NAG Library Manual
Keywords Ordered by Routine Name (internal)
Keyword Search (public)

Keyword Index for the NAG Library Manual, Mark 26

The following is a list of keywords and their related routines with details of the mark of introduction, a short description of its purpose and a list of related keywords to assist with the selection of a routine document.

Keyword Document Name Mark of Introduction Details
1 F 1 , hypergeometric function S22BAF   24  nagf_specfun_1f1_real
Real confluent hypergeometric function F 1 1 a ; b ; x
Related keywords: approximations of special functionsconfluent hypergeometric functionhypergeometric function
S22BBF   24  nagf_specfun_1f1_real_scaled
Real confluent hypergeometric function F 1 1 a ; b ; x in scaled form
Related keywords: approximations of special functionsconfluent hypergeometric functionhypergeometric function
1 -norm F04YDF   24  nagf_linsys_real_gen_norm_rcomm
Norm estimation (for use in condition estimation), real rectangular matrix
Related keywords: big datadata analyticsnorm, matrixreal, m by n matrixsimultaneous linear equations
F04ZDF   24  nagf_linsys_complex_gen_norm_rcomm
Norm estimation (for use in condition estimation), complex rectangular matrix
Related keywords: big datacomplex, m by n matrixdata analyticsnorm, matrixsimultaneous linear equations
F06RAF   15  nagf_blas_dlange
1 -norm, -norm, Frobenius norm, largest absolute element, real general matrix
Related keywords: BLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrixreal, m by n matrix
F06RBF   15  nagf_blas_dlangb
1 -norm, -norm, Frobenius norm, largest absolute element, real band matrix
Related keywords: BLASFrobenius norminfinity-normlinear algebra support routinesmatrix, bandnorm, matrixreal, band, m by n matrix
F06RCF   15  nagf_blas_dlansy
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix
Related keywords: BLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrixreal, indefinite, symmetric matrix
F06RDF   15  nagf_blas_dlansp
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage
Related keywords: BLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrixreal, indefinite, symmetric matrix
F06REF   15  nagf_blas_dlansb
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric band matrix
Related keywords: BLASFrobenius norminfinity-normlinear algebra support routinesmatrix, bandnorm, matrixreal, band, symmetric matrix
F06RJF   15  nagf_blas_dlantr
1 -norm, -norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix
Related keywords: BLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrixreal, trapezoidal matrixreal, triangular matrix
F06RKF   15  nagf_blas_dlantp
1 -norm, -norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage
Related keywords: BLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrixreal, triangular matrix
F06RLF   15  nagf_blas_dlantb
1 -norm, -norm, Frobenius norm, largest absolute element, real triangular band matrix
Related keywords: BLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrixreal, band, triangular matrix
F06RMF   15  nagf_blas_dlanhs
1 -norm, -norm, Frobenius norm, largest absolute element, real upper Hessenberg matrix
Related keywords: BLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrixreal, Hessenberg matrix
F06RNF   21  nagf_blas_dlangt
1 -norm, -norm, Frobenius norm, largest absolute element, real tridiagonal matrix
Related keywords: BLASFrobenius norminfinity-normlinear algebra support routinesmatrix, bandnorm, matrixreal, tridiagonal matrix
F06RPF   21  nagf_blas_dlanst
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix
Related keywords: BLASFrobenius norminfinity-normlinear algebra support routinesmatrix, bandnorm, matrixreal, symmetric, tridiagonal matrix
F06UAF   15  nagf_blas_zlange
1 -norm, -norm, Frobenius norm, largest absolute element, complex general matrix
Related keywords: BLAScomplex, m by n matrixFrobenius norminfinity-normlinear algebra support routines
F06UBF   15  nagf_blas_zlangb
1 -norm, -norm, Frobenius norm, largest absolute element, complex band matrix
Related keywords: BLAScomplex, band matrixFrobenius norminfinity-normlinear algebra support routinesmatrix, band
F06UCF   15  nagf_blas_zlanhe
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix
Related keywords: BLAScomplex, band matrixFrobenius norminfinity-normlinear algebra support routines
F06UDF   15  nagf_blas_zlanhp
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage
Related keywords: BLAScomplex, Hermitian matrixFrobenius norminfinity-normlinear algebra support routines
F06UEF   15  nagf_blas_zlanhb
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian band matrix
Related keywords: BLAScomplex, band, Hermitian matrixFrobenius norminfinity-normlinear algebra support routinesmatrix, band
F06UFF   15  nagf_blas_zlansy
1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix
Related keywords: BLAScomplex, symmetric matrixFrobenius norminfinity-normlinear algebra support routines
F06UGF   15  nagf_blas_zlansp
1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage
Related keywords: BLAScomplex, symmetric matrixFrobenius norminfinity-normlinear algebra support routines
F06UHF   15  nagf_blas_zlansb
1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric band matrix
Related keywords: BLAScomplex, band, symmetric matrixFrobenius norminfinity-normlinear algebra support routinesmatrix, band
F06UJF   15  nagf_blas_zlantr
1 -norm, -norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix
Related keywords: BLAScomplex, trapezoidal matrixcomplex, triangular matrixFrobenius norminfinity-normlinear algebra support routines
F06UKF   15  nagf_blas_zlantp
1 -norm, -norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage
Related keywords: BLAScomplex, triangular matrixFrobenius norminfinity-normlinear algebra support routines
F06ULF   15  nagf_blas_zlantb
1 -norm, -norm, Frobenius norm, largest absolute element, complex triangular band matrix
Related keywords: BLAScomplex, band, triangular matrixFrobenius norminfinity-normlinear algebra support routinesmatrix, band
F06UMF   15  nagf_blas_zlanhs
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hessenberg matrix
Related keywords: BLAScomplex, Hessenberg matrixFrobenius norminfinity-normlinear algebra support routines
F06UNF   21  nagf_blas_zlangt
1 -norm, -norm, Frobenius norm, largest absolute element, complex tridiagonal matrix
Related keywords: BLAScomplex, triangular matrixFrobenius norminfinity-normlinear algebra support routinesmatrix, band
F06UPF   21  nagf_blas_zlanht
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian tridiagonal matrix
Related keywords: BLAScomplex, Hermitian, tridiagonal matrixFrobenius norminfinity-normlinear algebra support routinesmatrix, band
F06WAF   23  nagf_blas_dlansf
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format
Related keywords: BLASBLASblas, real matricesdlansfFrobenius norminfinity-normlinear algebra support routineslinear algebra support routines;real, symmetric matrix
F06WNF   23  nagf_blas_zlanhf
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format
Related keywords: BLASBLASblas, complex matricescomplex, Hermitian matrixFrobenius norminfinity-normlinear algebra support routineslinear algebra support routines;zlanhf
F11MLF   21  nagf_sparse_direct_real_gen_norm
1 -norm, -norm, largest absolute element, real, square, sparse matrix
Related keywords: absolute valuebig datadata analyticsinfinity-normlarge scale linear systemsnorm, matrixreal, sparse matrix
F16RBF   23  nagf_blast_dgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, real band matrix
Related keywords: absolute valueabsolute valuebanded matrixFrobenius normfurther linear algebra support routinesinfinity-normmatrix, bandnorm, matrixreal, band, m by n matrix
F16UBF   23  nagf_blast_zgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, complex band matrix
Related keywords: absolute valuebanded matrixcomplex, band matrixFrobenius normfurther linear algebra support routinesinfinity-normmatrix, bandnorm, matrix
2 F 1 , hypergeometric function S22BEF   25  nagf_specfun_2f1_real
Real Gauss hypergeometric function F 1 2 a , b ; c ; x
Related keywords: approximations of special functionsGauss hypergeometric functionhypergeometric function
S22BFF   25  nagf_specfun_2f1_real_scaled
Real Gauss hypergeometric function F 1 2 a , b ; c ; x in scaled form
Related keywords: approximations of special functionsGauss hypergeometric functionhypergeometric function
abscissae D01BCF   nagf_quad_1d_gauss_wgen
Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule
Related keywords: cubaturefinanceintegration, non-adaptivequadratureweights and abscissae
D01TBF   24  nagf_quad_1d_gauss_wres
Pre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule
Related keywords: quadratureweights and abscissae
D01TDF   26  nagf_quad_1d_gauss_wrec
Calculation of weights and abscissae for Gaussian quadrature rules, method of Golub and Welsch
Related keywords: cubatureGaussianGolubGolub and Welschintegrationnon-adaptivequadratureweights and abscissaeWelsch
D01TEF   26  nagf_quad_1d_gauss_recm
Generates recursion coefficients needed by D01TDF to calculate a Gaussian quadrature rule
Related keywords: cubatureGaussianGolubGolub and Welschintegrationnon-adaptivequadraturerecursion coefficientsWelsch
absolute value F11MLF   21  nagf_sparse_direct_real_gen_norm
1 -norm, -norm, largest absolute element, real, square, sparse matrix
Related keywords: 1-normbig datadata analyticsinfinity-normlarge scale linear systemsnorm, matrixreal, sparse matrix
F16DQF   22  nagf_blast_iamax_val
Maximum absolute value and location, integer vector
Related keywords: further linear algebra support routinesmaximum value
F16DRF   22  nagf_blast_iamin_val
Minimum absolute value and location, integer vector
Related keywords: further linear algebra support routinesminimum value
F16JQF   22  nagf_blast_damax_val
Maximum absolute value and location, real vector
Related keywords: blasblas_damax_valfurther linear algebra support routinesmaximum value
F16JRF   22  nagf_blast_damin_val
Minimum absolute value and location, real vector
Related keywords: blasblas_damin_valfurther linear algebra support routinesminimum value
F16JSF   22  nagf_blast_zamax_val
Maximum absolute value and location, complex vector
Related keywords: blasblas_zamax_valfurther linear algebra support routinesmaximum value
F16JTF   22  nagf_blast_zamin_val
Minimum absolute value and location, complex vector
Related keywords: blasblas_zamin_valfurther linear algebra support routinesminimum value
F16RBF   23  nagf_blast_dgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, real band matrix
Related keywords: 1-normbanded matrixFrobenius normfurther linear algebra support routinesinfinity-normmatrix, bandnorm, matrixreal, band, m by n matrix
F16UBF   23  nagf_blast_zgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, complex band matrix
Related keywords: 1-normbanded matrixcomplex, band matrixFrobenius normfurther linear algebra support routinesinfinity-normmatrix, bandnorm, matrix
ACORN G05KFF   22  nagf_rand_init_repeat
Initializes a pseudorandom number generator to give a repeatable sequence
Related keywords: big datadata analyticsmersenne twisterMRG32k3aoptions, computationalrandom number generatorsrandom numbersWichmann Hill
G05KGF   22  nagf_rand_init_nonrepeat
Initializes a pseudorandom number generator to give a non-repeatable sequence
Related keywords: big datadata analyticsmersenne twisterMRG32k3aoptions, computationalrandom number generatorsrandom numbersWichmann Hill
active-set E04NCF   12  nagf_opt_lsq_lincon_solve_old
Linear programming (LP) convex quadratic programming (QP) or linearly-constrained linear least squares problem, dense
Related keywords: convex optimizationdata fittingfinanceleast squaresmaximizing a functionminimizing a functionnonlinear least squaresoptimizationQP, quadratic programming
active-set method E04MFF   16  nagf_opt_lp_solve_old
Linear programming (LP), dense, active-set method
Related keywords: financeLP, linear programmingmaximizing a functionminimizing a functionoptimization
E04NFF   16  nagf_opt_qp_dense_solve_old
General (possibly non-convex) quadratic programming (QP), dense, active-set method
Related keywords: financemaximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04NQF   21  nagf_opt_qpconvex2_sparse_solve
Linear programming (LP) or convex quadratic programming (QP), sparse, active-set method, recommended
Related keywords: financeLP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programmingservice routinesparse convex QP prolem
Adams' method D02CJF   13  nagf_ode_ivp_adams_zero_simple
Ordinary differential equations, initial value problem, Adams' method, until function of solution is zero, intermediate output (simple driver)
Related keywords: first-order systeminitial value problemIVP, initial value problemNonstiffODE, ordinary differential equationsstop at roots
D02QFF   13  nagf_ode_ivp_adams_roots
Ordinary differential equations, initial value problem, Adams' method with root-finding (direct communication, comprehensive)
Related keywords: IVP, initial value problemODE, ordinary differential equations
D02QGF   13  nagf_ode_ivp_adams_roots_revcom
Ordinary differential equations, initial value problem, Adams' method with root-finding (reverse communication, comprehensive)
Related keywords: IVP, initial value problemODE, ordinary differential equations
D02QWF   13  nagf_ode_ivp_adams_setup
Ordinary differential equations, initial value problem, setup for D02QFF and D02QGF
Related keywords: IVP, initial value problemODE, ordinary differential equations
D02QXF   13  nagf_ode_ivp_adams_diag
Ordinary differential equations, initial value problem, diagnostics for D02QFF and D02QGF
Related keywords: IVP, initial value problemODE, ordinary differential equations
D02QYF   13  nagf_ode_ivp_adams_rootdiag
Ordinary differential equations, initial value problem, root-finding diagnostics for D02QFF and D02QGF
Related keywords: IVP, initial value problemODE, ordinary differential equations
D02QZF   13  nagf_ode_ivp_adams_interp
Ordinary differential equations, initial value problem, interpolation for D02QFF or D02QGF
Related keywords: interpolationIVP, initial value problemODE, ordinary differential equations
adaptive grid, PDE D03PRF   16  nagf_pde_1d_parab_remesh_keller
General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretization, remeshing, one space variable
Related keywords: DAE, differential algebraic equationsKeller box discretizationmethod of linesPDE, partial differential equations
D03PSF   17  nagf_pde_1d_parab_convdiff_remesh
General system of convection-diffusion PDEs, coupled DAEs, method of lines, upwind scheme, remeshing, one space variable
Related keywords: convection-diffusion, PDEDAE, differential algebraic equationshyperbolic equationmethod of linesone-dimensionalparabolic partial differential equationPDE, partial differential equations
AD callback X10BBF   26 
Insert the location of the AD callback into the callback data object
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationcallback data objectinsertlocation
additional precision accumulation X03AAF   nagf_dot_real_prec
Real inner product added to initial value, basic/additional precision
Related keywords: dot productextended precision accumulationinner productinner productsscalar product
X03ABF   nagf_dot_complex_prec
Complex inner product added to initial value, basic/additional precision
Related keywords: dot productextended precision accumulationinner productinner productsscalar product
additive Schwarz preconditioner F11DFF   24  nagf_sparse_real_gen_precon_bdilu
Real sparse nonsymmetric linear system, incomplete L U factorization of local or overlapping diagonal blocks
Related keywords: big datadata analyticsincomplete L U factorizationlarge scale linear systemslinear equations, pre-conditionersreal, sparse matrix
F11DGF   24  nagf_sparse_real_gen_solve_bdilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DFF
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DTF   24  nagf_sparse_complex_gen_precon_bdilu
Complex, sparse, non-Hermitian linear system, incomplete L U factorization of local or overlapping diagonal blocks
Related keywords: big datacomplex, sparse matrixdata analyticsincomplete L U factorizationlarge scale linear systemslinear equations, pre-conditioners
F11DUF   24  nagf_sparse_complex_gen_solve_bdilu
Solution of complex, sparse, non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DTF
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
adjoint derivatives X10 Chapter Introduction     Automatic Differentiation Utilities
Related keywords: AD utility operationsautomatic differentiation
AD scalar X10BEF   26 
Write an integer (working precision) scalar to the callback data object
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationcallback data ojbectinteger scalarworking precisionwrite
X10BFF   26 
Write a real (working precision) scalar to the callback data object
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationcallback data objectreal scalarworking precisionwrite
X10BJF   26 
Write a scalar of type nagad_a1w_w_rtype to the callback data object
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationcallback data objectnagad_a1w_w_rtypewrite
X10CEF   26 
Read an integer scalar from the callback data object
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationcallback data objectinteger scalarread
X10CFF   26 
Read a real (working precision) scalar from the callback data object
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationcallback data objectreadreal scalarworking precision
X10CJF   26 
Read a scalar of type nagad_a1w_w_rtype from the callback data object
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationcallback dataobjectnagad_a1w_w_rtyperead
AD utility operations X10 Chapter Introduction     Automatic Differentiation Utilities
Related keywords: adjoint derivativesautomatic differentiation
Advancing-front method D06ACF   20  nagf_mesh_2d_gen_front
Generates a two-dimensional mesh using an Advancing-front method
Related keywords: mesh generationtriangular mesh
advisory messages X04ABF   nagf_file_set_unit_advisory
Return or set unit number for advisory messages
Related keywords: input utilitiesoutput utilities
affine mesh transformation D06DAF   20  nagf_mesh_2d_transform_affine
Generates a mesh resulting from an affine transformation of a given mesh
Related keywords: mesh generation
Ai S17AUF   24  nagf_specfun_airy_ai_real_vector
Airy function vectorized Ai x
Related keywords: Airy functionapproximations of special functions
Ai , Airy function S17AGF   nagf_specfun_airy_ai_real
Airy function Ai x
Related keywords: Airy functionapproximations of special functionsfinance
S17DGF   13  nagf_specfun_airy_ai_complex
Airy functions Ai z and Ai z , complex z
Related keywords: Airy function Ai , derivative Airy functionapproximations of special functionsfinance
Airy function S17AGF   nagf_specfun_airy_ai_real
Airy function Ai x
Related keywords: Ai , Airy functionapproximations of special functionsfinance
S17AHF   nagf_specfun_airy_bi_real
Airy function Bi x
Related keywords: approximations of special functions Bi , Airy functionfinance
S17AJF   nagf_specfun_airy_ai_deriv
Airy function Ai x
Related keywords: Ai , derivative Airy functionapproximations of special functionsfinance
S17AKF   nagf_specfun_airy_bi_deriv
Airy function Bi x
Related keywords: approximations of special functions Bi , derivative Airy functionfinance
S17AUF   24  nagf_specfun_airy_ai_real_vector
Airy function vectorized Ai x
Related keywords: Ai approximations of special functions
S17AVF   24  nagf_specfun_airy_bi_real_vector
Airy function vectorized Bi x
Related keywords: approximations of special functions Bi
S17AWF   24  nagf_specfun_airy_ai_deriv_vector
Derivatives of the Airy function, vectorized Ai x
Related keywords: Ai , derivative Airy functionapproximations of special functions
S17AXF   24  nagf_specfun_airy_bi_deriv_vector
Derivatives of the Airy function, vectorized Bi x
Related keywords: approximations of special functions Bi , derivative Airy function
S17DGF   13  nagf_specfun_airy_ai_complex
Airy functions Ai z and Ai z , complex z
Related keywords: Ai , Airy function Ai , derivative Airy functionapproximations of special functionsfinance
S17DHF   13  nagf_specfun_airy_bi_complex
Airy functions Bi z and Bi z , complex z
Related keywords: approximations of special functions Bi , Airy function Bi , derivative Airy functionfinance
Aitken's method E01AAF   nagf_interp_1d_aitken
Interpolated values, Aitken's technique, unequally spaced data, one variable
Related keywords: financeinterpolation
Ai , derivative Airy function S17AJF   nagf_specfun_airy_ai_deriv
Airy function Ai x
Related keywords: Airy functionapproximations of special functionsfinance
S17AWF   24  nagf_specfun_airy_ai_deriv_vector
Derivatives of the Airy function, vectorized Ai x
Related keywords: Airy functionapproximations of special functions
S17DGF   13  nagf_specfun_airy_ai_complex
Airy functions Ai z and Ai z , complex z
Related keywords: Ai , Airy functionAiry functionapproximations of special functionsfinance
algorithmic mode X10ACF   26 
Set the algorithmic mode
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationset
X10ADF   26 
Get the algorithmic mode
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationget
allocate G03EJF   16  nagf_mv_cluster_hier_indicator
Computes cluster indicator variable (for use after G03ECF)
Related keywords: big datacluster analysisdata analyticshierarchical cluster analysismultivariate methods
American options S30QCF   22  nagf_specfun_opt_amer_bs_price
American option, Bjerksund and Stensland pricing formula
Related keywords: approximations of special functionsBjerksund and Stensland pricing formulafinance
analysis of variance G04 Chapter Introduction     Analysis of Variance
Anderson acceleration C05MDF   26  nagf_roots_sys_func_aa_rcomm
Solution of a system of nonlinear equations using Anderson acceleration (reverse communication)
Related keywords: root-findingroots of transcendental equationszeros of transcendental functions
Anderson–Darling test statistic G08CHF   23  nagf_nonpar_gofstat_anddar
Calculates the Anderson–Darling goodness-of-fit test statistic
Related keywords: nonparametric statistics
G08CJF   23  nagf_nonpar_gofstat_anddar_unif
Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of uniformly distributed data
Related keywords: nonparametric statistics
G08CKF   23  nagf_nonpar_gofstat_anddar_normal
Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of a fully-unspecified Normal distribution
Related keywords: Gaussian distributionnonparametric statisticsNormal distributionprobability
G08CLF   23  nagf_nonpar_gofstat_anddar_exp
Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of an unspecified exponential distribution
Related keywords: exponential distributionnonparametric statisticsprobability
Andrew's sine wave G02HAF   13  nagf_correg_robustm
Robust regression, standard M -estimates
Related keywords: big datacorrelation analysisdata analyticsfinanceHampel's piecewise linear functionHuber type regressionKrasker–Welsch weightsMallows type regressionMaronna's weights M -estimatesnonlinear regressionpolynomial regressionregressionregression analysisrobust regressionScheppe type regressionTukey's bi-weight
ANOVA G04AGF   nagf_anova_hier2
Two-way analysis of variance, hierarchical classification, subgroups of unequal size
Related keywords: analysis of variancehierarchical classificationtwo-way analysis of variance
G04BBF   16  nagf_anova_random
Analysis of variance, randomized block or completely randomized design, treatment means and standard errors
Related keywords: analysis of variancecompletely randomized designrandomized block designstandard errorstreatment means
G04BCF   17  nagf_anova_rowcol
Analysis of variance, general row and column design, treatment means and standard errors
Related keywords: analysis of variancestandard errorstreatment means
G04CAF   16  nagf_anova_factorial
Analysis of variance, complete factorial design, treatment means and standard errors
Related keywords: analysis of variancefactorial designstandard errorstreatment means
G08AEF   nagf_nonpar_test_friedman
Friedman two-way analysis of variance on k matched samples
Related keywords: Friedman two-way analysis of variancenonparametric statistics
G08AFF   nagf_nonpar_test_kruskal
Kruskal–Wallis one-way analysis of variance on k samples of unequal size
Related keywords: Kruskal–Wallis analysis of variancenonparametric statistics
approximations of special functions S Chapter Introduction     Approximations of Special Functions
arccos S09ABF   nagf_specfun_arccos
arccos x
Related keywords: approximations of special functionsfinanceinverse circular cosine
arcsine S09AAF   nagf_specfun_arcsin
arcsin x
Related keywords: approximations of special functionsfinanceinverse circular sine
ARIMA G13ADF   nagf_tsa_uni_arima_prelim
Univariate time series, preliminary estimation, seasonal ARIMA model
Related keywords: big datadata analyticsfinancetime seriestime series analysisunivariate time series
G13AEF   nagf_tsa_uni_arima_estim
Univariate time series, estimation, seasonal ARIMA model (comprehensive)
Related keywords: big datadata analyticstime seriestime series analysisunivariate time series
G13AFF   nagf_tsa_uni_arima_estim_easy
Univariate time series, estimation, seasonal ARIMA model (easy-to-use)
Related keywords: big datadata analyticsfinancetime seriestime series analysisunivariate time series
G13BAF   10  nagf_tsa_multi_filter_arima
Multivariate time series, filtering (pre-whitening) by an ARIMA model
Related keywords: big datadata analyticsfilteringfinancemultivariate time seriespre-whitening, filteringtime seriestime series analysis
G13BEF   11  nagf_tsa_multi_inputmod_estim
Multivariate time series, estimation of multi-input model
Related keywords: big datadata analyticsexact likelihoodfinancemarginal likelihoodmultivariate time seriesnonlinear least squarestime seriestime series analysisunivariate time series
ARMA G05PHF   22  nagf_rand_times_arma
Generates a realization of a time series from an ARMA model
Related keywords: big datadata analyticsfinancerandom number generatorstime series
G13ASF   13  nagf_tsa_uni_arima_resid
Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF
Related keywords: autocorrelation functionbig dataBox–Jenkins modelsBox–Ljung portmanteau statisticdata analyticsfinancesignificancestandard errorstime seriestime series analysisunivariate time series
Asian option S30SAF   22  nagf_specfun_opt_asian_geom_price
Asian option, geometric continuous average rate pricing formula
Related keywords: approximations of special functionsderivative, optionsfinanceoption pricing
S30SBF   22  nagf_specfun_opt_asian_geom_greeks
Asian option, geometric continuous average rate pricing formula with Greeks
Related keywords: approximations of special functionsderivative, optionsfinanceGreeks, optionsoption pricing
autocorrelation coefficients G13ABF   nagf_tsa_uni_autocorr
Univariate time series, sample autocorrelation function
Related keywords: big datadata analyticsfinancemeantest statistictime seriestime series analysisunivariate time seriesvariance
G13ACF   nagf_tsa_uni_autocorr_part
Univariate time series, partial autocorrelations from autocorrelations
Related keywords: autoregressive parametersbig datadata analyticserror variance ratiosfinancepartial autocorrelation coefficientstime seriestime series analysisunivariate time series
autocorrelation function G13ASF   13  nagf_tsa_uni_arima_resid
Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF
Related keywords: ARMAbig dataBox–Jenkins modelsBox–Ljung portmanteau statisticdata analyticsfinancesignificancestandard errorstime seriestime series analysisunivariate time series
automatic D01ESF   25  nagf_quad_md_sgq_multi_vec
Multi-dimensional quadrature using sparse grids
Related keywords: multidimensionalmultiple integrandsquadraturesparsevectorized
automatic differentiation X10 Chapter Introduction     Automatic Differentiation Utilities
Related keywords: adjoint derivativesAD utility operations
autoregressive parameters G13ACF   nagf_tsa_uni_autocorr_part
Univariate time series, partial autocorrelations from autocorrelations
Related keywords: autocorrelation coefficientsbig datadata analyticserror variance ratiosfinancepartial autocorrelation coefficientstime seriestime series analysisunivariate time series
backward difference formula D02EJF   12  nagf_ode_ivp_bdf_zero_simple
Ordinary differential equations, stiff initial value problem, backward differentiation formulae method, until function of solution is zero, intermediate output (simple driver)
Related keywords: BDF, backward differentiation formulainitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NBF   12  nagf_ode_ivp_stiff_exp_fulljac
Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
Related keywords: initial value problemIVP, initial value problemJacobianODE, ordinary differential equationsstiff differential equations
D02NCF   12  nagf_ode_ivp_stiff_exp_bandjac
Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
Related keywords: BDF, backward differentiation formulainitial value problemJacobianODE, ordinary differential equationsstiff differential equations
D02NDF   12  nagf_ode_ivp_stiff_exp_sparjac
Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
Related keywords: BDF, backward differentiation formulainitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NGF   12  nagf_ode_ivp_stiff_imp_fulljac
Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
Related keywords: BDF, backward differentiation formulaimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemJacobianODE, ordinary differential equationsstiff differential equations
D02NHF   12  nagf_ode_ivp_stiff_imp_bandjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
Related keywords: BDF, backward differentiation formulaimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemJacobianODE, ordinary differential equationsstiff differential equations
D02NJF   12  nagf_ode_ivp_stiff_imp_sparjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
Related keywords: BDF, backward differentiation formuladiscretised systemimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemJacobianODEODE, ordinary differential equationsstiff differential equations
D02NMF   12  nagf_ode_ivp_stiff_exp_revcom
Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
Related keywords: BDF, backward differentiation formulainitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NNF   12  nagf_ode_ivp_stiff_imp_revcom
Implicit/algebraic ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
Related keywords: implicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NVF   12  nagf_ode_ivp_stiff_bdf
Ordinary differential equations, initial value problem, backward differentiation formulae method, setup for d02m–n routines
Related keywords: initial value problemODE, ordinary differential equationsstiff differential equations
D02XJF   12  nagf_ode_ivp_stiff_nat_interp
Ordinary differential equations, initial value problem, interpolation for d02m–n routines (BLEND and BDF methods only), natural interpolant
Related keywords: Blend methodinitial value probleminterpolationODE, ordinary differential equations
backward error F02JCF   25  nagf_eigen_real_gen_quad
Solves the quadratic eigenvalue problem for real matrices
Related keywords: balancingbig datacondition numberdata analyticseigenproblem, quadraticeigenvalueseigenvalues and eigenvectorseigenvectors
F02JQF   25  nagf_eigen_complex_gen_quad
Solves the quadratic eigenvalue problem for complex matrices
Related keywords: balancingbig datacondition numberdata analyticseigenproblem, quadraticeigenvalueseigenvalues and eigenvectorseigenvectors
F07ABF   21  nagf_lapacklin_dgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
Related keywords: condition number, matrixDGESVXerror bound, matrixfinanceforward errorLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
F07AHF   15  nagf_lapacklin_dgerfs
Refined solution with error bounds of real system of linear equations, multiple right-hand sides
Related keywords: DGERFSerror bound, matrixforward errorLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
F07APF   21  nagf_lapacklin_zgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
Related keywords: complex, nonsymmetric matrixcondition number, matrixerror bound, matrixfinanceforward errorLAPACKlinear equations L U decompositionZGESVX
F07AVF   15  nagf_lapacklin_zgerfs
Refined solution with error bounds of complex system of linear equations, multiple right-hand sides
Related keywords: complex, nonsymmetric matrixforward errorLAPACKlinear equationsZGERFS
F07BBF   21  nagf_lapacklin_dgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
Related keywords: condition number, matrixDGBSVXerror bound, matrixforward errorLAPACKlinear equations L U decompositionmatrix, bandreal, band matrix
F07BHF   15  nagf_lapacklin_dgbrfs
Refined solution with error bounds of real band system of linear equations, multiple right-hand sides
Related keywords: DGBRFSforward errorLAPACKlinear equations L U decompositionmatrix, bandreal, band matrix
F07BPF   21  nagf_lapacklin_zgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
Related keywords: complex, band matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equations L U decompositionmatrix, bandZGBSVX
F07BVF   15  nagf_lapacklin_zgbrfs
Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides
Related keywords: complex, band matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZGBRFS
F07CBF   21  nagf_lapacklin_dgtsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
Related keywords: condition number, matrixDGTSVXerror bound, matrixforward errorLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
F07CHF   22  nagf_lapacklin_dgtrfs
Refined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides
Related keywords: DGTCONforward errorLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
F07CPF   21  nagf_lapacklin_zgtsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations
Related keywords: complex, tridiagonal matrixforward errorLAPACKlinear equations L U decompositionmatrix, bandZGTSVX
F07CVF   22  nagf_lapacklin_zgtrfs
Refined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides
Related keywords: complex, tridiagonal matrixforward errorLAPACKlinear equations L U decompositionmatrix, bandZGTRFS
F07FBF   21  nagf_lapacklin_dposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations
Related keywords: Cholesky decompositioncondition number, matrixDPOSVXerror bound, matrixfinanceforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FHF   15  nagf_lapacklin_dporfs
Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides
Related keywords: Cholesky decompositionDPORFSforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FPF   21  nagf_lapacklin_zposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixcondition number, matrixerror bound, matrixfinanceforward errorLAPACKlinear equationsZPOSVX
F07FVF   15  nagf_lapacklin_zporfs
Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixerror bound, matrixforward errorLAPACKlinear equationsZPORFS
F07GBF   21  nagf_lapacklin_dppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations, packed storage
Related keywords: Cholesky decompositioncondition number, matrixDPPSVXerror bound, matrixforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GHF   15  nagf_lapacklin_dpprfs
Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides, packed storage
Related keywords: Cholesky decompositionDPPRFSforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GPF   21  nagf_lapacklin_zppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations, packed storage
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsZPPSVX
F07GVF   15  nagf_lapacklin_zpprfs
Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides, packed storage
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixerror bound, matrixforward errorLAPACKlinear equationsZPPRFS
F07HBF   21  nagf_lapacklin_dpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite banded system of linear equations
Related keywords: Cholesky decompositioncondition number, matrixDPBSVXerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
F07HHF   15  nagf_lapacklin_dpbrfs
Refined solution with error bounds of real symmetric positive definite band system of linear equations, multiple right-hand sides
Related keywords: Cholesky decompositionDPBRFSforward errorLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
F07HPF   21  nagf_lapacklin_zpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite banded system of linear equations
Related keywords: Cholesky decompositioncomplex, band, Hermitian, positive-definite matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZPBSVX
F07HVF   15  nagf_lapacklin_zpbrfs
Refined solution with error bounds of complex Hermitian positive definite band system of linear equations, multiple right-hand sides
Related keywords: Cholesky decompositioncomplex, band, Hermitian, positive-definite matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZPBRFS
F07JBF   21  nagf_lapacklin_dptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations
Related keywords: Cholesky decompositioncondition number, matrixDPTSVXerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
F07JHF   22  nagf_lapacklin_dptrfs
Refined solution with error bounds of real symmetric positive definite tridiagonal system of linear equations, multiple right-hand sides
Related keywords: Cholesky decompositionDPTRFSforward errorLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
F07JPF   21  nagf_lapacklin_zptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZPTSVX
F07JVF   22  nagf_lapacklin_zptrfs
Refined solution with error bounds of complex Hermitian positive definite tridiagonal system of linear equations, multiple right-hand sides
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixforward errorLAPACKlinear equationsmatrix, bandZPTRFS
F07MBF   21  nagf_lapacklin_dsysvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations
Related keywords: diagonal pivoting methodDSYSVXforward errorLAPACKLDLT decompositionlinear equationsreal, indefinite, symmetric matrix UDU T decompositiuon
F07MHF   15  nagf_lapacklin_dsyrfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodDSYRFSforward errorLAPACKlinear equationsreal, indefinite, symmetric matrix
F07MPF   21  nagf_lapacklin_zhesvx
Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations
Related keywords: complex, Hermitian, indefinite matrixdiagonal pivoting methodforward errorLAPACK LDL H decompositionlinear equations UDU H decompositionZHESVX
F07MVF   15  nagf_lapacklin_zherfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equationsZHERFS
F07NPF   21  nagf_lapacklin_zsysvx
Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations
Related keywords: complex, symmetric matrixdiagonal pivoting methodforward errorLAPACK LDL H decompositionlinear equations UDU H decompositionZSYSVX
F07NVF   15  nagf_lapacklin_zsyrfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equationsZSYRFS
F07PBF   21  nagf_lapacklin_dspsvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage. Error bounds and a condition estimate are also computed
Related keywords: condition number, matrixdiagonal pivoting methodDSPSVXerror bound, matrixforward errorLAPACK LDL H decompositionlinear equationsreal, indefinite, symmetric matrix UDU H decomposition
F07PHF   15  nagf_lapacklin_dsprfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodDSPRFSforward errorLAPACKlinear equationsreal, indefinite, symmetric matrix
F07PPF   21  nagf_lapacklin_zhpsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, Hermitian, system of linear equations, error bounds and condition estimates. Packed storage
Related keywords: complex, Hermitian, indefinite matrixdiagonal pivoting methodforward errorinverse, matrixLAPACK LDL H decompositionlinear equations UDU H decompositionZHPSVX
F07PVF   15  nagf_lapacklin_zhprfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equationsZHPRFS
F07QPF   21  nagf_lapacklin_zspsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, symmetric, system of linear equations, error bounds and condition estimates. Packed storage
Related keywords: complex, symmetric matrixdiagonal pivoting methodforward errorLAPACK LDL T decompositionlinear equations UDU T decompositionZSPSVX
F07QVF   15  nagf_lapacklin_zsprfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equationsZSPRFS
F07THF   15  nagf_lapacklin_dtrrfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides
Related keywords: DTRRFSerror bound, matrixfinanceforward errorLAPACKlinear equationsreal, triangular matrix
F07TVF   15  nagf_lapacklin_ztrrfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides
Related keywords: complex, triangular matrixerror bound, matrixforward errorLAPACKlinear equationsZTRRFS
F07UHF   15  nagf_lapacklin_dtprfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage
Related keywords: DTPRFSerror bound, matrixforward errorLAPACKlinear equationsreal, triangular matrix
F07UVF   15  nagf_lapacklin_ztprfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
Related keywords: complex, triangular matrixerror bound, matrixforward errorLAPACKlinear equationsZTPRFS
F07VHF   15  nagf_lapacklin_dtbrfs
Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides
Related keywords: DTBRFSerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandreal, band, triangular matrix
F07VVF   15  nagf_lapacklin_ztbrfs
Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides
Related keywords: complex, band, triangular matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZTBRFS
F11MHF   21  nagf_sparse_direct_real_gen_refine
Refined solution with error bounds of real system of linear equations, multiple right-hand sides
Related keywords: big datadata analyticsforward errorlarge scale linear systemslinear equationsreal, sparse matrix
balancing F02JCF   25  nagf_eigen_real_gen_quad
Solves the quadratic eigenvalue problem for real matrices
Related keywords: backward errorbig datacondition numberdata analyticseigenproblem, quadraticeigenvalueseigenvalues and eigenvectorseigenvectors
F02JQF   25  nagf_eigen_complex_gen_quad
Solves the quadratic eigenvalue problem for complex matrices
Related keywords: backward errorbig datacondition numberdata analyticseigenproblem, quadraticeigenvalueseigenvalues and eigenvectorseigenvectors
F08NBF   21  nagf_lapackeig_dgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: condition number, matrixDGEEVXeigenproblemeigenvalueseigenvectorsfinanceforward errorLAPACKLAPACKleast squaresorthogonal transformations QR algorithmreal, nonsymmetric matrix
F08NHF   16  nagf_lapackeig_dgebal
Balances a real general matrix
Related keywords: DGEBALeigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08NJF   16  nagf_lapackeig_dgebak
Transforms eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF
Related keywords: DGEBAKeigenproblemeigenvectorsLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08NPF   21  nagf_lapackeig_zgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: complex, nonsymmetric matrixcondition number, matrixDGEEVeigenproblemeigenvalueseigenvectorsfinanceforward errorLAPACKLAPACKleast squares
F08NVF   16  nagf_lapackeig_zgebal
Balances a complex general matrix
Related keywords: complex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresZGEBAL
F08NWF   16  nagf_lapackeig_zgebak
Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF
Related keywords: complex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresZGEBAK
F08WBF   21  nagf_lapackeig_dggevx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: condition number, matrixDGGEVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsfinanceforward errorgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WHF   20  nagf_lapackeig_dggbal
Balances a pair of real, square, matrices
Related keywords: DGGHRDeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squares
F08WJF   20  nagf_lapackeig_dggbak
Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF
Related keywords: DGGBAKeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
F08WPF   21  nagf_lapackeig_zggevx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsfinanceforward errorgeneralized eigenproblemLAPACKLAPACKleast squaresZGGEVX
F08WVF   20  nagf_lapackeig_zggbal
Balances a pair of complex, square, matrices
Related keywords: complex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresZGGBAL
F08WWF   20  nagf_lapackeig_zggbak
Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF
Related keywords: complex, nonsymmetric matrixeigenproblemeigenvectorsLAPACKLAPACKleast squaresZGGBAL
banded matrix F16RBF   23  nagf_blast_dgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, real band matrix
Related keywords: 1-normabsolute valueabsolute valueFrobenius normfurther linear algebra support routinesinfinity-normmatrix, bandnorm, matrixreal, band, m by n matrix
F16UBF   23  nagf_blast_zgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, complex band matrix
Related keywords: 1-normabsolute valuecomplex, band matrixFrobenius normfurther linear algebra support routinesinfinity-normmatrix, bandnorm, matrix
barrier option S30FAF   22  nagf_specfun_opt_barrier_std_price
Standard barrier option pricing formula
Related keywords: approximations of special functionsderivative, optionsfinanceoption pricing
Bartlett lag window G13CAF   10  nagf_tsa_uni_spectrum_lag
Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: big datadata analyticsfinanceParzen lag windowrectangular lag windowsmoothingtime seriestime series analysisTukey lag windowunivariate time series
G13CCF   10  nagf_tsa_multi_spectrum_lag
Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: big datacross-spectrumdata analyticsfinancemultivariate time seriesParzen lag windowrectangular lag windowsmoothingtime seriestime series analysisTukey lag window
barycentering D06CAF   20  nagf_mesh_2d_smooth_bary
Uses a barycentering technique to smooth a given mesh
Related keywords: barycentricmesh generationsmoothing
barycentric D06CAF   20  nagf_mesh_2d_smooth_bary
Uses a barycentering technique to smooth a given mesh
Related keywords: barycenteringmesh generationsmoothing
Barycentric interpolation E01EBF   25  nagf_interp_2d_triang_bary_eval
Barycentric interpolation on function values provided on a two-dimensional scattered grid
Related keywords: Bilinear interpolationfinanceinterpolationInterpolationRenka and Cline methodScattered dataScattered data interpolationTriangulation
barycentric Lagrange interpolation D02UWF   23  nagf_ode_bvp_ps_lin_grid_vals
Interpolate a function from Chebyshev grid to uniform grid using barycentric Lagrange interpolation
Related keywords: Gauss–Lobatto gridinterpolationODE, ordinary differential equations
base X02BHF   12  nagf_machine_model_base
The floating-point model parameter, b
Related keywords: floating-point modelmachine constants
BDF, backward differentiation formula D02EJF   12  nagf_ode_ivp_bdf_zero_simple
Ordinary differential equations, stiff initial value problem, backward differentiation formulae method, until function of solution is zero, intermediate output (simple driver)
Related keywords: backward difference formulainitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NCF   12  nagf_ode_ivp_stiff_exp_bandjac
Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
Related keywords: backward difference formulainitial value problemJacobianODE, ordinary differential equationsstiff differential equations
D02NDF   12  nagf_ode_ivp_stiff_exp_sparjac
Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
Related keywords: backward difference formulainitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NGF   12  nagf_ode_ivp_stiff_imp_fulljac
Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
Related keywords: backward difference formulaimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemJacobianODE, ordinary differential equationsstiff differential equations
D02NHF   12  nagf_ode_ivp_stiff_imp_bandjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
Related keywords: backward difference formulaimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemJacobianODE, ordinary differential equationsstiff differential equations
D02NJF   12  nagf_ode_ivp_stiff_imp_sparjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
Related keywords: backward difference formuladiscretised systemimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemJacobianODEODE, ordinary differential equationsstiff differential equations
D02NMF   12  nagf_ode_ivp_stiff_exp_revcom
Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
Related keywords: backward difference formulainitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
Bessel function S17ACF   nagf_specfun_bessel_y0_real
Bessel function Y 0 x
Related keywords: approximations of special functionsfinance Y 0 x , Bessel function
S17ADF   nagf_specfun_bessel_y1_real
Bessel function Y 1 x
Related keywords: approximations of special functionsfinance Y 1 x , Bessel function
S17AEF   nagf_specfun_bessel_j0_real
Bessel function J 0 x
Related keywords: approximations of special functionsfinance J 0 , Bessel function
S17AFF   nagf_specfun_bessel_j1_real
Bessel function J 1 x
Related keywords: approximations of special functionsfinance J 1 , Bessel function
S17ALF   20  nagf_specfun_bessel_zeros
Zeros of Bessel functions J α x , J α x , Y α x or Y α x
Related keywords: approximations of special functionsfinancezeros of bessel functions
S17AQF   24  nagf_specfun_bessel_y0_real_vector
Bessel function vectorized Y 0 x
Related keywords: approximations of special functions Y 0 x , Bessel function
S17ARF   24  nagf_specfun_bessel_y1_real_vector
Bessel function vectorized Y 1 x
Related keywords: approximations of special functions Y 1 x , Bessel function
S17ASF   24  nagf_specfun_bessel_j0_real_vector
Bessel function vectorized J 0 x
Related keywords: approximations of special functions J 0 , Bessel function
S17ATF   24  nagf_specfun_bessel_j1_real_vector
Bessel function vectorized J 1 x
Related keywords: approximations of special functions J 1 , Bessel function
S17DCF   13  nagf_specfun_bessel_y_complex
Bessel functions Y ν + a z , real a 0 , complex z , ν = 0 , 1 , 2 ,
Related keywords: approximations of special functions
S17DEF   13  nagf_specfun_bessel_j_complex
Bessel functions J ν + a z , real a 0 , complex z , ν = 0 , 1 , 2 ,
Related keywords: approximations of special functions
best subset H05AAF   24  nagf_mip_best_subset_given_size_revcomm
Best n subsets of size p (reverse communication)
Related keywords: operations researchsubsetting, best
H05ABF   24  nagf_mip_best_subset_given_size
Best n subsets of size p (direct communication)
Related keywords: operations researchsubsetting, best
beta distribution G01EEF   14  nagf_stat_prob_beta
Computes upper and lower tail probabilities and probability density function for the beta distribution
Related keywords: CDF, cumulative distribution functionfinancelower tail probabilityprobabilitySimple Calculations on Statistical Dataupper tail probability
G01FEF   14  nagf_stat_inv_cdf_beta
Computes deviates for the beta distribution
Related keywords: deviatesfinanceinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01GEF   14  nagf_stat_prob_beta_noncentral
Computes probabilities for the non-central beta distribution
Related keywords: financelower tail probabilitySimple Calculations on Statistical Data
G01SEF   24  nagf_stat_prob_beta_vector
Computes a vector of probabilities for the beta distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticslower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01TEF   24  nagf_stat_inv_cdf_beta_vector
Computes a vector of deviates for the beta distribution
Related keywords: big datadata analyticsdeviatesinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G05SBF   22  nagf_rand_dist_beta
Generates a vector of pseudorandom numbers from a beta distribution
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
beta function S14CBF   24  nagf_specfun_beta_log_real
Logarithm of the beta function ln B a , b
Related keywords: approximations of special functionslog beta function
BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithm E04GBF   nagf_opt_lsq_uncon_quasi_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (comprehensive)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationquasi-Newton algorithmsum-of-squares minimization
E04GYF   18  nagf_opt_lsq_uncon_quasi_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationquasi-Newton algorithmsum-of-squares minimization
E04JYF   18  nagf_opt_bounds_quasi_func_easy
Bound constrained minimum, quasi-Newton algorithm, using function values only (easy-to-use)
Related keywords: financemaximizing a functionminimization, simple bound constraintsminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton algorithm
E04KYF   18  nagf_opt_bounds_quasi_deriv_easy
Bound constrained minimum, quasi-Newton algorithm, using first derivatives (easy-to-use)
Related keywords: financemaximizing a functionminimization, simple bound constraintsminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton algorithm
Bi S17AVF   24  nagf_specfun_airy_bi_real_vector
Airy function vectorized Bi x
Related keywords: Airy functionapproximations of special functions
Bi , Airy function S17AHF   nagf_specfun_airy_bi_real
Airy function Bi x
Related keywords: Airy functionapproximations of special functionsfinance
S17DHF   13  nagf_specfun_airy_bi_complex
Airy functions Bi z and Bi z , complex z
Related keywords: Airy functionapproximations of special functions Bi , derivative Airy functionfinance
Bi-CGSTAB F11BEF   19  nagf_sparse_real_gen_basic_solver
Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
Related keywords: big dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11BSF   19  nagf_sparse_complex_gen_basic_solver
Complex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
Related keywords: big dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DCF   18  nagf_sparse_real_gen_solve_ilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DAF
Related keywords: big dataCGS, conjugate gradient methoddata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DEF   18  nagf_sparse_real_gen_solve_jacssor
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsJacobi preconditioninglarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodSSOR method, symmetric successive over-relaxationTFQMR, transpose-free quasi-minimal residual method
F11DGF   24  nagf_sparse_real_gen_solve_bdilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DFF
Related keywords: additive Schwarz preconditionerbig dataCGS, conjugate gradient methoddata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DQF   19  nagf_sparse_complex_gen_solve_ilu
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DNF (Black Box)
Related keywords: big dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DSF   19  nagf_sparse_complex_gen_solve_jacssor
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box
Related keywords: big dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsiterative methods, linear equationsJacobi preconditioninglarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodSSOR method, symmetric successive over-relaxationTFQMR, transpose-free quasi-minimal residual method
F11DUF   24  nagf_sparse_complex_gen_solve_bdilu
Solution of complex, sparse, non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DTF
Related keywords: additive Schwarz preconditionerbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
bicubic spline E01DAF   14  nagf_interp_2d_spline_grid
Interpolating functions, fitting bicubic spline, data on rectangular grid
Related keywords: financeinterpolationtwo-dimensional
bicubic spline, partial derivative E02DHF   23  nagf_fit_2dspline_derivm
Evaluation of spline surface at mesh of points with derivatives
Related keywords: bicubic splinescurve and surface fitting
bicubic splines E02DAF   nagf_fit_2dspline_panel
Least squares surface fit, bicubic splines
Related keywords: B-splinescurve and surface fittingknotsleast squarestwo-dimensional spline approximation
E02DCF   13  nagf_fit_2dspline_grid
Least squares surface fit by bicubic splines with automatic knot placement, data on rectangular grid
Related keywords: B-splinescurve and surface fittingleast squaressmoothingtwo-dimensional spline approximation
E02DDF   13  nagf_fit_2dspline_sctr
Least squares surface fit by bicubic splines with automatic knot placement, scattered data
Related keywords: B-splinescurve and surface fittingleast squaresscattered datasmoothing
E02DEF   14  nagf_fit_2dspline_evalv
Evaluation of fitted bicubic spline at a vector of points
Related keywords: B-splinescurve and surface fittingfinance
E02DFF   14  nagf_fit_2dspline_evalm
Evaluation of fitted bicubic spline at a mesh of points
Related keywords: B-splinescurve and surface fittingfinancegridded data
E02DHF   23  nagf_fit_2dspline_derivm
Evaluation of spline surface at mesh of points with derivatives
Related keywords: bicubic spline, partial derivativecurve and surface fitting
big data F02 Chapter Introduction     Eigenvalues and Eigenvectors
Related keywords: data analyticseigenvalueseigenvectors
F04 Chapter Introduction     Simultaneous Linear Equations
Related keywords: data analyticssimultaneous linear equations
F11 Chapter Introduction     Large Scale Linear Systems
Related keywords: data analyticslarge scale linear systems
F12 Chapter Introduction     Large Scale Eigenproblems
Related keywords: data analyticslarge scale eigenproblems
G01ANF   23  nagf_stat_quantiles_stream_fixed
Calculates approximate quantiles from a data stream of known size
Related keywords: data analyticsdata streamquantilesSimple Calculations on Statistical Datastreaming
G01APF   23  nagf_stat_quantiles_stream_arbitrary
Calculates approximate quantiles from a data stream of unknown size
Related keywords: data analyticsdata streamquantilesSimple Calculations on Statistical Datastreaming
G01ATF   24  nagf_stat_summary_onevar
Computes univariate summary information: mean, variance, skewness, kurtosis
Related keywords: data analyticsdata streamkurtosismaximum valuemeanminimum valueSimple Calculations on Statistical Dataskewnessstandard deviationstreaming
G01AUF   24  nagf_stat_summary_onevar_combine
Combines multiple sets of summary information, for use after G01ATF
Related keywords: data analyticsdata streamSimple Calculations on Statistical Datastreamingsummary information
G01SAF   24  nagf_stat_prob_normal_vector
Computes a vector of probabilities for the standard Normal distribution
Related keywords: CDF, cumulative distribution functionconfidence intervaldata analyticsGaussian distributionlower tail probabilityNormal distributionsignificanceSimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01SBF   24  nagf_stat_prob_students_t_vector
Computes a vector of probabilities for the Student's t -distribution
Related keywords: CDF, cumulative distribution functionconfidence intervaldata analyticslower tail probabilitysignificanceSimple Calculations on Statistical DataStudent's t -distributiontwo-tail probabilityupper tail probability
G01SCF   24  nagf_stat_prob_chisq_vector
Computes a vector of probabilities for χ 2 distribution
Related keywords: CDF, cumulative distribution functionchi-squared distributiondata analyticslower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01SDF   24  nagf_stat_prob_f_vector
Computes a vector of probabilities for F -distribution
Related keywords: CDF, cumulative distribution functiondata analytics F -distributionlower tail probabilitySimple Calculations on Statistical Dataupper tail probabilityvariance-ratio distribution
G01SEF   24  nagf_stat_prob_beta_vector
Computes a vector of probabilities for the beta distribution
Related keywords: beta distributionCDF, cumulative distribution functiondata analyticslower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01SFF   24  nagf_stat_prob_gamma_vector
Computes a vector of probabilities for the gamma distribution
Related keywords: CDF, cumulative distribution functiondata analyticsgamma distributionlower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01SJF   24  nagf_stat_prob_binomial_vector
Computes a vector of probabilities for the binomial distribution
Related keywords: binomial distributionCDF, cumulative distribution functiondata analyticslower tail probabilitypoint probabilitySimple Calculations on Statistical Dataupper tail probability
G01SKF   24  nagf_stat_prob_poisson_vector
Computes a vector of probabilities for the Poisson distribution
Related keywords: CDF, cumulative distribution functiondata analyticslower tail probabilitypoint probabilityPoisson distributionSimple Calculations on Statistical Dataupper tail probability
G01SLF   24  nagf_stat_prob_hypergeom_vector
Computes a vector of probabilities for the hypergeometric distribution
Related keywords: CDF, cumulative distribution functiondata analyticshypergeometric distributionlower tail probabilitypoint probabilitySimple Calculations on Statistical Dataupper tail probability
G01TAF   24  nagf_stat_inv_cdf_normal_vector
Computes a vector of deviates for the standard Normal distribution
Related keywords: data analyticsdeviatesGaussian distributioninverse CDFinverse cumulative distribution functionNormal distributionSimple Calculations on Statistical Data
G01TBF   24  nagf_stat_inv_cdf_students_t_vector
Computes a vector of deviates for Student's t -distribution
Related keywords: data analyticsdeviatesinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical DataStudent's t -distribution
G01TCF   24  nagf_stat_inv_cdf_chisq_vector
Computes a vector of deviates for χ 2 distribution
Related keywords: chi-squared distributiondata analyticsdeviatesinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01TDF   24  nagf_stat_inv_cdf_f_vector
Computes a vector of deviates for F -distribution
Related keywords: data analyticsdeviates F -distributioninverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Datavariance-ratio distribution
G01TEF   24  nagf_stat_inv_cdf_beta_vector
Computes a vector of deviates for the beta distribution
Related keywords: beta distributiondata analyticsdeviatesinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01TFF   24  nagf_stat_inv_cdf_gamma_vector
Computes a vector of deviates for the gamma distribution
Related keywords: data analyticsdeviatesgamma distributioninverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01WAF   24  nagf_stat_moving_average
Computes the mean and standard deviation using a rolling window
Related keywords: data analyticsdata streammeanmoving averageSimple Calculations on Statistical Datastandard deviationstreaming
G02 Chapter Introduction     Correlation and Regression Analysis
Related keywords: correlation analysisdata analyticsnonlinear regressionpolynomial regressionregression analysis
G03AAF   14  nagf_mv_prin_comp
Performs principal component analysis
Related keywords: data analyticsfinancemultivariate methodsprincipal component analysis
G03EAF   16  nagf_mv_distance_mat
Computes distance matrix
Related keywords: data analyticsdistance matrixmultivariate methods
G03ECF   16  nagf_mv_cluster_hier
Hierarchical cluster analysis
Related keywords: cluster analysisdata analyticshierarchical cluster analysismultivariate methods
G03EFF   16  nagf_mv_cluster_kmeans
K -means cluster analysis
Related keywords: cluster analysisdata analytics K -means cluster analysismultivariate methods
G03EHF   16  nagf_mv_cluster_hier_dendrogram
Constructs dendrogram (for use after G03ECF)
Related keywords: data analyticsdendrogramhierarchical cluster analysismultivariate methods
G03EJF   16  nagf_mv_cluster_hier_indicator
Computes cluster indicator variable (for use after G03ECF)
Related keywords: allocatecluster analysisdata analyticshierarchical cluster analysismultivariate methods
G05 Chapter Introduction     Random Number Generators
Related keywords: data analyticsrandom number generators
G13 Chapter Introduction     Time Series Analysis
Related keywords: data analyticstime series analysis
M01 Chapter Introduction     Sorting and Searching
Related keywords: data analyticssearchingsorting
Bilinear interpolation E01EBF   25  nagf_interp_2d_triang_bary_eval
Barycentric interpolation on function values provided on a two-dimensional scattered grid
Related keywords: Barycentric interpolationfinanceinterpolationInterpolationRenka and Cline methodScattered dataScattered data interpolationTriangulation
bilinear matrix inequality E04RPF   26  nagf_opt_handle_set_quadmatineq
Define bilinear matrix terms to a problem initialized by E04RAF
Related keywords: BMIleast squares fittingmatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04SVF   26  nagf_opt_handle_solve_pennon
Run the Pennon solver on a compatible problem initialized by E04RAF and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI)
Related keywords: BMIgeneralized augmented Lagrangian methodLagrangianleast squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionmonitoring informationoptimizationoptimizationSDPsemidefinite programming
binary option S30CAF   22  nagf_specfun_opt_binary_con_price
Binary option, cash-or-nothing pricing formula
Related keywords: approximations of special functionscash-or-nothing optionderivative, optionsfinanceoption pricing
S30CBF   22  nagf_specfun_opt_binary_con_greeks
Binary option, cash-or-nothing pricing formula with Greeks
Related keywords: approximations of special functionscash-or-nothing optionderivative, optionsfinanceGreeks, optionsoption pricing
S30CCF   22  nagf_specfun_opt_binary_aon_price
Binary option, asset-or-nothing pricing formula
Related keywords: approximations of special functionscash-or-nothing optionderivative, optionsfinanceoption pricing
S30CDF   22  nagf_specfun_opt_binary_aon_greeks
Binary option, asset-or-nothing pricing formula with Greeks
Related keywords: approximations of special functionscash-or-nothing optionderivative, optionsfinanceGreeks, optionsoption pricing
binary search method M01NAF   22  nagf_sort_realvec_search
Binary search in set of real numbers
Related keywords: big datadata analyticssearchingsorting
M01NBF   22  nagf_sort_intvec_search
Binary search in set of integer numbers
Related keywords: big datadata analyticssearchingsorting
M01NCF   22  nagf_sort_charvec_search
Binary search in set of character data
Related keywords: big datadata analyticssearchingsorting
binary segmentation G13NDF   25  nagf_tsa_cp_binary
Change point detection, using binary segmentation
Related keywords: big datachange pointdata analyticstime seriestime series analysis
G13NEF   25  nagf_tsa_cp_binary_user
Change point detection, using binary segmentation, user supplied cost function
Related keywords: big datachange pointdata analyticstime seriestime series analysis
binomial distribution G01BJF   13  nagf_stat_prob_binomial
Binomial distribution function
Related keywords: CDF, cumulative distribution functionfinanceSimple Calculations on Statistical Data
G01SJF   24  nagf_stat_prob_binomial_vector
Computes a vector of probabilities for the binomial distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticslower tail probabilitypoint probabilitySimple Calculations on Statistical Dataupper tail probability
G05TAF   22  nagf_rand_int_binomial
Generates a vector of pseudorandom integers from a binomial distribution
Related keywords: big datadata analyticsfinancerandom integersrandom number generators
G07AAF   15  nagf_univar_ci_binomial
Computes confidence interval for the parameter of a binomial distribution
Related keywords: confidence intervalunivariate estimation
biorthogonal wavelet C09AAF   22  nagf_wav_1d_init
One-dimensional wavelet filter initialization
Related keywords: Daubechies waveletHaar waveletwaveletswavelets, one-dimensionalwavelet transforms
C09ABF   23  nagf_wav_2d_init
Two-dimensional wavelet filter initialization
Related keywords: Daubechies waveletHaar waveletwaveletswavelets, two-dimensionalwavelet transforms
C09ACF   24  nagf_wav_3d_init
Three-dimensional wavelet filter initialization
Related keywords: Daubechies waveletHaar waveletwaveletswavelets, three-dimensionalwavelet transforms
bisection method F08JBF   21  nagf_lapackeig_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: DSTEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QR algorithmreal, symmetric, tridiagonal matrix
F08JJF   16  nagf_lapackeig_dstebz
Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection
Related keywords: DSTEBZeigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
bivariate Normal distribution G01HAF   14  nagf_stat_prob_bivariate_normal
Computes probability for the bivariate Normal distribution
Related keywords: financelower tail probabilityNormal distributionSimple Calculations on Statistical Data
bivariate polynomial approximation E02CAF   nagf_fit_2dcheb_lines
Least squares surface fit by polynomials, data on lines parallel to one independent coordinate axis
Related keywords: Chebyshev polynomial approximationcurve and surface fittingdata-on-lines polynomial approximationleast squarespolynomial approximationtwo-dimensional polynomial approximation
E02CBF   nagf_fit_2dcheb_eval
Evaluation of fitted polynomial in two variables
Related keywords: Chebyshev polynomial approximationcurve and surface fittingpolynomial approximationtwo-dimensional polynomial approximation
bivariate spectra G13CEF   10  nagf_tsa_multi_spectrum_bivar
Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra
Related keywords: big datacoherency, squared, time seriescross amplitude spectrumdata analyticsfinancemultivariate time seriessquared coherencytime seriestime series analysis
bivariate Student's t -distribution G01HCF   23  nagf_stat_prob_bivariate_students_t
Computes probabilities for the bivariate Student's t -distribution
Related keywords: probabilitySimple Calculations on Statistical DataStudent's t -distribution
bivariate time series G13CFF   10  nagf_tsa_multi_gain_bivar
Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra
Related keywords: big datacross-spectrumdata analyticsfinancegain, time seriesmultivariate time seriesphase, time seriestime seriestime series analysis
Bi , derivative Airy function S17AKF   nagf_specfun_airy_bi_deriv
Airy function Bi x
Related keywords: Airy functionapproximations of special functionsfinance
S17AXF   24  nagf_specfun_airy_bi_deriv_vector
Derivatives of the Airy function, vectorized Bi x
Related keywords: Airy functionapproximations of special functions
S17DHF   13  nagf_specfun_airy_bi_complex
Airy functions Bi z and Bi z , complex z
Related keywords: Airy functionapproximations of special functions Bi , Airy functionfinance
Bjerksund and Stensland pricing formula S30QCF   22  nagf_specfun_opt_amer_bs_price
American option, Bjerksund and Stensland pricing formula
Related keywords: American optionsapproximations of special functionsfinance
Black–Scholes option pricing D03NCF   20  nagf_pde_1d_blackscholes_fd
Finite difference solution of the Black–Scholes equations
Related keywords: one-dimensionalparabolic partial differential equationPDE, partial differential equations
D03NDF   20  nagf_pde_1d_blackscholes_closed
Analytic solution of the Black–Scholes equations
Related keywords: parabolic partial differential equationPDE, partial differential equations
D03NEF   20  nagf_pde_1d_blackscholes_means
Compute average values for D03NDF
Related keywords: parabolic partial differential equationPDE, partial differential equations
S30AAF   22  nagf_specfun_opt_bsm_price
Black–Scholes–Merton option pricing formula
Related keywords: approximations of special functionsderivative, optionsfinanceoption pricing
S30ABF   22  nagf_specfun_opt_bsm_greeks
Black–Scholes–Merton option pricing formula with Greeks
Related keywords: approximations of special functionsderivative, optionsfinanceGreeks, optionsoption pricing
blas F16ECF   24  nagf_blast_daxpby
Real weighted vector addition
Related keywords: blas_daxpbyfurther linear algebra support routinessum, vector
F16EHF   22  nagf_blast_dwaxpby
Real weighted vector addition preserving input
Related keywords: blas_dwaxpbyfurther linear algebra support routinessum, vector
F16ELF   22  nagf_blast_dsum
Sum elements of real vector
Related keywords: blas_dsumfurther linear algebra support routinessum, vector
F16GCF   24  nagf_blast_zaxpby
Complex weighted vector addition
Related keywords: blas_zaxpbyfurther linear algebra support routinessum, vector
F16GHF   22  nagf_blast_zwaxpby
Complex weighted vector addition preserving input
Related keywords: blas_zwaxpbyfurther linear algebra support routinessum, vector
F16GLF   22  nagf_blast_zsum
Sum elements of complex vector
Related keywords: blas_zsumfurther linear algebra support routinessum, vector
F16JNF   22  nagf_blast_dmax_val
Maximum value and location, real vector
Related keywords: blas_dmax_valfurther linear algebra support routinesmaximum value
F16JPF   22  nagf_blast_dmin_val
Minimum value and location, real vector
Related keywords: blas_dmax_valfurther linear algebra support routinesminimum value
F16JQF   22  nagf_blast_damax_val
Maximum absolute value and location, real vector
Related keywords: absolute valueblas_damax_valfurther linear algebra support routinesmaximum value
F16JRF   22  nagf_blast_damin_val
Minimum absolute value and location, real vector
Related keywords: absolute valueblas_damin_valfurther linear algebra support routinesminimum value
F16JSF   22  nagf_blast_zamax_val
Maximum absolute value and location, complex vector
Related keywords: absolute valueblas_zamax_valfurther linear algebra support routinesmaximum value
F16JTF   22  nagf_blast_zamin_val
Minimum absolute value and location, complex vector
Related keywords: absolute valueblas_zamin_valfurther linear algebra support routinesminimum value
BLAS F06 Chapter Introduction     Linear Algebra Support Routines
Related keywords: linear algebra support routines
F06WAF   23  nagf_blas_dlansf
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format
Related keywords: 1-normblas, real matricesdlansfFrobenius norminfinity-normlinear algebra support routineslinear algebra support routines;real, symmetric matrix
F06WBF   23  nagf_blas_dtfsm
Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix, Rectangular Full Packed format
Related keywords: blas, real matricesdtfsmlinear algebra support routineslinear algebra support routines;linear equationsreal, triangular matrix
F06WNF   23  nagf_blas_zlanhf
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format
Related keywords: 1-normblas, complex matricescomplex, Hermitian matrixFrobenius norminfinity-normlinear algebra support routineslinear algebra support routines;zlanhf
F06WPF   23  nagf_blas_ztfsm
Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix, Rectangular Full Packed format
Related keywords: blas, complex matricescomplex, triangular matrixlinear algebra support routineslinear algebra support routines;linear equationsztfsm
blas_damax_val F16JQF   22  nagf_blast_damax_val
Maximum absolute value and location, real vector
Related keywords: absolute valueblasfurther linear algebra support routinesmaximum value
blas_damin_val F16JRF   22  nagf_blast_damin_val
Minimum absolute value and location, real vector
Related keywords: absolute valueblasfurther linear algebra support routinesminimum value
blas_daxpby F16ECF   24  nagf_blast_daxpby
Real weighted vector addition
Related keywords: blasfurther linear algebra support routinessum, vector
blas_dmax_val F16JNF   22  nagf_blast_dmax_val
Maximum value and location, real vector
Related keywords: blasfurther linear algebra support routinesmaximum value
F16JPF   22  nagf_blast_dmin_val
Minimum value and location, real vector
Related keywords: blasfurther linear algebra support routinesminimum value
blas_dsum F16ELF   22  nagf_blast_dsum
Sum elements of real vector
Related keywords: blasfurther linear algebra support routinessum, vector
blas_dwaxpby F16EHF   22  nagf_blast_dwaxpby
Real weighted vector addition preserving input
Related keywords: blasfurther linear algebra support routinessum, vector
blas_zamax_val F16JSF   22  nagf_blast_zamax_val
Maximum absolute value and location, complex vector
Related keywords: absolute valueblasfurther linear algebra support routinesmaximum value
blas_zamin_val F16JTF   22  nagf_blast_zamin_val
Minimum absolute value and location, complex vector
Related keywords: absolute valueblasfurther linear algebra support routinesminimum value
blas_zaxpby F16GCF   24  nagf_blast_zaxpby
Complex weighted vector addition
Related keywords: blasfurther linear algebra support routinessum, vector
blas_zsum F16GLF   22  nagf_blast_zsum
Sum elements of complex vector
Related keywords: blasfurther linear algebra support routinessum, vector
blas_zwaxpby F16GHF   22  nagf_blast_zwaxpby
Complex weighted vector addition preserving input
Related keywords: blasfurther linear algebra support routinessum, vector
blas, complex matrices F06GAF   12  nagf_blas_zdotu
Dot product of two complex vectors, unconjugated
Related keywords: BLASinner productlinear algebra support routineszdotu
F06GBF   12  nagf_blas_zdotc
Dot product of two complex vectors, conjugated
Related keywords: BLASinner productlinear algebra support routineszdotc
F06GCF   12  nagf_blas_zaxpy
Add scalar times complex vector to complex vector
Related keywords: BLASelementary arithmeticlinear algebra support routineszaxpy
F06GDF   12  nagf_blas_zscal
Multiply complex vector by complex scalar
Related keywords: BLASelementary arithmeticlinear algebra support routineszscal
F06GFF   12  nagf_blas_zcopy
Copy complex vector
Related keywords: BLASelementary arithmeticlinear algebra support routineszcopy
F06GGF   12  nagf_blas_zswap
Swap two complex vectors
Related keywords: BLASelementary arithmeticlinear algebra support routineszswap
F06GRF   14  nagf_blas_zdotui
Dot product of a complex sparse and a full vector, unconjugated
Related keywords: BLASinner productlinear algebra support routineszdotui
F06GSF   14  nagf_blas_zdotci
Dot product of a complex sparse and a full vector, conjugated
Related keywords: BLASinner productlinear algebra support routineszdotci
F06GTF   14  nagf_blas_zaxpyi
Add scalar times complex sparse vector to a full vector
Related keywords: BLASinner productlinear algebra support routineszaxpyi
F06GUF   14  nagf_blas_zgthr
Gather complex sparse vector
Related keywords: BLASelementary arithmeticlinear algebra support routineszgthr
F06GVF   14  nagf_blas_zgthrz
Gather and set to zero complex sparse vector
Related keywords: BLASelementary arithmeticlinear algebra support routineszgthrz
F06GWF   14  nagf_blas_zsctr
Scatter complex sparse vector
Related keywords: BLASelementary arithmeticlinear algebra support routineszsctr
F06HMF   21  nagf_blas_zrot
Apply plane rotation with real cosine and complex sine
Related keywords: BLASlinear algebra support routinesrotation, elementaryzrot
F06JDF   12  nagf_blas_zdscal
Multiply complex vector by real scalar
Related keywords: BLASelementary arithmeticlinear algebra support routineszdscal
F06JJF   12  nagf_blas_dznrm2
Compute Euclidean norm of complex vector
Related keywords: BLASdznrm2Euclidean normfinancelinear algebra support routines
F06JKF   12  nagf_blas_dzasum
Sum absolute values of complex vector elements
Related keywords: BLASdzasumelementary arithmeticlinear algebra support routines
F06JMF   12  nagf_blas_izamax
Index, complex vector element with largest absolute value
Related keywords: BLASelementary arithmeticizamaxlinear algebra support routines
F06SAF   12  nagf_blas_zgemv
Matrix-vector product, complex rectangular matrix
Related keywords: BLAScomplex, m by n matrixlinear algebra support routinesmultiply, matrixzgemv
F06SBF   12  nagf_blas_zgbmv
Matrix-vector product, complex rectangular band matrix
Related keywords: BLAScomplex, band, m by n matrixlinear algebra support routinesmatrix, bandmultiply, matrixzgbmv
F06SCF   12  nagf_blas_zhemv
Matrix-vector product, complex Hermitian matrix
Related keywords: BLAScomplex, Hermitian matrixlinear algebra support routinesmultiply, matrixzhemv
F06SDF   12  nagf_blas_zhbmv
Matrix-vector product, complex Hermitian band matrix
Related keywords: BLAScomplex, band, Hermitian matrixlinear algebra support routinesmatrix, bandmultiply, matrixzhbmv
F06SEF   12  nagf_blas_zhpmv
Matrix-vector product, complex Hermitian packed matrix
Related keywords: BLAScomplex, Hermitian matrixlinear algebra support routinesmultiply, matrixzhpmv
F06SFF   12  nagf_blas_ztrmv
Matrix-vector product, complex triangular matrix
Related keywords: BLAScomplex, triangular matrixlinear algebra support routinesmultiply, matrixztrmv
F06SGF   12  nagf_blas_ztbmv
Matrix-vector product, complex triangular band matrix
Related keywords: BLAScomplex, band, triangular matrixlinear algebra support routinesmatrix, bandmultiply, matrixztbmv
F06SHF   12  nagf_blas_ztpmv
Matrix-vector product, complex triangular packed matrix
Related keywords: BLAScomplex, triangular matrixlinear algebra support routinesmultiply, matrixztpmv
F06SJF   12  nagf_blas_ztrsv
System of equations, complex triangular matrix
Related keywords: BLAScomplex, triangular matrixlinear algebra support routineslinear equationsztrsv
F06SKF   12  nagf_blas_ztbsv
System of equations, complex triangular band matrix
Related keywords: BLAScomplex, band, triangular matrixlinear algebra support routineslinear equationsmatrix, bandztbsv
F06SLF   12  nagf_blas_ztpsv
System of equations, complex triangular packed matrix
Related keywords: BLAScomplex, triangular matrixlinear algebra support routineslinear equationsztbsv
F06SMF   12  nagf_blas_zgeru
Rank-1 update, complex rectangular matrix, unconjugated vector
Related keywords: BLAScomplex, m by n matrixlinear algebra support routinesrank k matrix updateszgeru
F06SNF   12  nagf_blas_zgerc
Rank-1 update, complex rectangular matrix, conjugated vector
Related keywords: BLAScomplex, m by n matrixlinear algebra support routinesrank k matrix updateszgerc
F06SPF   12  nagf_blas_zher
Rank-1 update, complex Hermitian matrix
Related keywords: BLAScomplex, Hermitian matrixlinear algebra support routinesrank k matrix updateszher
F06SQF   12  nagf_blas_zhpr
Rank-1 update, complex Hermitian packed matrix
Related keywords: BLAScomplex, Hermitian matrixlinear algebra support routinesrank k matrix updateszhpr
F06SRF   12  nagf_blas_zher2
Rank-2 update, complex Hermitian matrix
Related keywords: BLAScomplex, Hermitian matrixlinear algebra support routinesrank k matrix updateszher2
F06SSF   12  nagf_blas_zhpr2
Rank-2 update, complex Hermitian packed matrix
Related keywords: BLAScomplex, Hermitian matrixlinear algebra support routinesrank k matrix updateszhpr2
F06WNF   23  nagf_blas_zlanhf
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format
Related keywords: 1-normBLASBLAScomplex, Hermitian matrixFrobenius norminfinity-normlinear algebra support routineslinear algebra support routines;zlanhf
F06WPF   23  nagf_blas_ztfsm
Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix, Rectangular Full Packed format
Related keywords: BLASBLAScomplex, triangular matrixlinear algebra support routineslinear algebra support routines;linear equationsztfsm
F06WQF   23  nagf_blas_zhfrk
Rank- k update of a complex Hermitian matrix, Rectangular Full Packed format
Related keywords: BLAScomplex, Hermitian, indefinite matrixlinear algebra support routinesrank k matrix updateszherk
F06ZAF   14  nagf_blas_zgemm
Matrix-matrix product, two complex rectangular matrices
Related keywords: BLAScomplex, m by n matrixlinear algebra support routinesmultiply, matrixzgemm
F06ZCF   14  nagf_blas_zhemm
Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix
Related keywords: BLAScomplex, Hermitian, indefinite matrixcomplex, m by n matrixlinear algebra support routinesmultiply, matrixzgemm
F06ZFF   14  nagf_blas_ztrmm
Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix
Related keywords: BLAScomplex, m by n matrixcomplex, triangular matrixlinear algebra support routinesmultiply, matrixztrmm
F06ZJF   14  nagf_blas_ztrsm
Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix
Related keywords: BLAScomplex, triangular matrixlinear algebra support routineslinear least squaresztrsm
F06ZPF   14  nagf_blas_zherk
Rank- k update of a complex Hermitian matrix
Related keywords: BLAScomplex, Hermitian, indefinite matrixlinear algebra support routinesrank k matrix updateszherk
F06ZRF   14  nagf_blas_zher2k
Rank- 2 k update of a complex Hermitian matrix
Related keywords: BLAScomplex, Hermitian, indefinite matrixlinear algebra support routinesrank k matrix updateszher2k
F06ZTF   14  nagf_blas_zsymm
Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix
Related keywords: BLAScomplex, m by n matrixcomplex, symmetric matrixlinear algebra support routinesmultiply, matrixzsymm
F06ZUF   14  nagf_blas_zsyrk
Rank- k update of a complex symmetric matrix
Related keywords: BLAScomplex, symmetric matrixlinear algebra support routinesrank k matrix updateszher2k
F06ZWF   14  nagf_blas_zsyr2k
Rank- 2 k update of a complex symmetric matrix
Related keywords: BLAScomplex, symmetric matrixlinear algebra support routinesrank k matrix updateszsyr2k
blas, real matrices F06AAF   12  nagf_blas_drotg
Generate real plane rotation
Related keywords: BLASdrotglinear algebra support routinesrotation, elementary
F06EAF   12  nagf_blas_ddot
Dot product of two real vectors
Related keywords: BLASddotfinanceinner productlinear algebra support routines
F06ECF   12  nagf_blas_daxpy
Add scalar times real vector to real vector
Related keywords: BLASdaxpyelementary arithmeticlinear algebra support routines
F06EDF   12  nagf_blas_dscal
Multiply real vector by scalar
Related keywords: BLASdscalelementary arithmeticlinear algebra support routines
F06EFF   12  nagf_blas_dcopy
Copy real vector
Related keywords: BLASdcopyelementary arithmeticfinancelinear algebra support routines
F06EGF   12  nagf_blas_dswap
Swap two real vectors
Related keywords: BLASdswapelementary arithmeticlinear algebra support routines
F06EJF   12  nagf_blas_dnrm2
Compute Euclidean norm of real vector
Related keywords: BLASdnrm2elementary arithmeticEuclidean normfinancelinear algebra support routines
F06EKF   12  nagf_blas_dasum
Sum absolute values of real vector elements
Related keywords: BLASdasumelementary arithmeticlinear algebra support routines
F06EPF   12  nagf_blas_drot
Apply real plane rotation
Related keywords: BLASdrotlinear algebra support routinesrotation, elementary
F06ERF   14  nagf_blas_ddoti
Dot product of a real sparse and a full vector
Related keywords: BLASddotiinner productlinear algebra support routines
F06ETF   14  nagf_blas_daxpyi
Add scalar times real sparse vector to a full vector
Related keywords: BLASdaxpyelementary arithmeticlinear algebra support routines
F06EUF   14  nagf_blas_dgthr
Gather real sparse vector
Related keywords: BLASdgthrelementary arithmeticlinear algebra support routines
F06EVF   14  nagf_blas_dgthrz
Gather and set to zero real sparse vector
Related keywords: BLASdgthrzelementary arithmeticlinear algebra support routines
F06EWF   14  nagf_blas_dsctr
Scatter real sparse vector
Related keywords: BLASdgthrzelementary arithmeticlinear algebra support routines
F06EXF   14  nagf_blas_droti
Apply plane rotation to a real sparse and a full vector
Related keywords: BLASdrotilinear algebra support routinesrotation, elementary
F06JLF   12  nagf_blas_idamax
Index, real vector element with largest absolute value
Related keywords: BLASelementary arithmeticidamaxlinear algebra support routines
F06PAF   12  nagf_blas_dgemv
Matrix-vector product, real rectangular matrix
Related keywords: BLASdgemvfinancelinear algebra support routinesmultiply, matrixreal, m by n matrix
F06PBF   12  nagf_blas_dgbmv
Matrix-vector product, real rectangular band matrix
Related keywords: BLASdgbmvlinear algebra support routinesmatrix, bandmultiply, matrixreal, band, m by n matrix
F06PCF   12  nagf_blas_dsymv
Matrix-vector product, real symmetric matrix
Related keywords: BLASdsymvlinear algebra support routinesmultiply, matrixreal, indefinite, symmetric matrix
F06PDF   12  nagf_blas_dsbmv
Matrix-vector product, real symmetric band matrix
Related keywords: BLASdsbmvlinear algebra support routinesmatrix, bandmultiply, matrixreal, band, symmetric matrix
F06PEF   12  nagf_blas_dspmv
Matrix-vector product, real symmetric packed matrix
Related keywords: BLASdspmvlinear algebra support routinesmultiply, matrixreal, indefinite, symmetric matrix
F06PFF   12  nagf_blas_dtrmv
Matrix-vector product, real triangular matrix
Related keywords: BLASdtrmvlinear algebra support routinesmultiply, matrixreal, triangular matrix
F06PGF   12  nagf_blas_dtbmv
Matrix-vector product, real triangular band matrix
Related keywords: BLASdtbmvlinear algebra support routinesmatrix, bandmultiply, matrixreal, band, triangular matrix
F06PHF   12  nagf_blas_dtpmv
Matrix-vector product, real triangular packed matrix
Related keywords: BLASdtpmvlinear algebra support routinesmultiply, matrixreal, triangular matrix
F06PJF   12  nagf_blas_dtrsv
System of equations, real triangular matrix
Related keywords: BLASdtrsvfinancelinear algebra support routineslinear equationsreal, triangular matrix
F06PKF   12  nagf_blas_dtbsv
System of equations, real triangular band matrix
Related keywords: BLASdtbsvlinear algebra support routineslinear equationsmatrix, bandreal, band, triangular matrix
F06PLF   12  nagf_blas_dtpsv
System of equations, real triangular packed matrix
Related keywords: BLASdtpsvlinear algebra support routineslinear equationsreal, triangular matrix
F06PMF   12  nagf_blas_dger
Rank-1 update, real rectangular matrix
Related keywords: BLASdgerlinear algebra support routinesrank k matrix updatesreal, m by n matrix
F06PPF   12  nagf_blas_dsyr
Rank-1 update, real symmetric matrix
Related keywords: BLASdsyrlinear algebra support routinesrank k matrix updatesreal, indefinite, symmetric matrix
F06PQF   12  nagf_blas_dspr
Rank-1 update, real symmetric packed matrix
Related keywords: BLASdsprlinear algebra support routinesrank k matrix updatesreal, indefinite, symmetric matrix
F06PRF   12  nagf_blas_dsyr2
Rank-2 update, real symmetric matrix
Related keywords: BLASdsyr2linear algebra support routinesrank k matrix updatesreal, indefinite, symmetric matrix
F06PSF   12  nagf_blas_dspr2
Rank-2 update, real symmetric packed matrix
Related keywords: BLASdspr2linear algebra support routinesrank k matrix updatesreal, indefinite, symmetric matrix
F06WAF   23  nagf_blas_dlansf
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format
Related keywords: 1-normBLASBLASdlansfFrobenius norminfinity-normlinear algebra support routineslinear algebra support routines;real, symmetric matrix
F06WBF   23  nagf_blas_dtfsm
Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix, Rectangular Full Packed format
Related keywords: BLASBLASdtfsmlinear algebra support routineslinear algebra support routines;linear equationsreal, triangular matrix
F06WCF   23  nagf_blas_dsfrk
Rank- k update of a real symmetric matrix, Rectangular Full Packed format
Related keywords: BLASdsfrklinear algebra support routinesrank k matrix updatesreal, indefinite, symmetric matrix
F06YAF   14  nagf_blas_dgemm
Matrix-matrix product, two real rectangular matrices
Related keywords: BLASdgemmfinancelinear algebra support routinesmultiply, matrixreal, m by n matrix
F06YCF   14  nagf_blas_dsymm
Matrix-matrix product, one real symmetric matrix, one real rectangular matrix
Related keywords: BLASdsymmlinear algebra support routinesmultiply, matrixreal, indefinite, symmetric matrixreal, m by n matrix
F06YFF   14  nagf_blas_dtrmm
Matrix-matrix product, one real triangular matrix, one real rectangular matrix
Related keywords: BLASdsymmlinear algebra support routinesmultiply, matrixreal, m by n matrixreal, triangular matrix
F06YJF   14  nagf_blas_dtrsm
Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix
Related keywords: BLASfinancelinear algebra support routineslinear equationsreal, triangular matrix
F06YPF   14  nagf_blas_dsyrk
Rank- k update of a real symmetric matrix
Related keywords: BLASdsyrklinear algebra support routinesreal, indefinite, symmetric matrix
F06YRF   14  nagf_blas_dsyr2k
Rank- 2 k update of a real symmetric matrix
Related keywords: BLASdsyr2klinear algebra support routinesrank k matrix updatesreal, indefinite, symmetric matrix
Blend method D02NWF   12  nagf_ode_ivp_stiff_blend
Ordinary differential equations, initial value problem, Blend method, setup for d02m–n routines
Related keywords: initial value problemODE, ordinary differential equationsstiff differential equations
D02XJF   12  nagf_ode_ivp_stiff_nat_interp
Ordinary differential equations, initial value problem, interpolation for d02m–n routines (BLEND and BDF methods only), natural interpolant
Related keywords: backward difference formulainitial value probleminterpolationODE, ordinary differential equations
Blom scores G01DHF   15  nagf_stat_ranks_and_scores
Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores
Related keywords: exponential scoresfinancerank scoresSavage scoresSimple Calculations on Statistical DataTukey scoresvan der Waerden scores
BMI E04RPF   26  nagf_opt_handle_set_quadmatineq
Define bilinear matrix terms to a problem initialized by E04RAF
Related keywords: bilinear matrix inequalityleast squares fittingmatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04SVF   26  nagf_opt_handle_solve_pennon
Run the Pennon solver on a compatible problem initialized by E04RAF and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI)
Related keywords: bilinear matrix inequalitygeneralized augmented Lagrangian methodLagrangianleast squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionmonitoring informationoptimizationoptimizationSDPsemidefinite programming
BOBYQA method E04JCF   23  nagf_opt_bounds_bobyqa_func
Bound constrained minimum, model-based algorithm, using function values only
Related keywords: financemaximizing a functionminimization, simple bound constraintsminimizing a functionNLPnonlinear programmingoptimization
boundary mesh D06BAF   20  nagf_mesh_2d_gen_boundary
Generates a boundary mesh
Related keywords: mesh generation
boundary value problem D02AGF   nagf_ode_bvp_shoot_genpar_intern
Ordinary differential equations, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined
Related keywords: BVPODE, ordinary differential equationsshooting method, ODE
D02GAF   nagf_ode_bvp_fd_nonlin_fixedbc
Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem
Related keywords: BVPfinite difference method, ODEODE, ordinary differential equations
D02GBF   nagf_ode_bvp_fd_lin_gen
Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, general linear problem
Related keywords: BVPfinite difference method, ODEODE, ordinary differential equations
D02HAF   nagf_ode_bvp_shoot_bval
Ordinary differential equations, boundary value problem, shooting and matching, boundary values to be determined
Related keywords: BVPODE, ordinary differential equationsshooting method, ODE
D02HBF   nagf_ode_bvp_shoot_genpar
Ordinary differential equations, boundary value problem, shooting and matching, general parameters to be determined
Related keywords: BVPODE, ordinary differential equationsshooting method, ODE
D02JAF   nagf_ode_bvp_coll_nth
Ordinary differential equations, boundary value problem, collocation and least squares, single n th-order linear equation
Related keywords: BVPcollocation methodODE, ordinary differential equations
D02JBF   nagf_ode_bvp_coll_sys
Ordinary differential equations, boundary value problem, collocation and least squares, system of first-order linear equations
Related keywords: BVPcollocation methodODE, ordinary differential equations
D02KAF   nagf_ode_sl2_reg_finite
Second-order Sturm–Liouville problem, regular system, finite range, eigenvalue only
Related keywords: BVPeigenproblemODE, ordinary differential equationsSturm–Liouville equations
D02KDF   nagf_ode_sl2_breaks_vals
Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points
Related keywords: BVPeigenproblemgeneralODE, ordinary differential equationsSturm–Liouville equations
D02KEF   nagf_ode_sl2_breaks_funs
Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points
Related keywords: BVPeigenproblemODE, ordinary differential equationsSturm–Liouville equations
D02SAF   nagf_ode_bvp_shoot_genpar_algeq
Ordinary differential equations, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined
Related keywords: BVPODE, ordinary differential equationsparameterized first ordershooting method, ODEtwo-point boundary value problem
D02TLF   25  nagf_ode_bvp_coll_nlin_solve
Ordinary differential equations, general nonlinear boundary value problem, collocation technique (thread safe)
Related keywords: BVPdifferential equationsnonlinear mixed orderODE, ordinary differential equationsordinary differential equationstwo-point boundary value problem
D02UEF   23  nagf_ode_bvp_ps_lin_solve
Solve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation
Related keywords: BVPGauss–Lobatto gridODE, ordinary differential equationspseudo-spectral method
bound box E04RHF   26  nagf_opt_handle_set_simplebounds
Define bounds of variables of a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
bounded influence G02HBF   13  nagf_correg_robustm_wts
Robust regression, compute weights for use with G02HDF
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysisrobust regression
G02HDF   13  nagf_correg_robustm_user
Robust regression, compute regression with user-supplied functions and weights
Related keywords: big datacorrelation analysisdata analyticsfinanceiterative weighted least squares M -estimatesnonlinear regressionpolynomial regressionregression analysisrobust regression
box and whisker plot G01ASF   14  nagf_stat_plot_box_whisker
Constructs a box and whisker plot
Related keywords: Simple Calculations on Statistical Data
Box–Jenkins models G13ASF   13  nagf_tsa_uni_arima_resid
Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF
Related keywords: ARMAautocorrelation functionbig dataBox–Ljung portmanteau statisticdata analyticsfinancesignificancestandard errorstime seriestime series analysisunivariate time series
Box–Ljung portmanteau statistic G13ASF   13  nagf_tsa_uni_arima_resid
Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF
Related keywords: ARMAautocorrelation functionbig dataBox–Jenkins modelsdata analyticsfinancesignificancestandard errorstime seriestime series analysisunivariate time series
branch and bound H02BBF   14  nagf_mip_ilp_dense
Integer LP problem (dense)
Related keywords: financeinteger programmingmixed integer programmingoperations research
H02BFF   16  nagf_mip_ilp_mpsx
Interpret MPSX data file defining IP or LP problem, optimize and print solution
Related keywords: integer programmingmixed integer programmingMPSX formatoperations research
H02CBF   19  nagf_mip_iqp_dense
Integer QP problem (dense)
Related keywords: financeinteger programminginteger quadratic programmixed integer programmingoperations researchQP, quadratic programming
H02CEF   19  nagf_mip_iqp_sparse
Integer LP or QP problem (sparse), using E04NKF
Related keywords: financeinteger programminginteger quadratic programmixed integer programmingoperations researchQP, quadratic programming
Brent algorithm C05AUF   23  nagf_roots_contfn_brent_interval
Zero of continuous function, Brent algorithm, from a given starting value, binary search for interval
Related keywords: financeroot-findingroots of transcendental equationszeros of transcendental functions
C05AYF   23  nagf_roots_contfn_brent
Zero of continuous function in a given interval, Brent algorithm
Related keywords: financeroot-findingroots of transcendental equationszeros of transcendental functions
C05AZF   nagf_roots_contfn_brent_rcomm
Zero of continuous function in a given interval, Brent algorithm (reverse communication)
Related keywords: financeroot-findingroots of transcendental equationszeros of transcendental functions
brownian bridge G05XAF   24  nagf_rand_bb_init
Initializes the Brownian bridge generator
Related keywords: big datadata analyticsoptions, computationalrandom number generators
G05XBF   24  nagf_rand_bb
Generate paths for a free or non-free Wiener process using the Brownian bridge algorithm
Related keywords: big datadata analyticsrandom number generatorsWiener process
G05XCF   24  nagf_rand_bb_inc_init
Initializes the generator which backs out the increments of sample paths generated by a Brownian bridge algorithm
Related keywords: big datadata analyticsoptions, computationalrandom number generators
G05XDF   24  nagf_rand_bb_inc
Backs out the increments from sample paths generated by a Brownian bridge algorithm
Related keywords: big datadata analyticsrandom number generators
G05XEF   24  nagf_rand_bb_make_bridge_order
Creates a Brownian bridge construction order out of a set of input times
Related keywords: big datadata analyticsrandom number generators
Brownian motion G05ZTF   24  nagf_rand_field_fracbm_generate
Generates realizations of fractional Brownian motion
Related keywords: big datadata analyticsfractional Brownian motionrandom number generators
Browns Exponential G13AMF   22  nagf_tsa_uni_smooth_exp
Univariate time series, exponential smoothing
Related keywords: big datadata analyticsexponential smoothingfinanceHolt WinterLinear Holttime seriestime series analysisunivariate time series
B-splines E02BAF   nagf_fit_1dspline_knots
Least squares curve cubic spline fit (including interpolation)
Related keywords: cubic splinescurve and surface fittingknotsleast squares
E02BBF   nagf_fit_1dspline_eval
Evaluation of fitted cubic spline, function only
Related keywords: cubic splinescurve and surface fittingfinance
E02BEF   13  nagf_fit_1dspline_auto
Least squares cubic spline curve fit, automatic knot placement
Related keywords: cubic splinescurve and surface fittingleast squaressmoothing
E02DAF   nagf_fit_2dspline_panel
Least squares surface fit, bicubic splines
Related keywords: bicubic splinescurve and surface fittingknotsleast squarestwo-dimensional spline approximation
E02DCF   13  nagf_fit_2dspline_grid
Least squares surface fit by bicubic splines with automatic knot placement, data on rectangular grid
Related keywords: bicubic splinescurve and surface fittingleast squaressmoothingtwo-dimensional spline approximation
E02DDF   13  nagf_fit_2dspline_sctr
Least squares surface fit by bicubic splines with automatic knot placement, scattered data
Related keywords: bicubic splinescurve and surface fittingleast squaresscattered datasmoothing
E02DEF   14  nagf_fit_2dspline_evalv
Evaluation of fitted bicubic spline at a vector of points
Related keywords: bicubic splinescurve and surface fittingfinance
E02DFF   14  nagf_fit_2dspline_evalm
Evaluation of fitted bicubic spline at a mesh of points
Related keywords: bicubic splinescurve and surface fittingfinancegridded data
b-splines, derivative E02BCF   nagf_fit_1dspline_deriv
Evaluation of fitted cubic spline, function and derivatives
Related keywords: cubic splinescurve and surface fittingfinance
E02BFF   24  nagf_fit_1dspline_deriv_vector
Evaluation of fitted cubic spline, function and optionally derivatives at a vector of points
Related keywords: cubic splinescurve and surface fitting
b-splines, integral E02BDF   nagf_fit_1dspline_integ
Evaluation of fitted cubic spline, definite integral
Related keywords: cubic splinescurve and surface fitting
Bunch–Kaufman factorization F07MDF   15  nagf_lapacklin_dsytrf
Bunch–Kaufman factorization of real symmetric indefinite matrix
Related keywords: diagonal pivoting methodDSYTRFLAPACKlinear equationsreal, indefinite, symmetric matrix
F07MEF   15  nagf_lapacklin_dsytrs
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MDF
Related keywords: diagonal pivoting methodDSYTRSLAPACKlinear equationsreal, indefinite, symmetric matrix
F07MGF   15  nagf_lapacklin_dsycon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MDF
Related keywords: condition number, matrixdiagonal pivoting methodDSYCONLAPACKlinear equationsreal, indefinite, symmetric matrix
F07MHF   15  nagf_lapacklin_dsyrfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides
Related keywords: backward errordiagonal pivoting methodDSYRFSforward errorLAPACKlinear equationsreal, indefinite, symmetric matrix
F07MJF   15  nagf_lapacklin_dsytri
Inverse of real symmetric indefinite matrix, matrix already factorized by F07MDF
Related keywords: diagonal pivoting methodDSYTRIinverse, matrixLAPACKlinear equationsreal, indefinite, symmetric matrix
F07MRF   15  nagf_lapacklin_zhetrf
Bunch–Kaufman factorization of complex Hermitian indefinite matrix
Related keywords: complex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACKlinear equationsZHETRF
F07MSF   15  nagf_lapacklin_zhetrs
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MRF
Related keywords: complex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACKlinear equationsZHETRS
F07MUF   15  nagf_lapacklin_zhecon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07MRF
Related keywords: complex, Hermitian, indefinite matrixcondition number, matrixdiagonal pivoting methodLAPACKlinear equationsZHECON
F07MVF   15  nagf_lapacklin_zherfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, Hermitian, indefinite matrixdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equationsZHERFS
F07MWF   15  nagf_lapacklin_zhetri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07MRF
Related keywords: complex, Hermitian, indefinite matrixdiagonal pivoting methodinverse, matrixLAPACKlinear equationsZHETRI
F07NRF   15  nagf_lapacklin_zsytrf
Bunch–Kaufman factorization of complex symmetric matrix
Related keywords: complex, symmetric matrixdiagonal pivoting methodLAPACKlinear equationsZSYTRF
F07NSF   15  nagf_lapacklin_zsytrs
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07NRF
Related keywords: complex, symmetric matrixdiagonal pivoting methodLAPACKlinear equationsZSYTRS
F07NUF   15  nagf_lapacklin_zsycon
Estimate condition number of complex symmetric matrix, matrix already factorized by F07NRF
Related keywords: complex, symmetric matrixcondition number, matrixdiagonal pivoting methodLAPACKlinear equationsZSYCON
F07NVF   15  nagf_lapacklin_zsyrfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, symmetric matrixdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equationsZSYRFS
F07NWF   15  nagf_lapacklin_zsytri
Inverse of complex symmetric matrix, matrix already factorized by F07NRF
Related keywords: complex, symmetric matrixdiagonal pivoting methodinverse, matrixLAPACKlinear equationsZSYTRI
F07PDF   15  nagf_lapacklin_dsptrf
Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage
Related keywords: diagonal pivoting methodDSPTRFLAPACKlinear equationsreal, indefinite, symmetric matrix
F07PEF   15  nagf_lapacklin_dsptrs
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PDF, packed storage
Related keywords: diagonal pivoting methodDSPTRSLAPACKlinear equationsreal, indefinite, symmetric matrix
F07PGF   15  nagf_lapacklin_dspcon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage
Related keywords: condition number, matrixdiagonal pivoting methodDSPCONLAPACKlinear equationsreal, indefinite, symmetric matrix
F07PHF   15  nagf_lapacklin_dsprfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errordiagonal pivoting methodDSPRFSforward errorLAPACKlinear equationsreal, indefinite, symmetric matrix
F07PJF   15  nagf_lapacklin_dsptri
Inverse of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage
Related keywords: diagonal pivoting methodDSPTRIinverse, matrixLAPACKlinear equationsreal, indefinite, symmetric matrix
F07PRF   15  nagf_lapacklin_zhptrf
Bunch–Kaufman factorization of complex Hermitian indefinite matrix, packed storage
Related keywords: complex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACKlinear equationsZHPTRF
F07PSF   15  nagf_lapacklin_zhptrs
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PRF, packed storage
Related keywords: complex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACKlinear equationsZHPTRS
F07PUF   15  nagf_lapacklin_zhpcon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07PRF, packed storage
Related keywords: complex, Hermitian, indefinite matrixcondition number, matrixdiagonal pivoting methodLAPACKlinear equationsZHPCON
F07PVF   15  nagf_lapacklin_zhprfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorcomplex, Hermitian, indefinite matrixdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equationsZHPRFS
F07PWF   15  nagf_lapacklin_zhptri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07PRF, packed storage
Related keywords: complex, Hermitian, indefinite matrixdiagonal pivoting methodinverse, matrixLAPACKlinear equationsZHPTRI
F07QRF   15  nagf_lapacklin_zsptrf
Bunch–Kaufman factorization of complex symmetric matrix, packed storage
Related keywords: complex, symmetric matrixdiagonal pivoting methodLAPACKlinear equationsZSPTRF
F07QSF   15  nagf_lapacklin_zsptrs
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07QRF, packed storage
Related keywords: complex, symmetric matrixdiagonal pivoting methodLAPACKlinear equationsZSPTRS
F07QUF   15  nagf_lapacklin_zspcon
Estimate condition number of complex symmetric matrix, matrix already factorized by F07QRF, packed storage
Related keywords: complex, symmetric matrixcondition number, matrixdiagonal pivoting methodLAPACKlinear equationsZSPCON
F07QVF   15  nagf_lapacklin_zsprfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorcomplex, symmetric matrixdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equationsZSPRFS
F07QWF   15  nagf_lapacklin_zsptri
Inverse of complex symmetric matrix, matrix already factorized by F07QRF, packed storage
Related keywords: complex, symmetric matrixdiagonal pivoting methodinverse, matrixLAPACKlinear equationsZSPTRI
BVLS, bounded variable least squares E04PCF   24  nagf_opt_bnd_lin_lsq
Computes the least squares solution to a set of linear equations subject to fixed upper and lower bounds on the variables. An option is provided to return a minimal length solution if a solution is not unique
Related keywords: data fittingfinancemaximizing a functionminimizing a functionNNLS, non-negative least squaresnonlinear least squaresnon-negative least squaresoptimization
BVP D02AGF   nagf_ode_bvp_shoot_genpar_intern
Ordinary differential equations, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined
Related keywords: boundary value problemODE, ordinary differential equationsshooting method, ODE
D02GAF   nagf_ode_bvp_fd_nonlin_fixedbc
Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem
Related keywords: boundary value problemfinite difference method, ODEODE, ordinary differential equations
D02GBF   nagf_ode_bvp_fd_lin_gen
Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, general linear problem
Related keywords: boundary value problemfinite difference method, ODEODE, ordinary differential equations
D02HAF   nagf_ode_bvp_shoot_bval
Ordinary differential equations, boundary value problem, shooting and matching, boundary values to be determined
Related keywords: boundary value problemODE, ordinary differential equationsshooting method, ODE
D02HBF   nagf_ode_bvp_shoot_genpar
Ordinary differential equations, boundary value problem, shooting and matching, general parameters to be determined
Related keywords: boundary value problemODE, ordinary differential equationsshooting method, ODE
D02JAF   nagf_ode_bvp_coll_nth
Ordinary differential equations, boundary value problem, collocation and least squares, single n th-order linear equation
Related keywords: boundary value problemcollocation methodODE, ordinary differential equations
D02JBF   nagf_ode_bvp_coll_sys
Ordinary differential equations, boundary value problem, collocation and least squares, system of first-order linear equations
Related keywords: boundary value problemcollocation methodODE, ordinary differential equations
D02KAF   nagf_ode_sl2_reg_finite
Second-order Sturm–Liouville problem, regular system, finite range, eigenvalue only
Related keywords: boundary value problemeigenproblemODE, ordinary differential equationsSturm–Liouville equations
D02KDF   nagf_ode_sl2_breaks_vals
Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points
Related keywords: boundary value problemeigenproblemgeneralODE, ordinary differential equationsSturm–Liouville equations
D02KEF   nagf_ode_sl2_breaks_funs
Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points
Related keywords: boundary value problemeigenproblemODE, ordinary differential equationsSturm–Liouville equations
D02SAF   nagf_ode_bvp_shoot_genpar_algeq
Ordinary differential equations, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined
Related keywords: boundary value problemODE, ordinary differential equationsparameterized first ordershooting method, ODEtwo-point boundary value problem
D02TLF   25  nagf_ode_bvp_coll_nlin_solve
Ordinary differential equations, general nonlinear boundary value problem, collocation technique (thread safe)
Related keywords: boundary value problemdifferential equationsnonlinear mixed orderODE, ordinary differential equationsordinary differential equationstwo-point boundary value problem
D02UEF   23  nagf_ode_bvp_ps_lin_solve
Solve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation
Related keywords: boundary value problemGauss–Lobatto gridODE, ordinary differential equationspseudo-spectral method
BVP, boundary value problem D02RAF   nagf_ode_bvp_fd_nonlin_gen
Ordinary differential equations, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility
Related keywords: finite difference method, ODEODE, ordinary differential equations
D02TGF   nagf_ode_bvp_coll_nth_comp
n th-order linear ordinary differential equations, boundary value problem, collocation and least squares
Related keywords: collocation methodODE, ordinary differential equations
D02TVF   17  nagf_ode_bvp_coll_nlin_setup
Ordinary differential equations, general nonlinear boundary value problem, setup for D02TLF
Related keywords: collocation methodODE, ordinary differential equations
D02TXF   17  nagf_ode_bvp_coll_nlin_contin
Ordinary differential equations, general nonlinear boundary value problem, continuation facility for D02TLF
Related keywords: collocation methodODE, ordinary differential equations
D02TYF   17  nagf_ode_bvp_coll_nlin_interp
Ordinary differential equations, general nonlinear boundary value problem, interpolation for D02TLF
Related keywords: collocation methodinterpolationODE, ordinary differential equations
D02TZF   17  nagf_ode_bvp_coll_nlin_diag
Ordinary differential equations, general nonlinear boundary value problem, diagnostics for D02TLF
Related keywords: collocation methodinterpolationODE, ordinary differential equations
calibration E04FFF   26  nagf_opt_handle_solve_dfls
Derivative-free (DFO) solver for a nonlinear least squares objective function with bounded variables
Related keywords: data fittingderivative-free optimizationDFODFOmaximizing a functionminimizing a functionnonlinear least squaresnonlinear least squaresoptimizationoptimizationsum of squares
E04RMF   26  nagf_opt_handle_set_nlnls
Define a nonlinear least squares objective function to a problem initialized by E04RAF
Related keywords: data fittingderivative-free optimizationDFOleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinear least squaresoptimizationoptimizationoptimizationsum of squares
callback algorithmic mode X10BCF   26 
Set the callback algorithmic mode
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationset
X10BDF   26 
Get the callback algorithmic mode
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationget
callback dataobject X10CJF   26 
Read a scalar of type nagad_a1w_w_rtype from the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationnagad_a1w_w_rtyperead
callback data object X10BAF   26 
Create a callback data object
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationcreate
X10BBF   26 
Insert the location of the AD callback into the callback data object
Related keywords: AD callbackadjoint derivativesAD utility operationsautomatic differentiationinsertlocation
X10BFF   26 
Write a real (working precision) scalar to the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationreal scalarworking precisionwrite
X10BJF   26 
Write a scalar of type nagad_a1w_w_rtype to the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationnagad_a1w_w_rtypewrite
X10CEF   26 
Read an integer scalar from the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationinteger scalarread
X10CFF   26 
Read a real (working precision) scalar from the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationreadreal scalarworking precision
callback data ojbect X10BEF   26 
Write an integer (working precision) scalar to the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationinteger scalarworking precisionwrite
canonical correlation analysis G03ADF   14  nagf_mv_canon_corr
Performs canonical correlation analysis
Related keywords: multivariate methods
canonical discrimination analysis G03ACF   14  nagf_mv_canon_var
Performs canonical variate analysis
Related keywords: canonical variate analysismultivariate methods
canonical variate analysis G03ACF   14  nagf_mv_canon_var
Performs canonical variate analysis
Related keywords: canonical discrimination analysismultivariate methods
G03BAF   15  nagf_mv_rot_orthomax
Computes orthogonal rotations for loading matrix, generalized orthomax criterion
Related keywords: factor analysismultivariate methodsorthogonal transformationsorthomax criterion
cash-or-nothing option S30CAF   22  nagf_specfun_opt_binary_con_price
Binary option, cash-or-nothing pricing formula
Related keywords: approximations of special functionsbinary optionderivative, optionsfinanceoption pricing
S30CBF   22  nagf_specfun_opt_binary_con_greeks
Binary option, cash-or-nothing pricing formula with Greeks
Related keywords: approximations of special functionsbinary optionderivative, optionsfinanceGreeks, optionsoption pricing
S30CCF   22  nagf_specfun_opt_binary_aon_price
Binary option, asset-or-nothing pricing formula
Related keywords: approximations of special functionsbinary optionderivative, optionsfinanceoption pricing
S30CDF   22  nagf_specfun_opt_binary_aon_greeks
Binary option, asset-or-nothing pricing formula with Greeks
Related keywords: approximations of special functionsbinary optionderivative, optionsfinanceGreeks, optionsoption pricing
Cauchy distribution G05SCF   22  nagf_rand_dist_cauchy
Generates a vector of pseudorandom numbers from a Cauchy distribution
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
Cauchy principal value D01AQF   nagf_quad_1d_fin_wcauchy
One-dimensional quadrature, adaptive, finite interval, weight function 1 / x - c , Cauchy principal value (Hilbert transform)
Related keywords: financeGauss–Kronrod quadratureHilbert transformintegration, adaptiveQAWCQUADPACKquadraturequadrature, adaptive
CDF, cumulative distribution function G01BJF   13  nagf_stat_prob_binomial
Binomial distribution function
Related keywords: binomial distributionfinanceSimple Calculations on Statistical Data
G01BKF   13  nagf_stat_prob_poisson
Poisson distribution function
Related keywords: financePoisson distributionSimple Calculations on Statistical Data
G01BLF   13  nagf_stat_prob_hypergeom
Hypergeometric distribution function
Related keywords: financehypergeometric distributionSimple Calculations on Statistical Data
G01EAF   15  nagf_stat_prob_normal
Computes probabilities for the standard Normal distribution
Related keywords: financelower tail probabilityNormal distributionprobabilitySimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01EBF   14  nagf_stat_prob_students_t
Computes probabilities for Student's t -distribution
Related keywords: financelower tail probabilityprobabilitySimple Calculations on Statistical DataStudent's t -distributiontwo-tail probabilityupper tail probability
G01ECF   14  nagf_stat_prob_chisq
Computes probabilities for χ 2 distribution
Related keywords: chi-squared distributionfinancelower tail probabilityprobabilitySimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01EDF   14  nagf_stat_prob_f
Computes probabilities for F -distribution
Related keywords: F -distributionfinancelower tail probabilityprobabilitySimple Calculations on Statistical Dataupper tail probabilityvariance-ratio distribution
G01EEF   14  nagf_stat_prob_beta
Computes upper and lower tail probabilities and probability density function for the beta distribution
Related keywords: beta distributionfinancelower tail probabilityprobabilitySimple Calculations on Statistical Dataupper tail probability
G01EFF   14  nagf_stat_prob_gamma
Computes probabilities for the gamma distribution
Related keywords: financegamma distributionlower tail probabilityprobabilitySimple Calculations on Statistical Dataupper tail probability
G01EMF   15  nagf_stat_prob_studentized_range
Computes probability for the Studentized range statistic
Related keywords: financeprobabilitySimple Calculations on Statistical DataStudentized range statistic
G01EPF   15  nagf_stat_prob_durbin_watson
Computes bounds for the significance of a Durbin–Watson statistic
Related keywords: Durbin–Watson statisticfinancesignificanceSimple Calculations on Statistical Data
G01ERF   16  nagf_stat_prob_vonmises
Computes probability for von Mises distribution
Related keywords: financelower tail probabilitySimple Calculations on Statistical Datavon Mises distribution
G01SAF   24  nagf_stat_prob_normal_vector
Computes a vector of probabilities for the standard Normal distribution
Related keywords: big dataconfidence intervaldata analyticsGaussian distributionlower tail probabilityNormal distributionsignificanceSimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01SBF   24  nagf_stat_prob_students_t_vector
Computes a vector of probabilities for the Student's t -distribution
Related keywords: big dataconfidence intervaldata analyticslower tail probabilitysignificanceSimple Calculations on Statistical DataStudent's t -distributiontwo-tail probabilityupper tail probability
G01SCF   24  nagf_stat_prob_chisq_vector
Computes a vector of probabilities for χ 2 distribution
Related keywords: big datachi-squared distributiondata analyticslower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01SDF   24  nagf_stat_prob_f_vector
Computes a vector of probabilities for F -distribution
Related keywords: big datadata analytics F -distributionlower tail probabilitySimple Calculations on Statistical Dataupper tail probabilityvariance-ratio distribution
G01SEF   24  nagf_stat_prob_beta_vector
Computes a vector of probabilities for the beta distribution
Related keywords: beta distributionbig datadata analyticslower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01SFF   24  nagf_stat_prob_gamma_vector
Computes a vector of probabilities for the gamma distribution
Related keywords: big datadata analyticsgamma distributionlower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01SJF   24  nagf_stat_prob_binomial_vector
Computes a vector of probabilities for the binomial distribution
Related keywords: big databinomial distributiondata analyticslower tail probabilitypoint probabilitySimple Calculations on Statistical Dataupper tail probability
G01SKF   24  nagf_stat_prob_poisson_vector
Computes a vector of probabilities for the Poisson distribution
Related keywords: big datadata analyticslower tail probabilitypoint probabilityPoisson distributionSimple Calculations on Statistical Dataupper tail probability
G01SLF   24  nagf_stat_prob_hypergeom_vector
Computes a vector of probabilities for the hypergeometric distribution
Related keywords: big datadata analyticshypergeometric distributionlower tail probabilitypoint probabilitySimple Calculations on Statistical Dataupper tail probability
G05TDF   22  nagf_rand_int_general
Generates a vector of pseudorandom integers from a general discrete distribution
Related keywords: big datadata analyticsdistribution functionfinancerandom integersrandom number generators
censored data G07BBF   15  nagf_univar_estim_normal
Computes maximum likelihood estimates for parameters of the Normal distribution from grouped and/or censored data
Related keywords: Gaussian distributiongrouping datamaximum likelihoodNormal distributionunivariate estimation
central probability G01HBF   15  nagf_stat_prob_multi_normal
Computes probabilities for the multivariate Normal distribution
Related keywords: financelower tail probabilitymultivariate Normal distributionNormal distributionSimple Calculations on Statistical Dataupper tail probability
CGS, conjugate gradient method F11BEF   19  nagf_sparse_real_gen_basic_solver
Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
Related keywords: Bi-CGSTABbig datadata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11BSF   19  nagf_sparse_complex_gen_basic_solver
Complex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
Related keywords: Bi-CGSTABbig datacomplex, sparse matrixdata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DCF   18  nagf_sparse_real_gen_solve_ilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DAF
Related keywords: Bi-CGSTABbig datadata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DEF   18  nagf_sparse_real_gen_solve_jacssor
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: Bi-CGSTABbig datadata analyticsiterative methods, linear equationsJacobi preconditioninglarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodSSOR method, symmetric successive over-relaxationTFQMR, transpose-free quasi-minimal residual method
F11DGF   24  nagf_sparse_real_gen_solve_bdilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DFF
Related keywords: additive Schwarz preconditionerBi-CGSTABbig datadata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DQF   19  nagf_sparse_complex_gen_solve_ilu
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DNF (Black Box)
Related keywords: Bi-CGSTABbig datacomplex, sparse matrixdata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DSF   19  nagf_sparse_complex_gen_solve_jacssor
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box
Related keywords: Bi-CGSTABbig datacomplex, sparse matrixdata analyticsiterative methods, linear equationsJacobi preconditioninglarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodSSOR method, symmetric successive over-relaxationTFQMR, transpose-free quasi-minimal residual method
F11DUF   24  nagf_sparse_complex_gen_solve_bdilu
Solution of complex, sparse, non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DTF
Related keywords: additive Schwarz preconditionerBi-CGSTABbig datacomplex, sparse matrixdata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11GEF   20  nagf_sparse_real_symm_basic_solver
Real sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos method or the MINRES algorithm
Related keywords: big datadata analyticsiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodMINRES, iterative linear equation solverreal, sparse, symmetric matrix
F11GSF   20  nagf_sparse_complex_herm_basic_solver
Complex sparse Hermitian linear systems, preconditioned conjugate gradient or Lanczos
Related keywords: big datacomplex, Hermitian, sparse matrixdata analyticsiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemslinear equations, iterative method
F11JCF   17  nagf_sparse_real_symm_solve_ichol
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JAF (Black Box)
Related keywords: big datadata analyticsincomplete Cholesky factorizationiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse, symmetric matrix
F11JEF   17  nagf_sparse_real_symm_solve_jacssor
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big datadata analyticsiterative methods, linear equationsJacobi preconditioningLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse, symmetric matrixSSOR method, symmetric successive over-relaxation
change point G13NAF   25  nagf_tsa_cp_pelt
Change point detection, using the PELT algorithm
Related keywords: big datadata analyticspelttime seriestime series analysis
G13NBF   25  nagf_tsa_cp_pelt_user
Change points detection using the PELT algorithm, user supplied cost function
Related keywords: big datadata analyticspelttime seriestime series analysis
G13NDF   25  nagf_tsa_cp_binary
Change point detection, using binary segmentation
Related keywords: big databinary segmentationdata analyticstime seriestime series analysis
G13NEF   25  nagf_tsa_cp_binary_user
Change point detection, using binary segmentation, user supplied cost function
Related keywords: big databinary segmentationdata analyticstime seriestime series analysis
Chebyshev polynomial approximation E02CAF   nagf_fit_2dcheb_lines
Least squares surface fit by polynomials, data on lines parallel to one independent coordinate axis
Related keywords: bivariate polynomial approximationcurve and surface fittingdata-on-lines polynomial approximationleast squarespolynomial approximationtwo-dimensional polynomial approximation
E02CBF   nagf_fit_2dcheb_eval
Evaluation of fitted polynomial in two variables
Related keywords: bivariate polynomial approximationcurve and surface fittingpolynomial approximationtwo-dimensional polynomial approximation
Chebyshev polynomial interpolation D02UAF   23  nagf_ode_bvp_ps_lin_coeffs
Coefficients of Chebyshev interpolating polynomial from function values on Chebyshev grid
Related keywords: Gauss–Lobatto gridinterpolationODE, ordinary differential equations
D02UBF   23  nagf_ode_bvp_ps_lin_cgl_vals
Function or low-order-derivative values on Chebyshev grid from coefficients of Chebyshev interpolating polynomial
Related keywords: Chebyshev series, solutionGauss–Lobatto gridinterpolationODE, ordinary differential equations
E01AEF   nagf_interp_1d_cheb
Interpolating functions, polynomial interpolant, data may include derivative values, one variable
Related keywords: interpolation
Chebyshev series, differentiation E02AHF   nagf_fit_1dcheb_deriv
Derivative of fitted polynomial in Chebyshev series form
Related keywords: curve and surface fitting
Chebyshev series, evaluation C06DCF   23  nagf_sum_chebyshev
Sum of a Chebyshev series at a set of points
Related keywords: summation of series
D02UZF   23  nagf_ode_bvp_ps_lin_cheb_eval
Chebyshev polynomial evaluation, T k x
Related keywords: ODE, ordinary differential equations
E02AKF   nagf_fit_1dcheb_eval2
Evaluation of fitted polynomial in one variable from Chebyshev series form
Related keywords: curve and surface fitting
Chebyshev series, integration E02AJF   nagf_fit_1dcheb_integ
Integral of fitted polynomial in Chebyshev series form
Related keywords: curve and surface fitting
Chebyshev series, solution D02UBF   23  nagf_ode_bvp_ps_lin_cgl_vals
Function or low-order-derivative values on Chebyshev grid from coefficients of Chebyshev interpolating polynomial
Related keywords: Chebyshev polynomial interpolationGauss–Lobatto gridinterpolationODE, ordinary differential equations
Chebyshev series approximation D02UYF   23  nagf_ode_bvp_ps_lin_quad_weights
Clenshaw–Curtis quadrature weights for integration using computed Chebyshev coefficients
Related keywords: Clenshaw–Curtis quadratureODE, ordinary differential equationsweights and abscissae
check derivative C05ZDF   23  nagf_roots_sys_deriv_check
Check user's routine for calculating first derivatives of a set of nonlinear functions of several variables
Related keywords: financeroots of transcendental equations
E04HCF   nagf_opt_check_deriv
Check user's routine for calculating first derivatives of function
Related keywords: financemaximizing a functionminimization, unconstrainedminimizing a functionoptimizationservice routine
E04HDF   nagf_opt_check_deriv2
Check user's routine for calculating second derivatives of function
Related keywords: financemaximizing a functionminimization, unconstrainedminimizing a functionoptimizationservice routine
chi-squared distribution G01AFF   nagf_stat_contingency_table
Two-way contingency table analysis, with χ 2 /Fisher's exact test
Related keywords: contingency tablefinanceFisher's exact testSimple Calculations on Statistical Datatwo-way contingency tableYates' correction
G01ECF   14  nagf_stat_prob_chisq
Computes probabilities for χ 2 distribution
Related keywords: CDF, cumulative distribution functionfinancelower tail probabilityprobabilitySimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01FCF   14  nagf_stat_inv_cdf_chisq
Computes deviates for the χ 2 distribution
Related keywords: deviatesfinanceinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01GCF   14  nagf_stat_prob_chisq_noncentral
Computes probabilities for the non-central χ 2 distribution
Related keywords: financelower tail probabilitySimple Calculations on Statistical Data
G01JCF   14  nagf_stat_prob_chisq_noncentral_lincomb
Computes probability for a positive linear combination of χ 2 variables
Related keywords: financelower tail probabilitySimple Calculations on Statistical Data
G01JDF   15  nagf_stat_prob_chisq_lincomb
Computes lower tail probability for a linear combination of (central) χ 2 variables
Related keywords: financeImhof's methodlower tail probabilityPan's methodSimple Calculations on Statistical Data
G01SCF   24  nagf_stat_prob_chisq_vector
Computes a vector of probabilities for χ 2 distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticslower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01TCF   24  nagf_stat_inv_cdf_chisq_vector
Computes a vector of deviates for χ 2 distribution
Related keywords: big datadata analyticsdeviatesinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G05SDF   22  nagf_rand_dist_chisq
Generates a vector of pseudorandom numbers from a χ 2 distribution
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
chi squared statistics G11AAF   16  nagf_contab_chisq
χ 2 statistics for two-way contingency table
Related keywords: contingency tablecontingency table analysis
G13DNF   15  nagf_tsa_multi_corrmat_partlag
Multivariate time series, sample partial lag correlation matrices, χ 2 statistics and significance levels
Related keywords: big datadata analyticsmultivariate time seriespartial lagsignificancetime seriestime series analysis
chi squared test G08CGF   14  nagf_nonpar_test_chisq
Performs the χ 2 goodness-of-fit test, for standard continuous distributions
Related keywords: nonparametric statistics
Cholesky decomposition F07FAF   21  nagf_lapacklin_dposv
Computes the solution to a real symmetric positive definite system of linear equations
Related keywords: DPOSVfinanceLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FBF   21  nagf_lapacklin_dposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations
Related keywords: backward errorcondition number, matrixDPOSVXerror bound, matrixfinanceforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FCF   23  nagf_lapacklin_dsposv
Computes the solution to a real symmetric positive definite system of linear equations using mixed precision arithmetic
Related keywords: DSPOSVLAPACKlinear equationsmixed-precisionreal, positive-definite, symmetric matrix
F07FDF   15  nagf_lapacklin_dpotrf
Cholesky factorization of real symmetric positive definite matrix
Related keywords: DPOTRFfinanceLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FEF   15  nagf_lapacklin_dpotrs
Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FDF
Related keywords: DPOTRSfinanceLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FHF   15  nagf_lapacklin_dporfs
Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides
Related keywords: backward errorDPORFSforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FJF   15  nagf_lapacklin_dpotri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07FDF
Related keywords: DPOTRIfinanceinverse, matrixLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FNF   21  nagf_lapacklin_zposv
Computes the solution to a complex Hermitian positive definite system of linear equations
Related keywords: complex, Hermitian, positive-definite matrixLAPACKlinear equationsZPOSV
F07FPF   21  nagf_lapacklin_zposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations
Related keywords: backward errorcomplex, Hermitian, positive-definite matrixcondition number, matrixerror bound, matrixfinanceforward errorLAPACKlinear equationsZPOSVX
F07FQF   23  nagf_lapacklin_zcposv
Computes the solution to a complex Hermitian positive definite system of linear equations using mixed precision arithmetic
Related keywords: complex, Hermitian, positive-definite matrixLAPACKlinear equationsmixed-precisionZCPOSV
F07FRF   15  nagf_lapacklin_zpotrf
Cholesky factorization of complex Hermitian positive definite matrix
Related keywords: complex, Hermitian, positive-definite matrixLAPACKlinear equationsZPOTRF
F07FSF   15  nagf_lapacklin_zpotrs
Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FRF
Related keywords: complex, Hermitian, positive-definite matrixLAPACKlinear equationsZPOTRS
F07FUF   15  nagf_lapacklin_zpocon
Estimate condition number of complex Hermitian positive definite matrix, matrix already factorized by F07FRF
Related keywords: complex, Hermitian, positive-definite matrixcondition number, matrixLAPACKlinear equationsZPOCON
F07FVF   15  nagf_lapacklin_zporfs
Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, Hermitian, positive-definite matrixerror bound, matrixforward errorLAPACKlinear equationsZPORFS
F07GAF   21  nagf_lapacklin_dppsv
Computes the solution to a real symmetric positive definite system of linear equations, packed storage
Related keywords: DPPSVLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GBF   21  nagf_lapacklin_dppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations, packed storage
Related keywords: backward errorcondition number, matrixDPPSVXerror bound, matrixforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GDF   15  nagf_lapacklin_dpptrf
Cholesky factorization of real symmetric positive definite matrix, packed storage
Related keywords: DPPTRFLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GEF   15  nagf_lapacklin_dpptrs
Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GDF, packed storage
Related keywords: DPPTRSLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GGF   15  nagf_lapacklin_dppcon
Estimate condition number of real symmetric positive definite matrix, matrix already factorized by F07GDF, packed storage
Related keywords: condition number, matrixDPPCONLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GHF   15  nagf_lapacklin_dpprfs
Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorDPPRFSforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GJF   15  nagf_lapacklin_dpptri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07GDF, packed storage
Related keywords: DPPTRIinverse, matrixLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GNF   21  nagf_lapacklin_zppsv
Computes the solution to a complex Hermitian positive definite system of linear equations, packed storage
Related keywords: complex, Hermitian, positive-definite matrixLAPACKlinear equationsZPPSV
F07GPF   21  nagf_lapacklin_zppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations, packed storage
Related keywords: backward errorcomplex, Hermitian, positive-definite matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsZPPSVX
F07GRF   15  nagf_lapacklin_zpptrf
Cholesky factorization of complex Hermitian positive definite matrix, packed storage
Related keywords: complex, Hermitian, positive-definite matrixLAPACKlinear equationsZPPTRF
F07GSF   15  nagf_lapacklin_zpptrs
Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GRF, packed storage
Related keywords: complex, Hermitian, positive-definite matrixLAPACKlinear equationsZPPTRS
F07GVF   15  nagf_lapacklin_zpprfs
Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorcomplex, Hermitian, positive-definite matrixerror bound, matrixforward errorLAPACKlinear equationsZPPRFS
F07GWF   15  nagf_lapacklin_zpptri
Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07GRF, packed storage
Related keywords: complex, Hermitian, positive-definite matrixinverse, matrixLAPACKlinear equationsZPPTRI
F07HAF   21  nagf_lapacklin_dpbsv
Computes the solution to a real symmetric positive definite banded system of linear equations
Related keywords: DPBSVLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
F07HBF   21  nagf_lapacklin_dpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite banded system of linear equations
Related keywords: backward errorcondition number, matrixDPBSVXerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
F07HDF   15  nagf_lapacklin_dpbtrf
Cholesky factorization of real symmetric positive definite band matrix
Related keywords: DPBTRFfinanceLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
F07HEF   15  nagf_lapacklin_dpbtrs
Solution of real symmetric positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HDF
Related keywords: DPBTRSfinanceLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
F07HHF   15  nagf_lapacklin_dpbrfs
Refined solution with error bounds of real symmetric positive definite band system of linear equations, multiple right-hand sides
Related keywords: backward errorDPBRFSforward errorLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
F07HNF   21  nagf_lapacklin_zpbsv
Computes the solution to a complex Hermitian positive definite banded system of linear equations
Related keywords: complex, band, Hermitian, positive-definite matrixLAPACKlinear equationsmatrix, bandZPBSV
F07HPF   21  nagf_lapacklin_zpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite banded system of linear equations
Related keywords: backward errorcomplex, band, Hermitian, positive-definite matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZPBSVX
F07HRF   15  nagf_lapacklin_zpbtrf
Cholesky factorization of complex Hermitian positive definite band matrix
Related keywords: complex, band, Hermitian, positive-definite matrixLAPACKlinear equationsmatrix, bandZPBTRF
F07HSF   15  nagf_lapacklin_zpbtrs
Solution of complex Hermitian positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HRF
Related keywords: complex, band, Hermitian, positive-definite matrixLAPACKlinear equationsmatrix, bandZPBTRS
F07HVF   15  nagf_lapacklin_zpbrfs
Refined solution with error bounds of complex Hermitian positive definite band system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, band, Hermitian, positive-definite matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZPBRFS
F07JAF   21  nagf_lapacklin_dptsv
Computes the solution to a real symmetric positive definite tridiagonal system of linear equations
Related keywords: DPTSVLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
F07JBF   21  nagf_lapacklin_dptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations
Related keywords: backward errorcondition number, matrixDPTSVXerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
F07JDF   22  nagf_lapacklin_dpttrf
Computes the LDL T factorization of a real symmetric positive definite tridiagonal matrix
Related keywords: DPTTRFLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
F07JEF   22  nagf_lapacklin_dpttrs
Solves a real symmetric positive definite tridiagonal system using the LDL T factorization computed by F07JDF
Related keywords: DPTTRSLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
F07JHF   22  nagf_lapacklin_dptrfs
Refined solution with error bounds of real symmetric positive definite tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorDPTRFSforward errorLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
F07JNF   21  nagf_lapacklin_zptsv
Computes the solution to a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: complex, Hermitian, positive-definite, tridiagonal matrixLAPACKlinear equationsmatrix, bandZPTSV
F07JPF   21  nagf_lapacklin_zptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: backward errorcomplex, Hermitian, positive-definite, tridiagonal matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZPTSVX
F07JRF   22  nagf_lapacklin_zpttrf
Computes the LDL H factorization of a complex Hermitian positive definite tridiagonal matrix
Related keywords: complex, Hermitian, positive-definite, tridiagonal matrixLAPACKlinear equationsmatrix, bandZPPTRF
F07JSF   22  nagf_lapacklin_zpttrs
Solves a complex Hermitian positive definite tridiagonal system using the LDL H factorization computed by F07JRF
Related keywords: complex, Hermitian, positive-definite, tridiagonal matrixLAPACKlinear equationsmatrix, bandZPPTRS
F07JUF   22  nagf_lapacklin_zptcon
Computes the reciprocal of the condition number of a complex Hermitian positive definite tridiagonal system using the LDL H factorization computed by F07JRF
Related keywords: complex, Hermitian, positive-definite, tridiagonal matrixcondition number, matrixLAPACKlinear equationsmatrix, bandZPTCON
F07JVF   22  nagf_lapacklin_zptrfs
Refined solution with error bounds of complex Hermitian positive definite tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, Hermitian, positive-definite, tridiagonal matrixforward errorLAPACKlinear equationsmatrix, bandZPTRFS
F07KDF   23  nagf_lapacklin_dpstrf
Cholesky factorization, with complete pivoting, of a real, symmetric, positive semidefinite matrix
Related keywords: DPSTRFLAPACKlinear equationsreal, positive-semidefinite, symmetric matrix
F07KRF   23  nagf_lapacklin_zpstrf
Cholesky factorization of complex Hermitian positive semidefinite matrix
Related keywords: complex, Hermitian, positive-semidefinite matrixLAPACKlinear equationsZPSTRF
F07WDF   23  nagf_lapacklin_dpftrf
Cholesky factorization of real symmetric positive definite matrix, Rectangular Full Packed format
Related keywords: DPFTRFLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07WEF   23  nagf_lapacklin_dpftrs
Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by F07WDF, Rectangular Full Packed format
Related keywords: DPFTRSLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07WJF   23  nagf_lapacklin_dpftri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07WDF, Rectangular Full Packed format
Related keywords: DPETRIinverse, matrixLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07WRF   23  nagf_lapacklin_zpftrf
Cholesky factorization of complex Hermitian positive definite matrix, Rectangular Full Packed format
Related keywords: complex, Hermitian, positive-definite matrixLAPACKlinear equationsZPFTRF
F07WSF   23  nagf_lapacklin_zpftrs
Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by F07WRF, Rectangular Full Packed format
Related keywords: complex, Hermitian, positive-definite matrixLAPACKlinear equationsZPFTRS
F07WWF   23  nagf_lapacklin_zpftri
Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07WRF, Rectangular Full Packed format
Related keywords: complex, Hermitian, positive-definite matrixLAPACKlinear equationsZPETRI
F08UFF   19  nagf_lapackeig_dpbstf
Computes a split Cholesky factorization of real symmetric positive definite band matrix A
Related keywords: DPBSTFDSBGSTeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
circular tangent S07AAF   nagf_specfun_tan
tan x
Related keywords: approximations of special functionsfinancetangent, circular tan x
classical metric scaling G03FAF   17  nagf_mv_multidimscal_metric
Performs principal coordinate analysis, classical metric scaling
Related keywords: multivariate methodsprincipal coordinate analysis
classification variable G04EAF   17  nagf_anova_dummyvars
Computes orthogonal polynomials or dummy variables for factor/classification variable
Related keywords: analysis of variancedesign of experimentsexperimental designfactor variable
G11BAF   17  nagf_contab_tabulate_stat
Computes multiway table from set of classification factors using selected statistic
Related keywords: contingency table analysisfactor variabletable
G11BBF   17  nagf_contab_tabulate_percentile
Computes multiway table from set of classification factors using given percentile/quantile
Related keywords: contingency table analysisfactor variabletable
Clayton/Cook–Johnson copula G05REF   23  nagf_rand_copula_clayton_bivar
Generates a matrix of pseudorandom numbers from a bivariate Clayton/Cook–Johnson copula
Related keywords: big datacopuladata analyticsrandom number generatorsrandom numbers
G05RHF   23  nagf_rand_copula_clayton
Generates a matrix of pseudorandom numbers from a multivariate Clayton/Cook–Johnson copula
Related keywords: big datacopuladata analyticsrandom number generatorsrandom numbers
Clenshaw–Curtis quadrature D02UYF   23  nagf_ode_bvp_ps_lin_quad_weights
Clenshaw–Curtis quadrature weights for integration using computed Chebyshev coefficients
Related keywords: Chebyshev series approximationODE, ordinary differential equationsweights and abscissae
close file X04ADF   19  nagf_file_close
Close file associated with given unit number
Related keywords: file closinginput utilitiesoutput utilities
cluster analysis G03ECF   16  nagf_mv_cluster_hier
Hierarchical cluster analysis
Related keywords: big datadata analyticshierarchical cluster analysismultivariate methods
G03EFF   16  nagf_mv_cluster_kmeans
K -means cluster analysis
Related keywords: big datadata analytics K -means cluster analysismultivariate methods
G03EJF   16  nagf_mv_cluster_hier_indicator
Computes cluster indicator variable (for use after G03ECF)
Related keywords: allocatebig datadata analyticshierarchical cluster analysismultivariate methods
G03GAF   24  nagf_mv_gaussian_mixture
Fits a Gaussian mixture model
Related keywords: Gaussian mixture modelmultivariate methods
cn, Jacobian elliptic function S21CAF   15  nagf_specfun_jacellip_real
Jacobian elliptic functions sn, cn and dn of real argument
Related keywords: approximations of special functionsdn, Jacobian elliptic functionelliptic functionsfinanceJacobian elliptic functionssn, Jacobian elliptic functions
S21CBF   20  nagf_specfun_jacellip_complex
Jacobian elliptic functions sn, cn and dn of complex argument
Related keywords: approximations of special functionsdn, Jacobian elliptic functionelliptic functionsfinanceJacobian elliptic functionssn, Jacobian elliptic functions
Cochran Q test G08ALF   15  nagf_nonpar_test_cochranq
Performs the Cochran Q test on cross-classified binary data
Related keywords: cross-classifiednonparametric statistics
coefficients C09EYF   25  nagf_wav_2d_coeff_ext
Two-dimensional discrete wavelet transform coefficient extraction
Related keywords: extracttwo-dimensionalwaveletwavelet transforms
C09EZF   25  nagf_wav_2d_coeff_ins
Two-dimensional discrete wavelet transform coefficient insertion
Related keywords: inserttwo-dimensionalwaveletwavelet transforms
C09FYF   25  nagf_wav_3d_coeff_ext
Three-dimensional discrete wavelet transform coefficient extraction
Related keywords: extractthree-dimensionalwaveletwavelet transforms
C09FZF   25  nagf_wav_3d_coeff_ins
Three-dimensional discrete wavelet transform coefficient insertion
Related keywords: insertthree-dimensionalwaveletwavelet transforms
coherency, squared, time series G13CEF   10  nagf_tsa_multi_spectrum_bivar
Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra
Related keywords: big databivariate spectracross amplitude spectrumdata analyticsfinancemultivariate time seriessquared coherencytime seriestime series analysis
collocation method D02JAF   nagf_ode_bvp_coll_nth
Ordinary differential equations, boundary value problem, collocation and least squares, single n th-order linear equation
Related keywords: boundary value problemBVPODE, ordinary differential equations
D02JBF   nagf_ode_bvp_coll_sys
Ordinary differential equations, boundary value problem, collocation and least squares, system of first-order linear equations
Related keywords: boundary value problemBVPODE, ordinary differential equations
D02TGF   nagf_ode_bvp_coll_nth_comp
n th-order linear ordinary differential equations, boundary value problem, collocation and least squares
Related keywords: BVP, boundary value problemODE, ordinary differential equations
D02TVF   17  nagf_ode_bvp_coll_nlin_setup
Ordinary differential equations, general nonlinear boundary value problem, setup for D02TLF
Related keywords: BVP, boundary value problemODE, ordinary differential equations
D02TXF   17  nagf_ode_bvp_coll_nlin_contin
Ordinary differential equations, general nonlinear boundary value problem, continuation facility for D02TLF
Related keywords: BVP, boundary value problemODE, ordinary differential equations
D02TYF   17  nagf_ode_bvp_coll_nlin_interp
Ordinary differential equations, general nonlinear boundary value problem, interpolation for D02TLF
Related keywords: BVP, boundary value probleminterpolationODE, ordinary differential equations
D02TZF   17  nagf_ode_bvp_coll_nlin_diag
Ordinary differential equations, general nonlinear boundary value problem, diagnostics for D02TLF
Related keywords: BVP, boundary value probleminterpolationODE, ordinary differential equations
D03PDF   15  nagf_pde_1d_parab_coll_old
General system of parabolic PDEs, method of lines, Chebyshev C 0 collocation, one space variable
Related keywords: method of linesparabolic partial differential equationPDE, partial differential equations
communalities, maximum likelihood G03CAF   15  nagf_mv_factor
Computes maximum likelihood estimates of the parameters of a factor analysis model, factor loadings, communalities and residual correlations
Related keywords: factor analysisfactor loadingsmaximum likelihoodmultivariate methodsresidual correlations
complement error function S15ADF   nagf_specfun_erfc_real
Complement of error function erfc x
Related keywords: approximations of special functionserror functionfinance
S15AGF   22  nagf_specfun_erfcx_real
Scaled complement of error function, erfcx x
Related keywords: approximations of special functionserror functionfinance
S15DDF   14  nagf_specfun_erfc_complex
Scaled complex complement of error function, exp - z 2 erfc - i z
Related keywords: approximations of special functionserror function
complement of cumulative Normal distribution S15ACF   nagf_specfun_compcdf_normal
Complement of cumulative Normal distribution function Q x
Related keywords: approximations of special functionscumulative Normal distributionerror functionfinance
complement of incomplete beta function S14CCF   24  nagf_specfun_beta_incomplete
Incomplete beta function I x a , b and its complement 1 - I x
Related keywords: approximations of special functionsincomplete beta function
complete CS decomposition F08RAF   25  nagf_lapackeig_dorcsd
Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
Related keywords: DORCSDeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresreal, orthogonal matrix
F08RNF   25  nagf_lapackeig_zuncsd
Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices
Related keywords: complex, unitary matrixeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresZUNCSD
completely randomized design G04BBF   16  nagf_anova_random
Analysis of variance, randomized block or completely randomized design, treatment means and standard errors
Related keywords: analysis of varianceANOVArandomized block designstandard errorstreatment means
complex, band, Hermitian, positive-definite matrix F04CFF   21  nagf_linsys_complex_posdef_band_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite banded system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationsmatrix, bandsimultaneous linear equations
F07HNF   21  nagf_lapacklin_zpbsv
Computes the solution to a complex Hermitian positive definite banded system of linear equations
Related keywords: Cholesky decompositionLAPACKlinear equationsmatrix, bandZPBSV
F07HPF   21  nagf_lapacklin_zpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite banded system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZPBSVX
F07HRF   15  nagf_lapacklin_zpbtrf
Cholesky factorization of complex Hermitian positive definite band matrix
Related keywords: Cholesky decompositionLAPACKlinear equationsmatrix, bandZPBTRF
F07HSF   15  nagf_lapacklin_zpbtrs
Solution of complex Hermitian positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HRF
Related keywords: Cholesky decompositionLAPACKlinear equationsmatrix, bandZPBTRS
F07HTF   22  nagf_lapacklin_zpbequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite banded matrix and reduce its condition number
Related keywords: equilibrationLAPACKlinear equationsmatrix, bandscalingZPBEQU
F07HUF   15  nagf_lapacklin_zpbcon
Estimate condition number of complex Hermitian positive definite band matrix, matrix already factorized by F07HRF
Related keywords: condition number, matrixLAPACKlinear equationsmatrix, bandZPBCON
F07HVF   15  nagf_lapacklin_zpbrfs
Refined solution with error bounds of complex Hermitian positive definite band system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositionerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZPBRFS
F08UNF   21  nagf_lapackeig_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBGV
F08UPF   21  nagf_lapackeig_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBGVX
F08UQF   21  nagf_lapackeig_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBGVD
F08USF   19  nagf_lapackeig_zhbgst
Performs a reduction of complex Hermitian-definite banded generalized eigenproblem A x = λ B x to standard form C y = λ y , such that C has the same bandwidth as A
Related keywords: eigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBGST
F08UTF   19  nagf_lapackeig_zpbstf
Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
Related keywords: eigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandSplit Cholesky factorizationZPBSTF
complex, band, Hermitian matrix F06SDF   12  nagf_blas_zhbmv
Matrix-vector product, complex Hermitian band matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesmatrix, bandmultiply, matrixzhbmv
F06UEF   15  nagf_blas_zlanhb
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian band matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesmatrix, band
F08HNF   21  nagf_lapackeig_zhbev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
Related keywords: eigenproblemLAPACKLAPACKleast squaresmatrix, band QR algorithmunitary transformationsZHBEV
F08HPF   21  nagf_lapackeig_zhbevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
Related keywords: eigenproblemLAPACKLAPACKleast squaresmatrix, bandunitary transformationsZHBEVX
F08HQF   19  nagf_lapackeig_zhbevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithmZHBEVD
F08HSF   16  nagf_lapackeig_zhbtrd
Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
Related keywords: eigenproblemLAPACKLAPACKleast squaresmatrix, bandunitary transformationsZHBTRD
complex, band, m by n matrix F06SBF   12  nagf_blas_zgbmv
Matrix-vector product, complex rectangular band matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesmatrix, bandmultiply, matrixzgbmv
complex, band, symmetric matrix F06UHF   15  nagf_blas_zlansb
1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric band matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesmatrix, band
complex, band, triangular matrix F06SGF   12  nagf_blas_ztbmv
Matrix-vector product, complex triangular band matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesmatrix, bandmultiply, matrixztbmv
F06SKF   12  nagf_blas_ztbsv
System of equations, complex triangular band matrix
Related keywords: BLASblas, complex matriceslinear algebra support routineslinear equationsmatrix, bandztbsv
F06ULF   15  nagf_blas_zlantb
1 -norm, -norm, Frobenius norm, largest absolute element, complex triangular band matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesmatrix, band
F07VSF   15  nagf_lapacklin_ztbtrs
Solution of complex band triangular system of linear equations, multiple right-hand sides
Related keywords: LAPACKlinear equationsmatrix, bandZTBTRS
F07VUF   15  nagf_lapacklin_ztbcon
Estimate condition number of complex band triangular matrix
Related keywords: condition number, matrixLAPACKlinear equationsmatrix, bandZTBCON
F07VVF   15  nagf_lapacklin_ztbrfs
Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZTBRFS
complex, band matrix F04CBF   21  nagf_linsys_complex_band_solve
Computes the solution, estimated condition number and error-bound to a complex banded system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationsmatrix, bandsimultaneous linear equations
F06UBF   15  nagf_blas_zlangb
1 -norm, -norm, Frobenius norm, largest absolute element, complex band matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesmatrix, band
F06UCF   15  nagf_blas_zlanhe
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routines
F07BNF   21  nagf_lapacklin_zgbsv
Computes the solution to a complex banded system of linear equations
Related keywords: LAPACKlinear equations L U decompositionmatrix, bandZGBSV
F07BPF   21  nagf_lapacklin_zgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
Related keywords: backward errorcondition number, matrixerror bound, matrixforward errorLAPACKlinear equations L U decompositionmatrix, bandZGBSVX
F07BSF   15  nagf_lapacklin_zgbtrs
Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by F07BRF
Related keywords: LAPACKlinear equations L U decompositionmatrix, bandZGBTRS
F07BTF   22  nagf_lapacklin_zgbequ
Computes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number
Related keywords: equilibrationLAPACKlinear equationsmatrix, bandscalingZGBEQU
F07BUF   15  nagf_lapacklin_zgbcon
Estimate condition number of complex band matrix, matrix already factorized by F07BRF
Related keywords: condition number, matrixLAPACKlinear equationsmatrix, bandZGBEQU
F07BVF   15  nagf_lapacklin_zgbrfs
Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides
Related keywords: backward errorerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZGBRFS
F12ATF   24  nagf_sparseig_complex_band_init
Initialization routine for F12AUF computing selected eigenvalues and, optionally, eigenvectors of a complex banded (standard or generalized) eigenproblem
Related keywords: big datadata analyticseigenproblem, initializationlarge scale eigenproblems
F12AUF   24  nagf_sparseig_complex_band_solve
Selected eigenvalues and, optionally, eigenvectors of complex non-Hermitian banded eigenproblem, driver
Related keywords: big datadata analyticseigenproblem, bandedeigenvalueseigenvectorslarge scale eigenproblems
F16UBF   23  nagf_blast_zgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, complex band matrix
Related keywords: 1-normabsolute valuebanded matrixFrobenius normfurther linear algebra support routinesinfinity-normmatrix, bandnorm, matrix
complex, Hermitian, indefinite matrix F01FDF   23  nagf_matop_complex_herm_matrix_exp
Complex Hermitian matrix exponential
Related keywords: exponential, matrixfinanceinversionmatrix exponentialmatrix operations
F01FFF   23  nagf_matop_complex_herm_matrix_fun
Function of a complex Hermitian matrix
Related keywords: financefunctions, matrixinversionmatrix functionsmatrix operations
F04CHF   21  nagf_linsys_complex_herm_solve
Computes the solution and error-bound to a complex Hermitian system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationssimultaneous linear equations
F04CJF   21  nagf_linsys_complex_herm_packed_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian system of linear equations, packed storage
Related keywords: big datadata analyticsforward errorlinear equationssimultaneous linear equations
F06WQF   23  nagf_blas_zhfrk
Rank- k update of a complex Hermitian matrix, Rectangular Full Packed format
Related keywords: BLASblas, complex matriceslinear algebra support routinesrank k matrix updateszherk
F06ZCF   14  nagf_blas_zhemm
Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix
Related keywords: BLASblas, complex matricescomplex, m by n matrixlinear algebra support routinesmultiply, matrixzgemm
F06ZPF   14  nagf_blas_zherk
Rank- k update of a complex Hermitian matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesrank k matrix updateszherk
F06ZRF   14  nagf_blas_zher2k
Rank- 2 k update of a complex Hermitian matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesrank k matrix updateszher2k
F07MNF   21  nagf_lapacklin_zhesv
Computes the solution to a complex Hermitian system of linear equations
Related keywords: diagonal pivoting methodLAPACK LDL H decompositionlinear equations UDU H decompositionZHESV
F07MPF   21  nagf_lapacklin_zhesvx
Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations
Related keywords: backward errordiagonal pivoting methodforward errorLAPACK LDL H decompositionlinear equations UDU H decompositionZHESVX
F07MRF   15  nagf_lapacklin_zhetrf
Bunch–Kaufman factorization of complex Hermitian indefinite matrix
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodLAPACKlinear equationsZHETRF
F07MSF   15  nagf_lapacklin_zhetrs
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MRF
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodLAPACKlinear equationsZHETRS
F07MUF   15  nagf_lapacklin_zhecon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07MRF
Related keywords: Bunch–Kaufman factorizationcondition number, matrixdiagonal pivoting methodLAPACKlinear equationsZHECON
F07MVF   15  nagf_lapacklin_zherfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
Related keywords: backward errorBunch–Kaufman factorizationdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equationsZHERFS
F07MWF   15  nagf_lapacklin_zhetri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07MRF
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodinverse, matrixLAPACKlinear equationsZHETRI
F07PNF   21  nagf_lapacklin_zhpsv
Computes the solution to a complex Hermitian system of linear equations, packed storage
Related keywords: diagonal pivoting methodinverse, matrixLAPACK LDL H decompositionlinear equations UDU H decompositionZHPSV
F07PPF   21  nagf_lapacklin_zhpsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, Hermitian, system of linear equations, error bounds and condition estimates. Packed storage
Related keywords: backward errordiagonal pivoting methodforward errorinverse, matrixLAPACK LDL H decompositionlinear equations UDU H decompositionZHPSVX
F07PRF   15  nagf_lapacklin_zhptrf
Bunch–Kaufman factorization of complex Hermitian indefinite matrix, packed storage
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodLAPACKlinear equationsZHPTRF
F07PSF   15  nagf_lapacklin_zhptrs
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PRF, packed storage
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodLAPACKlinear equationsZHPTRS
F07PUF   15  nagf_lapacklin_zhpcon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07PRF, packed storage
Related keywords: Bunch–Kaufman factorizationcondition number, matrixdiagonal pivoting methodLAPACKlinear equationsZHPCON
F07PVF   15  nagf_lapacklin_zhprfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorBunch–Kaufman factorizationdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equationsZHPRFS
F07PWF   15  nagf_lapacklin_zhptri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07PRF, packed storage
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodinverse, matrixLAPACKlinear equationsZHPTRI
F08FLF   22  nagf_lapackeig_ddisna
Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix
Related keywords: condition number, matrixDDISNAeigenproblemeigenvectorsfinanceLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08FNF   21  nagf_lapackeig_zheev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresZHEEV
F08FPF   21  nagf_lapackeig_zheevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
Related keywords: eigenproblemeigenvalueseigenvectorsfinanceLAPACKLAPACKleast squaresZHEEVX
F08FQF   19  nagf_lapackeig_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenvalueseigenvectorsfinanceLAPACKLAPACKleast squaresZHEEVD
F08FRF   21  nagf_lapackeig_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresrelatively robust representationsunitary transformationsZHEEVR
F08FSF   16  nagf_lapackeig_zhetrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformationsZHETRD
F08GNF   21  nagf_lapackeig_zhpev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresZHPEV
F08GPF   21  nagf_lapackeig_zhpevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresZHPEVX
F08GQF   19  nagf_lapackeig_zhpevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: divide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresPal–Walker–Kahan ( QL or QR ) algorithmZHPEVD
F08GSF   16  nagf_lapackeig_zhptrd
Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformationsZHPTRD
F08XSF   20  nagf_lapackeig_zhgeqz
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices
Related keywords: eigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresQZ algorithmZHGEQZ
complex, Hermitian, positive-definite, tridiagonal matrix F04CGF   21  nagf_linsys_complex_posdef_tridiag_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationsmatrix, bandsimultaneous linear equations
F07JNF   21  nagf_lapacklin_zptsv
Computes the solution to a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: Cholesky decompositionLAPACKlinear equationsmatrix, bandZPTSV
F07JPF   21  nagf_lapacklin_zptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZPTSVX
F07JRF   22  nagf_lapacklin_zpttrf
Computes the LDL H factorization of a complex Hermitian positive definite tridiagonal matrix
Related keywords: Cholesky decompositionLAPACKlinear equationsmatrix, bandZPPTRF
F07JSF   22  nagf_lapacklin_zpttrs
Solves a complex Hermitian positive definite tridiagonal system using the LDL H factorization computed by F07JRF
Related keywords: Cholesky decompositionLAPACKlinear equationsmatrix, bandZPPTRS
F07JUF   22  nagf_lapacklin_zptcon
Computes the reciprocal of the condition number of a complex Hermitian positive definite tridiagonal system using the LDL H factorization computed by F07JRF
Related keywords: Cholesky decompositioncondition number, matrixLAPACKlinear equationsmatrix, bandZPTCON
F07JVF   22  nagf_lapacklin_zptrfs
Refined solution with error bounds of complex Hermitian positive definite tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositionforward errorLAPACKlinear equationsmatrix, bandZPTRFS
complex, Hermitian, positive-definite matrix F04CDF   21  nagf_linsys_complex_posdef_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationssimultaneous linear equations
F04CEF   21  nagf_linsys_complex_posdef_packed_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite system of linear equations, packed storage
Related keywords: big datadata analyticsforward errorlinear equationssimultaneous linear equations
F07FNF   21  nagf_lapacklin_zposv
Computes the solution to a complex Hermitian positive definite system of linear equations
Related keywords: Cholesky decompositionLAPACKlinear equationsZPOSV
F07FPF   21  nagf_lapacklin_zposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixerror bound, matrixfinanceforward errorLAPACKlinear equationsZPOSVX
F07FQF   23  nagf_lapacklin_zcposv
Computes the solution to a complex Hermitian positive definite system of linear equations using mixed precision arithmetic
Related keywords: Cholesky decompositionLAPACKlinear equationsmixed-precisionZCPOSV
F07FRF   15  nagf_lapacklin_zpotrf
Cholesky factorization of complex Hermitian positive definite matrix
Related keywords: Cholesky decompositionLAPACKlinear equationsZPOTRF
F07FSF   15  nagf_lapacklin_zpotrs
Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FRF
Related keywords: Cholesky decompositionLAPACKlinear equationsZPOTRS
F07FTF   22  nagf_lapacklin_zpoequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number
Related keywords: equilibrationLAPACKlinear equationsscalingZPOEQU
F07FUF   15  nagf_lapacklin_zpocon
Estimate condition number of complex Hermitian positive definite matrix, matrix already factorized by F07FRF
Related keywords: Cholesky decompositioncondition number, matrixLAPACKlinear equationsZPOCON
F07FVF   15  nagf_lapacklin_zporfs
Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositionerror bound, matrixforward errorLAPACKlinear equationsZPORFS
F07FWF   15  nagf_lapacklin_zpotri
Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07FRF
Related keywords: inverse, matrixLAPACKlinear equationsZPOTRI
F07GNF   21  nagf_lapacklin_zppsv
Computes the solution to a complex Hermitian positive definite system of linear equations, packed storage
Related keywords: Cholesky decompositionLAPACKlinear equationsZPPSV
F07GPF   21  nagf_lapacklin_zppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations, packed storage
Related keywords: backward errorCholesky decompositioncondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsZPPSVX
F07GRF   15  nagf_lapacklin_zpptrf
Cholesky factorization of complex Hermitian positive definite matrix, packed storage
Related keywords: Cholesky decompositionLAPACKlinear equationsZPPTRF
F07GSF   15  nagf_lapacklin_zpptrs
Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GRF, packed storage
Related keywords: Cholesky decompositionLAPACKlinear equationsZPPTRS
F07GTF   22  nagf_lapacklin_zppequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number, packed storage
Related keywords: equilibrationLAPACKlinear equationsscalingZPPEQU
F07GUF   15  nagf_lapacklin_zppcon
Estimate condition number of complex Hermitian positive definite matrix, matrix already factorized by F07GRF, packed storage
Related keywords: condition number, matrixLAPACKlinear equationsZPPCON
F07GVF   15  nagf_lapacklin_zpprfs
Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorCholesky decompositionerror bound, matrixforward errorLAPACKlinear equationsZPPRFS
F07GWF   15  nagf_lapacklin_zpptri
Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07GRF, packed storage
Related keywords: Cholesky decompositioninverse, matrixLAPACKlinear equationsZPPTRI
F07WRF   23  nagf_lapacklin_zpftrf
Cholesky factorization of complex Hermitian positive definite matrix, Rectangular Full Packed format
Related keywords: Cholesky decompositionLAPACKlinear equationsZPFTRF
F07WSF   23  nagf_lapacklin_zpftrs
Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by F07WRF, Rectangular Full Packed format
Related keywords: Cholesky decompositionLAPACKlinear equationsZPFTRS
F07WWF   23  nagf_lapacklin_zpftri
Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07WRF, Rectangular Full Packed format
Related keywords: Cholesky decompositionLAPACKlinear equationsZPETRI
F08SNF   21  nagf_lapackeig_zhegv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHEGV
F08SPF   21  nagf_lapackeig_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHEGVX
F08SQF   21  nagf_lapackeig_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHEGVD
F08SSF   16  nagf_lapackeig_zhegst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , B factorized by F07FRF
Related keywords: eigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresZHEGST
F08TNF   21  nagf_lapackeig_zhpgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHPGV
F08TPF   21  nagf_lapackeig_zhpgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHPGVX
F08TQF   21  nagf_lapackeig_zhpgvd
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHPGVD
F08TSF   16  nagf_lapackeig_zhpgst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , packed storage, B factorized by F07GRF
Related keywords: eigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresZHPGVD
complex, Hermitian, positive-semidefinite matrix F07KRF   23  nagf_lapacklin_zpstrf
Cholesky factorization of complex Hermitian positive semidefinite matrix
Related keywords: Cholesky decompositionLAPACKlinear equationsZPSTRF
complex, Hermitian, sparse matrix F11GRF   20  nagf_sparse_complex_herm_basic_setup
Complex sparse Hermitian linear systems, setup for F11GSF
Related keywords: big datadata analyticslarge scale linear systemslinear equations, iterative method, setup
F11GSF   20  nagf_sparse_complex_herm_basic_solver
Complex sparse Hermitian linear systems, preconditioned conjugate gradient or Lanczos
Related keywords: big dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemslinear equations, iterative method
F11GTF   20  nagf_sparse_complex_herm_basic_diag
Complex sparse Hermitian linear systems, diagnostic for F11GSF
Related keywords: big datadata analyticslarge scale linear systemslinear equations, iterative method, diagnostic
F11JNF   19  nagf_sparse_complex_herm_precon_ilu
Complex sparse Hermitian matrix, incomplete Cholesky factorization
Related keywords: big datadata analyticsincomplete Cholesky factorizationlarge scale linear systems
F11JPF   19  nagf_sparse_complex_herm_precon_ilu_solve
Solution of complex linear system involving incomplete Cholesky preconditioning matrix generated by F11JNF
Related keywords: big datadata analyticsincomplete Cholesky factorizationlarge scale linear systemslinear equations, pre-conditioners
F11JQF   19  nagf_sparse_complex_herm_solve_ilu
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JNF (Black Box)
Related keywords: big dataconjugate gradient methoddata analyticsiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodsparse linear equations
F11JRF   19  nagf_sparse_complex_herm_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse Hermitian matrix
Related keywords: big datadata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodsparse linear equationsSSOR method, symmetric successive over-relaxation
F11JSF   19  nagf_sparse_complex_herm_solve_jacssor
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big dataconjugate gradient methoddata analyticsiterative methods, linear equationsJacobi methodLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodsparse linear equationsSSOR method, symmetric successive over-relaxation
F11XSF   19  nagf_sparse_complex_herm_matvec
Complex sparse Hermitian matrix-vector multiply
Related keywords: big datadata analyticslarge scale linear systemsmultiply, matrix
F11ZPF   19  nagf_sparse_complex_herm_sort
Complex sparse Hermitian matrix reorder routine
Related keywords: big datadata analyticslarge scale linear systemsmatrix, reorder
complex, Hermitian, tridiagonal matrix F06UPF   21  nagf_blas_zlanht
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian tridiagonal matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesmatrix, band
complex, Hermitian matrix F06SCF   12  nagf_blas_zhemv
Matrix-vector product, complex Hermitian matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesmultiply, matrixzhemv
F06SEF   12  nagf_blas_zhpmv
Matrix-vector product, complex Hermitian packed matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesmultiply, matrixzhpmv
F06SPF   12  nagf_blas_zher
Rank-1 update, complex Hermitian matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesrank k matrix updateszher
F06SQF   12  nagf_blas_zhpr
Rank-1 update, complex Hermitian packed matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesrank k matrix updateszhpr
F06SRF   12  nagf_blas_zher2
Rank-2 update, complex Hermitian matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesrank k matrix updateszher2
F06SSF   12  nagf_blas_zhpr2
Rank-2 update, complex Hermitian packed matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesrank k matrix updateszhpr2
F06TMF   13  nagf_blas_zhesrc
Unitary similarity transformation of Hermitian matrix as a sequence of plane rotations
Related keywords: BLASlinear algebra support routinesrotation, elementary
F06UDF   15  nagf_blas_zlanhp
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routines
F06WNF   23  nagf_blas_zlanhf
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format
Related keywords: 1-normBLASBLASblas, complex matricesFrobenius norminfinity-normlinear algebra support routineslinear algebra support routines;zlanhf
complex, Hessenberg matrix F06TRF   13  nagf_blas_zuhqr
Q R or R Q factorization by sequence of plane rotations, complex upper Hessenberg matrix
Related keywords: BLASlinear algebra support routines QR factorizationrotation, elementaryRQ factorizations
F06UMF   15  nagf_blas_zlanhs
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hessenberg matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routines
F08PSF   16  nagf_lapackeig_zhseqr
Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
Related keywords: eigenproblemeigenvaluesLAPACKLAPACKleast squaresSchur formZHSEQR
F08PXF   16  nagf_lapackeig_zhsein
Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
Related keywords: eigenproblemeigenvectorsinverse iterationLAPACKLAPACKleast squaresZHSEIN
complex, m by n matrix F01RJF   14  nagf_matop_complex_gen_rq
R Q factorization of complex m by n matrix m n
Related keywords: inversionmatrix operations R Q factorizations
F04ZDF   24  nagf_linsys_complex_gen_norm_rcomm
Norm estimation (for use in condition estimation), complex rectangular matrix
Related keywords: 1 -normbig datadata analyticsnorm, matrixsimultaneous linear equations
F06SAF   12  nagf_blas_zgemv
Matrix-vector product, complex rectangular matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesmultiply, matrixzgemv
F06SMF   12  nagf_blas_zgeru
Rank-1 update, complex rectangular matrix, unconjugated vector
Related keywords: BLASblas, complex matriceslinear algebra support routinesrank k matrix updateszgeru
F06SNF   12  nagf_blas_zgerc
Rank-1 update, complex rectangular matrix, conjugated vector
Related keywords: BLASblas, complex matriceslinear algebra support routinesrank k matrix updateszgerc
F06TFF   13  nagf_blas_zmcopy
Matrix copy, complex rectangular or trapezoidal matrix
Related keywords: BLAScomplex, trapezoidal matrixelementary arithmeticlinear algebra support routines
F06THF   13  nagf_blas_zmload
Matrix initialization, complex rectangular matrix
Related keywords: BLASelementary arithmeticlinear algebra support routines
F06TXF   13  nagf_blas_zgesrc
Apply sequence of plane rotations, complex rectangular matrix, real cosine and complex sine
Related keywords: BLASlinear algebra support routinesrotation, elementary
F06TYF   13  nagf_blas_zgesrs
Apply sequence of plane rotations, complex rectangular matrix, complex cosine and real sine
Related keywords: BLASlinear algebra support routinesrotation, elementary
F06UAF   15  nagf_blas_zlange
1 -norm, -norm, Frobenius norm, largest absolute element, complex general matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routines
F06VJF   13  nagf_blas_zgeap
Permute rows or columns, complex rectangular matrix, permutations represented by an integer array
Related keywords: BLASlinear algebra support routinespermutation
F06VKF   13  nagf_blas_zgeapr
Permute rows or columns, complex rectangular matrix, permutations represented by a real array
Related keywords: BLASlinear algebra support routinespermutation
F06VXF   13  nagf_blas_zsgesr
Apply sequence of plane rotations, complex rectangular matrix, real cosine and sine
Related keywords: BLASlinear algebra support routinesrotation, elementary
F06ZAF   14  nagf_blas_zgemm
Matrix-matrix product, two complex rectangular matrices
Related keywords: BLASblas, complex matriceslinear algebra support routinesmultiply, matrixzgemm
F06ZCF   14  nagf_blas_zhemm
Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian, indefinite matrixlinear algebra support routinesmultiply, matrixzgemm
F06ZFF   14  nagf_blas_ztrmm
Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix
Related keywords: BLASblas, complex matricescomplex, triangular matrixlinear algebra support routinesmultiply, matrixztrmm
F06ZTF   14  nagf_blas_zsymm
Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix
Related keywords: BLASblas, complex matricescomplex, symmetric matrixlinear algebra support routinesmultiply, matrixzsymm
F07ARF   15  nagf_lapacklin_zgetrf
L U factorization of complex m by n matrix
Related keywords: financeLAPACKlinear equations L U decompositionZGETRF
F07BRF   15  nagf_lapacklin_zgbtrf
L U factorization of complex m by n band matrix
Related keywords: LAPACKlinear equations L U decompositionmatrix, bandZGBSVX
F08ANF   21  nagf_lapackeig_zgels
Solves a complex linear least problem of full rank
Related keywords: eigenproblemfinanceLAPACKLAPACKleast squareslinear least squares LQ decompositionoverdetermined linear equations QR factorizationunderdetermined linear systemZGELS
F08APF   25  nagf_lapackeig_zgeqrt
Performs a Q R factorization of complex general rectangular matrix using recursive algorithm
Related keywords: eigenproblemexplicit blockingLAPACKleast squaresQR factorizationrecursive QRZGEQRT
F08ASF   16  nagf_lapackeig_zgeqrf
Performs a Q R factorization of complex general rectangular matrix
Related keywords: eigenproblemLAPACKLAPACKleast squares QR factorizationZGEQRF
F08AVF   16  nagf_lapackeig_zgelqf
Performs a L Q factorization of complex general rectangular matrix
Related keywords: eigenproblemLAPACKLAPACKleast squares LQ factorizationZGELQF
F08BNF   21  nagf_lapackeig_zgelsy
Computes the minimum-norm solution to a complex linear least squares problem
Related keywords: eigenproblemLAPACKLAPACKleast squareslinear least squaresminimal least squaresZGELSY
F08BSF   16  nagf_lapackeig_zgeqpf
Q R factorization, with column pivoting, of complex general rectangular matrix
Related keywords: eigenproblemLAPACKLAPACKleast squares QR factorizationZGEQPF
F08BTF   22  nagf_lapackeig_zgeqp3
Q R factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix
Related keywords: eigenproblemLAPACKLAPACKleast squares QR factorizationZGEQP3
F08CSF   22  nagf_lapackeig_zgeqlf
Q L factorization of complex general rectangular matrix
Related keywords: eigenproblemLAPACKLAPACKleast squares QL factorizationZGEQLF
F08CVF   22  nagf_lapackeig_zgerqf
R Q factorization of complex general rectangular matrix
Related keywords: eigenproblemLAPACKLAPACKleast squaresRQ factorizationsZGERQF
F08KNF   21  nagf_lapackeig_zgelss
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
Related keywords: eigenproblemLAPACKLAPACKleast squareslinear least squaresminimal least squaresSVD, singular value decompositionZGELSS
F08KQF   21  nagf_lapackeig_zgelsd
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemLAPACKLAPACKleast squareslinear least squaresminimal least squaresSVD, singular value decompositionZGELSD
F08KSF   16  nagf_lapackeig_zgebrd
Performs a unitary reduction of complex general rectangular matrix to bidiagonal form
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformationsZGEBRD
F08VSF   22  nagf_lapackeig_zggsvp
Produces unitary matrices that simultaneously reduce the complex, m by n , matrix A and the complex, p by n , matrix B to upper triangular form
Related keywords: eigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresorthogonal transformationsSVD, generalizedZGGSVP
F08VUF   26  nagf_lapackeig_zggsvp3
Produces unitary matrices, using BLAS-3, that simultaneously reduce the complex, m by n , matrix A and the complex, p by n , matrix B to upper triangular form
Related keywords: eigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresorthogonal transformationsSVD, generalizedZGGSVP3
F08ZNF   21  nagf_lapackeig_zgglse
Solves the complex linear equality-constrained least squares (LSE) problem
Related keywords: eigenproblemLAPACKLAPACKleast squareslinear least squaresRQ factorizationsZGGLSE
F08ZPF   21  nagf_lapackeig_zggglm
Solves a complex general Gauss–Markov linear model (GLM) problem
Related keywords: eigenproblemGauss–Markov linear modelLAPACKLAPACKleast squaresZGGGLM
F08ZSF   22  nagf_lapackeig_zggqrf
Computes a generalized Q R factorization of a complex matrix pair
Related keywords: eigenproblemLAPACKLAPACKleast squares QR factorizationZGGQRF
F08ZTF   22  nagf_lapackeig_zggrqf
Computes a generalized R Q factorization of a complex matrix pair
Related keywords: eigenproblemLAPACKLAPACKleast squaresRQ factorizationsZGGRQF
complex, nonsymmetric matrix F01CWF   14  nagf_matop_complex_addsub
Sum or difference of two complex matrices, optional scaling and transposition
Related keywords: inversionmatrix operationssum, matrixtranspose, matrix
F01FCF   23  nagf_matop_complex_gen_matrix_exp
Complex matrix exponential
Related keywords: exponential, matrixfinanceinversionmatrix exponentialmatrix operations
F01FJF   24  nagf_matop_complex_gen_matrix_log
Complex matrix logarithm
Related keywords: inversionlogarithm, matrixmatrix logarithmmatrix operations
F01FKF   24  nagf_matop_complex_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm)
Related keywords: cosh, matrixcosine, matrixexponential, matrixfunctions, matrixinversionmatrix operationssine, matrixsinh, matrix
F01FLF   24  nagf_matop_complex_gen_matrix_fun_num
Function of a complex matrix (using numerical differentiation)
Related keywords: functions, matrixinversionmatrix functionsmatrix operations
F01FMF   24  nagf_matop_complex_gen_matrix_fun_usd
Function of a complex matrix (using user-supplied derivatives)
Related keywords: functions, matrixinversionmatrix functionsmatrix operations
F01FNF   25  nagf_matop_complex_gen_matrix_sqrt
Complex matrix square root
Related keywords: inversionmatrix operations
F01HAF   24  nagf_matop_complex_gen_matrix_actexp
Action of a complex matrix exponential on a complex matrix
Related keywords: exponential, matrixinversionmatrix exponentialmatrix operationsproduct, matrices
F01HBF   24  nagf_matop_complex_gen_matrix_actexp_rcomm
Action of a complex matrix exponential on a complex matrix (reverse communication)
Related keywords: exponential, matrixinversionmatrix exponentialmatrix operationsproduct, matrices
F01KAF   24  nagf_matop_complex_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix
Related keywords: condition number, matrixcosh, matrixcosine, matrixexponential, matrixinversionlogarithm, matrixmatrix operationssine, matrixsinh, matrix
F01KBF   24  nagf_matop_complex_gen_matrix_cond_num
Condition number for a function of a complex matrix (using numerical differentiation)
Related keywords: condition number, matrixinversionmatrix functionsmatrix operations
F01KCF   24  nagf_matop_complex_gen_matrix_cond_usd
Condition number for a function of a complex matrix (using user-supplied derivatives)
Related keywords: condition number, matrixinversionmatrix functionsmatrix operations
F01KDF   25  nagf_matop_complex_gen_matrix_cond_sqrt
Condition number for square root of complex matrix
Related keywords: condition numberinversionmatrix operations
F01KGF   25  nagf_matop_complex_gen_matrix_cond_exp
Condition number for complex matrix exponential
Related keywords: condition numberinversionmatrix operations
F01KHF   25  nagf_matop_complex_gen_matrix_frcht_exp
Fréchet derivative of complex matrix exponential
Related keywords: Fréchet derivativeinversionmatrix operations
F01KJF   25  nagf_matop_complex_gen_matrix_cond_log
Condition number for complex matrix logarithm
Related keywords: condition numberinversionmatrix operations
F01KKF   25  nagf_matop_complex_gen_matrix_frcht_log
Fréchet derivative of complex matrix logarithm
Related keywords: Fréchet derivativeinversionmatrix operations
F01LEF   11  nagf_matop_real_gen_tridiag_lu
L U factorization of real tridiagonal matrix
Related keywords: inversionLU decompositionmatrix, bandmatrix operations
F01ZBF   14  nagf_matop_complex_tri_pack
Convert complex matrix between packed triangular and square storage formats
Related keywords: convert matrix storage formatsinversionmatrix operations
F01ZDF   14  nagf_matop_complex_band_pack
Convert complex matrix between packed banded and rectangular storage formats
Related keywords: convert matrix storage formatsinversionmatrix operations
F02GCF   17  nagf_eigen_complex_gen_eigsys
Selected eigenvalues and eigenvectors of complex nonsymmetric matrix (Black Box)
Related keywords: big datadata analyticseigenvalueseigenvectors
F03BNF   23  nagf_det_complex_gen
Determinant of complex matrix previously L U factorized
Related keywords: determinant
F04CAF   21  nagf_linsys_complex_square_solve
Computes the solution, estimated condition number and error-bound to a complex system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationssimultaneous linear equations
F07ANF   21  nagf_lapacklin_zgesv
Computes the solution to a complex system of linear equations
Related keywords: LAPACKlinear equations L U decompositionZGESV
F07APF   21  nagf_lapacklin_zgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
Related keywords: backward errorcondition number, matrixerror bound, matrixfinanceforward errorLAPACKlinear equations L U decompositionZGESVX
F07AQF   22  nagf_lapacklin_zcgesv
Computes the solution to a complex system of linear equations using mixed precision arithmetic
Related keywords: LAPACKlinear equationsmixed-precisionZCGESV
F07ASF   15  nagf_lapacklin_zgetrs
Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by F07ARF
Related keywords: financeLAPACKlinear equations L U decompositionZGETRS
F07ATF   22  nagf_lapacklin_zgeequ
Computes row and column scalings intended to equilibrate a general complex matrix and reduce its condition number
Related keywords: equilibrationLAPACKlinear equationsscalingZGEEQU
F07AUF   15  nagf_lapacklin_zgecon
Estimate condition number of complex matrix, matrix already factorized by F07ARF
Related keywords: condition number, matrixLAPACKlinear equationsZGECON
F07AVF   15  nagf_lapacklin_zgerfs
Refined solution with error bounds of complex system of linear equations, multiple right-hand sides
Related keywords: backward errorforward errorLAPACKlinear equationsZGERFS
F07AWF   15  nagf_lapacklin_zgetri
Inverse of complex matrix, matrix already factorized by F07ARF
Related keywords: inverse, matrixLAPACKlinear equationsZGETRI
F08KPF   21  nagf_lapackeig_zgesvd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
Related keywords: eigenproblemfinanceLAPACKLAPACKleast squaresSVD, singular value decompositionZGESVD
F08KRF   21  nagf_lapackeig_zgesdd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemLAPACKLAPACKleast squaresSVD, singular value decompositionZGESDD
F08NNF   21  nagf_lapackeig_zgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
Related keywords: DGEEVeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares
F08NPF   21  nagf_lapackeig_zgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGEEVeigenproblemeigenvalueseigenvectorsfinanceforward errorLAPACKLAPACKleast squares
F08NSF   16  nagf_lapackeig_zgehrd
Performs a unitary reduction of complex general matrix to upper Hessenberg form
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformationsZGEHRD
F08NVF   16  nagf_lapackeig_zgebal
Balances a complex general matrix
Related keywords: balancingeigenproblemLAPACKLAPACKleast squaresZGEBAL
F08NWF   16  nagf_lapackeig_zgebak
Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF
Related keywords: balancingeigenproblemLAPACKLAPACKleast squaresZGEBAK
F08PNF   21  nagf_lapackeig_zgees
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
Related keywords: eigenproblemeigenvaluesLAPACKLAPACKleast squaresSchur formSchur vectorsZGEES
F08VNF   21  nagf_lapackeig_zggsvd
Computes the generalized singular value decomposition of a complex matrix pair
Related keywords: eigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresSVD, generalizedZGGSVD
F08VQF   26  nagf_lapackeig_zggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair
Related keywords: eigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresSVD, generalizedZGGSVD3
F08WNF   21  nagf_lapackeig_zggev
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZGGEV
F08WPF   21  nagf_lapackeig_zggevx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsfinanceforward errorgeneralized eigenproblemLAPACKLAPACKleast squaresZGGEVX
F08WQF   26  nagf_lapackeig_zggev3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZGGEV3
F08WSF   20  nagf_lapackeig_zgghrd
Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformationsZGGHRD
F08WTF   26  nagf_lapackeig_zgghd3
Performs, using BLAS-3, a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformationsZGGHD3
F08WVF   20  nagf_lapackeig_zggbal
Balances a pair of complex, square, matrices
Related keywords: balancingeigenproblemLAPACKLAPACKleast squaresZGGBAL
F08WWF   20  nagf_lapackeig_zggbak
Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF
Related keywords: balancingeigenproblemeigenvectorsLAPACKLAPACKleast squaresZGGBAL
F08XNF   21  nagf_lapackeig_zgges
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: eigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresSchur vectorsZGGES
F08XPF   21  nagf_lapackeig_zggesx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: condition number, matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresSchur vectorsZGGES
F08XQF   26  nagf_lapackeig_zgges3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: eigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresSchur vectorsZGGES3
F08YTF   22  nagf_lapackeig_ztgexc
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
Related keywords: eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresunitary transformationsZTGEXC
F08YUF   22  nagf_lapackeig_ztgsen
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Related keywords: condition number, matrixeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresunitary transformationsZTGEXC
F08YYF   22  nagf_lapackeig_ztgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
Related keywords: condition number, matrixeigenproblemgeneralized Schur formLAPACKLAPACKleast squaresZTGSNA
complex, sparse matrix F11BRF   19  nagf_sparse_complex_gen_basic_setup
Complex sparse non-Hermitian linear systems, setup for F11BSF
Related keywords: big datadata analyticslarge scale linear systemslinear equations, iterative method, setup
F11BSF   19  nagf_sparse_complex_gen_basic_solver
Complex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11BTF   19  nagf_sparse_complex_gen_basic_diag
Complex sparse non-Hermitian linear systems, diagnostic for F11BSF
Related keywords: big datadata analyticslarge scale linear systemslinear equations, iterative method, diagnostic
F11DNF   19  nagf_sparse_complex_gen_precon_ilu
Complex sparse non-Hermitian linear systems, incomplete L U factorization
Related keywords: big datadata analyticsincomplete L U factorizationlarge scale linear systemslinear equations, pre-conditioners
F11DPF   19  nagf_sparse_complex_gen_precon_ilu_solve
Solution of complex linear system involving incomplete L U preconditioning matrix generated by F11DNF
Related keywords: big datadata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative method
F11DQF   19  nagf_sparse_complex_gen_solve_ilu
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DNF (Black Box)
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DRF   19  nagf_sparse_complex_gen_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse non-Hermitian matrix
Related keywords: big datadata analyticslarge scale linear systemslinear equations, pre-conditionersSSOR method, symmetric successive over-relaxation
F11DSF   19  nagf_sparse_complex_gen_solve_jacssor
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsJacobi preconditioninglarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodSSOR method, symmetric successive over-relaxationTFQMR, transpose-free quasi-minimal residual method
F11DTF   24  nagf_sparse_complex_gen_precon_bdilu
Complex, sparse, non-Hermitian linear system, incomplete L U factorization of local or overlapping diagonal blocks
Related keywords: additive Schwarz preconditionerbig datadata analyticsincomplete L U factorizationlarge scale linear systemslinear equations, pre-conditioners
F11DUF   24  nagf_sparse_complex_gen_solve_bdilu
Solution of complex, sparse, non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DTF
Related keywords: additive Schwarz preconditionerBi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DXF   20  nagf_sparse_complex_gen_precon_jacobi
Complex, sparse, Hermitian or non-Hermitian, linear systems, line Jacobi preconditioner
Related keywords: big datadata analyticsJacobi preconditioninglarge scale linear systemslinear equations, pre-conditioners
F11XNF   19  nagf_sparse_complex_gen_matvec
Complex sparse non-Hermitian matrix-vector multiply
Related keywords: big datadata analyticslarge scale linear systemsmultiply, matrix
F11ZNF   19  nagf_sparse_complex_gen_sort
Complex sparse non-Hermitian matrix reorder routine
Related keywords: big datadata analyticslarge scale linear systemsmatrix, reorder
F12ANF   21  nagf_sparseig_complex_init
Initialization routine for (F12APF) computing selected eigenvalues and, optionally, eigenvectors of a complex sparse (standard or generalized) eigenproblem
Related keywords: big datadata analyticseigenproblem, initializationlarge scale eigenproblems
F12APF   21  nagf_sparseig_complex_iter
Selected eigenvalues and, optionally, eigenvectors of a complex sparse eigenproblem, reverse communication
Related keywords: big datadata analyticseigenvalueseigenvectorslarge scale eigenproblemssparse eigenproblemsparse generalized eigenproblem
F12AQF   21  nagf_sparseig_complex_proc
Selected eigenvalues and, optionally, eigenvectors of a complex sparse eigenproblem, postprocessing for F12APF
Related keywords: big datadata analyticslarge scale eigenproblemssparse eigenproblem, postprocessing
F12ARF   21  nagf_sparseig_complex_option
Set a single option from a string (F12APF/F12AQF)
Related keywords: big datadata analyticslarge scale eigenproblemssparse eigenproblem, options
F12ASF   21  nagf_sparseig_complex_monit
Provides monitoring information for F12APF
Related keywords: big datadata analyticseigenproblemlarge scale eigenproblemsmonitoring informationsparse eigenproblems, monitoring
complex, symmetric matrix F04DHF   21  nagf_linsys_complex_symm_solve
Computes the solution, estimated condition number and error-bound to a complex symmetric system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationssimultaneous linear equations
F04DJF   21  nagf_linsys_complex_symm_packed_solve
Computes the solution, estimated condition number and error-bound to a complex symmetric system of linear equations, packed storage
Related keywords: big datadata analyticsforward errorlinear equationssimultaneous linear equations
F06TAF   21  nagf_blas_zsymv
Matrix-vector product, complex symmetric matrix
Related keywords: BLASlinear algebra support routinesmultiply, matrix
F06TBF   21  nagf_blas_zsyr
Rank-1 update, complex symmetric matrix
Related keywords: BLASlinear algebra support routinesrank k matrix updates
F06TCF   21  nagf_blas_zspmv
Matrix-vector product, complex symmetric packed matrix
Related keywords: BLASlinear algebra support routinesmultiply, matrix
F06TDF   21  nagf_blas_zspr
Rank-1 update, complex symmetric packed matrix
Related keywords: BLASlinear algebra support routinesrank k matrix updates
F06UFF   15  nagf_blas_zlansy
1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routines
F06UGF   15  nagf_blas_zlansp
1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routines
F06ZTF   14  nagf_blas_zsymm
Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix
Related keywords: BLASblas, complex matricescomplex, m by n matrixlinear algebra support routinesmultiply, matrixzsymm
F06ZUF   14  nagf_blas_zsyrk
Rank- k update of a complex symmetric matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesrank k matrix updateszher2k
F06ZWF   14  nagf_blas_zsyr2k
Rank- 2 k update of a complex symmetric matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesrank k matrix updateszsyr2k
F07NNF   21  nagf_lapacklin_zsysv
Computes the solution to a complex symmetric system of linear equations
Related keywords: diagonal pivoting methodLAPACK LDL H decompositionlinear equations UDU H decompositionZSYSV
F07NPF   21  nagf_lapacklin_zsysvx
Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations
Related keywords: backward errordiagonal pivoting methodforward errorLAPACK LDL H decompositionlinear equations UDU H decompositionZSYSVX
F07NRF   15  nagf_lapacklin_zsytrf
Bunch–Kaufman factorization of complex symmetric matrix
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodLAPACKlinear equationsZSYTRF
F07NSF   15  nagf_lapacklin_zsytrs
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07NRF
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodLAPACKlinear equationsZSYTRS
F07NUF   15  nagf_lapacklin_zsycon
Estimate condition number of complex symmetric matrix, matrix already factorized by F07NRF
Related keywords: Bunch–Kaufman factorizationcondition number, matrixdiagonal pivoting methodLAPACKlinear equationsZSYCON
F07NVF   15  nagf_lapacklin_zsyrfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
Related keywords: backward errorBunch–Kaufman factorizationdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equationsZSYRFS
F07NWF   15  nagf_lapacklin_zsytri
Inverse of complex symmetric matrix, matrix already factorized by F07NRF
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodinverse, matrixLAPACKlinear equationsZSYTRI
F07QNF   21  nagf_lapacklin_zspsv
Computes the solution to a complex symmetric system of linear equations, packed storage
Related keywords: diagonal pivoting methodLAPACK LDL T decompositionlinear equations UDU T decompositionZSPSV
F07QPF   21  nagf_lapacklin_zspsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, symmetric, system of linear equations, error bounds and condition estimates. Packed storage
Related keywords: backward errordiagonal pivoting methodforward errorLAPACK LDL T decompositionlinear equations UDU T decompositionZSPSVX
F07QRF   15  nagf_lapacklin_zsptrf
Bunch–Kaufman factorization of complex symmetric matrix, packed storage
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodLAPACKlinear equationsZSPTRF
F07QSF   15  nagf_lapacklin_zsptrs
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07QRF, packed storage
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodLAPACKlinear equationsZSPTRS
F07QUF   15  nagf_lapacklin_zspcon
Estimate condition number of complex symmetric matrix, matrix already factorized by F07QRF, packed storage
Related keywords: Bunch–Kaufman factorizationcondition number, matrixdiagonal pivoting methodLAPACKlinear equationsZSPCON
F07QVF   15  nagf_lapacklin_zsprfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorBunch–Kaufman factorizationdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equationsZSPRFS
F07QWF   15  nagf_lapacklin_zsptri
Inverse of complex symmetric matrix, matrix already factorized by F07QRF, packed storage
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodinverse, matrixLAPACKlinear equationsZSPTRI
F11YEF   25  nagf_sparse_sym_rcm
Reverse Cuthill–McKee reordering of a sparse symmetric matrix in CCS format
Related keywords: big datadata analyticslarge scale linear systemspermutationreal, symmetric matrixsparsesparse matrix
complex, trapezoidal matrix F01RGF   14  nagf_matop_complex_trapez_rq
R Q factorization of complex m by n upper trapezoidal matrix m n
Related keywords: inversionmatrix operationsRQ factorizations
F06TFF   13  nagf_blas_zmcopy
Matrix copy, complex rectangular or trapezoidal matrix
Related keywords: BLAScomplex, m by n matrixelementary arithmeticlinear algebra support routines
F06UJF   15  nagf_blas_zlantr
1 -norm, -norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix
Related keywords: 1-normBLAScomplex, triangular matrixFrobenius norminfinity-normlinear algebra support routines
F08BVF   22  nagf_lapackeig_ztzrzf
Reduces a complex upper trapezoidal matrix to upper triangular form
Related keywords: eigenproblemLAPACKLAPACKleast squaresmatrix, upper trapezoidalmatrix, upper triangularZTZRZF
F08YSF   22  nagf_lapackeig_ztgsja
Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
Related keywords: complex, triangular matrixeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresZTGSJA
complex, triangular matrix F01FPF   25  nagf_matop_complex_tri_matrix_sqrt
Complex upper triangular matrix square root
Related keywords: inversionmatrix operations
F01VBF   23  nagf_matop_ztrttp
Copies a complex triangular matrix from full format to packed format
Related keywords: financeinversionLAPACKmatrix operationsZTRTTP
F01VDF   23  nagf_matop_ztpttr
Copies a complex triangular matrix from packed format to full format
Related keywords: financeinversionLAPACKmatrix operationsZTPTTR
F01VFF   23  nagf_matop_ztrttf
Copies a complex triangular matrix from full format to Rectangular Full Packed format
Related keywords: financeinversionLAPACKmatrix operationsZTRTTF
F01VHF   23  nagf_matop_ztfttr
Copies a complex triangular matrix from Rectangular Full Packed format to full format
Related keywords: financeinversionLAPACKmatrix operationsZTFTTR
F01VKF   23  nagf_matop_ztpttf
Copies a complex triangular matrix from packed format to Rectangular Full Packed format
Related keywords: financeinversionLAPACKmatrix operationsZTPTTF
F01VMF   23  nagf_matop_ztfttp
Copies a complex triangular matrix from Rectangular Full Packed format to packed format
Related keywords: financeinversionLAPACKmatrix operationsZTFTTP
F02XUF   13  nagf_eigen_complex_triang_svd
SVD of complex upper triangular matrix (Black Box)
Related keywords: big datadata analyticseigenvalueseigenvectorsSVD, singular value decomposition
F06SFF   12  nagf_blas_ztrmv
Matrix-vector product, complex triangular matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesmultiply, matrixztrmv
F06SHF   12  nagf_blas_ztpmv
Matrix-vector product, complex triangular packed matrix
Related keywords: BLASblas, complex matriceslinear algebra support routinesmultiply, matrixztpmv
F06SJF   12  nagf_blas_ztrsv
System of equations, complex triangular matrix
Related keywords: BLASblas, complex matriceslinear algebra support routineslinear equationsztrsv
F06SLF   12  nagf_blas_ztpsv
System of equations, complex triangular packed matrix
Related keywords: BLASblas, complex matriceslinear algebra support routineslinear equationsztbsv
F06TPF   13  nagf_blas_zutr1
Q R factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix
Related keywords: BLASlinear algebra support routines QR factorizationrank k matrix updates
F06TQF   13  nagf_blas_zutupd
Q R factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row
Related keywords: BLASlinear algebra support routines QR factorizationrotation, elementary
F06TSF   13  nagf_blas_zusqr
Q R or R Q factorization by sequence of plane rotations, complex upper spiked matrix
Related keywords: BLASlinear algebra support routines QR factorizationrotation, elementaryRQ factorizations
F06TTF   13  nagf_blas_zutsqr
Q R factorization of U P or R Q factorization of P U , U complex upper triangular, P a sequence of plane rotations
Related keywords: BLASlinear algebra support routines QR factorizationrotation, elementaryRQ factorizations
F06TVF   13  nagf_blas_zutsrh
Compute upper Hessenberg matrix by sequence of plane rotations, complex upper triangular matrix
Related keywords: BLASlinear algebra support routinesrotation, elementary
F06TWF   13  nagf_blas_zutsrs
Compute upper spiked matrix by sequence of plane rotations, complex upper triangular matrix
Related keywords: BLASlinear algebra support routinesrotation, elementary
F06UJF   15  nagf_blas_zlantr
1 -norm, -norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix
Related keywords: 1-normBLAScomplex, trapezoidal matrixFrobenius norminfinity-normlinear algebra support routines
F06UKF   15  nagf_blas_zlantp
1 -norm, -norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routines
F06UNF   21  nagf_blas_zlangt
1 -norm, -norm, Frobenius norm, largest absolute element, complex tridiagonal matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesmatrix, band
F06WPF   23  nagf_blas_ztfsm
Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix, Rectangular Full Packed format
Related keywords: BLASBLASblas, complex matriceslinear algebra support routineslinear algebra support routines;linear equationsztfsm
F06ZFF   14  nagf_blas_ztrmm
Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix
Related keywords: BLASblas, complex matricescomplex, m by n matrixlinear algebra support routinesmultiply, matrixztrmm
F06ZJF   14  nagf_blas_ztrsm
Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix
Related keywords: BLASblas, complex matriceslinear algebra support routineslinear least squaresztrsm
F07TSF   15  nagf_lapacklin_ztrtrs
Solution of complex triangular system of linear equations, multiple right-hand sides
Related keywords: LAPACKlinear equationsZTRTRS
F07TUF   15  nagf_lapacklin_ztrcon
Estimate condition number of complex triangular matrix
Related keywords: condition number, matrixLAPACKlinear equationsZTRCON
F07TVF   15  nagf_lapacklin_ztrrfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorerror bound, matrixforward errorLAPACKlinear equationsZTRRFS
F07TWF   15  nagf_lapacklin_ztrtri
Inverse of complex triangular matrix
Related keywords: inverse, matrixLAPACKlinear equationsZTRTRI
F07USF   15  nagf_lapacklin_ztptrs
Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
Related keywords: LAPACKlinear equationsZTPTRS
F07UUF   15  nagf_lapacklin_ztpcon
Estimate condition number of complex triangular matrix, packed storage
Related keywords: condition number, matrixLAPACKlinear equationsZTPCON
F07UVF   15  nagf_lapacklin_ztprfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorerror bound, matrixforward errorLAPACKlinear equationsZTPRFS
F07UWF   15  nagf_lapacklin_ztptri
Inverse of complex triangular matrix, packed storage
Related keywords: inverse, matrixLAPACKlinear equationsZTPTRI
F07WXF   23  nagf_lapacklin_ztftri
Inverse of complex triangular matrix, Rectangular Full Packed format
Related keywords: inverse, matrixLAPACKlinear equationsZTFTRI
F08QVF   16  nagf_lapackeig_ztrsyl
Solves the complex Sylvester matrix equation A X + X B = C , A and B are upper triangular or conjugate-transposes
Related keywords: eigenproblemLAPACKLAPACKleast squaresSylvester equationZTRSYL
F08QXF   16  nagf_lapackeig_ztrevc
Computes left and right eigenvectors of complex upper triangular matrix
Related keywords: eigenproblemeigenvectorsLAPACKLAPACKleast squaresZTREVC
F08QYF   16  nagf_lapackeig_ztrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
Related keywords: condition number, matrixDTRSNAeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares
F08YSF   22  nagf_lapackeig_ztgsja
Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
Related keywords: complex, trapezoidal matrixeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresZTGSJA
F08YVF   22  nagf_lapackeig_ztgsyl
Solves the complex generalized Sylvester equation
Related keywords: eigenproblemLAPACKLAPACKleast squaresSylvester equationZTGSYL
F08YXF   20  nagf_lapackeig_ztgevc
Computes left and right eigenvectors of a pair of complex upper triangular matrices
Related keywords: eigenproblemeigenvectorsgeneralized Schur formLAPACKLAPACKleast squaresZTGEVC
complex, triangular-pentagonal matrix F08BPF   25  nagf_lapackeig_ztpqrt
Q R factorization of complex triangular-pentagonal matrix
Related keywords: eigenproblemexplicit blockingLAPACKleast squaresQR factorizationrecursive QRZTPQRT
complex, tridiagonal matrix F04CCF   21  nagf_linsys_complex_tridiag_solve
Computes the solution, estimated condition number and error-bound to a complex tridiagonal system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationsmatrix, bandsimultaneous linear equations
F07CNF   21  nagf_lapacklin_zgtsv
Computes the solution to a complex tridiagonal system of linear equations
Related keywords: LAPACKlinear equations L U decompositionmatrix, bandZGTSV
F07CPF   21  nagf_lapacklin_zgtsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations
Related keywords: backward errorforward errorLAPACKlinear equations L U decompositionmatrix, bandZGTSVX
F07CRF   22  nagf_lapacklin_zgttrf
L U factorization of complex tridiagonal matrix
Related keywords: LAPACKlinear equations L U decompositionmatrix, bandZGTTRF
F07CSF   22  nagf_lapacklin_zgttrs
Solves a complex tridiagonal system of linear equations using the L U factorization computed by F07CDF
Related keywords: LAPACKlinear equations L U decompositionmatrix, bandZGTTRS
F07CUF   22  nagf_lapacklin_zgtcon
Estimates the reciprocal of the condition number of a complex tridiagonal matrix using the L U factorization computed by F07CDF
Related keywords: condition number, matrixLAPACKlinear equations L U decompositionmatrix, bandZGTCON
F07CVF   22  nagf_lapacklin_zgtrfs
Refined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorforward errorLAPACKlinear equations L U decompositionmatrix, bandZGTRFS
complex, unitary matrix F08RNF   25  nagf_lapackeig_zuncsd
Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices
Related keywords: complete CS decompositioneigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresZUNCSD
complex arithmetic A02 Chapter Introduction     Complex Arithmetic
complex exponential S01EAF   14  nagf_specfun_exp_complex
Complex exponential, e z
Related keywords: approximations of special functionsexponential
complex Fourier transform C06FFF   11  nagf_sum_fft_complex_multid_1d_sep
One-dimensional complex discrete Fourier transform of multidimensional data
Related keywords: Fast Fourier TransformFFTsummation of series
C06FJF   11  nagf_sum_fft_complex_multid_sep
Multidimensional complex discrete Fourier transform of multidimensional data
Related keywords: Fast Fourier TransformFFTsummation of series
C06FXF   17  nagf_sum_fft_complex_3d_sep
Three-dimensional complex discrete Fourier transform
Related keywords: Fast Fourier TransformFFTsummation of series
conditional logistic analysis G11CAF   19  nagf_contab_condl_logistic
Returns parameter estimates for the conditional analysis of stratified data
Related keywords: contingency table analysislogistic analysisparameter estimatesstratified data
condition number F01JDF   25  nagf_matop_real_gen_matrix_cond_sqrt
Condition number for square root of real matrix
Related keywords: inversionmatrix operationsreal, nonsymmetric matrix
F01JEF   25  nagf_matop_real_gen_matrix_cond_pow
Condition number for real matrix power
Related keywords: inversionmatrix operationsmatrix operations including inversion
F01JGF   25  nagf_matop_real_gen_matrix_cond_exp
Condition number for real matrix exponential
Related keywords: inversionmatrix operationsreal, nonsymmetric matrix
F01JJF   25  nagf_matop_real_gen_matrix_cond_log
Condition number for real matrix logarithm
Related keywords: inversionmatrix operationsreal, nonsymmetric matrix
F01KDF   25  nagf_matop_complex_gen_matrix_cond_sqrt
Condition number for square root of complex matrix
Related keywords: complex, nonsymmetric matrixinversionmatrix operations
F01KEF   25  nagf_matop_complex_gen_matrix_cond_pow
Condition number for complex matrix power
Related keywords: eigenvalues and eigenvectorsinversionmatrix operationsmatrix operations including inversion
F01KGF   25  nagf_matop_complex_gen_matrix_cond_exp
Condition number for complex matrix exponential
Related keywords: complex, nonsymmetric matrixinversionmatrix operations
F01KJF   25  nagf_matop_complex_gen_matrix_cond_log
Condition number for complex matrix logarithm
Related keywords: complex, nonsymmetric matrixinversionmatrix operations
F02JCF   25  nagf_eigen_real_gen_quad
Solves the quadratic eigenvalue problem for real matrices
Related keywords: backward errorbalancingbig datadata analyticseigenproblem, quadraticeigenvalueseigenvalues and eigenvectorseigenvectors
F02JQF   25  nagf_eigen_complex_gen_quad
Solves the quadratic eigenvalue problem for complex matrices
Related keywords: backward errorbalancingbig datadata analyticseigenproblem, quadraticeigenvalueseigenvalues and eigenvectorseigenvectors
condition number, matrix F01JAF   24  nagf_matop_real_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix
Related keywords: cosh, matrixcosine, matrixexponential, matrixinversionlogarithm, matrixmatrix operationsreal, nonsymmetric matrixsine, matrixsinh, matrix
F01JBF   24  nagf_matop_real_gen_matrix_cond_num
Condition number for a function of a real matrix (using numerical differentiation)
Related keywords: inversionmatrix functionsmatrix operationsreal, nonsymmetric matrix
F01JCF   24  nagf_matop_real_gen_matrix_cond_usd
Condition number for a function of a real matrix (using user-supplied derivatives)
Related keywords: inversionmatrix functionsmatrix operationsreal, nonsymmetric matrix
F01KAF   24  nagf_matop_complex_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix
Related keywords: complex, nonsymmetric matrixcosh, matrixcosine, matrixexponential, matrixinversionlogarithm, matrixmatrix operationssine, matrixsinh, matrix
F01KBF   24  nagf_matop_complex_gen_matrix_cond_num
Condition number for a function of a complex matrix (using numerical differentiation)
Related keywords: complex, nonsymmetric matrixinversionmatrix functionsmatrix operations
F01KCF   24  nagf_matop_complex_gen_matrix_cond_usd
Condition number for a function of a complex matrix (using user-supplied derivatives)
Related keywords: complex, nonsymmetric matrixinversionmatrix functionsmatrix operations
F07ABF   21  nagf_lapacklin_dgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
Related keywords: backward errorDGESVXerror bound, matrixfinanceforward errorLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
F07AGF   15  nagf_lapacklin_dgecon
Estimate condition number of real matrix, matrix already factorized by F07ADF
Related keywords: DGECONLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
F07APF   21  nagf_lapacklin_zgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
Related keywords: backward errorcomplex, nonsymmetric matrixerror bound, matrixfinanceforward errorLAPACKlinear equations L U decompositionZGESVX
F07AUF   15  nagf_lapacklin_zgecon
Estimate condition number of complex matrix, matrix already factorized by F07ARF
Related keywords: complex, nonsymmetric matrixLAPACKlinear equationsZGECON
F07BBF   21  nagf_lapacklin_dgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
Related keywords: backward errorDGBSVXerror bound, matrixforward errorLAPACKlinear equations L U decompositionmatrix, bandreal, band matrix
F07BGF   15  nagf_lapacklin_dgbcon
Estimate condition number of real band matrix, matrix already factorized by F07BDF
Related keywords: DGBCONLAPACKlinear equationsmatrix, bandreal, band matrix
F07BPF   21  nagf_lapacklin_zgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
Related keywords: backward errorcomplex, band matrixerror bound, matrixforward errorLAPACKlinear equations L U decompositionmatrix, bandZGBSVX
F07BUF   15  nagf_lapacklin_zgbcon
Estimate condition number of complex band matrix, matrix already factorized by F07BRF
Related keywords: complex, band matrixLAPACKlinear equationsmatrix, bandZGBEQU
F07CBF   21  nagf_lapacklin_dgtsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
Related keywords: backward errorDGTSVXerror bound, matrixforward errorLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
F07CGF   22  nagf_lapacklin_dgtcon
Estimates the reciprocal of the condition number of a real tridiagonal matrix using the L U factorization computed by F07CDF
Related keywords: DGTCONLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
F07CUF   22  nagf_lapacklin_zgtcon
Estimates the reciprocal of the condition number of a complex tridiagonal matrix using the L U factorization computed by F07CDF
Related keywords: complex, tridiagonal matrixLAPACKlinear equations L U decompositionmatrix, bandZGTCON
F07FBF   21  nagf_lapacklin_dposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations
Related keywords: backward errorCholesky decompositionDPOSVXerror bound, matrixfinanceforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FGF   15  nagf_lapacklin_dpocon
Estimate condition number of real symmetric positive definite matrix, matrix already factorized by F07FDF
Related keywords: DPOCONLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FPF   21  nagf_lapacklin_zposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite matrixerror bound, matrixfinanceforward errorLAPACKlinear equationsZPOSVX
F07FUF   15  nagf_lapacklin_zpocon
Estimate condition number of complex Hermitian positive definite matrix, matrix already factorized by F07FRF
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixLAPACKlinear equationsZPOCON
F07GBF   21  nagf_lapacklin_dppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations, packed storage
Related keywords: backward errorCholesky decompositionDPPSVXerror bound, matrixforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GGF   15  nagf_lapacklin_dppcon
Estimate condition number of real symmetric positive definite matrix, matrix already factorized by F07GDF, packed storage
Related keywords: Cholesky decompositionDPPCONLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GPF   21  nagf_lapacklin_zppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations, packed storage
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite matrixerror bound, matrixforward errorLAPACKlinear equationsZPPSVX
F07GUF   15  nagf_lapacklin_zppcon
Estimate condition number of complex Hermitian positive definite matrix, matrix already factorized by F07GRF, packed storage
Related keywords: complex, Hermitian, positive-definite matrixLAPACKlinear equationsZPPCON
F07HBF   21  nagf_lapacklin_dpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite banded system of linear equations
Related keywords: backward errorCholesky decompositionDPBSVXerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
F07HGF   15  nagf_lapacklin_dpbcon
Estimate condition number of real symmetric positive definite band matrix, matrix already factorized by F07HDF
Related keywords: DPBCONLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
F07HPF   21  nagf_lapacklin_zpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite banded system of linear equations
Related keywords: backward errorCholesky decompositioncomplex, band, Hermitian, positive-definite matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZPBSVX
F07HUF   15  nagf_lapacklin_zpbcon
Estimate condition number of complex Hermitian positive definite band matrix, matrix already factorized by F07HRF
Related keywords: complex, band, Hermitian, positive-definite matrixLAPACKlinear equationsmatrix, bandZPBCON
F07JBF   21  nagf_lapacklin_dptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations
Related keywords: backward errorCholesky decompositionDPTSVXerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
F07JGF   22  nagf_lapacklin_dptcon
Computes the reciprocal of the condition number of a real symmetric positive definite tridiagonal system using the LDL T factorization computed by F07JDF
Related keywords: DPTCONLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
F07JPF   21  nagf_lapacklin_zptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZPTSVX
F07JUF   22  nagf_lapacklin_zptcon
Computes the reciprocal of the condition number of a complex Hermitian positive definite tridiagonal system using the LDL H factorization computed by F07JRF
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixLAPACKlinear equationsmatrix, bandZPTCON
F07MGF   15  nagf_lapacklin_dsycon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MDF
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodDSYCONLAPACKlinear equationsreal, indefinite, symmetric matrix
F07MUF   15  nagf_lapacklin_zhecon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07MRF
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACKlinear equationsZHECON
F07NUF   15  nagf_lapacklin_zsycon
Estimate condition number of complex symmetric matrix, matrix already factorized by F07NRF
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methodLAPACKlinear equationsZSYCON
F07PBF   21  nagf_lapacklin_dspsvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage. Error bounds and a condition estimate are also computed
Related keywords: backward errordiagonal pivoting methodDSPSVXerror bound, matrixforward errorLAPACK LDL H decompositionlinear equationsreal, indefinite, symmetric matrix UDU H decomposition
F07PGF   15  nagf_lapacklin_dspcon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodDSPCONLAPACKlinear equationsreal, indefinite, symmetric matrix
F07PUF   15  nagf_lapacklin_zhpcon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07PRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACKlinear equationsZHPCON
F07QUF   15  nagf_lapacklin_zspcon
Estimate condition number of complex symmetric matrix, matrix already factorized by F07QRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methodLAPACKlinear equationsZSPCON
F07TGF   15  nagf_lapacklin_dtrcon
Estimate condition number of real triangular matrix
Related keywords: DTRCONLAPACKlinear equationsreal, triangular matrix
F07TUF   15  nagf_lapacklin_ztrcon
Estimate condition number of complex triangular matrix
Related keywords: complex, triangular matrixLAPACKlinear equationsZTRCON
F07UGF   15  nagf_lapacklin_dtpcon
Estimate condition number of real triangular matrix, packed storage
Related keywords: DTPCONLAPACKlinear equationsreal, triangular matrix
F07UUF   15  nagf_lapacklin_ztpcon
Estimate condition number of complex triangular matrix, packed storage
Related keywords: complex, triangular matrixLAPACKlinear equationsZTPCON
F07VGF   15  nagf_lapacklin_dtbcon
Estimate condition number of real band triangular matrix
Related keywords: DTBCONLAPACKlinear equationsmatrix, bandreal, band, triangular matrix
F07VUF   15  nagf_lapacklin_ztbcon
Estimate condition number of complex band triangular matrix
Related keywords: complex, band, triangular matrixLAPACKlinear equationsmatrix, bandZTBCON
F08FLF   22  nagf_lapackeig_ddisna
Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix
Related keywords: complex, Hermitian, indefinite matrixDDISNAeigenproblemeigenvectorsfinanceLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08NBF   21  nagf_lapackeig_dgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingDGEEVXeigenproblemeigenvalueseigenvectorsfinanceforward errorLAPACKLAPACKleast squaresorthogonal transformations QR algorithmreal, nonsymmetric matrix
F08NPF   21  nagf_lapackeig_zgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixDGEEVeigenproblemeigenvalueseigenvectorsfinanceforward errorLAPACKLAPACKleast squares
F08PBF   21  nagf_lapackeig_dgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: DGEESeigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur formSchur vectors
F08PPF   21  nagf_lapackeig_zgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also computes a reciprocal condition number for the average of the selected eigenvalues and for the right invariant subspace corresponding to these eigenvalues
Related keywords: eigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur formSchur vectorsZGEESX
F08QGF   16  nagf_lapackeig_dtrsen
Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
Related keywords: DTREXCeigenproblemLAPACKLAPACKleast squaresorthogonal transformationsSchur form
F08QLF   16  nagf_lapackeig_dtrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
Related keywords: DTRSNAeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, quasi-triangular matrix
F08QUF   16  nagf_lapackeig_ztrsen
Reorders a Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
Related keywords: eigenproblemLAPACKLAPACKleast squaresSchur formZTRSEN
F08QYF   16  nagf_lapackeig_ztrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
Related keywords: complex, triangular matrixDTRSNAeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares
F08WBF   21  nagf_lapackeig_dggevx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingDGGEVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsfinanceforward errorgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WPF   21  nagf_lapackeig_zggevx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsfinanceforward errorgeneralized eigenproblemLAPACKLAPACKleast squaresZGGEVX
F08XBF   21  nagf_lapackeig_dggesx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: DGGESXeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form, generalizedSchur vectors
F08XPF   21  nagf_lapackeig_zggesx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresSchur vectorsZGGES
F08YGF   22  nagf_lapackeig_dtgsen
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Related keywords: DTGSENeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresorthogonal transformationsreal, nonsymmetric matrix
F08YLF   22  nagf_lapackeig_dtgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
Related keywords: DTGSNAeigenproblemgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08YUF   22  nagf_lapackeig_ztgsen
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Related keywords: complex, nonsymmetric matrixeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresunitary transformationsZTGEXC
F08YYF   22  nagf_lapackeig_ztgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
Related keywords: complex, nonsymmetric matrixeigenproblemgeneralized Schur formLAPACKLAPACKleast squaresZTGSNA
F11MGF   21  nagf_sparse_direct_real_gen_cond
Estimate condition number of real matrix, matrix already factorized by F11MEF
Related keywords: big datadata analyticslarge scale linear systemsreal, sparse matrix
confidence interval G01SAF   24  nagf_stat_prob_normal_vector
Computes a vector of probabilities for the standard Normal distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticsGaussian distributionlower tail probabilityNormal distributionsignificanceSimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01SBF   24  nagf_stat_prob_students_t_vector
Computes a vector of probabilities for the Student's t -distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticslower tail probabilitysignificanceSimple Calculations on Statistical DataStudent's t -distributiontwo-tail probabilityupper tail probability
G04DBF   17  nagf_anova_confidence
Computes confidence intervals for differences between means computed by G04BBF or G04BCF
Related keywords: analysis of variancedesign of experimentsexperimental design
G07AAF   15  nagf_univar_ci_binomial
Computes confidence interval for the parameter of a binomial distribution
Related keywords: binomial distributionunivariate estimation
G07ABF   15  nagf_univar_ci_poisson
Computes confidence interval for the parameter of a Poisson distribution
Related keywords: Poisson distributionunivariate estimation
G07CAF   15  nagf_univar_ttest_2normal
Computes t -test statistic for a difference in means between two Normal populations, confidence interval
Related keywords: Gaussian distributionNormal distributiont-test statisticunivariate estimation
G07EAF   16  nagf_univar_robust_1var_ci
Robust confidence intervals, one-sample
Related keywords: robust estimationunivariate estimation
G07EBF   16  nagf_univar_robust_2var_ci
Robust confidence intervals, two-sample
Related keywords: robust estimationunivariate estimation
configuration data object X10AAF   26 
Create a configuration data object
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationcreate
X10ABF   26 
Remove a configuration data object
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationremove
confluent hypergeometric function S22BAF   24  nagf_specfun_1f1_real
Real confluent hypergeometric function F 1 1 a ; b ; x
Related keywords: 1 F 1 , hypergeometric functionapproximations of special functionshypergeometric function
S22BBF   24  nagf_specfun_1f1_real_scaled
Real confluent hypergeometric function F 1 1 a ; b ; x in scaled form
Related keywords: 1 F 1 , hypergeometric functionapproximations of special functionshypergeometric function
conjugate gradient method E04DGF   12  nagf_opt_uncon_conjgrd_comp_old
Unconstrained minimum, preconditioned conjugate gradient algorithm, using first derivatives (comprehensive)
Related keywords: financemaximizing a functionminimization, unconstrainedminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton
F11JQF   19  nagf_sparse_complex_herm_solve_ilu
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JNF (Black Box)
Related keywords: big datacomplex, Hermitian, sparse matrixdata analyticsiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodsparse linear equations
F11JSF   19  nagf_sparse_complex_herm_solve_jacssor
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big datacomplex, Hermitian, sparse matrixdata analyticsiterative methods, linear equationsJacobi methodLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodsparse linear equationsSSOR method, symmetric successive over-relaxation
constants and utilities X06 Chapter Introduction     OpenMP Utilities
Related keywords: openMPthread
X06AAF   25  nagf_omp_set_num_threads
Sets the number of threads for OpenMP parallel regions
Related keywords: openMPopenMPthreadthread
X06ABF   25  nagf_omp_get_num_threads
The number of OpenMP threads in the current team
Related keywords: openMPopenMPthreadthread
X06ACF   25  nagf_omp_get_max_threads
An upper bound on the number of threads in the next parallel region
Related keywords: openMPopenMPthreadthread
X06ADF   25  nagf_omp_get_thread_num
The OpenMP thread number of the calling thread
Related keywords: openMPopenMPthreadthread
X06AFF   25  nagf_omp_in_parallel
Tests for an active OpenMP parallel region
Related keywords: openMPopenMPthreadthread
X06AGF   25  nagf_omp_set_nested
Enables or disables nested OpenMP parallelism
Related keywords: openMPopenMPthreadthread
X06AHF   25  nagf_omp_get_nested
Tests the status of nested OpenMP parallelism
Related keywords: openMPopenMPthreadthread
X06XAF   26  nagf_omp_using_threaded_impl
Tests whether a threaded NAG Library is being used
Related keywords: openMPopenMPthreadthread
contingency table G01AFF   nagf_stat_contingency_table
Two-way contingency table analysis, with χ 2 /Fisher's exact test
Related keywords: chi-squared distributionfinanceFisher's exact testSimple Calculations on Statistical Datatwo-way contingency tableYates' correction
G11AAF   16  nagf_contab_chisq
χ 2 statistics for two-way contingency table
Related keywords: chi squared statisticscontingency table analysis
contingency table analysis G11 Chapter Introduction     Contingency Table Analysis
convection-diffusion, PDE D03PFF   17  nagf_pde_1d_parab_convdiff
General system of convection-diffusion PDEs with source terms in conservative form, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable
Related keywords: method of linespartial differential equationsPDE, partial differential equations
D03PLF   17  nagf_pde_1d_parab_convdiff_dae
General system of convection-diffusion PDEs with source terms in conservative form, coupled DAEs, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable
Related keywords: DAE, differential algebraic equationspartial differential equationsPDE, partial differential equations
D03PSF   17  nagf_pde_1d_parab_convdiff_remesh
General system of convection-diffusion PDEs, coupled DAEs, method of lines, upwind scheme, remeshing, one space variable
Related keywords: adaptive grid, PDEDAE, differential algebraic equationshyperbolic equationmethod of linesone-dimensionalparabolic partial differential equationPDE, partial differential equations
convert matrix storage formats F01ZAF   14  nagf_matop_real_tri_pack
Convert real matrix between packed triangular and square storage formats
Related keywords: inversionmatrix operationsreal, nonsymmetric matrix
F01ZBF   14  nagf_matop_complex_tri_pack
Convert complex matrix between packed triangular and square storage formats
Related keywords: complex, nonsymmetric matrixinversionmatrix operations
F01ZCF   14  nagf_matop_real_band_pack
Convert real matrix between packed banded and rectangular storage formats
Related keywords: inversionmatrix operationsreal, nonsymmetric matrix
F01ZDF   14  nagf_matop_complex_band_pack
Convert complex matrix between packed banded and rectangular storage formats
Related keywords: complex, nonsymmetric matrixinversionmatrix operations
convex optimization E04NCF   12  nagf_opt_lsq_lincon_solve_old
Linear programming (LP) convex quadratic programming (QP) or linearly-constrained linear least squares problem, dense
Related keywords: active-setdata fittingfinanceleast squaresmaximizing a functionminimizing a functionnonlinear least squaresoptimizationQP, quadratic programming
E04NDF   12  nagf_opt_lsq_lincon_option_file_old
Supply values for E04NCF from external file
Related keywords: least squaresmaximizing a functionminimizing a functionoptimizationoptions, computationalQP, quadratic programming
convolution C06FKF   11  nagf_sum_convcorr_real
Circular convolution or correlation of two real vectors, no restrictions on n
Related keywords: correlationFast Fourier TransformFFTsummation of series
convolution, vectors C06PKF   19  nagf_sum_convcorr_complex
Circular convolution or correlation of two complex vectors
Related keywords: summation of series
copula G05RCF   22  nagf_rand_copula_students_t
Generates a matrix of pseudorandom numbers from a Student's t -copula
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbersstudent's t-copula
G05RDF   22  nagf_rand_copula_normal
Generates a matrix of pseudorandom numbers from a Gaussian copula
Related keywords: big datadata analyticsfinanceGaussian copularandom number generatorsrandom numbers
G05REF   23  nagf_rand_copula_clayton_bivar
Generates a matrix of pseudorandom numbers from a bivariate Clayton/Cook–Johnson copula
Related keywords: big dataClayton/Cook–Johnson copuladata analyticsrandom number generatorsrandom numbers
G05RFF   23  nagf_rand_copula_frank_bivar
Generates a matrix of pseudorandom numbers from a bivariate Frank copula
Related keywords: big datadata analyticsFrank copularandom number generatorsrandom numbers
G05RGF   23  nagf_rand_copula_plackett_bivar
Generates a matrix of pseudorandom numbers from a bivariate Plackett copula
Related keywords: big datadata analyticsPlackett copularandom number generatorsrandom numbers
G05RHF   23  nagf_rand_copula_clayton
Generates a matrix of pseudorandom numbers from a multivariate Clayton/Cook–Johnson copula
Related keywords: big dataClayton/Cook–Johnson copuladata analyticsrandom number generatorsrandom numbers
G05RJF   23  nagf_rand_copula_frank
Generates a matrix of pseudorandom numbers from a multivariate Frank copula
Related keywords: big datadata analyticsFrank copularandom number generatorsrandom numbers
G05RKF   23  nagf_rand_copula_gumbel
Generates a matrix of pseudorandom numbers from a Gumbel–Hougaard copula
Related keywords: big datadata analyticsGumbel–Hougard copularandom number generatorsrandom numbers
copy, vectors and matrices F06QFF   13  nagf_blas_dmcopy
Matrix copy, real rectangular or trapezoidal matrix
Related keywords: BLASelementary arithmeticfinancelinear algebra support routinesreal, m by n matrixreal, trapezoidal matrix
correlation C06FKF   11  nagf_sum_convcorr_real
Circular convolution or correlation of two real vectors, no restrictions on n
Related keywords: convolutionFast Fourier TransformFFTsummation of series
correlation analysis G02 Chapter Introduction     Correlation and Regression Analysis
Related keywords: big datadata analyticsnonlinear regressionpolynomial regressionregression analysis
correlation coefficients G02BAF   nagf_correg_coeffs_pearson
Pearson product-moment correlation coefficients, all variables, no missing values
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionPearson product moment correlationpolynomial regressionregression analysis
G02BBF   nagf_correg_coeffs_pearson_miss_case
Pearson product-moment correlation coefficients, all variables, casewise treatment of missing values
Related keywords: big datacorrelation analysisdata analyticsfinancemissing valuesnonlinear regressionPearson product moment correlationpolynomial regressionregression analysis
G02BCF   nagf_correg_coeffs_pearson_miss_pair
Pearson product-moment correlation coefficients, all variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysisdata analyticsfinancemissing valuesnonlinear regressionPearson product moment correlationpolynomial regressionregression analysis
G02BNF   nagf_correg_coeffs_kspearman_overwrite
Kendall/Spearman non-parametric rank correlation coefficients, no missing values, overwriting input data
Related keywords: big datacorrelation analysisdata analyticsfinanceKendall's tau correlation coefficientnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02BPF   nagf_correg_coeffs_kspearman_miss_case_overwrite
Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data
Related keywords: big datacorrelation analysisdata analyticsfinanceKendall's tau correlation coefficientmissing valuesnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02BQF   nagf_correg_coeffs_kspearman
Kendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data
Related keywords: big datacorrelation analysisdata analyticsfinanceKendall's tau correlation coefficientnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02BRF   nagf_correg_coeffs_kspearman_miss_case
Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data
Related keywords: big datacorrelation analysisdata analyticsfinanceKendall's tau correlation coefficientmissing valuesnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02BSF   nagf_correg_coeffs_kspearman_miss_pair
Kendall/Spearman non-parametric rank correlation coefficients, pairwise treatment of missing values
Related keywords: big datacorrelation analysisdata analyticsfinanceKendall's tau correlation coefficientmissing valuesnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
correlation-like coefficients G02BDF   nagf_correg_coeffs_zero
Correlation-like coefficients (about zero), all variables, no missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BEF   nagf_correg_coeffs_zero_miss_case
Correlation-like coefficients (about zero), all variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BFF   nagf_correg_coeffs_zero_miss_pair
Correlation-like coefficients (about zero), all variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BKF   nagf_correg_coeffs_zero_subset
Correlation-like coefficients (about zero), subset of variables, no missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BLF   nagf_correg_coeffs_zero_subset_miss_case
Correlation-like coefficients (about zero), subset of variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BMF   nagf_correg_coeffs_zero_subset_miss_pair
Correlation-like coefficients (about zero), subset of variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
correlation matrix G02AAF   22  nagf_correg_corrmat_nearest
Computes the nearest correlation matrix to a real square matrix, using the method of Qi and Sun
Related keywords: big datacorrelation analysisdata analyticsfinancenearest correlation matrixnonlinear regressionpolynomial regressionQi and Sun algorithmregression analysis
G02ABF   23  nagf_correg_corrmat_nearest_bounded
Computes the nearest correlation matrix to a real square matrix, augmenting G02AAF to incorporate weights and bounds
Related keywords: big datacorrelation analysisdata analyticsfinancenearest correlation matrixnonlinear regressionpolynomial regressionQi and Sun algorithmregression analysis
G02AEF   23  nagf_correg_corrmat_nearest_kfactor
Computes the nearest correlation matrix with k -factor structure to a real square matrix
Related keywords: big datacorrelation analysisdata analyticsfinance k -factor structurenearest correlation matrixnonlinear regressionpolynomial regressionQi and Sun algorithmregression analysis
G02AJF   24  nagf_correg_corrmat_h_weight
Computes the nearest correlation matrix to a real square matrix, using element-wise weighting
Related keywords: big datacorrelation analysisdata analyticsnearest correlation matrixnonlinear regressionpolynomial regressionQi and Sun algorithmregression analysis
G02ANF   25  nagf_correg_corrmat_shrinking
Computes a correlation matrix from an approximate matrix with fixed submatrix
Related keywords: big datacorrelation analysisdata analyticsnearest correlation matrixnonlinear regressionpolynomial regressionregression analysisshrinking method
G02APF   26  nagf_correg_corrmat_target
Computes a correlation matrix from an approximate one using a specified target matrix
Related keywords: big datacorrelation analysisdata analyticselementwise weightsnearest correlation matrixnonlinear regressionpolynomial regressionregression analysisshrinkageshrinking method
G02HKF   14  nagf_correg_robustm_corr_huber
Calculates a robust estimation of a covariance matrix, Huber's weight function
Related keywords: big datacorrelation analysisdata analyticsfinanceHuber's weight functionnonlinear regressionpolynomial regressionregression analysis
G02HLF   14  nagf_correg_robustm_corr_user_deriv
Calculates a robust estimation of a covariance matrix, user-supplied weight function plus derivatives
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysisrobust estimation
G02HMF   14  nagf_correg_robustm_corr_user
Calculates a robust estimation of a covariance matrix, user-supplied weight function
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysisrobust estimation
G13DDF   22  nagf_tsa_multi_varma_estimate
Multivariate time series, estimation of VARMA model
Related keywords: big datadata analyticsfinancemaximum likelihoodmultivariate time seriesstandard errorstime seriestime series analysisVARMA, vector autoregressive moving average model
cosh, matrix F01EKF   24  nagf_matop_real_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm)
Related keywords: cosine, matrixexponential, matrixfunctions, matrixinversionmatrix operationsreal, nonsymmetric matrixsine, matrixsinh, matrix
F01FKF   24  nagf_matop_complex_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm)
Related keywords: complex, nonsymmetric matrixcosine, matrixexponential, matrixfunctions, matrixinversionmatrix operationssine, matrixsinh, matrix
F01JAF   24  nagf_matop_real_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix
Related keywords: condition number, matrixcosine, matrixexponential, matrixinversionlogarithm, matrixmatrix operationsreal, nonsymmetric matrixsine, matrixsinh, matrix
F01KAF   24  nagf_matop_complex_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix
Related keywords: complex, nonsymmetric matrixcondition number, matrixcosine, matrixexponential, matrixinversionlogarithm, matrixmatrix operationssine, matrixsinh, matrix
cosine, matrix F01EKF   24  nagf_matop_real_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm)
Related keywords: cosh, matrixexponential, matrixfunctions, matrixinversionmatrix operationsreal, nonsymmetric matrixsine, matrixsinh, matrix
F01FKF   24  nagf_matop_complex_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm)
Related keywords: complex, nonsymmetric matrixcosh, matrixexponential, matrixfunctions, matrixinversionmatrix operationssine, matrixsinh, matrix
F01JAF   24  nagf_matop_real_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix
Related keywords: condition number, matrixcosh, matrixexponential, matrixinversionlogarithm, matrixmatrix operationsreal, nonsymmetric matrixsine, matrixsinh, matrix
F01KAF   24  nagf_matop_complex_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix
Related keywords: complex, nonsymmetric matrixcondition number, matrixcosh, matrixexponential, matrixinversionlogarithm, matrixmatrix operationssine, matrixsinh, matrix
cosine integral, Ci x S13ACF   nagf_specfun_integral_cos
Cosine integral Ci x
Related keywords: approximations of special functionsfinance
cosine transform C06RBF   19  nagf_sum_fft_real_cosine_simple
Discrete cosine transform (easy-to-use)
Related keywords: summation of series
C06RDF   19  nagf_sum_fft_real_qtrcosine_simple
Discrete quarter-wave cosine transform (easy-to-use)
Related keywords: summation of series
C06RFF   25  nagf_sum_fft_cosine
Multiple discrete cosine transforms, simple
Related keywords: Discrete Fourier TransformsFast Fourier TransformFFTFourier Transforms, realsummation of series
C06RHF   25  nagf_sum_fft_qtrcosine
Multiple discrete quarter-wave cosine transforms, simple
Related keywords: Discrete Fourier TransformsFast Fourier TransformFFTFourier Transforms, realquarter-wavesummation of series
covariance matrix E04YCF   11  nagf_opt_lsq_uncon_covariance
Covariance matrix for nonlinear least squares problem (unconstrained)
Related keywords: maximizing a functionminimizing a functionnonlinear least squaresoptimizationservice routine
F04YAF   11  nagf_linsys_real_gen_lsq_covmat
Covariance matrix for linear least squares problems, m real equations in n unknowns
Related keywords: big datadata analyticsleast squaresreal, m by n matrixsimultaneous linear equations
G01DCF   12  nagf_stat_normal_scores_var
Normal scores, approximate variance-covariance matrix
Related keywords: financeNormal scoresSimple Calculations on Statistical Datavariance-covariance matrix
Cox proportional hazard model G12BAF   17  nagf_surviv_coxmodel
Fits Cox's proportional hazard model
Related keywords: survival analysis
G12ZAF   19  nagf_surviv_coxmodel_risksets
Creates the risk sets associated with the Cox proportional hazards model for fixed covariates
Related keywords: risk setssurvival analysis
CPU time X05BAF   14  nagf_time_cpu
Return the CPU time
Related keywords: data and time utilitiestime, cpu
C P values G02ECF   14  nagf_correg_linregm_rssq_stat
Calculates R 2 and C P values from residual sums of squares
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionpolynomial regression R 2 valuesregression analysissum of squares
create X10AAF   26 
Create a configuration data object
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationconfiguration data object
X10BAF   26 
Create a callback data object
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationcallback data object
cross amplitude spectrum G13CEF   10  nagf_tsa_multi_spectrum_bivar
Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra
Related keywords: big databivariate spectracoherency, squared, time seriesdata analyticsfinancemultivariate time seriessquared coherencytime seriestime series analysis
cross-classified G08ALF   15  nagf_nonpar_test_cochranq
Performs the Cochran Q test on cross-classified binary data
Related keywords: Cochran Q testnonparametric statistics
cross-correlation G13BCF   10  nagf_tsa_multi_xcorr
Multivariate time series, cross-correlations
Related keywords: big datadata analyticsfinancemultivariate time seriestime seriestime series analysis
G13DMF   15  nagf_tsa_multi_corrmat_cross
Multivariate time series, sample cross-correlation or cross-covariance matrices
Related keywords: big datacross-covariancedata analyticsmultivariate time seriestime seriestime series analysis
cross-covariance G13DMF   15  nagf_tsa_multi_corrmat_cross
Multivariate time series, sample cross-correlation or cross-covariance matrices
Related keywords: big datacross-correlationdata analyticsmultivariate time seriestime seriestime series analysis
cross-product G02MBF   25  nagf_correg_lars_xtx
Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) and forward stagewise regression using the cross-products matrix
Related keywords: big datacorrelation analysisdata analyticsforward stagewiseLARSLASSOleast angle regressionmodel selectionnonlinear regressionpolynomial regressionregression analysis
cross-products G01ABF   nagf_stat_summary_2var
Means, corrected sums of squares and cross-products, etc., two variables, from raw data
Related keywords: maximum valuemeanminimum valueproduct-moment correlation coefficientsSimple Calculations on Statistical Datasum of squares
G02BDF   nagf_correg_coeffs_zero
Correlation-like coefficients (about zero), all variables, no missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BEF   nagf_correg_coeffs_zero_miss_case
Correlation-like coefficients (about zero), all variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BFF   nagf_correg_coeffs_zero_miss_pair
Correlation-like coefficients (about zero), all variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BGF   nagf_correg_coeffs_pearson_subset
Pearson product-moment correlation coefficients, subset of variables, no missing values
Related keywords: big datacorrelation analysisdata analyticsfinancemeannonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviationsum of squares
G02BHF   nagf_correg_coeffs_pearson_subset_miss_case
Pearson product-moment correlation coefficients, subset of variables, casewise treatment of missing values
Related keywords: big datacorrelation analysisdata analyticsfinancemeanmissing valuesnonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviationsum of squares
G02BJF   nagf_correg_coeffs_pearson_subset_miss_pair
Pearson product-moment correlation coefficients, subset of variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysisdata analyticsfinancemeanmissing valuesnonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviationsum of squares
G02BKF   nagf_correg_coeffs_zero_subset
Correlation-like coefficients (about zero), subset of variables, no missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BLF   nagf_correg_coeffs_zero_subset_miss_case
Correlation-like coefficients (about zero), subset of variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BMF   nagf_correg_coeffs_zero_subset_miss_pair
Correlation-like coefficients (about zero), subset of variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BTF   14  nagf_correg_ssqmat_update
Update a weighted sum of squares matrix with a new observation
Related keywords: big datacorrelation analysisdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysissum of squares
G02BUF   14  nagf_correg_ssqmat
Computes a weighted sum of squares matrix
Related keywords: big datacorrelation analysisdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysissum of squaresWest's WV2 algorithm
G02BZF   24  nagf_correg_ssqmat_combine
Combines two sums of squares matrices, for use after G02BUF
Related keywords: big datacorrelation analysisdata analyticsdata streammeannonlinear regressionpolynomial regressionregression analysisstreamingsum of squares
cross-spectrum G13CCF   10  nagf_tsa_multi_spectrum_lag
Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: Bartlett lag windowbig datadata analyticsfinancemultivariate time seriesParzen lag windowrectangular lag windowsmoothingtime seriestime series analysisTukey lag window
G13CDF   10  nagf_tsa_multi_spectrum_daniell
Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window
Related keywords: big dataDaniell windowdata analyticsfinancemultivariate time seriessmoothingspectral smoothingtime seriestime series analysistrapezium frequency window
G13CFF   10  nagf_tsa_multi_gain_bivar
Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra
Related keywords: big databivariate time seriesdata analyticsfinancegain, time seriesmultivariate time seriesphase, time seriestime seriestime series analysis
cross-validation G05PVF   25  nagf_rand_kfold_xyw
Permutes a matrix, vector, vector triplet into a form suitable for K -fold cross validation
Related keywords: big dataCVdata analyticsjacknifek-foldleave-one-outLOOpermuterandom number generators
G05PWF   25  nagf_rand_subsamp_xyw
Permutes a matrix, vector, vector triplet into a form suitable for random sub-sampling validation
Related keywords: big datadata analyticspermuterandom number generatorsresamplesub-sample
Crump's method C06LAF   12  nagf_sum_invlaplace_crump
Inverse Laplace transform, Crump's method
Related keywords: inverse Laplace transformLaplace transformsummation of series
cubature D01BCF   nagf_quad_1d_gauss_wgen
Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule
Related keywords: abscissaefinanceintegration, non-adaptivequadratureweights and abscissae
D01TDF   26  nagf_quad_1d_gauss_wrec
Calculation of weights and abscissae for Gaussian quadrature rules, method of Golub and Welsch
Related keywords: abscissaeGaussianGolubGolub and Welschintegrationnon-adaptivequadratureweights and abscissaeWelsch
D01TEF   26  nagf_quad_1d_gauss_recm
Generates recursion coefficients needed by D01TDF to calculate a Gaussian quadrature rule
Related keywords: abscissaeGaussianGolubGolub and Welschintegrationnon-adaptivequadraturerecursion coefficientsWelsch
cubic polynomial C02AKF   20  nagf_zeros_cubic_real
All zeros of real cubic equation
Related keywords: root-findingzeros of polynomials
C02AMF   20  nagf_zeros_cubic_complex
All zeros of complex cubic equation
Related keywords: root-findingzeros of polynomials
cubic spline E01BAF   nagf_interp_1d_spline
Interpolating functions, cubic spline interpolant, one variable
Related keywords: financeinterpolationone-dimensional
cubic spline interpolation E01BEF   13  nagf_interp_1d_monotonic
Interpolating functions, monotonicity-preserving, piecewise cubic Hermite, one variable
Related keywords: financeHermite interpolationinterpolationmonotonicity-preserving spline
cubic splines E02BAF   nagf_fit_1dspline_knots
Least squares curve cubic spline fit (including interpolation)
Related keywords: B-splinescurve and surface fittingknotsleast squares
E02BBF   nagf_fit_1dspline_eval
Evaluation of fitted cubic spline, function only
Related keywords: B-splinescurve and surface fittingfinance
E02BCF   nagf_fit_1dspline_deriv
Evaluation of fitted cubic spline, function and derivatives
Related keywords: b-splines, derivativecurve and surface fittingfinance
E02BDF   nagf_fit_1dspline_integ
Evaluation of fitted cubic spline, definite integral
Related keywords: b-splines, integralcurve and surface fitting
E02BEF   13  nagf_fit_1dspline_auto
Least squares cubic spline curve fit, automatic knot placement
Related keywords: B-splinescurve and surface fittingleast squaressmoothing
E02BFF   24  nagf_fit_1dspline_deriv_vector
Evaluation of fitted cubic spline, function and optionally derivatives at a vector of points
Related keywords: b-splines, derivativecurve and surface fitting
cuboid D03ECF   nagf_pde_3d_ellip_fd
Elliptic PDE, solution of finite difference equations by SIP for seven-point three-dimensional molecule, iterate to convergence
Related keywords: elliptic partial differential equationsLaplace's equationPDE, partial differential equationsStone's strongly implicit procedure
cumulant G01NAF   16  nagf_stat_moments_quad_form
Cumulants and moments of quadratic forms in Normal variables
Related keywords: financeGaussian distributionmoments quadratic formmultivariate Normal distributionNormal distributionSimple Calculations on Statistical Data
cumulative Normal distribution S15ABF   nagf_specfun_cdf_normal
Cumulative Normal distribution function P x
Related keywords: approximations of special functionsfinanceGaussian distributionNormal distribution
S15ACF   nagf_specfun_compcdf_normal
Complement of cumulative Normal distribution function Q x
Related keywords: approximations of special functionscomplement of cumulative Normal distributionerror functionfinance
curve and surface fitting E02 Chapter Introduction     Curve and Surface Fitting
CV G05PVF   25  nagf_rand_kfold_xyw
Permutes a matrix, vector, vector triplet into a form suitable for K -fold cross validation
Related keywords: big datacross-validationdata analyticsjacknifek-foldleave-one-outLOOpermuterandom number generators
C x , Fresnel Integral S20ADF   nagf_specfun_fresnel_c
Fresnel integral C x
Related keywords: approximations of special functionsfinanceFresnel integral
S20ARF   24  nagf_specfun_fresnel_c_vector
Fresnel integral vectorized C x
Related keywords: approximations of special functionsFresnel integral
cycles M01ZCF   12  nagf_sort_permute_decompose
Decompose a permutation into cycles
Related keywords: big datadata analyticspermutationsearchingsorting
DAE, differential algebraic equations D02MCF   22  nagf_ode_dae_dassl_cont
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method continuation for D02NEF
Related keywords: DASSL, ordinary differential equationsimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NEF   22  nagf_ode_dae_dassl_gen
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator
Related keywords: DASSL, ordinary differential equationsimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equations
D03PHF   15  nagf_pde_1d_parab_dae_fd_old
General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable
Related keywords: finite difference discretizationmethod of linesparabolic partial differential equationpartial differential equationsPDE, partial differential equations
D03PJF   15  nagf_pde_1d_parab_dae_coll_old
General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C 0 collocation, one space variable
Related keywords: method of linesparabolic partial differential equationpartial differential equationsPDE, partial differential equations
D03PKF   16  nagf_pde_1d_parab_dae_keller
General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretization, one space variable
Related keywords: Keller box discretizationmethod of linespartial differential equationsPDE, partial differential equations
D03PLF   17  nagf_pde_1d_parab_convdiff_dae
General system of convection-diffusion PDEs with source terms in conservative form, coupled DAEs, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable
Related keywords: convection-diffusion, PDEpartial differential equationsPDE, partial differential equations
D03PPF   16  nagf_pde_1d_parab_remesh_fd_old
General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable
Related keywords: method of linesone-dimensionalparabolic partial differential equationPDE, partial differential equations
D03PRF   16  nagf_pde_1d_parab_remesh_keller
General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretization, remeshing, one space variable
Related keywords: adaptive grid, PDEKeller box discretizationmethod of linesPDE, partial differential equations
D03PSF   17  nagf_pde_1d_parab_convdiff_remesh
General system of convection-diffusion PDEs, coupled DAEs, method of lines, upwind scheme, remeshing, one space variable
Related keywords: adaptive grid, PDEconvection-diffusion, PDEhyperbolic equationmethod of linesone-dimensionalparabolic partial differential equationPDE, partial differential equations
Daniell window G13CBF   10  nagf_tsa_uni_spectrum_daniell
Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window
Related keywords: big datadata analyticsfinancesmoothingspectral smoothingtime seriestime series analysistrapezium frequency windowunivariate time series
G13CDF   10  nagf_tsa_multi_spectrum_daniell
Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window
Related keywords: big datacross-spectrumdata analyticsfinancemultivariate time seriessmoothingspectral smoothingtime seriestime series analysistrapezium frequency window
DASSL, ordinary differential equations D02MCF   22  nagf_ode_dae_dassl_cont
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method continuation for D02NEF
Related keywords: DAE, differential algebraic equationsimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02MVF   14  nagf_ode_ivp_stiff_dassl
Ordinary differential equations, initial value problem, DASSL method, setup for d02m–n routines
Related keywords: implicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02MWF   22  nagf_ode_dae_dassl_setup
Implicit ordinary differential equations/DAEs, initial value problem, setup for D02NEF
Related keywords: initial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NEF   22  nagf_ode_dae_dassl_gen
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator
Related keywords: DAE, differential algebraic equationsimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equations
dasum F06EKF   12  nagf_blas_dasum
Sum absolute values of real vector elements
Related keywords: BLASblas, real matriceselementary arithmeticlinear algebra support routines
data G22YBF   26  nagf_blgm_lm_describe_data
Describe a dataset
data analytics F02 Chapter Introduction     Eigenvalues and Eigenvectors
Related keywords: big dataeigenvalueseigenvectors
F04 Chapter Introduction     Simultaneous Linear Equations
Related keywords: big datasimultaneous linear equations
F11 Chapter Introduction     Large Scale Linear Systems
Related keywords: big datalarge scale linear systems
F12 Chapter Introduction     Large Scale Eigenproblems
Related keywords: big datalarge scale eigenproblems
G01ANF   23  nagf_stat_quantiles_stream_fixed
Calculates approximate quantiles from a data stream of known size
Related keywords: big datadata streamquantilesSimple Calculations on Statistical Datastreaming
G01APF   23  nagf_stat_quantiles_stream_arbitrary
Calculates approximate quantiles from a data stream of unknown size
Related keywords: big datadata streamquantilesSimple Calculations on Statistical Datastreaming
G01ATF   24  nagf_stat_summary_onevar
Computes univariate summary information: mean, variance, skewness, kurtosis
Related keywords: big datadata streamkurtosismaximum valuemeanminimum valueSimple Calculations on Statistical Dataskewnessstandard deviationstreaming
G01AUF   24  nagf_stat_summary_onevar_combine
Combines multiple sets of summary information, for use after G01ATF
Related keywords: big datadata streamSimple Calculations on Statistical Datastreamingsummary information
G01SAF   24  nagf_stat_prob_normal_vector
Computes a vector of probabilities for the standard Normal distribution
Related keywords: big dataCDF, cumulative distribution functionconfidence intervalGaussian distributionlower tail probabilityNormal distributionsignificanceSimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01SBF   24  nagf_stat_prob_students_t_vector
Computes a vector of probabilities for the Student's t -distribution
Related keywords: big dataCDF, cumulative distribution functionconfidence intervallower tail probabilitysignificanceSimple Calculations on Statistical DataStudent's t -distributiontwo-tail probabilityupper tail probability
G01SCF   24  nagf_stat_prob_chisq_vector
Computes a vector of probabilities for χ 2 distribution
Related keywords: big dataCDF, cumulative distribution functionchi-squared distributionlower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01SDF   24  nagf_stat_prob_f_vector
Computes a vector of probabilities for F -distribution
Related keywords: big dataCDF, cumulative distribution function F -distributionlower tail probabilitySimple Calculations on Statistical Dataupper tail probabilityvariance-ratio distribution
G01SEF   24  nagf_stat_prob_beta_vector
Computes a vector of probabilities for the beta distribution
Related keywords: beta distributionbig dataCDF, cumulative distribution functionlower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01SFF   24  nagf_stat_prob_gamma_vector
Computes a vector of probabilities for the gamma distribution
Related keywords: big dataCDF, cumulative distribution functiongamma distributionlower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01SJF   24  nagf_stat_prob_binomial_vector
Computes a vector of probabilities for the binomial distribution
Related keywords: big databinomial distributionCDF, cumulative distribution functionlower tail probabilitypoint probabilitySimple Calculations on Statistical Dataupper tail probability
G01SKF   24  nagf_stat_prob_poisson_vector
Computes a vector of probabilities for the Poisson distribution
Related keywords: big dataCDF, cumulative distribution functionlower tail probabilitypoint probabilityPoisson distributionSimple Calculations on Statistical Dataupper tail probability
G01SLF   24  nagf_stat_prob_hypergeom_vector
Computes a vector of probabilities for the hypergeometric distribution
Related keywords: big dataCDF, cumulative distribution functionhypergeometric distributionlower tail probabilitypoint probabilitySimple Calculations on Statistical Dataupper tail probability
G01TAF   24  nagf_stat_inv_cdf_normal_vector
Computes a vector of deviates for the standard Normal distribution
Related keywords: big datadeviatesGaussian distributioninverse CDFinverse cumulative distribution functionNormal distributionSimple Calculations on Statistical Data
G01TBF   24  nagf_stat_inv_cdf_students_t_vector
Computes a vector of deviates for Student's t -distribution
Related keywords: big datadeviatesinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical DataStudent's t -distribution
G01TCF   24  nagf_stat_inv_cdf_chisq_vector
Computes a vector of deviates for χ 2 distribution
Related keywords: big datachi-squared distributiondeviatesinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01TDF   24  nagf_stat_inv_cdf_f_vector
Computes a vector of deviates for F -distribution
Related keywords: big datadeviates F -distributioninverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Datavariance-ratio distribution
G01TEF   24  nagf_stat_inv_cdf_beta_vector
Computes a vector of deviates for the beta distribution
Related keywords: beta distributionbig datadeviatesinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01TFF   24  nagf_stat_inv_cdf_gamma_vector
Computes a vector of deviates for the gamma distribution
Related keywords: big datadeviatesgamma distributioninverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01WAF   24  nagf_stat_moving_average
Computes the mean and standard deviation using a rolling window
Related keywords: big datadata streammeanmoving averageSimple Calculations on Statistical Datastandard deviationstreaming
G02 Chapter Introduction     Correlation and Regression Analysis
Related keywords: big datacorrelation analysisnonlinear regressionpolynomial regressionregression analysis
G03AAF   14  nagf_mv_prin_comp
Performs principal component analysis
Related keywords: big datafinancemultivariate methodsprincipal component analysis
G03EAF   16  nagf_mv_distance_mat
Computes distance matrix
Related keywords: big datadistance matrixmultivariate methods
G03ECF   16  nagf_mv_cluster_hier
Hierarchical cluster analysis
Related keywords: big datacluster analysishierarchical cluster analysismultivariate methods
G03EFF   16  nagf_mv_cluster_kmeans
K -means cluster analysis
Related keywords: big datacluster analysis K -means cluster analysismultivariate methods
G03EHF   16  nagf_mv_cluster_hier_dendrogram
Constructs dendrogram (for use after G03ECF)
Related keywords: big datadendrogramhierarchical cluster analysismultivariate methods
G03EJF   16  nagf_mv_cluster_hier_indicator
Computes cluster indicator variable (for use after G03ECF)
Related keywords: allocatebig datacluster analysishierarchical cluster analysismultivariate methods
G05 Chapter Introduction     Random Number Generators
Related keywords: big datarandom number generators
G13 Chapter Introduction     Time Series Analysis
Related keywords: big datatime series analysis
M01 Chapter Introduction     Sorting and Searching
Related keywords: big datasearchingsorting
data and time utilities X05 Chapter Introduction     Date and Time Utilities
data fitting E04FCF   nagf_opt_lsq_uncon_mod_func_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (comprehensive)
Related keywords: derivative-free minimizationfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04FFF   26  nagf_opt_handle_solve_dfls
Derivative-free (DFO) solver for a nonlinear least squares objective function with bounded variables
Related keywords: calibrationderivative-free optimizationDFODFOmaximizing a functionminimizing a functionnonlinear least squaresnonlinear least squaresoptimizationoptimizationsum of squares
E04FYF   18  nagf_opt_lsq_uncon_mod_func_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (easy-to-use)
Related keywords: derivative-free minimizationfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04GBF   nagf_opt_lsq_uncon_quasi_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (comprehensive)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationquasi-Newton algorithmsum-of-squares minimization
E04GDF   nagf_opt_lsq_uncon_mod_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (comprehensive)
Related keywords: financeGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04GYF   18  nagf_opt_lsq_uncon_quasi_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationquasi-Newton algorithmsum-of-squares minimization
E04GZF   18  nagf_opt_lsq_uncon_mod_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (easy-to-use)
Related keywords: financeGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04HEF   nagf_opt_lsq_uncon_mod_deriv2_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive)
Related keywords: financeGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04HYF   18  nagf_opt_lsq_uncon_mod_deriv2_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use)
Related keywords: financeGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04NCF   12  nagf_opt_lsq_lincon_solve_old
Linear programming (LP) convex quadratic programming (QP) or linearly-constrained linear least squares problem, dense
Related keywords: active-setconvex optimizationfinanceleast squaresmaximizing a functionminimizing a functionnonlinear least squaresoptimizationQP, quadratic programming
E04PCF   24  nagf_opt_bnd_lin_lsq
Computes the least squares solution to a set of linear equations subject to fixed upper and lower bounds on the variables. An option is provided to return a minimal length solution if a solution is not unique
Related keywords: BVLS, bounded variable least squaresfinancemaximizing a functionminimizing a functionNNLS, non-negative least squaresnonlinear least squaresnon-negative least squaresoptimization
E04RMF   26  nagf_opt_handle_set_nlnls
Define a nonlinear least squares objective function to a problem initialized by E04RAF
Related keywords: calibrationderivative-free optimizationDFOleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinear least squaresoptimizationoptimizationoptimizationsum of squares
E04USF   14  nagf_opt_lsq_gencon_deriv_old
Minimum of a sum of squares, nonlinear constraints, dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: financemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear least squaresnonlinear programmingoptimizationquasi-Newton approximationsequential QP methodsum of squares
data-on-lines polynomial approximation E02CAF   nagf_fit_2dcheb_lines
Least squares surface fit by polynomials, data on lines parallel to one independent coordinate axis
Related keywords: bivariate polynomial approximationChebyshev polynomial approximationcurve and surface fittingleast squarespolynomial approximationtwo-dimensional polynomial approximation
data stream G01ANF   23  nagf_stat_quantiles_stream_fixed
Calculates approximate quantiles from a data stream of known size
Related keywords: big datadata analyticsquantilesSimple Calculations on Statistical Datastreaming
G01APF   23  nagf_stat_quantiles_stream_arbitrary
Calculates approximate quantiles from a data stream of unknown size
Related keywords: big datadata analyticsquantilesSimple Calculations on Statistical Datastreaming
G01ATF   24  nagf_stat_summary_onevar
Computes univariate summary information: mean, variance, skewness, kurtosis
Related keywords: big datadata analyticskurtosismaximum valuemeanminimum valueSimple Calculations on Statistical Dataskewnessstandard deviationstreaming
G01AUF   24  nagf_stat_summary_onevar_combine
Combines multiple sets of summary information, for use after G01ATF
Related keywords: big datadata analyticsSimple Calculations on Statistical Datastreamingsummary information
G01WAF   24  nagf_stat_moving_average
Computes the mean and standard deviation using a rolling window
Related keywords: big datadata analyticsmeanmoving averageSimple Calculations on Statistical Datastandard deviationstreaming
G02BZF   24  nagf_correg_ssqmat_combine
Combines two sums of squares matrices, for use after G02BUF
Related keywords: big datacorrelation analysiscross-productsdata analyticsmeannonlinear regressionpolynomial regressionregression analysisstreamingsum of squares
G13MEF   24  nagf_tsa_inhom_iema
Computes the iterated exponential moving average for a univariate inhomogeneous time series
Related keywords: big datadata analyticsexponential moving averagemoving averagestreamingtime seriestime series analysisunivariate time series
G13MFF   24  nagf_tsa_inhom_iema_all
Computes the iterated exponential moving average for a univariate inhomogeneous time series, intermediate results are also returned
Related keywords: big datadata analyticsexponential moving averagemoving averagestreamingtime seriestime series analysisunivariate time series
G13MGF   24  nagf_tsa_inhom_ma
Computes the exponential moving average for a univariate inhomogeneous time series
Related keywords: big datadata analyticsexponential moving averagemoving averagestreamingtime seriestime series analysisunivariate time series
date and time X05AAF   14  nagf_time_date_array
Return date and time as an array of integers
Related keywords: data and time utilitiestime
X05ABF   14  nagf_time_date_array_string
Convert array of integers representing date and time to character string
Related keywords: data and time utilitiestime
X05ACF   14  nagf_time_date_string_compare
Compare two character strings representing date and time
Related keywords: data and time utilitiestime
Daubechies wavelet C09AAF   22  nagf_wav_1d_init
One-dimensional wavelet filter initialization
Related keywords: biorthogonal waveletHaar waveletwaveletswavelets, one-dimensionalwavelet transforms
C09ABF   23  nagf_wav_2d_init
Two-dimensional wavelet filter initialization
Related keywords: biorthogonal waveletHaar waveletwaveletswavelets, two-dimensionalwavelet transforms
C09ACF   24  nagf_wav_3d_init
Three-dimensional wavelet filter initialization
Related keywords: biorthogonal waveletHaar waveletwaveletswavelets, three-dimensionalwavelet transforms
David's test G08BAF   nagf_nonpar_test_mooddavid
Mood's and David's tests on two samples of unequal size
Related keywords: dispersionMood's test for dispersion differencesnonparametric statistics
Dawson's integral S15AFF   nagf_specfun_dawson
Dawson's integral
Related keywords: approximations of special functionsfinance
daxpy F06ECF   12  nagf_blas_daxpy
Add scalar times real vector to real vector
Related keywords: BLASblas, real matriceselementary arithmeticlinear algebra support routines
F06ETF   14  nagf_blas_daxpyi
Add scalar times real sparse vector to a full vector
Related keywords: BLASblas, real matriceselementary arithmeticlinear algebra support routines
DBDSDC F08MDF   22  nagf_lapackeig_dbdsdc
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemLAPACKLAPACKleast squaresmatrix, band QR algorithmreal, bidiagonal matrixSVD, singular value decomposition
DBDSQR F08MEF   16  nagf_lapackeig_dbdsqr
Performs an SVD of real bidiagonal matrix reduced from real general matrix
Related keywords: differential qd algorithmeigenproblemLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, bidiagonal matrixSVD, singular value decomposition
dcopy F06EFF   12  nagf_blas_dcopy
Copy real vector
Related keywords: BLASblas, real matriceselementary arithmeticfinancelinear algebra support routines
DDISNA F08FLF   22  nagf_lapackeig_ddisna
Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix
Related keywords: complex, Hermitian, indefinite matrixcondition number, matrixeigenproblemeigenvectorsfinanceLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
ddot F06EAF   12  nagf_blas_ddot
Dot product of two real vectors
Related keywords: BLASblas, real matricesfinanceinner productlinear algebra support routines
ddoti F06ERF   14  nagf_blas_ddoti
Dot product of a real sparse and a full vector
Related keywords: BLASblas, real matricesinner productlinear algebra support routines
decimal digits X02BEF   nagf_machine_decimal_digits
The maximum number of decimal digits that can be represented
Related keywords: machine constants
decomposition, matrix F01BUF   nagf_matop_real_symm_posdef_fac
U L D L T U T factorization of real symmetric positive definite band matrix
Related keywords: inversionmatrix, bandmatrix operationsreal, band, positive-definite, symmetric matrix U L D L T U T decomposition
Delaunay–Voronoi process D06ABF   20  nagf_mesh_2d_gen_delaunay
Generates a two-dimensional mesh using a Delaunay–Voronoi process
Related keywords: mesh generationtriangular mesh
dendrogram G03EHF   16  nagf_mv_cluster_hier_dendrogram
Constructs dendrogram (for use after G03ECF)
Related keywords: big datadata analyticshierarchical cluster analysismultivariate methods
dense E04UCF   12  nagf_opt_nlp1_solve_old
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: financemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationsequential QP methodSQP
E04UFF   18  nagf_opt_nlp1_rcomm_old
Nonlinear programming (NLP), dense, active-set, SQP method, using function values and optionally first derivatives (reverse communication, comprehensive)
Related keywords: financemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationsequential QP methodSQP
E04WDF   21  nagf_opt_nlp2_solve
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: financemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationsequential QP methodSQP
derivative, Landau density function G01RTF   21  nagf_stat_pdf_landau_deriv
Landau derivative function ϕ λ
Related keywords: financeLandau density functionSimple Calculations on Statistical Data
derivative, options S30AAF   22  nagf_specfun_opt_bsm_price
Black–Scholes–Merton option pricing formula
Related keywords: approximations of special functionsBlack–Scholes option pricingfinanceoption pricing
S30ABF   22  nagf_specfun_opt_bsm_greeks
Black–Scholes–Merton option pricing formula with Greeks
Related keywords: approximations of special functionsBlack–Scholes option pricingfinanceGreeks, optionsoption pricing
S30BAF   22  nagf_specfun_opt_lookback_fls_price
Floating-strike lookback option pricing formula in the Black-Scholes-Merton model
Related keywords: approximations of special functionsfinancefloating-strike lookback optionoption pricing
S30BBF   22  nagf_specfun_opt_lookback_fls_greeks
Floating-strike lookback option pricing formula with Greeks in the Black-Scholes-Merton model
Related keywords: approximations of special functionsfinancefloating-strike lookback optionGreeks, optionsoption pricing
S30CAF   22  nagf_specfun_opt_binary_con_price
Binary option, cash-or-nothing pricing formula
Related keywords: approximations of special functionsbinary optioncash-or-nothing optionfinanceoption pricing
S30CBF   22  nagf_specfun_opt_binary_con_greeks
Binary option, cash-or-nothing pricing formula with Greeks
Related keywords: approximations of special functionsbinary optioncash-or-nothing optionfinanceGreeks, optionsoption pricing
S30CCF   22  nagf_specfun_opt_binary_aon_price
Binary option, asset-or-nothing pricing formula
Related keywords: approximations of special functionsbinary optioncash-or-nothing optionfinanceoption pricing
S30CDF   22  nagf_specfun_opt_binary_aon_greeks
Binary option, asset-or-nothing pricing formula with Greeks
Related keywords: approximations of special functionsbinary optioncash-or-nothing optionfinanceGreeks, optionsoption pricing
S30FAF   22  nagf_specfun_opt_barrier_std_price
Standard barrier option pricing formula
Related keywords: approximations of special functionsbarrier optionfinanceoption pricing
S30JAF   22  nagf_specfun_opt_jumpdiff_merton_price
Jump-diffusion, Merton's model, option pricing formula
Related keywords: approximations of special functionsfinancejump-diffusion model, option pricingMerton model, option pricingoption pricing
S30JBF   22  nagf_specfun_opt_jumpdiff_merton_greeks
Jump-diffusion, Merton's model, option pricing formula with Greeks
Related keywords: approximations of special functionsfinanceGreeks, optionsjump-diffusion model, option pricingMerton model, option pricingoption pricing
S30NAF   22  nagf_specfun_opt_heston_price
Heston's model option pricing formula
Related keywords: approximations of special functionsfinancefinanceHeston model, optionsoption pricing
S30NBF   23  nagf_specfun_opt_heston_greeks
Heston's model option pricing formula with Greeks
Related keywords: approximations of special functionsfinanceGreeks, optionsHeston model, optionsoption pricing
S30SAF   22  nagf_specfun_opt_asian_geom_price
Asian option, geometric continuous average rate pricing formula
Related keywords: approximations of special functionsAsian optionfinanceoption pricing
S30SBF   22  nagf_specfun_opt_asian_geom_greeks
Asian option, geometric continuous average rate pricing formula with Greeks
Related keywords: approximations of special functionsAsian optionfinanceGreeks, optionsoption pricing
derivative-free minimization E04ABF   nagf_opt_one_var_func_old
Minimum, function of one variable, using function values only
Related keywords: financemaximizing a functionminimization, unconstrainedminimizing a functionNLPnonlinear programmingone-dimensional quadratic interpolationoptimizationunivariate minimization
E04CBF   22  nagf_opt_uncon_simplex
Unconstrained minimum, Nelder–Mead simplex algorithm, using function values only
Related keywords: financemaximizing a functionminimization, unconstrainedminimizing a functionNelder–Mead algorithmNLPnonlinear programmingoptimizationsimplex algorithm
E04FCF   nagf_opt_lsq_uncon_mod_func_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (comprehensive)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04FYF   18  nagf_opt_lsq_uncon_mod_func_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (easy-to-use)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
derivative-free optimization E04FFF   26  nagf_opt_handle_solve_dfls
Derivative-free (DFO) solver for a nonlinear least squares objective function with bounded variables
Related keywords: calibrationdata fittingDFODFOmaximizing a functionminimizing a functionnonlinear least squaresnonlinear least squaresoptimizationoptimizationsum of squares
E04RMF   26  nagf_opt_handle_set_nlnls
Define a nonlinear least squares objective function to a problem initialized by E04RAF
Related keywords: calibrationdata fittingDFOleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinear least squaresoptimizationoptimizationoptimizationsum of squares
derivative of a Gaussian wavelet C09BAF   23  nagf_wav_1d_cont
One-dimensional real continuous wavelet transform
Related keywords: Mexican hat waveletMorlet waveletwavelet continuouswaveletswavelets, one-dimensionalwavelet transforms
derivatives, psi function S14ADF   14  nagf_specfun_polygamma_deriv
Scaled derivatives of ψ x
Related keywords: approximations of special functionsfinancepsi function
S14AEF   20  nagf_specfun_psi_deriv_real
Polygamma function ψ n x for real x
Related keywords: approximations of special functionsfinancepsi function
S14AFF   20  nagf_specfun_psi_deriv_complex
Polygamma function ψ n z for complex z
Related keywords: approximations of special functionsdigamma functionpolygamma functionpsi functiontrigamma function
design matrix G22YCF   26  nagf_blgm_lm_design_matrix
Construct a design matrix from a linear model specified using G22YAF
Related keywords: regression
G22YDF   26  nagf_blgm_lm_submodel
Construct a vector indicating which columns of a design matrix to include in a submodel specified using G22YAF
Related keywords: regression
design of experiments G04DAF   17  nagf_anova_contrasts
Computes sum of squares for contrast between means
Related keywords: analysis of varianceexperimental designsum of squares
G04DBF   17  nagf_anova_confidence
Computes confidence intervals for differences between means computed by G04BBF or G04BCF
Related keywords: analysis of varianceconfidence intervalexperimental design
G04EAF   17  nagf_anova_dummyvars
Computes orthogonal polynomials or dummy variables for factor/classification variable
Related keywords: analysis of varianceclassification variableexperimental designfactor variable
destroy G22ZAF   26  nagf_blgm_handle_free
Destroy a and deallocate all the memory used
Related keywords: freehandle
determinant F03 Chapter Introduction     Determinants
deviates G01FAF   15  nagf_stat_inv_cdf_normal
Computes deviates for the standard Normal distribution
Related keywords: financeinverse CDFinverse cumulative distribution functionNormal distributionSimple Calculations on Statistical Data
G01FBF   14  nagf_stat_inv_cdf_students_t
Computes deviates for Student's t -distribution
Related keywords: financeinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical DataStudent's t -distribution
G01FCF   14  nagf_stat_inv_cdf_chisq
Computes deviates for the χ 2 distribution
Related keywords: chi-squared distributionfinanceinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01FDF   14  nagf_stat_inv_cdf_f
Computes deviates for the F -distribution
Related keywords: F -distributionfinanceinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01FEF   14  nagf_stat_inv_cdf_beta
Computes deviates for the beta distribution
Related keywords: beta distributionfinanceinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01FFF   14  nagf_stat_inv_cdf_gamma
Computes deviates for the gamma distribution
Related keywords: financegamma distributioninverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01FMF   15  nagf_stat_inv_cdf_studentized_range
Computes deviates for the Studentized range statistic
Related keywords: financeinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical DataStudentized range statistic
G01TAF   24  nagf_stat_inv_cdf_normal_vector
Computes a vector of deviates for the standard Normal distribution
Related keywords: big datadata analyticsGaussian distributioninverse CDFinverse cumulative distribution functionNormal distributionSimple Calculations on Statistical Data
G01TBF   24  nagf_stat_inv_cdf_students_t_vector
Computes a vector of deviates for Student's t -distribution
Related keywords: big datadata analyticsinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical DataStudent's t -distribution
G01TCF   24  nagf_stat_inv_cdf_chisq_vector
Computes a vector of deviates for χ 2 distribution
Related keywords: big datachi-squared distributiondata analyticsinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01TDF   24  nagf_stat_inv_cdf_f_vector
Computes a vector of deviates for F -distribution
Related keywords: big datadata analytics F -distributioninverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Datavariance-ratio distribution
G01TEF   24  nagf_stat_inv_cdf_beta_vector
Computes a vector of deviates for the beta distribution
Related keywords: beta distributionbig datadata analyticsinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01TFF   24  nagf_stat_inv_cdf_gamma_vector
Computes a vector of deviates for the gamma distribution
Related keywords: big datadata analyticsgamma distributioninverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
DFO E04FFF   26  nagf_opt_handle_solve_dfls
Derivative-free (DFO) solver for a nonlinear least squares objective function with bounded variables
Related keywords: calibrationdata fittingderivative-free optimizationmaximizing a functionminimizing a functionnonlinear least squaresnonlinear least squaresoptimizationoptimizationsum of squares
E04RMF   26  nagf_opt_handle_set_nlnls
Define a nonlinear least squares objective function to a problem initialized by E04RAF
Related keywords: calibrationdata fittingderivative-free optimizationleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinear least squaresoptimizationoptimizationoptimizationsum of squares
DGBBRD F08LEF   19  nagf_lapackeig_dgbbrd
Performs a reduction of real rectangular band matrix to upper bidiagonal form
Related keywords: eigenproblemGivens rotationsLAPACKLAPACKleast squaresmatrix, bandreal, band, m by n matrix
DGBCON F07BGF   15  nagf_lapacklin_dgbcon
Estimate condition number of real band matrix, matrix already factorized by F07BDF
Related keywords: condition number, matrixLAPACKlinear equationsmatrix, bandreal, band matrix
DGBEQU F07BFF   22  nagf_lapacklin_dgbequ
Computes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number
Related keywords: equilibrationLAPACKlinear equationsmatrix, bandreal, band matrixscaling
dgbmv F06PBF   12  nagf_blas_dgbmv
Matrix-vector product, real rectangular band matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesmatrix, bandmultiply, matrixreal, band, m by n matrix
DGBRFS F07BHF   15  nagf_lapacklin_dgbrfs
Refined solution with error bounds of real band system of linear equations, multiple right-hand sides
Related keywords: backward errorforward errorLAPACKlinear equations L U decompositionmatrix, bandreal, band matrix
DGBSV F07BAF   21  nagf_lapacklin_dgbsv
Computes the solution to a real banded system of linear equations
Related keywords: LAPACKlinear equations L U decompositionmatrix, bandreal, band matrix
DGBSVX F07BBF   21  nagf_lapacklin_dgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
Related keywords: backward errorcondition number, matrixerror bound, matrixforward errorLAPACKlinear equations L U decompositionmatrix, bandreal, band matrix
DGBTRF F07BDF   15  nagf_lapacklin_dgbtrf
L U factorization of real m by n band matrix
Related keywords: LAPACKlinear equations L U decompositionmatrix, bandreal, band matrix
DGBTRS F07BEF   15  nagf_lapacklin_dgbtrs
Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by F07BDF
Related keywords: LAPACKlinear equations L U decompositionmatrix, bandreal, band matrix
DGEBAK F08NJF   16  nagf_lapackeig_dgebak
Transforms eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF
Related keywords: balancingeigenproblemeigenvectorsLAPACKLAPACKleast squaresreal, nonsymmetric matrix
DGEBAL F08NHF   16  nagf_lapackeig_dgebal
Balances a real general matrix
Related keywords: balancingeigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
DGEBRD F08KEF   16  nagf_lapackeig_dgebrd
Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal transformationsreal, m by n matrix
DGECON F07AGF   15  nagf_lapacklin_dgecon
Estimate condition number of real matrix, matrix already factorized by F07ADF
Related keywords: condition number, matrixLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
DGEEQU F07AFF   22  nagf_lapacklin_dgeequ
Computes row and column scalings intended to equilibrate a general real matrix and reduce its condition number
Related keywords: equilibrationLAPACKlinear equationsreal, nonsymmetric matrixscaling
DGEES F08PAF   21  nagf_lapackeig_dgees
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
Related keywords: eigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur formSchur vectors
F08PBF   21  nagf_lapackeig_dgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: condition number, matrixeigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur formSchur vectors
DGEEV F08NAF   21  nagf_lapackeig_dgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresorthogonal transformations QR algorithmreal, nonsymmetric matrix
F08NNF   21  nagf_lapackeig_zgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
Related keywords: complex, nonsymmetric matrixeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares
F08NPF   21  nagf_lapackeig_zgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixcondition number, matrixeigenproblemeigenvalueseigenvectorsfinanceforward errorLAPACKLAPACKleast squares
DGEEVX F08NBF   21  nagf_lapackeig_dgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixeigenproblemeigenvalueseigenvectorsfinanceforward errorLAPACKLAPACKleast squaresorthogonal transformations QR algorithmreal, nonsymmetric matrix
DGEHRD F08NEF   16  nagf_lapackeig_dgehrd
Performs an orthogonal reduction of real general matrix to upper Hessenberg form
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal transformationsreal, nonsymmetric matrix
DGEJSV F08KHF   23  nagf_lapackeig_dgejsv
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
Related keywords: eigenproblemJacobi methodLAPACKLAPACKleast squaresreal, nonsymmetric matrixsingular value decomposition
DGELQF F08AHF   16  nagf_lapackeig_dgelqf
Performs a L Q factorization of real general rectangular matrix
Related keywords: eigenproblemLAPACKLAPACKleast squares LQ factorizationreal, m by n matrix
DGELS F08AAF   21  nagf_lapackeig_dgels
Solves a real linear least squares problem of full rank
Related keywords: eigenproblemfinanceLAPACKLAPACKleast squareslinear least squares LQ decompositionoverdetermined linear equations QR factorizationreal, m by n matrixunderdetermined linear system
DGELSD F08KCF   21  nagf_lapackeig_dgelsd
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemfinanceLAPACKLAPACKleast squareslinear least squaresminimal least squaresreal, m by n matrixSVD, singular value decomposition
DGELSS F08KAF   21  nagf_lapackeig_dgelss
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
Related keywords: eigenproblemLAPACKLAPACKleast squareslinear least squaresminimal least squaresreal, m by n matrixSVD, singular value decomposition
DGELSY F08BAF   21  nagf_lapackeig_dgelsy
Computes the minimum-norm solution to a real linear least squares problem
Related keywords: eigenproblemfinanceLAPACKLAPACKleast squareslinear least squaresminimal least squaresreal, m by n matrix
dgemm F06YAF   14  nagf_blas_dgemm
Matrix-matrix product, two real rectangular matrices
Related keywords: BLASblas, real matricesfinancelinear algebra support routinesmultiply, matrixreal, m by n matrix
DGEMQRT F08ACF   25  nagf_lapackeig_dgemqrt
Applies the orthogonal transformation determined by F08ABF
Related keywords: eigenproblemexplicit blockingLAPACKleast squaresorthogonal transformationsQR factorizationrecursive QR
dgemv F06PAF   12  nagf_blas_dgemv
Matrix-vector product, real rectangular matrix
Related keywords: BLASblas, real matricesfinancelinear algebra support routinesmultiply, matrixreal, m by n matrix
DGEQLF F08CEF   22  nagf_lapackeig_dgeqlf
Q L factorization of real general rectangular matrix
Related keywords: eigenproblemLAPACKLAPACKleast squares QL factorizationreal, m by n matrix
DGEQP3 F08BFF   22  nagf_lapackeig_dgeqp3
Q R factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
Related keywords: eigenproblemfinanceLAPACKLAPACKleast squaresorthogonal transformations QR factorizationreal, m by n matrix
DGEQPF F08BEF   16  nagf_lapackeig_dgeqpf
Q R factorization, with column pivoting, of real general rectangular matrix
Related keywords: eigenproblemfinanceLAPACKLAPACKleast squaresorthogonal transformations QR factorizationreal, m by n matrix
DGEQRF F08AEF   16  nagf_lapackeig_dgeqrf
Performs a Q R factorization of real general rectangular matrix
Related keywords: eigenproblemfinanceLAPACKLAPACKleast squares QR factorizationreal, m by n matrix
DGEQRT F08ABF   25  nagf_lapackeig_dgeqrt
Performs a Q R factorization of real general rectangular matrix, with explicit blocking
Related keywords: eigenproblemexplicit blockingLAPACKleast squaresQR factorizationreal, m by n matrixrecursive QR
dger F06PMF   12  nagf_blas_dger
Rank-1 update, real rectangular matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesrank k matrix updatesreal, m by n matrix
DGERFS F07AHF   15  nagf_lapacklin_dgerfs
Refined solution with error bounds of real system of linear equations, multiple right-hand sides
Related keywords: backward errorerror bound, matrixforward errorLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
DGERQF F08CHF   22  nagf_lapackeig_dgerqf
R Q factorization of real general rectangular matrix
Related keywords: eigenproblemLAPACKLAPACKleast squaresreal, m by n matrixRQ factorizations
DGESDD F08KDF   21  nagf_lapackeig_dgesdd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemfinanceLAPACKLAPACKleast squaresreal, nonsymmetric matrixSVD, singular value decomposition
DGESV F07AAF   21  nagf_lapacklin_dgesv
Computes the solution to a real system of linear equations
Related keywords: financeLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
DGESVD F08KBF   21  nagf_lapackeig_dgesvd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
Related keywords: eigenproblemfinanceLAPACKLAPACKleast squaresreal, nonsymmetric matrixSVD, singular value decomposition
DGESVJ F08KJF   23  nagf_lapackeig_dgesvj
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
Related keywords: eigenproblemJacobi methodLAPACKLAPACKleast squaresreal, nonsymmetric matrixsingular value decomposition
DGESVX F07ABF   21  nagf_lapacklin_dgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
Related keywords: backward errorcondition number, matrixerror bound, matrixfinanceforward errorLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
DGETRF F07ADF   15  nagf_lapacklin_dgetrf
L U factorization of real m by n matrix
Related keywords: financeLAPACKlinear equations L U decompositionreal, m by n matrix
DGETRI F07AJF   15  nagf_lapacklin_dgetri
Inverse of real matrix, matrix already factorized by F07ADF
Related keywords: financeinverse, matrixLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
DGETRS F07AEF   15  nagf_lapacklin_dgetrs
Solution of real system of linear equations, multiple right-hand sides, matrix already factorized by F07ADF
Related keywords: LAPACKlinear equations L U decompositionreal, nonsymmetric matrix
DGGBAK F08WJF   20  nagf_lapackeig_dggbak
Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF
Related keywords: balancingeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
DGGES F08XAF   21  nagf_lapackeig_dgges
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: eigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form, generalizedSchur vectors
DGGES3 F08XCF   26  nagf_lapackeig_dgges3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: eigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form, generalizedSchur vectors
DGGESX F08XBF   21  nagf_lapackeig_dggesx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: condition number, matrixeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form, generalizedSchur vectors
DGGEV F08WAF   21  nagf_lapackeig_dggev
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WCF   26  nagf_lapackeig_dggev3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
DGGEVX F08WBF   21  nagf_lapackeig_dggevx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsfinanceforward errorgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
DGGGLM F08ZBF   21  nagf_lapackeig_dggglm
Solves a real general Gauss–Markov linear model (GLM) problem
Related keywords: eigenproblemGauss–Markov linear modelLAPACKLAPACKleast squares QR factorizationreal, m by n matrix
DGGHD3 F08WFF   26  nagf_lapackeig_dgghd3
Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Related keywords: eigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresorthogonal transformationsreal, nonsymmetric matrix
DGGHRD F08WEF   20  nagf_lapackeig_dgghrd
Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Related keywords: eigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresorthogonal transformationsreal, nonsymmetric matrix
F08WHF   20  nagf_lapackeig_dggbal
Balances a pair of real, square, matrices
Related keywords: balancingeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squares
DGGLSE F08ZAF   21  nagf_lapackeig_dgglse
Solves the real linear equality-constrained least squares (LSE) problem
Related keywords: eigenproblemLAPACKLAPACKleast squareslinear least squaresreal, m by n matrixRQ factorizations
DGGQRF F08ZEF   22  nagf_lapackeig_dggqrf
Computes a generalized Q R factorization of a real matrix pair
Related keywords: eigenproblemLAPACKLAPACKleast squares QR factorizationreal, m by n matrix
DGGRQF F08ZFF   22  nagf_lapackeig_dggrqf
Computes a generalized R Q factorization of a real matrix pair
Related keywords: eigenproblemLAPACKLAPACKleast squaresreal, m by n matrixRQ factorizations
DGGSVD F08VAF   21  nagf_lapackeig_dggsvd
Computes the generalized singular value decomposition of a real matrix pair
Related keywords: eigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresreal, nonsymmetric matrixSVD, generalized
DGGSVD3 F08VCF   26  nagf_lapackeig_dggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair
Related keywords: eigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresreal, nonsymmetric matrixSVD, generalized
DGGSVP F08VEF   22  nagf_lapackeig_dggsvp
Produces orthogonal matrices that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
Related keywords: eigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresorthogonal transformationsreal, m by n matrixSVD, generalized
DGGSVP3 F08VGF   26  nagf_lapackeig_dggsvp3
Produces orthogonal matrices, using BLAS-3, that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
Related keywords: eigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresorthogonal transformationsreal, m by n matrixSVD, generalized
DGTCON F07CGF   22  nagf_lapacklin_dgtcon
Estimates the reciprocal of the condition number of a real tridiagonal matrix using the L U factorization computed by F07CDF
Related keywords: condition number, matrixLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
F07CHF   22  nagf_lapacklin_dgtrfs
Refined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorforward errorLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
dgthr F06EUF   14  nagf_blas_dgthr
Gather real sparse vector
Related keywords: BLASblas, real matriceselementary arithmeticlinear algebra support routines
dgthrz F06EVF   14  nagf_blas_dgthrz
Gather and set to zero real sparse vector
Related keywords: BLASblas, real matriceselementary arithmeticlinear algebra support routines
F06EWF   14  nagf_blas_dsctr
Scatter real sparse vector
Related keywords: BLASblas, real matriceselementary arithmeticlinear algebra support routines
DGTSV F07CAF   21  nagf_lapacklin_dgtsv
Computes the solution to a real tridiagonal system of linear equations
Related keywords: financeLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
DGTSVX F07CBF   21  nagf_lapacklin_dgtsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
Related keywords: backward errorcondition number, matrixerror bound, matrixforward errorLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
DGTTRF F07CDF   22  nagf_lapacklin_dgttrf
L U factorization of real tridiagonal matrix
Related keywords: financeLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
DGTTRS F07CEF   22  nagf_lapacklin_dgttrs
Solves a real tridiagonal system of linear equations using the L U factorization computed by F07CDF
Related keywords: financeLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
DHGEQZ F08XEF   20  nagf_lapackeig_dhgeqz
Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
Related keywords: eigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresreal, Hessenberg matrix
DHSEIN F08PKF   16  nagf_lapackeig_dhsein
Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
Related keywords: eigenproblemeigenvectorsinverse iterationLAPACKLAPACKleast squaresreal, Hessenberg matrix
DHSEQR F08PEF   16  nagf_lapackeig_dhseqr
Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
Related keywords: eigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form
diagonal pivoting method F07MAF   21  nagf_lapacklin_dsysv
Computes the solution to a real symmetric system of linear equations
Related keywords: DSYSVLAPACKLDLT decompositionlinear equationsreal, indefinite, symmetric matrix UDU T decompositiuon
F07MBF   21  nagf_lapacklin_dsysvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations
Related keywords: backward errorDSYSVXforward errorLAPACKLDLT decompositionlinear equationsreal, indefinite, symmetric matrix UDU T decompositiuon
F07MDF   15  nagf_lapacklin_dsytrf
Bunch–Kaufman factorization of real symmetric indefinite matrix
Related keywords: Bunch–Kaufman factorizationDSYTRFLAPACKlinear equationsreal, indefinite, symmetric matrix
F07MEF   15  nagf_lapacklin_dsytrs
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MDF
Related keywords: Bunch–Kaufman factorizationDSYTRSLAPACKlinear equationsreal, indefinite, symmetric matrix
F07MGF   15  nagf_lapacklin_dsycon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MDF
Related keywords: Bunch–Kaufman factorizationcondition number, matrixDSYCONLAPACKlinear equationsreal, indefinite, symmetric matrix
F07MHF   15  nagf_lapacklin_dsyrfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides
Related keywords: backward errorBunch–Kaufman factorizationDSYRFSforward errorLAPACKlinear equationsreal, indefinite, symmetric matrix
F07MJF   15  nagf_lapacklin_dsytri
Inverse of real symmetric indefinite matrix, matrix already factorized by F07MDF
Related keywords: Bunch–Kaufman factorizationDSYTRIinverse, matrixLAPACKlinear equationsreal, indefinite, symmetric matrix
F07MNF   21  nagf_lapacklin_zhesv
Computes the solution to a complex Hermitian system of linear equations
Related keywords: complex, Hermitian, indefinite matrixLAPACK LDL H decompositionlinear equations UDU H decompositionZHESV
F07MPF   21  nagf_lapacklin_zhesvx
Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations
Related keywords: backward errorcomplex, Hermitian, indefinite matrixforward errorLAPACK LDL H decompositionlinear equations UDU H decompositionZHESVX
F07MRF   15  nagf_lapacklin_zhetrf
Bunch–Kaufman factorization of complex Hermitian indefinite matrix
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixLAPACKlinear equationsZHETRF
F07MSF   15  nagf_lapacklin_zhetrs
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MRF
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixLAPACKlinear equationsZHETRS
F07MUF   15  nagf_lapacklin_zhecon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07MRF
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixcondition number, matrixLAPACKlinear equationsZHECON
F07MVF   15  nagf_lapacklin_zherfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
Related keywords: backward errorBunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixerror bound, matrixforward errorLAPACKlinear equationsZHERFS
F07MWF   15  nagf_lapacklin_zhetri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07MRF
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixinverse, matrixLAPACKlinear equationsZHETRI
F07NNF   21  nagf_lapacklin_zsysv
Computes the solution to a complex symmetric system of linear equations
Related keywords: complex, symmetric matrixLAPACK LDL H decompositionlinear equations UDU H decompositionZSYSV
F07NPF   21  nagf_lapacklin_zsysvx
Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations
Related keywords: backward errorcomplex, symmetric matrixforward errorLAPACK LDL H decompositionlinear equations UDU H decompositionZSYSVX
F07NRF   15  nagf_lapacklin_zsytrf
Bunch–Kaufman factorization of complex symmetric matrix
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixLAPACKlinear equationsZSYTRF
F07NSF   15  nagf_lapacklin_zsytrs
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07NRF
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixLAPACKlinear equationsZSYTRS
F07NUF   15  nagf_lapacklin_zsycon
Estimate condition number of complex symmetric matrix, matrix already factorized by F07NRF
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixcondition number, matrixLAPACKlinear equationsZSYCON
F07NVF   15  nagf_lapacklin_zsyrfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
Related keywords: backward errorBunch–Kaufman factorizationcomplex, symmetric matrixerror bound, matrixforward errorLAPACKlinear equationsZSYRFS
F07NWF   15  nagf_lapacklin_zsytri
Inverse of complex symmetric matrix, matrix already factorized by F07NRF
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixinverse, matrixLAPACKlinear equationsZSYTRI
F07PAF   21  nagf_lapacklin_dspsv
Computes the solution to a real symmetric system of linear equations, packed storage
Related keywords: DSPSVLAPACK LDL T decompositionlinear equationsreal, indefinite, symmetric matrix UDU T decomposition
F07PBF   21  nagf_lapacklin_dspsvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage. Error bounds and a condition estimate are also computed
Related keywords: backward errorcondition number, matrixDSPSVXerror bound, matrixforward errorLAPACK LDL H decompositionlinear equationsreal, indefinite, symmetric matrix UDU H decomposition
F07PDF   15  nagf_lapacklin_dsptrf
Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage
Related keywords: Bunch–Kaufman factorizationDSPTRFLAPACKlinear equationsreal, indefinite, symmetric matrix
F07PEF   15  nagf_lapacklin_dsptrs
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PDF, packed storage
Related keywords: Bunch–Kaufman factorizationDSPTRSLAPACKlinear equationsreal, indefinite, symmetric matrix
F07PGF   15  nagf_lapacklin_dspcon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage
Related keywords: Bunch–Kaufman factorizationcondition number, matrixDSPCONLAPACKlinear equationsreal, indefinite, symmetric matrix
F07PHF   15  nagf_lapacklin_dsprfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorBunch–Kaufman factorizationDSPRFSforward errorLAPACKlinear equationsreal, indefinite, symmetric matrix
F07PJF   15  nagf_lapacklin_dsptri
Inverse of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage
Related keywords: Bunch–Kaufman factorizationDSPTRIinverse, matrixLAPACKlinear equationsreal, indefinite, symmetric matrix
F07PNF   21  nagf_lapacklin_zhpsv
Computes the solution to a complex Hermitian system of linear equations, packed storage
Related keywords: complex, Hermitian, indefinite matrixinverse, matrixLAPACK LDL H decompositionlinear equations UDU H decompositionZHPSV
F07PPF   21  nagf_lapacklin_zhpsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, Hermitian, system of linear equations, error bounds and condition estimates. Packed storage
Related keywords: backward errorcomplex, Hermitian, indefinite matrixforward errorinverse, matrixLAPACK LDL H decompositionlinear equations UDU H decompositionZHPSVX
F07PRF   15  nagf_lapacklin_zhptrf
Bunch–Kaufman factorization of complex Hermitian indefinite matrix, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixLAPACKlinear equationsZHPTRF
F07PSF   15  nagf_lapacklin_zhptrs
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixLAPACKlinear equationsZHPTRS
F07PUF   15  nagf_lapacklin_zhpcon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07PRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixcondition number, matrixLAPACKlinear equationsZHPCON
F07PVF   15  nagf_lapacklin_zhprfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorBunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixerror bound, matrixforward errorLAPACKlinear equationsZHPRFS
F07PWF   15  nagf_lapacklin_zhptri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07PRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixinverse, matrixLAPACKlinear equationsZHPTRI
F07QNF   21  nagf_lapacklin_zspsv
Computes the solution to a complex symmetric system of linear equations, packed storage
Related keywords: complex, symmetric matrixLAPACK LDL T decompositionlinear equations UDU T decompositionZSPSV
F07QPF   21  nagf_lapacklin_zspsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, symmetric, system of linear equations, error bounds and condition estimates. Packed storage
Related keywords: backward errorcomplex, symmetric matrixforward errorLAPACK LDL T decompositionlinear equations UDU T decompositionZSPSVX
F07QRF   15  nagf_lapacklin_zsptrf
Bunch–Kaufman factorization of complex symmetric matrix, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixLAPACKlinear equationsZSPTRF
F07QSF   15  nagf_lapacklin_zsptrs
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07QRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixLAPACKlinear equationsZSPTRS
F07QUF   15  nagf_lapacklin_zspcon
Estimate condition number of complex symmetric matrix, matrix already factorized by F07QRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixcondition number, matrixLAPACKlinear equationsZSPCON
F07QVF   15  nagf_lapacklin_zsprfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorBunch–Kaufman factorizationcomplex, symmetric matrixerror bound, matrixforward errorLAPACKlinear equationsZSPRFS
F07QWF   15  nagf_lapacklin_zsptri
Inverse of complex symmetric matrix, matrix already factorized by F07QRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixinverse, matrixLAPACKlinear equationsZSPTRI
Dickey–Fuller G13AWF   25  nagf_tsa_uni_dickey_fuller_unit
Computes (augmented) Dickey–Fuller unit root test statistic
Related keywords: big datadata analyticstime series analysisunit root
Dickey–Fuller G01EWF   25  nagf_stat_prob_dickey_fuller_unit
Computes probabilities for the Dickey–Fuller unit root test
Related keywords: probabilitiesSimple Calculations on Statistical Datastatistical distribution functionsunit root
differencing, time series G13AAF   nagf_tsa_uni_diff
Univariate time series, seasonal and non-seasonal differencing
Related keywords: big datadata analyticsfinancenon-seasonal differencingseasonal differencingtime seriestime series analysisunivariate time series
differential equations D02TLF   25  nagf_ode_bvp_coll_nlin_solve
Ordinary differential equations, general nonlinear boundary value problem, collocation technique (thread safe)
Related keywords: boundary value problemBVPnonlinear mixed orderODE, ordinary differential equationsordinary differential equationstwo-point boundary value problem
differential qd algorithm F08MEF   16  nagf_lapackeig_dbdsqr
Performs an SVD of real bidiagonal matrix reduced from real general matrix
Related keywords: DBDSQReigenproblemLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, bidiagonal matrixSVD, singular value decomposition
F08MSF   16  nagf_lapackeig_zbdsqr
Performs an SVD of real bidiagonal matrix reduced from complex general matrix
Related keywords: eigenproblemLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, bidiagonal matrixSVD, singular value decompositionZBDSQR
differentiation, numerical D04AAF   nagf_numdiff_fwd
Numerical differentiation, derivatives up to order 14 , function of one real variable
Related keywords: numerical differentiation
D04BAF   23  nagf_numdiff_rcomm
Numerical differentiation, user-supplied function values, derivatives up to order 14 , derivatives with respect to one real variable
Related keywords: numerical differentiation
D04BBF   23  nagf_numdiff_sample
Generates sample points for function evaluations by D04BAF
Related keywords: numerical differentiation
digamma function S14AFF   20  nagf_specfun_psi_deriv_complex
Polygamma function ψ n z for complex z
Related keywords: approximations of special functionsderivatives, psi functionpolygamma functionpsi functiontrigamma function
Dijkstra's algorithm, shortest path H03ADF   18  nagf_mip_shortestpath
Shortest path problem, Dijkstra's algorithm
Related keywords: operations researchshortest path
Dirichlet distribution G05SEF   22  nagf_rand_dist_dirichlet
Generates a vector of pseudorandom numbers from a Dirichlet distribution
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
discrete C06PQF   19  nagf_sum_fft_realherm_1d_multi_col
Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using column ordered complex storage format for Hermitian sequences
Related keywords: Fast Fourier TransformFFTone-dimensionalsummation of series
C09DAF   25  nagf_wav_1d_mxolap_fwd
One-dimensional maximal overlap discrete wavelet transform (MODWT)
Related keywords: maximal-overlapstationarywavelet transforms
C09DBF   25  nagf_wav_1d_mxolap_inv
One-dimensional inverse maximal overlap discrete wavelet transform (IMODWT)
Related keywords: inversemaximal-overlapstationarywavelet transforms
C09DCF   25  nagf_wav_1d_mxolap_multi_fwd
One-dimensional multi-level maximal overlap discrete wavelet transform (MODWT)
Related keywords: maximal-overlapmulti-levelstationarywavelet transforms
C09DDF   25  nagf_wav_1d_mxolap_multi_inv
One-dimensional inverse multi-level maximal overlap discrete wavelet transform (IMODWT)
Related keywords: inversemaximal-overlapmulti-levelstationarywavelet transforms
Discrete Fourier Transforms C06REF   25  nagf_sum_fft_sine
Multiple discrete sine transforms, simple
Related keywords: Fast Fourier TransformFFTFourier Transforms, realsine transformsummation of series
C06RFF   25  nagf_sum_fft_cosine
Multiple discrete cosine transforms, simple
Related keywords: cosine transformFast Fourier TransformFFTFourier Transforms, realsummation of series
C06RGF   25  nagf_sum_fft_qtrsine
Multiple discrete quarter-wave sine transforms, simple
Related keywords: Fast Fourier TransformFFTFourier Transforms, realquarter-wavesine transformsummation of series
C06RHF   25  nagf_sum_fft_qtrcosine
Multiple discrete quarter-wave cosine transforms, simple
Related keywords: cosine transformFast Fourier TransformFFTFourier Transforms, realquarter-wavesummation of series
discrete transform C09CAF   22  nagf_wav_1d_sngl_fwd
One-dimensional discrete wavelet transform
Related keywords: financewaveletswavelets, one-dimensionalwavelet transforms
C09CBF   22  nagf_wav_1d_sngl_inv
One-dimensional inverse discrete wavelet transform
Related keywords: financewaveletswavelets, one-dimensionalwavelet transforms
C09EAF   23  nagf_wav_2d_sngl_fwd
Two-dimensional discrete wavelet transform
Related keywords: waveletswavelets, two-dimensionalwavelet transforms
C09EBF   23  nagf_wav_2d_sngl_inv
Two-dimensional inverse discrete wavelet transform
Related keywords: waveletswavelets, two-dimensionalwavelet transforms
C09ECF   23  nagf_wav_2d_multi_fwd
Two-dimensional multi-level discrete wavelet transform
Related keywords: multi-level discrete transformwaveletswavelets, two-dimensionalwavelet transforms
C09EDF   23  nagf_wav_2d_multi_inv
Two-dimensional inverse multi-level discrete wavelet transform
Related keywords: multi-level discrete transformwaveletswavelets, two-dimensionalwavelet transforms
C09FAF   24  nagf_wav_3d_sngl_fwd
Three-dimensional discrete wavelet transform
Related keywords: waveletswavelets, three-dimensionalwavelet transforms
C09FBF   24  nagf_wav_3d_sngl_inv
Three-dimensional inverse discrete wavelet transform
Related keywords: waveletswavelets, three-dimensionalwavelet transforms
C09FCF   24  nagf_wav_3d_multi_fwd
Three-dimensional multi-level discrete wavelet transform
Related keywords: multi-level discrete transformwaveletswavelets, three-dimensionalwavelet transforms
C09FDF   24  nagf_wav_3d_mxolap_multi_inv
Three-dimensional inverse multi-level discrete wavelet transform
Related keywords: multi-level discrete transformwaveletswavelets, three-dimensionalwavelet transforms
discretised system C05QSF   23  nagf_roots_sparsys_func_easy
Solution of a sparse system of nonlinear equations using function values only (easy-to-use)
Related keywords: root-findingroots of transcendental equationssparse nonlinear systemzeros of transcendental functions
D02NJF   12  nagf_ode_ivp_stiff_imp_sparjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulaimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemJacobianODEODE, ordinary differential equationsstiff differential equations
F11MEF   21  nagf_sparse_direct_real_gen_lu
L U factorization of real sparse matrix
Related keywords: big datadata analyticslarge scale linear systemsLU decompositionreal, sparse matrixsparse linear system
F11MFF   21  nagf_sparse_direct_real_gen_solve
Solution of real sparse simultaneous linear equations (coefficient matrix already factorized)
Related keywords: big datadata analyticslarge scale linear systemslinear equationsreal, sparse matrixsparse linear system
discretization, PDE D03EEF   13  nagf_pde_2d_ellip_discret
Discretize a second-order elliptic PDE on a rectangle
Related keywords: elliptic partial differential equationsPDE, partial differential equations
discriminant analysis G03DAF   15  nagf_mv_discrim
Computes test statistic for equality of within-group covariance matrices and matrices for discriminant analysis
Related keywords: multivariate methodstest statistic
G03DBF   15  nagf_mv_discrim_mahal
Computes Mahalanobis squared distances for group or pooled variance-covariance matrices (for use after G03DAF)
Related keywords: Mahalanobis distancesmultivariate methods
G03DCF   15  nagf_mv_discrim_group
Allocates observations to groups according to selected rules (for use after G03DAF)
Related keywords: multivariate methods
dispersion G08BAF   nagf_nonpar_test_mooddavid
Mood's and David's tests on two samples of unequal size
Related keywords: David's testMood's test for dispersion differencesnonparametric statistics
distance matrix G03EAF   16  nagf_mv_distance_mat
Computes distance matrix
Related keywords: big datadata analyticsmultivariate methods
distribution function G05TDF   22  nagf_rand_int_general
Generates a vector of pseudorandom integers from a general discrete distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticsfinancerandom integersrandom number generators
divide-and-conquer method F08FCF   19  nagf_lapackeig_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
Related keywords: DSYEVDeigenproblemeigenvalueseigenvectorsfinanceLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08FQF   19  nagf_lapackeig_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvalueseigenvectorsfinanceLAPACKLAPACKleast squaresZHEEVD
F08GCF   19  nagf_lapackeig_dspevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: DSPEVDeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresPal–Walker–Kahan ( QL or QR ) algorithmreal, indefinite, symmetric matrix
F08GQF   19  nagf_lapackeig_zhpevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresPal–Walker–Kahan ( QL or QR ) algorithmZHPEVD
F08HCF   19  nagf_lapackeig_dsbevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: DSBEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithmreal, band, symmetric matrix
F08HQF   19  nagf_lapackeig_zhbevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
Related keywords: complex, band, Hermitian matrixeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithmZHBEVD
F08JCF   19  nagf_lapackeig_dstevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
Related keywords: DSTEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithmreal, symmetric, tridiagonal matrix
F08JHF   22  nagf_lapackeig_dstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
Related keywords: DSTEDCeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JVF   22  nagf_lapackeig_zstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares QL algorithm QR algorithmreal, symmetric, tridiagonal matrixZSTEDC
F08KCF   21  nagf_lapackeig_dgelsd
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
Related keywords: DGELSDeigenproblemfinanceLAPACKLAPACKleast squareslinear least squaresminimal least squaresreal, m by n matrixSVD, singular value decomposition
F08KDF   21  nagf_lapackeig_dgesdd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
Related keywords: DGESDDeigenproblemfinanceLAPACKLAPACKleast squaresreal, nonsymmetric matrixSVD, singular value decomposition
F08KQF   21  nagf_lapackeig_zgelsd
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squareslinear least squaresminimal least squaresSVD, singular value decompositionZGELSD
F08KRF   21  nagf_lapackeig_zgesdd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
Related keywords: complex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresSVD, singular value decompositionZGESDD
F08MDF   22  nagf_lapackeig_dbdsdc
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
Related keywords: DBDSDCeigenproblemLAPACKLAPACKleast squaresmatrix, band QR algorithmreal, bidiagonal matrixSVD, singular value decomposition
F08SCF   21  nagf_lapackeig_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: DSYGVDeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08SQF   21  nagf_lapackeig_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHEGVD
F08TCF   21  nagf_lapackeig_dspgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: DSPGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TQF   21  nagf_lapackeig_zhpgvd
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHPGVD
F08UCF   21  nagf_lapackeig_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: DSBGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UQF   21  nagf_lapackeig_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBGVD
division, complex A02ACF   nagf_complex_divide
Quotient of two complex numbers
Related keywords: complex arithmetic
dlansf F06WAF   23  nagf_blas_dlansf
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format
Related keywords: 1-normBLASBLASblas, real matricesFrobenius norminfinity-normlinear algebra support routineslinear algebra support routines;real, symmetric matrix
dn, Jacobian elliptic function S21CAF   15  nagf_specfun_jacellip_real
Jacobian elliptic functions sn, cn and dn of real argument
Related keywords: approximations of special functionscn, Jacobian elliptic functionelliptic functionsfinanceJacobian elliptic functionssn, Jacobian elliptic functions
S21CBF   20  nagf_specfun_jacellip_complex
Jacobian elliptic functions sn, cn and dn of complex argument
Related keywords: approximations of special functionscn, Jacobian elliptic functionelliptic functionsfinanceJacobian elliptic functionssn, Jacobian elliptic functions
dnrm2 F06EJF   12  nagf_blas_dnrm2
Compute Euclidean norm of real vector
Related keywords: BLASblas, real matriceselementary arithmeticEuclidean normfinancelinear algebra support routines
DOPGTR F08GFF   16  nagf_lapackeig_dopgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generationorthogonal transformations
DOPMTR F08GGF   16  nagf_lapackeig_dopmtr
Applies the orthogonal transformation determined by F08GEF
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal transformations
DORCSD F08RAF   25  nagf_lapackeig_dorcsd
Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
Related keywords: complete CS decompositioneigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresreal, orthogonal matrix
DORGBR F08KFF   16  nagf_lapackeig_dorgbr
Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generationorthogonal matrix, generationorthogonal transformations
DORGHR F08NFF   16  nagf_lapackeig_dorghr
Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generationorthogonal matrix, generation
DORGLQ F08AJF   16  nagf_lapackeig_dorglq
Forms all or part of orthogonal Q from L Q factorization determined by F08AHF
Related keywords: eigenproblemLAPACKLAPACKleast squares LQ factorizationorthogonal matrix, generationorthogonal transformations
DORGQL F08CFF   22  nagf_lapackeig_dorgql
Form all or part of orthogonal Q from Q L factorization determined by F08CEF
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generationorthogonal transformations QL factorization
DORGQR F08AFF   16  nagf_lapackeig_dorgqr
Forms all or part of orthogonal Q from Q R factorization determined by F08AEF F08BEF F08BFF
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generationorthogonal transformations QR factorization
DORGRQ F08CJF   22  nagf_lapackeig_dorgrq
Form all or part of orthogonal Q from R Q factorization determined by F08CHF
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generationorthogonal transformationsRQ factorizations
F08CKF   22  nagf_lapackeig_dormrq
Applies the orthogonal transformation determined by F08CHF
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal transformationsRQ factorizations
DORGTR F08FFF   16  nagf_lapackeig_dorgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generationorthogonal transformations
DORMBR F08KGF   16  nagf_lapackeig_dormbr
Applies the orthogonal transformations from reduction to bidiagonal form determined by F08KEF
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal transformations
DORMHR F08NGF   16  nagf_lapackeig_dormhr
Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal transformations
DORMLQ F08AKF   16  nagf_lapackeig_dormlq
Applies the orthogonal transformation determined by F08AHF
Related keywords: eigenproblemLAPACKLAPACKleast squares LQ factorizationorthogonal transformations
DORMQL F08CGF   22  nagf_lapackeig_dormql
Applies the orthogonal transformation determined by F08CEF
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal transformations QL factorization
DORMQR F08AGF   16  nagf_lapackeig_dormqr
Applies an orthogonal transformation determined by F08AEF F08BEF F08BFF
Related keywords: eigenproblemfinanceLAPACKLAPACKleast squaresorthogonal transformations QR factorization
DORMRZ F08BKF   22  nagf_lapackeig_dormrz
Applies the orthogonal transformation determined by F08BHF
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal transformations
DORMTR F08FGF   16  nagf_lapackeig_dormtr
Applies the orthogonal transformation determined by F08FEF
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal transformations
dot product F16EAF   25  nagf_blast_ddot
Dot product of two vectors, allows scaling and accumulation
Related keywords: further linear algebra support routinesinner product
X03AAF   nagf_dot_real_prec
Real inner product added to initial value, basic/additional precision
Related keywords: additional precision accumulationextended precision accumulationinner productinner productsscalar product
X03ABF   nagf_dot_complex_prec
Complex inner product added to initial value, basic/additional precision
Related keywords: additional precision accumulationextended precision accumulationinner productinner productsscalar product
DPBCON F07HGF   15  nagf_lapacklin_dpbcon
Estimate condition number of real symmetric positive definite band matrix, matrix already factorized by F07HDF
Related keywords: condition number, matrixLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
DPBEQU F07HFF   22  nagf_lapacklin_dpbequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite banded matrix and reduce its condition number
Related keywords: equilibrationLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrixscaling
DPBRFS F07HHF   15  nagf_lapacklin_dpbrfs
Refined solution with error bounds of real symmetric positive definite band system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositionforward errorLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
DPBSTF F08UFF   19  nagf_lapackeig_dpbstf
Computes a split Cholesky factorization of real symmetric positive definite band matrix A
Related keywords: Cholesky decompositionDSBGSTeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
DPBSV F07HAF   21  nagf_lapacklin_dpbsv
Computes the solution to a real symmetric positive definite banded system of linear equations
Related keywords: Cholesky decompositionLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
DPBSVX F07HBF   21  nagf_lapacklin_dpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite banded system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
DPBTRF F07HDF   15  nagf_lapacklin_dpbtrf
Cholesky factorization of real symmetric positive definite band matrix
Related keywords: Cholesky decompositionfinanceLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
DPBTRS F07HEF   15  nagf_lapacklin_dpbtrs
Solution of real symmetric positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HDF
Related keywords: Cholesky decompositionfinanceLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
DPETRI F07WJF   23  nagf_lapacklin_dpftri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07WDF, Rectangular Full Packed format
Related keywords: Cholesky decompositioninverse, matrixLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPFTRF F07WDF   23  nagf_lapacklin_dpftrf
Cholesky factorization of real symmetric positive definite matrix, Rectangular Full Packed format
Related keywords: Cholesky decompositionLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPFTRS F07WEF   23  nagf_lapacklin_dpftrs
Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by F07WDF, Rectangular Full Packed format
Related keywords: Cholesky decompositionLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPOCON F07FGF   15  nagf_lapacklin_dpocon
Estimate condition number of real symmetric positive definite matrix, matrix already factorized by F07FDF
Related keywords: condition number, matrixLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPOEQU F07FFF   22  nagf_lapacklin_dpoequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number
Related keywords: equilibrationLAPACKlinear equationsreal, positive-definite, symmetric matrixscaling
DPORFS F07FHF   15  nagf_lapacklin_dporfs
Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositionforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPOSV F07FAF   21  nagf_lapacklin_dposv
Computes the solution to a real symmetric positive definite system of linear equations
Related keywords: Cholesky decompositionfinanceLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPOSVX F07FBF   21  nagf_lapacklin_dposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixerror bound, matrixfinanceforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPOTRF F07FDF   15  nagf_lapacklin_dpotrf
Cholesky factorization of real symmetric positive definite matrix
Related keywords: Cholesky decompositionfinanceLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPOTRI F07FJF   15  nagf_lapacklin_dpotri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07FDF
Related keywords: Cholesky decompositionfinanceinverse, matrixLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPOTRS F07FEF   15  nagf_lapacklin_dpotrs
Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FDF
Related keywords: Cholesky decompositionfinanceLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPPCON F07GGF   15  nagf_lapacklin_dppcon
Estimate condition number of real symmetric positive definite matrix, matrix already factorized by F07GDF, packed storage
Related keywords: Cholesky decompositioncondition number, matrixLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPPEQU F07GFF   22  nagf_lapacklin_dppequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number, packed storage
Related keywords: equilibrationLAPACKlinear equationsreal, positive-definite, symmetric matrixscaling
DPPRFS F07GHF   15  nagf_lapacklin_dpprfs
Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorCholesky decompositionforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPPSV F07GAF   21  nagf_lapacklin_dppsv
Computes the solution to a real symmetric positive definite system of linear equations, packed storage
Related keywords: Cholesky decompositionLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPPSVX F07GBF   21  nagf_lapacklin_dppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations, packed storage
Related keywords: backward errorCholesky decompositioncondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPPTRF F07GDF   15  nagf_lapacklin_dpptrf
Cholesky factorization of real symmetric positive definite matrix, packed storage
Related keywords: Cholesky decompositionLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPPTRI F07GJF   15  nagf_lapacklin_dpptri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07GDF, packed storage
Related keywords: Cholesky decompositioninverse, matrixLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPPTRS F07GEF   15  nagf_lapacklin_dpptrs
Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GDF, packed storage
Related keywords: Cholesky decompositionLAPACKlinear equationsreal, positive-definite, symmetric matrix
DPSTRF F07KDF   23  nagf_lapacklin_dpstrf
Cholesky factorization, with complete pivoting, of a real, symmetric, positive semidefinite matrix
Related keywords: Cholesky decompositionLAPACKlinear equationsreal, positive-semidefinite, symmetric matrix
DPTCON F07JGF   22  nagf_lapacklin_dptcon
Computes the reciprocal of the condition number of a real symmetric positive definite tridiagonal system using the LDL T factorization computed by F07JDF
Related keywords: condition number, matrixLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
DPTEQR F08JGF   16  nagf_lapackeig_dpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
DPTRFS F07JHF   22  nagf_lapacklin_dptrfs
Refined solution with error bounds of real symmetric positive definite tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositionforward errorLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
DPTSV F07JAF   21  nagf_lapacklin_dptsv
Computes the solution to a real symmetric positive definite tridiagonal system of linear equations
Related keywords: Cholesky decompositionLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
DPTSVX F07JBF   21  nagf_lapacklin_dptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
DPTTRF F07JDF   22  nagf_lapacklin_dpttrf
Computes the LDL T factorization of a real symmetric positive definite tridiagonal matrix
Related keywords: Cholesky decompositionLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
DPTTRS F07JEF   22  nagf_lapacklin_dpttrs
Solves a real symmetric positive definite tridiagonal system using the LDL T factorization computed by F07JDF
Related keywords: Cholesky decompositionLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
dqds algorithm F08FDF   21  nagf_lapackeig_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
Related keywords: DSYEVReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, indefinite, symmetric matrixrelatively robust representations
F08JDF   21  nagf_lapackeig_dstevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
Related keywords: DSTEVReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrixrelatively robust representations
F08JLF   22  nagf_lapackeig_dstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
Related keywords: DSTEGReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrixrelatively robust representations
F08JYF   22  nagf_lapackeig_zstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrixrelatively robust representationsZSTEGR
drot F06EPF   12  nagf_blas_drot
Apply real plane rotation
Related keywords: BLASblas, real matriceslinear algebra support routinesrotation, elementary
drotg F06AAF   12  nagf_blas_drotg
Generate real plane rotation
Related keywords: BLASblas, real matriceslinear algebra support routinesrotation, elementary
droti F06EXF   14  nagf_blas_droti
Apply plane rotation to a real sparse and a full vector
Related keywords: BLASblas, real matriceslinear algebra support routinesrotation, elementary
DSBEV F08HAF   21  nagf_lapackeig_dsbev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
Related keywords: eigenproblemLAPACKLAPACKleast squaresmatrix, band QR algorithmreal, band, symmetric matrix
DSBEVX F08HBF   21  nagf_lapackeig_dsbevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, band, symmetric matrix
F08HCF   19  nagf_lapackeig_dsbevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: divide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithmreal, band, symmetric matrix
DSBGST F08UEF   19  nagf_lapackeig_dsbgst
Performs a reduction of real symmetric-definite banded generalized eigenproblem A x = λ B x to standard form C y = λ y , such that C has the same bandwidth as A
Related keywords: eigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UFF   19  nagf_lapackeig_dpbstf
Computes a split Cholesky factorization of real symmetric positive definite band matrix A
Related keywords: Cholesky decompositionDPBSTFeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
DSBGV F08UAF   21  nagf_lapackeig_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
DSBGVX F08UBF   21  nagf_lapackeig_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UCF   21  nagf_lapackeig_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
dsbmv F06PDF   12  nagf_blas_dsbmv
Matrix-vector product, real symmetric band matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesmatrix, bandmultiply, matrixreal, band, symmetric matrix
DSBTRD F08HEF   16  nagf_lapackeig_dsbtrd
Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
Related keywords: eigenproblemLAPACKLAPACKleast squaresmatrix, bandorthogonal transformationsreal, band, symmetric matrix
dscal F06EDF   12  nagf_blas_dscal
Multiply real vector by scalar
Related keywords: BLASblas, real matriceselementary arithmeticlinear algebra support routines
dsfrk F06WCF   23  nagf_blas_dsfrk
Rank- k update of a real symmetric matrix, Rectangular Full Packed format
Related keywords: BLASblas, real matriceslinear algebra support routinesrank k matrix updatesreal, indefinite, symmetric matrix
DSGESV F07ACF   22  nagf_lapacklin_dsgesv
Computes the solution to a real system of linear equations using mixed precision arithmetic
Related keywords: LAPACKlinear equationsmixed-precisionreal, nonsymmetric matrix
DSPCON F07PGF   15  nagf_lapacklin_dspcon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage
Related keywords: Bunch–Kaufman factorizationcondition number, matrixdiagonal pivoting methodLAPACKlinear equationsreal, indefinite, symmetric matrix
DSPEV F08GAF   21  nagf_lapackeig_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresorthogonal transformations QR algorithmreal, indefinite, symmetric matrix
DSPEVD F08GCF   19  nagf_lapackeig_dspevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: divide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresPal–Walker–Kahan ( QL or QR ) algorithmreal, indefinite, symmetric matrix
DSPEVX F08GBF   21  nagf_lapackeig_dspevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresorthogonal transformationsreal, indefinite, symmetric matrix
DSPGV F08TAF   21  nagf_lapackeig_dspgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
DSPGVX F08TBF   21  nagf_lapackeig_dspgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TCF   21  nagf_lapackeig_dspgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TEF   16  nagf_lapackeig_dspgst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , packed storage, B factorized by F07GDF
Related keywords: eigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
dspmv F06PEF   12  nagf_blas_dspmv
Matrix-vector product, real symmetric packed matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesmultiply, matrixreal, indefinite, symmetric matrix
DSPOSV F07FCF   23  nagf_lapacklin_dsposv
Computes the solution to a real symmetric positive definite system of linear equations using mixed precision arithmetic
Related keywords: Cholesky decompositionLAPACKlinear equationsmixed-precisionreal, positive-definite, symmetric matrix
dspr F06PQF   12  nagf_blas_dspr
Rank-1 update, real symmetric packed matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesrank k matrix updatesreal, indefinite, symmetric matrix
dspr2 F06PSF   12  nagf_blas_dspr2
Rank-2 update, real symmetric packed matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesrank k matrix updatesreal, indefinite, symmetric matrix
DSPRFS F07PHF   15  nagf_lapacklin_dsprfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorBunch–Kaufman factorizationdiagonal pivoting methodforward errorLAPACKlinear equationsreal, indefinite, symmetric matrix
DSPSV F07PAF   21  nagf_lapacklin_dspsv
Computes the solution to a real symmetric system of linear equations, packed storage
Related keywords: diagonal pivoting methodLAPACK LDL T decompositionlinear equationsreal, indefinite, symmetric matrix UDU T decomposition
DSPSVX F07PBF   21  nagf_lapacklin_dspsvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage. Error bounds and a condition estimate are also computed
Related keywords: backward errorcondition number, matrixdiagonal pivoting methoderror bound, matrixforward errorLAPACK LDL H decompositionlinear equationsreal, indefinite, symmetric matrix UDU H decomposition
DSPTRD F08GEF   16  nagf_lapackeig_dsptrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal transformationsreal, indefinite, symmetric matrix
DSPTRF F07PDF   15  nagf_lapacklin_dsptrf
Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodLAPACKlinear equationsreal, indefinite, symmetric matrix
DSPTRI F07PJF   15  nagf_lapacklin_dsptri
Inverse of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodinverse, matrixLAPACKlinear equationsreal, indefinite, symmetric matrix
DSPTRS F07PEF   15  nagf_lapacklin_dsptrs
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PDF, packed storage
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodLAPACKlinear equationsreal, indefinite, symmetric matrix
DSTEBZ F08JJF   16  nagf_lapackeig_dstebz
Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection
Related keywords: bisection methodeigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
DSTEDC F08JHF   22  nagf_lapackeig_dstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
DSTEGR F08JLF   22  nagf_lapackeig_dstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
Related keywords: dqds algorithmeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrixrelatively robust representations
DSTEIN F08JKF   16  nagf_lapackeig_dstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
Related keywords: eigenproblemeigenvectorsinverse iterationLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
DSTEQR F08JEF   16  nagf_lapackeig_dsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit Q L or Q R algorithm
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
DSTERF F08JFF   16  nagf_lapackeig_dsterf
Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the Q L or Q R algorithm
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
DSTEV F08JAF   21  nagf_lapackeig_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
DSTEVR F08JDF   21  nagf_lapackeig_dstevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
Related keywords: dqds algorithmeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrixrelatively robust representations
DSTEVX F08JBF   21  nagf_lapackeig_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: bisection methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QR algorithmreal, symmetric, tridiagonal matrix
F08JCF   19  nagf_lapackeig_dstevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithmreal, symmetric, tridiagonal matrix
dswap F06EGF   12  nagf_blas_dswap
Swap two real vectors
Related keywords: BLASblas, real matriceselementary arithmeticlinear algebra support routines
DSYCON F07MGF   15  nagf_lapacklin_dsycon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MDF
Related keywords: Bunch–Kaufman factorizationcondition number, matrixdiagonal pivoting methodLAPACKlinear equationsreal, indefinite, symmetric matrix
DSYEV F08FAF   21  nagf_lapackeig_dsyev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Related keywords: eigenproblemeigenvalueseigenvectorsfinanceLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
DSYEVD F08FCF   19  nagf_lapackeig_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenvalueseigenvectorsfinanceLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
DSYEVR F08FDF   21  nagf_lapackeig_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
Related keywords: dqds algorithmeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, indefinite, symmetric matrixrelatively robust representations
DSYEVX F08FBF   21  nagf_lapackeig_dsyevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Related keywords: eigenproblemeigenvalueseigenvectorsfinanceLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
DSYGST F08SEF   16  nagf_lapackeig_dsygst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , B factorized by F07FDF
Related keywords: eigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
DSYGV F08SAF   21  nagf_lapackeig_dsygv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
DSYGVD F08SCF   21  nagf_lapackeig_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
DSYGVX F08SBF   21  nagf_lapackeig_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Related keywords: eigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
dsymm F06YCF   14  nagf_blas_dsymm
Matrix-matrix product, one real symmetric matrix, one real rectangular matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesmultiply, matrixreal, indefinite, symmetric matrixreal, m by n matrix
F06YFF   14  nagf_blas_dtrmm
Matrix-matrix product, one real triangular matrix, one real rectangular matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesmultiply, matrixreal, m by n matrixreal, triangular matrix
dsymv F06PCF   12  nagf_blas_dsymv
Matrix-vector product, real symmetric matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesmultiply, matrixreal, indefinite, symmetric matrix
dsyr F06PPF   12  nagf_blas_dsyr
Rank-1 update, real symmetric matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesrank k matrix updatesreal, indefinite, symmetric matrix
dsyr2 F06PRF   12  nagf_blas_dsyr2
Rank-2 update, real symmetric matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesrank k matrix updatesreal, indefinite, symmetric matrix
dsyr2k F06YRF   14  nagf_blas_dsyr2k
Rank- 2 k update of a real symmetric matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesrank k matrix updatesreal, indefinite, symmetric matrix
DSYRFS F07MHF   15  nagf_lapacklin_dsyrfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides
Related keywords: backward errorBunch–Kaufman factorizationdiagonal pivoting methodforward errorLAPACKlinear equationsreal, indefinite, symmetric matrix
dsyrk F06YPF   14  nagf_blas_dsyrk
Rank- k update of a real symmetric matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesreal, indefinite, symmetric matrix
DSYSV F07MAF   21  nagf_lapacklin_dsysv
Computes the solution to a real symmetric system of linear equations
Related keywords: diagonal pivoting methodLAPACKLDLT decompositionlinear equationsreal, indefinite, symmetric matrix UDU T decompositiuon
DSYSVX F07MBF   21  nagf_lapacklin_dsysvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations
Related keywords: backward errordiagonal pivoting methodforward errorLAPACKLDLT decompositionlinear equationsreal, indefinite, symmetric matrix UDU T decompositiuon
DSYTRD F08FEF   16  nagf_lapackeig_dsytrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal transformationsreal, indefinite, symmetric matrix
DSYTRF F07MDF   15  nagf_lapacklin_dsytrf
Bunch–Kaufman factorization of real symmetric indefinite matrix
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodLAPACKlinear equationsreal, indefinite, symmetric matrix
DSYTRI F07MJF   15  nagf_lapacklin_dsytri
Inverse of real symmetric indefinite matrix, matrix already factorized by F07MDF
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodinverse, matrixLAPACKlinear equationsreal, indefinite, symmetric matrix
DSYTRS F07MEF   15  nagf_lapacklin_dsytrs
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MDF
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodLAPACKlinear equationsreal, indefinite, symmetric matrix
DTBCON F07VGF   15  nagf_lapacklin_dtbcon
Estimate condition number of real band triangular matrix
Related keywords: condition number, matrixLAPACKlinear equationsmatrix, bandreal, band, triangular matrix
dtbmv F06PGF   12  nagf_blas_dtbmv
Matrix-vector product, real triangular band matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesmatrix, bandmultiply, matrixreal, band, triangular matrix
DTBRFS F07VHF   15  nagf_lapacklin_dtbrfs
Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandreal, band, triangular matrix
dtbsv F06PKF   12  nagf_blas_dtbsv
System of equations, real triangular band matrix
Related keywords: BLASblas, real matriceslinear algebra support routineslinear equationsmatrix, bandreal, band, triangular matrix
DTBTRS F07VEF   15  nagf_lapacklin_dtbtrs
Solution of real band triangular system of linear equations, multiple right-hand sides
Related keywords: LAPACKlinear equationsmatrix, bandreal, band, triangular matrix
dtfsm F06WBF   23  nagf_blas_dtfsm
Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix, Rectangular Full Packed format
Related keywords: BLASBLASblas, real matriceslinear algebra support routineslinear algebra support routines;linear equationsreal, triangular matrix
DTFTRI F07WKF   23  nagf_lapacklin_dtftri
Inverse of real triangular matrix, Rectangular Full Packed format
Related keywords: inverse, matrixLAPACKlinear equationsreal, triangular matrix
DTFTTP F01VLF   23  nagf_matop_dtfttp
Copies a real triangular matrix from Rectangular Full Packed format to packed format
Related keywords: financeinversionLAPACKmatrix operationsreal, triangular matrix
DTFTTR F01VGF   23  nagf_matop_dtfttr
Copies a real triangular matrix from Rectangular Full Packed format to full format
Related keywords: financeinversionLAPACKmatrix operationsreal, triangular matrix
DTGEVC F08YKF   20  nagf_lapackeig_dtgevc
Computes right and left generalized eigenvectors of the matrix pair A , B which is assumed to be in generalized upper Schur form
Related keywords: eigenproblemeigenvectorsgeneralized Schur formLAPACKLAPACKleast squares
DTGEXC F08YFF   22  nagf_lapackeig_dtgexc
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
Related keywords: eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresorthogonal transformations
DTGSEN F08YGF   22  nagf_lapackeig_dtgsen
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Related keywords: condition number, matrixeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresorthogonal transformationsreal, nonsymmetric matrix
DTGSJA F08YEF   22  nagf_lapackeig_dtgsja
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
Related keywords: eigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresreal, trapezoidal matrixreal, triangular matrixSVD, generalized
DTGSNA F08YLF   22  nagf_lapackeig_dtgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
Related keywords: condition number, matrixeigenproblemgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrix
DTGSYL F08YHF   22  nagf_lapackeig_dtgsyl
Solves the real-valued, generalized, quasi-trangular, Sylvester equation
Related keywords: eigenproblemLAPACKLAPACKleast squaresreal, quasi-triangular matrixSylvester equation
DTPCON F07UGF   15  nagf_lapacklin_dtpcon
Estimate condition number of real triangular matrix, packed storage
Related keywords: condition number, matrixLAPACKlinear equationsreal, triangular matrix
DTPMQRT F08BCF   25  nagf_lapackeig_dtpmqrt
Applies the orthogonal transformation determined by F08BBF
Related keywords: eigenproblemexplicit blockingLAPACKleast squaresorthogonal transformationsQR factorizationrecursive QR
dtpmv F06PHF   12  nagf_blas_dtpmv
Matrix-vector product, real triangular packed matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesmultiply, matrixreal, triangular matrix
DTPQRT F08BBF   25  nagf_lapackeig_dtpqrt
Q R factorization of real general triangular-pentagonal matrix
Related keywords: eigenproblemexplicit blockingLAPACKleast squaresQR factorizationreal, triangular-pentagonal matrixrecursive QR
DTPRFS F07UHF   15  nagf_lapacklin_dtprfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorerror bound, matrixforward errorLAPACKlinear equationsreal, triangular matrix
dtpsv F06PLF   12  nagf_blas_dtpsv
System of equations, real triangular packed matrix
Related keywords: BLASblas, real matriceslinear algebra support routineslinear equationsreal, triangular matrix
DTPTRI F07UJF   15  nagf_lapacklin_dtptri
Inverse of real triangular matrix, packed storage
Related keywords: inverse, matrixLAPACKlinear equationsreal, triangular matrix
DTPTRS F07UEF   15  nagf_lapacklin_dtptrs
Solution of real triangular system of linear equations, multiple right-hand sides, packed storage
Related keywords: LAPACKlinear equationsreal, triangular matrix
DTPTTF F01VJF   23  nagf_matop_dtpttf
Copies a real triangular matrix from packed format to Rectangular Full Packed format
Related keywords: financeinversionLAPACKmatrix operationsreal, triangular matrix
DTPTTR F01VCF   23  nagf_matop_dtpttr
Copies a real triangular matrix from packed format to full format
Related keywords: financeinversionLAPACKmatrix operationsreal, triangular matrix
DTRCON F07TGF   15  nagf_lapacklin_dtrcon
Estimate condition number of real triangular matrix
Related keywords: condition number, matrixLAPACKlinear equationsreal, triangular matrix
DTREVC F08QKF   16  nagf_lapackeig_dtrevc
Computes left and right eigenvectors of real upper quasi-triangular matrix
Related keywords: eigenproblemeigenvectorsLAPACKLAPACKleast squaresreal, quasi-triangular matrix
DTREXC F08QFF   16  nagf_lapackeig_dtrexc
Reorders a Schur factorization of real matrix using orthogonal similarity transformation
Related keywords: eigenproblemLAPACKLAPACKleast squaresorthogonal transformationsreal, nonsymmetric matrixSchur form
F08QGF   16  nagf_lapackeig_dtrsen
Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
Related keywords: condition number, matrixeigenproblemLAPACKLAPACKleast squaresorthogonal transformationsSchur form
dtrmv F06PFF   12  nagf_blas_dtrmv
Matrix-vector product, real triangular matrix
Related keywords: BLASblas, real matriceslinear algebra support routinesmultiply, matrixreal, triangular matrix
DTRRFS F07THF   15  nagf_lapacklin_dtrrfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorerror bound, matrixfinanceforward errorLAPACKlinear equationsreal, triangular matrix
DTRSNA F08QLF   16  nagf_lapackeig_dtrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
Related keywords: condition number, matrixeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, quasi-triangular matrix
F08QYF   16  nagf_lapackeig_ztrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
Related keywords: complex, triangular matrixcondition number, matrixeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares
dtrsv F06PJF   12  nagf_blas_dtrsv
System of equations, real triangular matrix
Related keywords: BLASblas, real matricesfinancelinear algebra support routineslinear equationsreal, triangular matrix
DTRSYL F08QHF   16  nagf_lapackeig_dtrsyl
Solves the real Sylvester matrix equation A X + X B = C , A and B are upper quasi-triangular or transposes
Related keywords: eigenproblemLAPACKLAPACKleast squaresreal, quasi-triangular matrixSylvester equation
DTRTRI F07TJF   15  nagf_lapacklin_dtrtri
Inverse of real triangular matrix
Related keywords: financeinverse, matrixLAPACKlinear equationsreal, triangular matrix
DTRTRS F07TEF   15  nagf_lapacklin_dtrtrs
Solution of real triangular system of linear equations, multiple right-hand sides
Related keywords: financeLAPACKlinear equationsreal, triangular matrix
DTRTTP F01VAF   23  nagf_matop_dtrttp
Copies a real triangular matrix from full format to packed format
Related keywords: financeinversionLAPACKmatrix operationsreal, triangular matrix
F01VEF   23  nagf_matop_dtrttf
Copies a real triangular matrix from full format to Rectangular Full Packed format
Related keywords: financeinversionLAPACKmatrix operationsreal, triangular matrix
DTZRZF F08BHF   22  nagf_lapackeig_dtzrzf
Reduces a real upper trapezoidal matrix to upper triangular form
Related keywords: eigenproblemLAPACKLAPACKleast squaresmatrix, upper trapezoidalmatrix, upper triangularorthogonal transformationsreal, trapezoidal matrix
Durbin–Watson statistic G01EPF   15  nagf_stat_prob_durbin_watson
Computes bounds for the significance of a Durbin–Watson statistic
Related keywords: CDF, cumulative distribution functionfinancesignificanceSimple Calculations on Statistical Data
G02FCF   15  nagf_correg_linregm_stat_durbwat
Computes Durbin–Watson test statistic
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysissignificance
dzasum F06JKF   12  nagf_blas_dzasum
Sum absolute values of complex vector elements
Related keywords: BLASblas, complex matriceselementary arithmeticlinear algebra support routines
dznrm2 F06JJF   12  nagf_blas_dznrm2
Compute Euclidean norm of complex vector
Related keywords: BLASblas, complex matricesEuclidean normfinancelinear algebra support routines
EGARCH G05PGF   22  nagf_rand_times_garch_exp
Generates a realization of a time series from an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsfinancerandom number generatorstime series
G13FGF   20  nagf_tsa_uni_garch_exp_estim
Univariate time series, parameter estimation for an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsexponential GARCHfinanceGARCHtime seriestime series analysisunivariate time series
G13FHF   20  nagf_tsa_uni_garch_exp_forecast
Univariate time series, forecast function for an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsexponential GARCHfinanceforecastingGARCHtime seriestime series analysisunivariate time series
eigenproblem D02KAF   nagf_ode_sl2_reg_finite
Second-order Sturm–Liouville problem, regular system, finite range, eigenvalue only
Related keywords: boundary value problemBVPODE, ordinary differential equationsSturm–Liouville equations
D02KDF   nagf_ode_sl2_breaks_vals
Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points
Related keywords: boundary value problemBVPgeneralODE, ordinary differential equationsSturm–Liouville equations
D02KEF   nagf_ode_sl2_breaks_funs
Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points
Related keywords: boundary value problemBVPODE, ordinary differential equationsSturm–Liouville equations
F02FKF   25  nagf_eigen_real_symm_sparse_arnoldi
Selected eigenvalues and eigenvectors of a real symmetric sparse matrix
Related keywords: big datadata analyticseigenvalueseigenvalueseigenvectorseigenvectorslarge scale eigenproblemsmatrix, sparsereal, sparse, symmetric matrixsparse eigenproblem
F08 Chapter Introduction     Least Squares and Eigenvalue Problems (LAPACK)
Related keywords: LAPACKleast squares
F12AAF   21  nagf_sparseig_real_init
Initialization routine for (F12ABF) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse (standard or generalized) eigenproblem
Related keywords: big datadata analyticseigenproblem, initializationlarge scale eigenproblemsreal, sparse matrix
F12ABF   21  nagf_sparseig_real_iter
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, reverse communication
Related keywords: big datadata analyticseigenvalueseigenvectorslarge scale eigenproblemsreal, sparse matrixsparse eigenproblem
F12ACF   21  nagf_sparseig_real_proc
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, postprocessing for F12ABF
Related keywords: big datadata analyticseigenvalueseigenvectorslarge scale eigenproblemsreal, sparse matrixsparse eigenproblem
F12AEF   21  nagf_sparseig_real_monit
Provides monitoring information for F12ABF
Related keywords: big datadata analyticslarge scale eigenproblemsmonitoring informationreal, sparse matrixsparse eigenproblems, monitoring
F12ASF   21  nagf_sparseig_complex_monit
Provides monitoring information for F12APF
Related keywords: big datacomplex, sparse matrixdata analyticslarge scale eigenproblemsmonitoring informationsparse eigenproblems, monitoring
eigenproblem, banded F12AGF   21  nagf_sparseig_real_band_solve
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded eigenproblem, driver
Related keywords: big datadata analyticseigenvalueseigenvectorslarge scale eigenproblemsreal, band matrix
F12AUF   24  nagf_sparseig_complex_band_solve
Selected eigenvalues and, optionally, eigenvectors of complex non-Hermitian banded eigenproblem, driver
Related keywords: big datacomplex, band matrixdata analyticseigenvalueseigenvectorslarge scale eigenproblems
F12FGF   21  nagf_sparseig_real_symm_band_solve
Selected eigenvalues and, optionally, eigenvectors of a real symmetric banded eigenproblem, driver
Related keywords: big datadata analyticseigenvalueseigenvectorslarge scale eigenproblemsreal, band, symmetric matrix
eigenproblem, generalized F01BVF   nagf_matop_real_symm_posdef_geneig
Reduction to standard form, generalized real symmetric-definite banded eigenproblem
Related keywords: generalized eigenprobleminversionmatrix, bandmatrix operationsreal, band, positive-definite, symmetric matrix
F08SAF   21  nagf_lapackeig_dsygv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Related keywords: DSYGVeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08SBF   21  nagf_lapackeig_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Related keywords: DSYGVXeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08SCF   21  nagf_lapackeig_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodDSYGVDeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08SEF   16  nagf_lapackeig_dsygst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , B factorized by F07FDF
Related keywords: DSYGSTeigenproblemgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08SNF   21  nagf_lapackeig_zhegv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHEGV
F08SPF   21  nagf_lapackeig_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHEGVX
F08SQF   21  nagf_lapackeig_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: complex, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHEGVD
F08SSF   16  nagf_lapackeig_zhegst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , B factorized by F07FRF
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemgeneralized eigenproblemLAPACKLAPACKleast squaresZHEGST
F08TAF   21  nagf_lapackeig_dspgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Related keywords: DSPGVeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TBF   21  nagf_lapackeig_dspgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Related keywords: DSPGVXeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TCF   21  nagf_lapackeig_dspgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: divide-and-conquer methodDSPGVXeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TEF   16  nagf_lapackeig_dspgst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , packed storage, B factorized by F07GDF
Related keywords: DSPGVXeigenproblemgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TNF   21  nagf_lapackeig_zhpgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHPGV
F08TPF   21  nagf_lapackeig_zhpgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHPGVX
F08TQF   21  nagf_lapackeig_zhpgvd
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: complex, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHPGVD
F08TSF   16  nagf_lapackeig_zhpgst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , packed storage, B factorized by F07GRF
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemgeneralized eigenproblemLAPACKLAPACKleast squaresZHPGVD
F08UAF   21  nagf_lapackeig_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: DSBGVeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UBF   21  nagf_lapackeig_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: DSBGVXeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UCF   21  nagf_lapackeig_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodDSBGVXeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UEF   19  nagf_lapackeig_dsbgst
Performs a reduction of real symmetric-definite banded generalized eigenproblem A x = λ B x to standard form C y = λ y , such that C has the same bandwidth as A
Related keywords: DSBGSTeigenproblemgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UFF   19  nagf_lapackeig_dpbstf
Computes a split Cholesky factorization of real symmetric positive definite band matrix A
Related keywords: Cholesky decompositionDPBSTFDSBGSTeigenproblemgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UNF   21  nagf_lapackeig_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBGV
F08UPF   21  nagf_lapackeig_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBGVX
F08UQF   21  nagf_lapackeig_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: complex, band, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBGVD
F08USF   19  nagf_lapackeig_zhbgst
Performs a reduction of complex Hermitian-definite banded generalized eigenproblem A x = λ B x to standard form C y = λ y , such that C has the same bandwidth as A
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBGST
F08UTF   19  nagf_lapackeig_zpbstf
Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandSplit Cholesky factorizationZPBSTF
F08WAF   21  nagf_lapackeig_dggev
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: DGGEVeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WBF   21  nagf_lapackeig_dggevx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGGEVXeigenproblemeigenvalueseigenvectorsfinanceforward errorgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WCF   26  nagf_lapackeig_dggev3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: DGGEVeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WEF   20  nagf_lapackeig_dgghrd
Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Related keywords: DGGHRDeigenproblemgeneralized eigenproblemLAPACKLAPACKleast squaresorthogonal transformationsreal, nonsymmetric matrix
F08WFF   26  nagf_lapackeig_dgghd3
Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Related keywords: DGGHD3eigenproblemgeneralized eigenproblemLAPACKLAPACKleast squaresorthogonal transformationsreal, nonsymmetric matrix
F08WHF   20  nagf_lapackeig_dggbal
Balances a pair of real, square, matrices
Related keywords: balancingDGGHRDeigenproblemgeneralized eigenproblemLAPACKLAPACKleast squares
F08WJF   20  nagf_lapackeig_dggbak
Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF
Related keywords: balancingDGGBAKeigenproblemeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
F08WNF   21  nagf_lapackeig_zggev
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZGGEV
F08WPF   21  nagf_lapackeig_zggevx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixcondition number, matrixeigenproblemeigenvalueseigenvectorsfinanceforward errorgeneralized eigenproblemLAPACKLAPACKleast squaresZGGEVX
F08WQF   26  nagf_lapackeig_zggev3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZGGEV3
F08XNF   21  nagf_lapackeig_zgges
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresSchur vectorsZGGES
F08XPF   21  nagf_lapackeig_zggesx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresSchur vectorsZGGES
F08XQF   26  nagf_lapackeig_zgges3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresSchur vectorsZGGES3
F08XSF   20  nagf_lapackeig_zhgeqz
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresQZ algorithmZHGEQZ
eigenproblem, initialization F12AAF   21  nagf_sparseig_real_init
Initialization routine for (F12ABF) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse (standard or generalized) eigenproblem
Related keywords: big datadata analyticseigenproblemlarge scale eigenproblemsreal, sparse matrix
F12AFF   21  nagf_sparseig_real_band_init
Initialization routine for (F12AGF) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded (standard or generalized) eigenproblem
Related keywords: big datadata analyticslarge scale eigenproblemsreal, band matrix
F12ANF   21  nagf_sparseig_complex_init
Initialization routine for (F12APF) computing selected eigenvalues and, optionally, eigenvectors of a complex sparse (standard or generalized) eigenproblem
Related keywords: big datacomplex, sparse matrixdata analyticslarge scale eigenproblems
F12ATF   24  nagf_sparseig_complex_band_init
Initialization routine for F12AUF computing selected eigenvalues and, optionally, eigenvectors of a complex banded (standard or generalized) eigenproblem
Related keywords: big datacomplex, band matrixdata analyticslarge scale eigenproblems
F12FAF   21  nagf_sparseig_real_symm_init
Initialization routine for (F12FBF) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse (standard or generalized) eigenproblem
Related keywords: big datadata analyticslarge scale eigenproblemsreal, sparse, symmetric matrix
F12FFF   21  nagf_sparseig_real_symm_band_init
Initialization routine for (F12FGF) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric banded (standard or generalized) eigenproblem
Related keywords: big datadata analyticslarge scale eigenproblemsreal, band, symmetric matrix
eigenproblem, quadratic F02JCF   25  nagf_eigen_real_gen_quad
Solves the quadratic eigenvalue problem for real matrices
Related keywords: backward errorbalancingbig datacondition numberdata analyticseigenvalueseigenvalues and eigenvectorseigenvectors
F02JQF   25  nagf_eigen_complex_gen_quad
Solves the quadratic eigenvalue problem for complex matrices
Related keywords: backward errorbalancingbig datacondition numberdata analyticseigenvalueseigenvalues and eigenvectorseigenvectors
eigenvalues F02 Chapter Introduction     Eigenvalues and Eigenvectors
Related keywords: big datadata analyticseigenvectors
F02FKF   25  nagf_eigen_real_symm_sparse_arnoldi
Selected eigenvalues and eigenvectors of a real symmetric sparse matrix
Related keywords: big datadata analyticseigenproblemeigenvectorseigenvectorslarge scale eigenproblemsmatrix, sparsereal, sparse, symmetric matrixsparse eigenproblem
F06BPF   12  nagf_blas_deig2
Compute eigenvalue of 2 by 2 real symmetric matrix
Related keywords: BLASelementary arithmeticlinear algebra support routines
F08FAF   21  nagf_lapackeig_dsyev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Related keywords: DSYEVeigenproblemeigenvectorsfinanceLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08FBF   21  nagf_lapackeig_dsyevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Related keywords: DSYEVXeigenproblemeigenvectorsfinanceLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08FCF   19  nagf_lapackeig_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
Related keywords: divide-and-conquer methodDSYEVDeigenproblemeigenvectorsfinanceLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08FDF   21  nagf_lapackeig_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
Related keywords: dqds algorithmDSYEVReigenproblemeigenvectorsLAPACKLAPACKleast squaresreal, indefinite, symmetric matrixrelatively robust representations
F08FNF   21  nagf_lapackeig_zheev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvectorsLAPACKLAPACKleast squaresZHEEV
F08FPF   21  nagf_lapackeig_zheevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvectorsfinanceLAPACKLAPACKleast squaresZHEEVX
F08FQF   19  nagf_lapackeig_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
Related keywords: complex, Hermitian, indefinite matrixdivide-and-conquer methodeigenproblemeigenvectorsfinanceLAPACKLAPACKleast squaresZHEEVD
F08FRF   21  nagf_lapackeig_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvectorsLAPACKLAPACKleast squaresrelatively robust representationsunitary transformationsZHEEVR
F08GAF   21  nagf_lapackeig_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Related keywords: DSPEVeigenproblemeigenvectorsLAPACKLAPACKleast squaresorthogonal transformations QR algorithmreal, indefinite, symmetric matrix
F08GBF   21  nagf_lapackeig_dspevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Related keywords: DSPEVXeigenproblemeigenvectorsLAPACKLAPACKleast squaresorthogonal transformationsreal, indefinite, symmetric matrix
F08GCF   19  nagf_lapackeig_dspevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: divide-and-conquer methodDSPEVDeigenproblemeigenvectorsLAPACKLAPACKleast squaresPal–Walker–Kahan ( QL or QR ) algorithmreal, indefinite, symmetric matrix
F08GNF   21  nagf_lapackeig_zhpev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvectorsLAPACKLAPACKleast squaresZHPEV
F08GPF   21  nagf_lapackeig_zhpevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvectorsLAPACKLAPACKleast squaresZHPEVX
F08GQF   19  nagf_lapackeig_zhpevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: complex, Hermitian, indefinite matrixdivide-and-conquer methodeigenproblemeigenvectorsLAPACKLAPACKleast squaresPal–Walker–Kahan ( QL or QR ) algorithmZHPEVD
F08HBF   21  nagf_lapackeig_dsbevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
Related keywords: DSBEVXeigenproblemeigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, band, symmetric matrix
F08HCF   19  nagf_lapackeig_dsbevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: divide-and-conquer methodDSBEVXeigenproblemeigenvectorsLAPACKLAPACKleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithmreal, band, symmetric matrix
F08HQF   19  nagf_lapackeig_zhbevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
Related keywords: complex, band, Hermitian matrixdivide-and-conquer methodeigenproblemeigenvectorsLAPACKLAPACKleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithmZHBEVD
F08JAF   21  nagf_lapackeig_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: DSTEVeigenproblemeigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JBF   21  nagf_lapackeig_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: bisection methodDSTEVXeigenproblemeigenvectorsLAPACKLAPACKleast squaresmatrix, band QR algorithmreal, symmetric, tridiagonal matrix
F08JCF   19  nagf_lapackeig_dstevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
Related keywords: divide-and-conquer methodDSTEVXeigenproblemeigenvectorsLAPACKLAPACKleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithmreal, symmetric, tridiagonal matrix
F08JDF   21  nagf_lapackeig_dstevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
Related keywords: dqds algorithmDSTEVReigenproblemeigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrixrelatively robust representations
F08JEF   16  nagf_lapackeig_dsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit Q L or Q R algorithm
Related keywords: DSTEQReigenproblemeigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JFF   16  nagf_lapackeig_dsterf
Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the Q L or Q R algorithm
Related keywords: DSTERFeigenproblemeigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JGF   16  nagf_lapackeig_dpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
Related keywords: DPTEQReigenproblemeigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
F08JHF   22  nagf_lapackeig_dstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
Related keywords: divide-and-conquer methodDSTEDCeigenproblemeigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JJF   16  nagf_lapackeig_dstebz
Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection
Related keywords: bisection methodDSTEBZeigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
F08JLF   22  nagf_lapackeig_dstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
Related keywords: dqds algorithmDSTEGReigenproblemeigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrixrelatively robust representations
F08JSF   16  nagf_lapackeig_zsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit Q L or Q R algorithm
Related keywords: eigenproblemeigenvectorsLAPACKLAPACKleast squares QR algorithmreal, symmetric, tridiagonal matrixZSTEQR
F08JUF   16  nagf_lapackeig_zpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
Related keywords: eigenproblemeigenvectorsLAPACKLAPACK LDL H decompositionleast squaresreal, symmetric, tridiagonal matrixZPTEQR
F08JVF   22  nagf_lapackeig_zstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenvectorsLAPACKLAPACKleast squares QL algorithm QR algorithmreal, symmetric, tridiagonal matrixZSTEDC
F08JYF   22  nagf_lapackeig_zstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
Related keywords: dqds algorithmeigenproblemeigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrixrelatively robust representationsZSTEGR
F08NAF   21  nagf_lapackeig_dgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
Related keywords: DGEEVeigenproblemeigenvectorsLAPACKLAPACKleast squaresorthogonal transformations QR algorithmreal, nonsymmetric matrix
F08NBF   21  nagf_lapackeig_dgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGEEVXeigenproblemeigenvectorsfinanceforward errorLAPACKLAPACKleast squaresorthogonal transformations QR algorithmreal, nonsymmetric matrix
F08NNF   21  nagf_lapackeig_zgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
Related keywords: complex, nonsymmetric matrixDGEEVeigenproblemeigenvectorsLAPACKLAPACKleast squares
F08NPF   21  nagf_lapackeig_zgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixcondition number, matrixDGEEVeigenproblemeigenvectorsfinanceforward errorLAPACKLAPACKleast squares
F08PAF   21  nagf_lapackeig_dgees
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
Related keywords: DGEESeigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur formSchur vectors
F08PBF   21  nagf_lapackeig_dgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: condition number, matrixDGEESeigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur formSchur vectors
F08PEF   16  nagf_lapackeig_dhseqr
Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
Related keywords: DHSEQReigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form
F08PNF   21  nagf_lapackeig_zgees
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresSchur formSchur vectorsZGEES
F08PPF   21  nagf_lapackeig_zgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also computes a reciprocal condition number for the average of the selected eigenvalues and for the right invariant subspace corresponding to these eigenvalues
Related keywords: condition number, matrixeigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur formSchur vectorsZGEESX
F08PSF   16  nagf_lapackeig_zhseqr
Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
Related keywords: complex, Hessenberg matrixeigenproblemLAPACKLAPACKleast squaresSchur formZHSEQR
F08QLF   16  nagf_lapackeig_dtrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
Related keywords: condition number, matrixDTRSNAeigenproblemeigenvectorsLAPACKLAPACKleast squaresreal, quasi-triangular matrix
F08QYF   16  nagf_lapackeig_ztrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
Related keywords: complex, triangular matrixcondition number, matrixDTRSNAeigenproblemeigenvectorsLAPACKLAPACKleast squares
F08SAF   21  nagf_lapackeig_dsygv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Related keywords: DSYGVeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08SBF   21  nagf_lapackeig_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Related keywords: DSYGVXeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08SCF   21  nagf_lapackeig_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodDSYGVDeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08SNF   21  nagf_lapackeig_zhegv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHEGV
F08SPF   21  nagf_lapackeig_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHEGVX
F08SQF   21  nagf_lapackeig_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: complex, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHEGVD
F08TAF   21  nagf_lapackeig_dspgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Related keywords: DSPGVeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TBF   21  nagf_lapackeig_dspgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Related keywords: DSPGVXeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TCF   21  nagf_lapackeig_dspgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: divide-and-conquer methodDSPGVXeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TNF   21  nagf_lapackeig_zhpgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHPGV
F08TPF   21  nagf_lapackeig_zhpgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHPGVX
F08TQF   21  nagf_lapackeig_zhpgvd
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: complex, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHPGVD
F08UAF   21  nagf_lapackeig_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: DSBGVeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UBF   21  nagf_lapackeig_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: DSBGVXeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UCF   21  nagf_lapackeig_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodDSBGVXeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UNF   21  nagf_lapackeig_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBGV
F08UPF   21  nagf_lapackeig_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBGVX
F08UQF   21  nagf_lapackeig_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: complex, band, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBGVD
F08WAF   21  nagf_lapackeig_dggev
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: DGGEVeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WBF   21  nagf_lapackeig_dggevx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGGEVXeigenproblemeigenproblem, generalizedeigenvectorsfinanceforward errorgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WCF   26  nagf_lapackeig_dggev3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: DGGEVeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WNF   21  nagf_lapackeig_zggev
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZGGEV
F08WPF   21  nagf_lapackeig_zggevx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixcondition number, matrixeigenproblemeigenproblem, generalizedeigenvectorsfinanceforward errorgeneralized eigenproblemLAPACKLAPACKleast squaresZGGEVX
F08WQF   26  nagf_lapackeig_zggev3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZGGEV3
F08XAF   21  nagf_lapackeig_dgges
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: DGGESeigenproblemgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form, generalizedSchur vectors
F08XBF   21  nagf_lapackeig_dggesx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: condition number, matrixDGGESXeigenproblemgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form, generalizedSchur vectors
F08XCF   26  nagf_lapackeig_dgges3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: DGGES3eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form, generalizedSchur vectors
F08XEF   20  nagf_lapackeig_dhgeqz
Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
Related keywords: DHGEQZeigenproblemgeneralized Schur formLAPACKLAPACKleast squaresreal, Hessenberg matrix
F08XNF   21  nagf_lapackeig_zgges
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresSchur vectorsZGGES
F08XPF   21  nagf_lapackeig_zggesx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemeigenproblem, generalizedgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresSchur vectorsZGGES
F08XQF   26  nagf_lapackeig_zgges3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresSchur vectorsZGGES3
F08XSF   20  nagf_lapackeig_zhgeqz
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenproblem, generalizedgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresQZ algorithmZHGEQZ
F08YGF   22  nagf_lapackeig_dtgsen
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Related keywords: condition number, matrixDTGSENeigenproblemgeneralized Schur formLAPACKLAPACKleast squaresorthogonal transformationsreal, nonsymmetric matrix
F08YUF   22  nagf_lapackeig_ztgsen
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemgeneralized Schur formLAPACKLAPACKleast squaresunitary transformationsZTGEXC
F12ABF   21  nagf_sparseig_real_iter
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, reverse communication
Related keywords: big datadata analyticseigenproblemeigenvectorslarge scale eigenproblemsreal, sparse matrixsparse eigenproblem
F12ACF   21  nagf_sparseig_real_proc
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, postprocessing for F12ABF
Related keywords: big datadata analyticseigenproblemeigenvectorslarge scale eigenproblemsreal, sparse matrixsparse eigenproblem
F12AGF   21  nagf_sparseig_real_band_solve
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded eigenproblem, driver
Related keywords: big datadata analyticseigenproblem, bandedeigenvectorslarge scale eigenproblemsreal, band matrix
F12APF   21  nagf_sparseig_complex_iter
Selected eigenvalues and, optionally, eigenvectors of a complex sparse eigenproblem, reverse communication
Related keywords: big datacomplex, sparse matrixdata analyticseigenvectorslarge scale eigenproblemssparse eigenproblemsparse generalized eigenproblem
F12AUF   24  nagf_sparseig_complex_band_solve
Selected eigenvalues and, optionally, eigenvectors of complex non-Hermitian banded eigenproblem, driver
Related keywords: big datacomplex, band matrixdata analyticseigenproblem, bandedeigenvectorslarge scale eigenproblems
F12FBF   21  nagf_sparseig_real_symm_iter
Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, reverse communication
Related keywords: big datadata analyticseigenvectorslarge scale eigenproblemsreal, sparse, symmetric matrixsparse eigenproblem
F12FGF   21  nagf_sparseig_real_symm_band_solve
Selected eigenvalues and, optionally, eigenvectors of a real symmetric banded eigenproblem, driver
Related keywords: big datadata analyticseigenproblem, bandedeigenvectorslarge scale eigenproblemsreal, band, symmetric matrix
eigenvalues and eigenvectors F01FQF   25  nagf_matop_complex_gen_matrix_pow
General power of a complex matrix
Related keywords: general powerinversionmatrix operationsmatrix operations including inversion
F01KEF   25  nagf_matop_complex_gen_matrix_cond_pow
Condition number for complex matrix power
Related keywords: condition numberinversionmatrix operationsmatrix operations including inversion
F01KFF   25  nagf_matop_complex_gen_matrix_frcht_pow
Fréchet derivative of complex matrix power
Related keywords: Fréchet derivativeinversionmatrix operationsmatrix operations including inversion
F02JCF   25  nagf_eigen_real_gen_quad
Solves the quadratic eigenvalue problem for real matrices
Related keywords: backward errorbalancingbig datacondition numberdata analyticseigenproblem, quadraticeigenvalueseigenvectors
F02JQF   25  nagf_eigen_complex_gen_quad
Solves the quadratic eigenvalue problem for complex matrices
Related keywords: backward errorbalancingbig datacondition numberdata analyticseigenproblem, quadraticeigenvalueseigenvectors
eigenvectors F02 Chapter Introduction     Eigenvalues and Eigenvectors
Related keywords: big datadata analyticseigenvalues
F02FKF   25  nagf_eigen_real_symm_sparse_arnoldi
Selected eigenvalues and eigenvectors of a real symmetric sparse matrix
Related keywords: big datadata analyticseigenproblemeigenvalueseigenvalueslarge scale eigenproblemsmatrix, sparsereal, sparse, symmetric matrixsparse eigenproblem
F08FAF   21  nagf_lapackeig_dsyev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Related keywords: DSYEVeigenproblemeigenvaluesfinanceLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08FBF   21  nagf_lapackeig_dsyevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Related keywords: DSYEVXeigenproblemeigenvaluesfinanceLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08FCF   19  nagf_lapackeig_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
Related keywords: divide-and-conquer methodDSYEVDeigenproblemeigenvaluesfinanceLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08FDF   21  nagf_lapackeig_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
Related keywords: dqds algorithmDSYEVReigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, indefinite, symmetric matrixrelatively robust representations
F08FLF   22  nagf_lapackeig_ddisna
Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix
Related keywords: complex, Hermitian, indefinite matrixcondition number, matrixDDISNAeigenproblemfinanceLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08FNF   21  nagf_lapackeig_zheev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvaluesLAPACKLAPACKleast squaresZHEEV
F08FPF   21  nagf_lapackeig_zheevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvaluesfinanceLAPACKLAPACKleast squaresZHEEVX
F08FQF   19  nagf_lapackeig_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
Related keywords: complex, Hermitian, indefinite matrixdivide-and-conquer methodeigenproblemeigenvaluesfinanceLAPACKLAPACKleast squaresZHEEVD
F08FRF   21  nagf_lapackeig_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvaluesLAPACKLAPACKleast squaresrelatively robust representationsunitary transformationsZHEEVR
F08GAF   21  nagf_lapackeig_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Related keywords: DSPEVeigenproblemeigenvaluesLAPACKLAPACKleast squaresorthogonal transformations QR algorithmreal, indefinite, symmetric matrix
F08GBF   21  nagf_lapackeig_dspevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Related keywords: DSPEVXeigenproblemeigenvaluesLAPACKLAPACKleast squaresorthogonal transformationsreal, indefinite, symmetric matrix
F08GCF   19  nagf_lapackeig_dspevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: divide-and-conquer methodDSPEVDeigenproblemeigenvaluesLAPACKLAPACKleast squaresPal–Walker–Kahan ( QL or QR ) algorithmreal, indefinite, symmetric matrix
F08GNF   21  nagf_lapackeig_zhpev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvaluesLAPACKLAPACKleast squaresZHPEV
F08GPF   21  nagf_lapackeig_zhpevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvaluesLAPACKLAPACKleast squaresZHPEVX
F08GQF   19  nagf_lapackeig_zhpevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: complex, Hermitian, indefinite matrixdivide-and-conquer methodeigenproblemeigenvaluesLAPACKLAPACKleast squaresPal–Walker–Kahan ( QL or QR ) algorithmZHPEVD
F08HBF   21  nagf_lapackeig_dsbevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
Related keywords: DSBEVXeigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, bandreal, band, symmetric matrix
F08HCF   19  nagf_lapackeig_dsbevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: divide-and-conquer methodDSBEVXeigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithmreal, band, symmetric matrix
F08HQF   19  nagf_lapackeig_zhbevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
Related keywords: complex, band, Hermitian matrixdivide-and-conquer methodeigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithmZHBEVD
F08JAF   21  nagf_lapackeig_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: DSTEVeigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JBF   21  nagf_lapackeig_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: bisection methodDSTEVXeigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, band QR algorithmreal, symmetric, tridiagonal matrix
F08JCF   19  nagf_lapackeig_dstevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
Related keywords: divide-and-conquer methodDSTEVXeigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithmreal, symmetric, tridiagonal matrix
F08JDF   21  nagf_lapackeig_dstevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
Related keywords: dqds algorithmDSTEVReigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrixrelatively robust representations
F08JEF   16  nagf_lapackeig_dsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit Q L or Q R algorithm
Related keywords: DSTEQReigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JFF   16  nagf_lapackeig_dsterf
Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the Q L or Q R algorithm
Related keywords: DSTERFeigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JGF   16  nagf_lapackeig_dpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
Related keywords: DPTEQReigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
F08JHF   22  nagf_lapackeig_dstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
Related keywords: divide-and-conquer methodDSTEDCeigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JKF   16  nagf_lapackeig_dstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
Related keywords: DSTEINeigenprobleminverse iterationLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
F08JLF   22  nagf_lapackeig_dstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
Related keywords: dqds algorithmDSTEGReigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrixrelatively robust representations
F08JSF   16  nagf_lapackeig_zsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit Q L or Q R algorithm
Related keywords: eigenproblemeigenvaluesLAPACKLAPACKleast squares QR algorithmreal, symmetric, tridiagonal matrixZSTEQR
F08JUF   16  nagf_lapackeig_zpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
Related keywords: eigenproblemeigenvaluesLAPACKLAPACK LDL H decompositionleast squaresreal, symmetric, tridiagonal matrixZPTEQR
F08JVF   22  nagf_lapackeig_zstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenvaluesLAPACKLAPACKleast squares QL algorithm QR algorithmreal, symmetric, tridiagonal matrixZSTEDC
F08JXF   16  nagf_lapackeig_zstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
Related keywords: eigenprobleminverse iterationLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrixZSTEIN
F08JYF   22  nagf_lapackeig_zstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
Related keywords: dqds algorithmeigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrixrelatively robust representationsZSTEGR
F08NAF   21  nagf_lapackeig_dgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
Related keywords: DGEEVeigenproblemeigenvaluesLAPACKLAPACKleast squaresorthogonal transformations QR algorithmreal, nonsymmetric matrix
F08NBF   21  nagf_lapackeig_dgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGEEVXeigenproblemeigenvaluesfinanceforward errorLAPACKLAPACKleast squaresorthogonal transformations QR algorithmreal, nonsymmetric matrix
F08NJF   16  nagf_lapackeig_dgebak
Transforms eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF
Related keywords: balancingDGEBAKeigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08NNF   21  nagf_lapackeig_zgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
Related keywords: complex, nonsymmetric matrixDGEEVeigenproblemeigenvaluesLAPACKLAPACKleast squares
F08NPF   21  nagf_lapackeig_zgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixcondition number, matrixDGEEVeigenproblemeigenvaluesfinanceforward errorLAPACKLAPACKleast squares
F08PKF   16  nagf_lapackeig_dhsein
Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
Related keywords: DHSEINeigenprobleminverse iterationLAPACKLAPACKleast squaresreal, Hessenberg matrix
F08PXF   16  nagf_lapackeig_zhsein
Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
Related keywords: complex, Hessenberg matrixeigenprobleminverse iterationLAPACKLAPACKleast squaresZHSEIN
F08QKF   16  nagf_lapackeig_dtrevc
Computes left and right eigenvectors of real upper quasi-triangular matrix
Related keywords: DTREVCeigenproblemLAPACKLAPACKleast squaresreal, quasi-triangular matrix
F08QLF   16  nagf_lapackeig_dtrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
Related keywords: condition number, matrixDTRSNAeigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, quasi-triangular matrix
F08QXF   16  nagf_lapackeig_ztrevc
Computes left and right eigenvectors of complex upper triangular matrix
Related keywords: complex, triangular matrixeigenproblemLAPACKLAPACKleast squaresZTREVC
F08QYF   16  nagf_lapackeig_ztrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
Related keywords: complex, triangular matrixcondition number, matrixDTRSNAeigenproblemeigenvaluesLAPACKLAPACKleast squares
F08SAF   21  nagf_lapackeig_dsygv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Related keywords: DSYGVeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08SBF   21  nagf_lapackeig_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Related keywords: DSYGVXeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08SCF   21  nagf_lapackeig_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodDSYGVDeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08SNF   21  nagf_lapackeig_zhegv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresZHEGV
F08SPF   21  nagf_lapackeig_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresZHEGVX
F08SQF   21  nagf_lapackeig_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: complex, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresZHEGVD
F08TAF   21  nagf_lapackeig_dspgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Related keywords: DSPGVeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TBF   21  nagf_lapackeig_dspgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Related keywords: DSPGVXeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TCF   21  nagf_lapackeig_dspgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: divide-and-conquer methodDSPGVXeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TNF   21  nagf_lapackeig_zhpgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresZHPGV
F08TPF   21  nagf_lapackeig_zhpgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresZHPGVX
F08TQF   21  nagf_lapackeig_zhpgvd
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: complex, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresZHPGVD
F08UAF   21  nagf_lapackeig_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: DSBGVeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UBF   21  nagf_lapackeig_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: DSBGVXeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UCF   21  nagf_lapackeig_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodDSBGVXeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UNF   21  nagf_lapackeig_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBGV
F08UPF   21  nagf_lapackeig_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBGVX
F08UQF   21  nagf_lapackeig_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: complex, band, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBGVD
F08WAF   21  nagf_lapackeig_dggev
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: DGGEVeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WBF   21  nagf_lapackeig_dggevx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGGEVXeigenproblemeigenproblem, generalizedeigenvaluesfinanceforward errorgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WCF   26  nagf_lapackeig_dggev3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: DGGEVeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WJF   20  nagf_lapackeig_dggbak
Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF
Related keywords: balancingDGGBAKeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squares
F08WNF   21  nagf_lapackeig_zggev
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresZGGEV
F08WPF   21  nagf_lapackeig_zggevx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixcondition number, matrixeigenproblemeigenproblem, generalizedeigenvaluesfinanceforward errorgeneralized eigenproblemLAPACKLAPACKleast squaresZGGEVX
F08WQF   26  nagf_lapackeig_zggev3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresZGGEV3
F08WWF   20  nagf_lapackeig_zggbak
Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF
Related keywords: balancingcomplex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresZGGBAL
F08YKF   20  nagf_lapackeig_dtgevc
Computes right and left generalized eigenvectors of the matrix pair A , B which is assumed to be in generalized upper Schur form
Related keywords: DTGEVCeigenproblemgeneralized Schur formLAPACKLAPACKleast squares
F08YXF   20  nagf_lapackeig_ztgevc
Computes left and right eigenvectors of a pair of complex upper triangular matrices
Related keywords: complex, triangular matrixeigenproblemgeneralized Schur formLAPACKLAPACKleast squaresZTGEVC
F12ABF   21  nagf_sparseig_real_iter
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, reverse communication
Related keywords: big datadata analyticseigenproblemeigenvalueslarge scale eigenproblemsreal, sparse matrixsparse eigenproblem
F12ACF   21  nagf_sparseig_real_proc
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, postprocessing for F12ABF
Related keywords: big datadata analyticseigenproblemeigenvalueslarge scale eigenproblemsreal, sparse matrixsparse eigenproblem
F12AGF   21  nagf_sparseig_real_band_solve
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded eigenproblem, driver
Related keywords: big datadata analyticseigenproblem, bandedeigenvalueslarge scale eigenproblemsreal, band matrix
F12APF   21  nagf_sparseig_complex_iter
Selected eigenvalues and, optionally, eigenvectors of a complex sparse eigenproblem, reverse communication
Related keywords: big datacomplex, sparse matrixdata analyticseigenvalueslarge scale eigenproblemssparse eigenproblemsparse generalized eigenproblem
F12AUF   24  nagf_sparseig_complex_band_solve
Selected eigenvalues and, optionally, eigenvectors of complex non-Hermitian banded eigenproblem, driver
Related keywords: big datacomplex, band matrixdata analyticseigenproblem, bandedeigenvalueslarge scale eigenproblems
F12FBF   21  nagf_sparseig_real_symm_iter
Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, reverse communication
Related keywords: big datadata analyticseigenvalueslarge scale eigenproblemsreal, sparse, symmetric matrixsparse eigenproblem
F12FGF   21  nagf_sparseig_real_symm_band_solve
Selected eigenvalues and, optionally, eigenvectors of a real symmetric banded eigenproblem, driver
Related keywords: big datadata analyticseigenproblem, bandedeigenvalueslarge scale eigenproblemsreal, band, symmetric matrix
elementary arithmetic F06BNF   12  nagf_blas_dpyth
Compute square root of a 2 + b 2 , real a and b
Related keywords: BLASfinancelinear algebra support routines
F06BPF   12  nagf_blas_deig2
Compute eigenvalue of 2 by 2 real symmetric matrix
Related keywords: BLASeigenvalueslinear algebra support routines
F06CCF   12  nagf_blas_zcsg
Recover cosine and sine from given complex tangent, real cosine
Related keywords: BLASlinear algebra support routines
F06CDF   12  nagf_blas_zcsgs
Recover cosine and sine from given complex tangent, real sine
Related keywords: BLASlinear algebra support routines
F06CLF   12  nagf_blas_zdiv
Compute quotient of two complex scalars, with overflow flag
Related keywords: BLASlinear algebra support routines
F06DBF   12  nagf_blas_iload
Broadcast scalar into integer vector
Related keywords: BLASfinancelinear algebra support routines
F06DFF   12  nagf_blas_icopy
Copy integer vector
Related keywords: BLASlinear algebra support routines
F06ECF   12  nagf_blas_daxpy
Add scalar times real vector to real vector
Related keywords: BLASblas, real matricesdaxpylinear algebra support routines
F06EDF   12  nagf_blas_dscal
Multiply real vector by scalar
Related keywords: BLASblas, real matricesdscallinear algebra support routines
F06EFF   12  nagf_blas_dcopy
Copy real vector
Related keywords: BLASblas, real matricesdcopyfinancelinear algebra support routines
F06EGF   12  nagf_blas_dswap
Swap two real vectors
Related keywords: BLASblas, real matricesdswaplinear algebra support routines
F06EJF   12  nagf_blas_dnrm2
Compute Euclidean norm of real vector
Related keywords: BLASblas, real matricesdnrm2Euclidean normfinancelinear algebra support routines
F06EKF   12  nagf_blas_dasum
Sum absolute values of real vector elements
Related keywords: BLASblas, real matricesdasumlinear algebra support routines
F06ETF   14  nagf_blas_daxpyi
Add scalar times real sparse vector to a full vector
Related keywords: BLASblas, real matricesdaxpylinear algebra support routines
F06EUF   14  nagf_blas_dgthr
Gather real sparse vector
Related keywords: BLASblas, real matricesdgthrlinear algebra support routines
F06EVF   14  nagf_blas_dgthrz
Gather and set to zero real sparse vector
Related keywords: BLASblas, real matricesdgthrzlinear algebra support routines
F06EWF   14  nagf_blas_dsctr
Scatter real sparse vector
Related keywords: BLASblas, real matricesdgthrzlinear algebra support routines
F06FAF   12  nagf_blas_dvcos
Compute cosine of angle between two real vectors
Related keywords: BLASlinear algebra support routines
F06FBF   12  nagf_blas_dload
Broadcast scalar into real vector
Related keywords: BLASlinear algebra support routines
F06FCF   12  nagf_blas_ddscl
Multiply real vector by diagonal matrix
Related keywords: BLASlinear algebra support routines
F06FDF   12  nagf_blas_axpzy
Multiply real vector by scalar, preserving input vector
Related keywords: BLASfinancelinear algebra support routines
F06FEF   21  nagf_blas_drscl
Multiply real vector by reciprocal of scalar
Related keywords: BLASlinear algebra support routines
F06FGF   12  nagf_blas_dnegv
Negate real vector
Related keywords: BLASlinear algebra support routines
F06FLF   12  nagf_blas_darang
Elements of real vector with largest and smallest absolute value
Related keywords: BLASlinear algebra support routines
F06GCF   12  nagf_blas_zaxpy
Add scalar times complex vector to complex vector
Related keywords: BLASblas, complex matriceslinear algebra support routineszaxpy
F06GDF   12  nagf_blas_zscal
Multiply complex vector by complex scalar
Related keywords: BLASblas, complex matriceslinear algebra support routineszscal
F06GFF   12  nagf_blas_zcopy
Copy complex vector
Related keywords: BLASblas, complex matriceslinear algebra support routineszcopy
F06GGF   12  nagf_blas_zswap
Swap two complex vectors
Related keywords: BLASblas, complex matriceslinear algebra support routineszswap
F06GUF   14  nagf_blas_zgthr
Gather complex sparse vector
Related keywords: BLASblas, complex matriceslinear algebra support routineszgthr
F06GVF   14  nagf_blas_zgthrz
Gather and set to zero complex sparse vector
Related keywords: BLASblas, complex matriceslinear algebra support routineszgthrz
F06GWF   14  nagf_blas_zsctr
Scatter complex sparse vector
Related keywords: BLASblas, complex matriceslinear algebra support routineszsctr
F06HBF   12  nagf_blas_zload
Broadcast scalar into complex vector
Related keywords: BLASlinear algebra support routines
F06HCF   12  nagf_blas_zdscl
Multiply complex vector by complex diagonal matrix
Related keywords: BLASlinear algebra support routines
F06HDF   12  nagf_blas_zaxpzy
Multiply complex vector by complex scalar, preserving input vector
Related keywords: BLASlinear algebra support routines
F06HGF   12  nagf_blas_znegv
Negate complex vector
Related keywords: BLASlinear algebra support routines
F06JDF   12  nagf_blas_zdscal
Multiply complex vector by real scalar
Related keywords: BLASblas, complex matriceslinear algebra support routineszdscal
F06JKF   12  nagf_blas_dzasum
Sum absolute values of complex vector elements
Related keywords: BLASblas, complex matricesdzasumlinear algebra support routines
F06JLF   12  nagf_blas_idamax
Index, real vector element with largest absolute value
Related keywords: BLASblas, real matricesidamaxlinear algebra support routines
F06JMF   12  nagf_blas_izamax
Index, complex vector element with largest absolute value
Related keywords: BLASblas, complex matricesizamaxlinear algebra support routines
F06KCF   12  nagf_blas_zddscl
Multiply complex vector by real diagonal matrix
Related keywords: BLASlinear algebra support routines
F06KDF   12  nagf_blas_zdaxpzy
Multiply complex vector by real scalar, preserving input vector
Related keywords: BLASlinear algebra support routines
F06KEF   21  nagf_blas_zdrscl
Multiply complex vector by reciprocal of real scalar
Related keywords: BLASlinear algebra support routines
F06KFF   12  nagf_blas_zdcopy
Copy real vector to complex vector
Related keywords: BLASlinear algebra support routines
F06KJF   12  nagf_blas_dzssq
Update Euclidean norm of complex vector in scaled form
Related keywords: BLASlinear algebra support routines
F06KLF   12  nagf_blas_idrank
Last non-negligible element of real vector
Related keywords: BLASlinear algebra support routines
F06QFF   13  nagf_blas_dmcopy
Matrix copy, real rectangular or trapezoidal matrix
Related keywords: BLAScopy, vectors and matricesfinancelinear algebra support routinesreal, m by n matrixreal, trapezoidal matrix
F06QHF   13  nagf_blas_dmload
Matrix initialization, real rectangular matrix
Related keywords: BLASfinancelinear algebra support routinesreal, m by n matrix
F06TFF   13  nagf_blas_zmcopy
Matrix copy, complex rectangular or trapezoidal matrix
Related keywords: BLAScomplex, m by n matrixcomplex, trapezoidal matrixlinear algebra support routines
F06THF   13  nagf_blas_zmload
Matrix initialization, complex rectangular matrix
Related keywords: BLAScomplex, m by n matrixlinear algebra support routines
elementary reflection F06FRF   12  nagf_blas_dnhousg
Generate real elementary reflection, NAG style
Related keywords: BLASlinear algebra support routines
F06FSF   12  nagf_blas_dlhousg
Generate real elementary reflection, LINPACK style
Related keywords: BLASlinear algebra support routines
F06FTF   12  nagf_blas_dnhous
Apply real elementary reflection, NAG style
Related keywords: BLASlinear algebra support routines
F06FUF   12  nagf_blas_dlhous
Apply real elementary reflection, LINPACK style
Related keywords: BLASlinear algebra support routines
F06HRF   12  nagf_blas_zhousg
Generate complex elementary reflection
Related keywords: BLASlinear algebra support routines
F06HTF   12  nagf_blas_zhous
Apply complex elementary reflection
Related keywords: BLASlinear algebra support routines
elementwise weights G02APF   26  nagf_correg_corrmat_target
Computes a correlation matrix from an approximate one using a specified target matrix
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsnearest correlation matrixnonlinear regressionpolynomial regressionregression analysisshrinkageshrinking method
elliptic functions S21CAF   15  nagf_specfun_jacellip_real
Jacobian elliptic functions sn, cn and dn of real argument
Related keywords: approximations of special functionscn, Jacobian elliptic functiondn, Jacobian elliptic functionfinanceJacobian elliptic functionssn, Jacobian elliptic functions
S21CBF   20  nagf_specfun_jacellip_complex
Jacobian elliptic functions sn, cn and dn of complex argument
Related keywords: approximations of special functionscn, Jacobian elliptic functiondn, Jacobian elliptic functionfinanceJacobian elliptic functionssn, Jacobian elliptic functions
elliptic integral S21BAF   nagf_specfun_ellipint_symm_1_degen
Degenerate symmetrised elliptic integral of 1st kind R C x , y
Related keywords: approximations of special functionsfinance
S21BBF   nagf_specfun_ellipint_symm_1
Symmetrised elliptic integral of 1st kind R F x , y , z
Related keywords: approximations of special functionsfinance
S21BCF   nagf_specfun_ellipint_symm_2
Symmetrised elliptic integral of 2nd kind R D x , y , z
Related keywords: approximations of special functionsfinance
S21BDF   nagf_specfun_ellipint_symm_3
Symmetrised elliptic integral of 3rd kind R J x , y , z , r
Related keywords: approximations of special functionsfinance
S21BEF   22  nagf_specfun_ellipint_legendre_1
Elliptic integral of 1st kind, Legendre form, F ϕ m
Related keywords: approximations of special functionsfinance
S21BFF   22  nagf_specfun_ellipint_legendre_2
Elliptic integral of 2nd kind, Legendre form, E ϕ m
Related keywords: approximations of special functionsfinance
S21BGF   22  nagf_specfun_ellipint_legendre_3
Elliptic integral of 3rd kind, Legendre form, Π n ; ϕ m
Related keywords: approximations of special functionsfinance
S21BHF   22  nagf_specfun_ellipint_complete_1
Complete elliptic integral of 1st kind, Legendre form, K m
Related keywords: approximations of special functionsfinance
S21BJF   22  nagf_specfun_ellipint_complete_2
Complete elliptic integral of 2nd kind, Legendre form, E m
Related keywords: approximations of special functionsfinance
S21DAF   20  nagf_specfun_ellipint_general_2
General elliptic integral of 2nd kind F z , k , a , b of complex argument
Related keywords: approximations of special functions
elliptic partial differential equations D03EAF   nagf_pde_2d_laplace
Elliptic PDE, Laplace's equation, two-dimensional arbitrary domain
Related keywords: Laplace's equationPDE, partial differential equations
D03EBF   nagf_pde_2d_ellip_fd
Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, iterate to convergence
Related keywords: Laplace's equationPDE, partial differential equationsStone's strongly implicit procedure
D03ECF   nagf_pde_3d_ellip_fd
Elliptic PDE, solution of finite difference equations by SIP for seven-point three-dimensional molecule, iterate to convergence
Related keywords: cuboidLaplace's equationPDE, partial differential equationsStone's strongly implicit procedure
D03EDF   12  nagf_pde_2d_ellip_mgrid
Elliptic PDE, solution of finite difference equations by a multigrid technique
Related keywords: multigrid methodPDE, partial differential equationsrectangulartwo-dimensional
D03EEF   13  nagf_pde_2d_ellip_discret
Discretize a second-order elliptic PDE on a rectangle
Related keywords: discretization, PDEPDE, partial differential equations
D03FAF   14  nagf_pde_3d_ellip_helmholtz
Elliptic PDE, Helmholtz equation, three-dimensional Cartesian coordinates
Related keywords: Helmholtz equation, PDEPDE, partial differential equations
D03UAF   nagf_pde_2d_ellip_fd_iter
Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, one iteration
Related keywords: five-point stencilPDE, partial differential equationsStone's strongly implicit procedure
D03UBF   nagf_pde_3d_ellip_fd_iter
Elliptic PDE, solution of finite difference equations by SIP, seven-point three-dimensional molecule, one iteration
Related keywords: PDE, partial differential equationsseven-point stencilStone's strongly implicit procedure
epsilon algorithm C06BAF   10  nagf_sum_accelerate
Acceleration of convergence of sequence, Shanks' transformation and epsilon algorithm
Related keywords: sequence, accelerateShanks' transformation, epsilon algorithmsummation of series
equilibration F07AFF   22  nagf_lapacklin_dgeequ
Computes row and column scalings intended to equilibrate a general real matrix and reduce its condition number
Related keywords: DGEEQULAPACKlinear equationsreal, nonsymmetric matrixscaling
F07ATF   22  nagf_lapacklin_zgeequ
Computes row and column scalings intended to equilibrate a general complex matrix and reduce its condition number
Related keywords: complex, nonsymmetric matrixLAPACKlinear equationsscalingZGEEQU
F07BFF   22  nagf_lapacklin_dgbequ
Computes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number
Related keywords: DGBEQULAPACKlinear equationsmatrix, bandreal, band matrixscaling
F07BTF   22  nagf_lapacklin_zgbequ
Computes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number
Related keywords: complex, band matrixLAPACKlinear equationsmatrix, bandscalingZGBEQU
F07FFF   22  nagf_lapacklin_dpoequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number
Related keywords: DPOEQULAPACKlinear equationsreal, positive-definite, symmetric matrixscaling
F07FTF   22  nagf_lapacklin_zpoequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number
Related keywords: complex, Hermitian, positive-definite matrixLAPACKlinear equationsscalingZPOEQU
F07GFF   22  nagf_lapacklin_dppequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number, packed storage
Related keywords: DPPEQULAPACKlinear equationsreal, positive-definite, symmetric matrixscaling
F07GTF   22  nagf_lapacklin_zppequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number, packed storage
Related keywords: complex, Hermitian, positive-definite matrixLAPACKlinear equationsscalingZPPEQU
F07HFF   22  nagf_lapacklin_dpbequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite banded matrix and reduce its condition number
Related keywords: DPBEQULAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrixscaling
F07HTF   22  nagf_lapacklin_zpbequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite banded matrix and reduce its condition number
Related keywords: complex, band, Hermitian, positive-definite matrixLAPACKlinear equationsmatrix, bandscalingZPBEQU
error bound, matrix F07ABF   21  nagf_lapacklin_dgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
Related keywords: backward errorcondition number, matrixDGESVXfinanceforward errorLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
F07AHF   15  nagf_lapacklin_dgerfs
Refined solution with error bounds of real system of linear equations, multiple right-hand sides
Related keywords: backward errorDGERFSforward errorLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
F07APF   21  nagf_lapacklin_zgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
Related keywords: backward errorcomplex, nonsymmetric matrixcondition number, matrixfinanceforward errorLAPACKlinear equations L U decompositionZGESVX
F07BBF   21  nagf_lapacklin_dgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
Related keywords: backward errorcondition number, matrixDGBSVXforward errorLAPACKlinear equations L U decompositionmatrix, bandreal, band matrix
F07BPF   21  nagf_lapacklin_zgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
Related keywords: backward errorcomplex, band matrixcondition number, matrixforward errorLAPACKlinear equations L U decompositionmatrix, bandZGBSVX
F07BVF   15  nagf_lapacklin_zgbrfs
Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, band matrixforward errorLAPACKlinear equationsmatrix, bandZGBRFS
F07CBF   21  nagf_lapacklin_dgtsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
Related keywords: backward errorcondition number, matrixDGTSVXforward errorLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
F07FBF   21  nagf_lapacklin_dposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixDPOSVXfinanceforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FPF   21  nagf_lapacklin_zposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite matrixcondition number, matrixfinanceforward errorLAPACKlinear equationsZPOSVX
F07FVF   15  nagf_lapacklin_zporfs
Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite matrixforward errorLAPACKlinear equationsZPORFS
F07GBF   21  nagf_lapacklin_dppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations, packed storage
Related keywords: backward errorCholesky decompositioncondition number, matrixDPPSVXforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GPF   21  nagf_lapacklin_zppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations, packed storage
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite matrixcondition number, matrixforward errorLAPACKlinear equationsZPPSVX
F07GVF   15  nagf_lapacklin_zpprfs
Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite matrixforward errorLAPACKlinear equationsZPPRFS
F07HBF   21  nagf_lapacklin_dpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite banded system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixDPBSVXforward errorLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
F07HPF   21  nagf_lapacklin_zpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite banded system of linear equations
Related keywords: backward errorCholesky decompositioncomplex, band, Hermitian, positive-definite matrixcondition number, matrixforward errorLAPACKlinear equationsmatrix, bandZPBSVX
F07HVF   15  nagf_lapacklin_zpbrfs
Refined solution with error bounds of complex Hermitian positive definite band system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositioncomplex, band, Hermitian, positive-definite matrixforward errorLAPACKlinear equationsmatrix, bandZPBRFS
F07JBF   21  nagf_lapacklin_dptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixDPTSVXforward errorLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
F07JPF   21  nagf_lapacklin_zptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixcondition number, matrixforward errorLAPACKlinear equationsmatrix, bandZPTSVX
F07MVF   15  nagf_lapacklin_zherfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
Related keywords: backward errorBunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methodforward errorLAPACKlinear equationsZHERFS
F07NVF   15  nagf_lapacklin_zsyrfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
Related keywords: backward errorBunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methodforward errorLAPACKlinear equationsZSYRFS
F07PBF   21  nagf_lapacklin_dspsvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage. Error bounds and a condition estimate are also computed
Related keywords: backward errorcondition number, matrixdiagonal pivoting methodDSPSVXforward errorLAPACK LDL H decompositionlinear equationsreal, indefinite, symmetric matrix UDU H decomposition
F07PVF   15  nagf_lapacklin_zhprfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorBunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methodforward errorLAPACKlinear equationsZHPRFS
F07QVF   15  nagf_lapacklin_zsprfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorBunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methodforward errorLAPACKlinear equationsZSPRFS
F07THF   15  nagf_lapacklin_dtrrfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorDTRRFSfinanceforward errorLAPACKlinear equationsreal, triangular matrix
F07TVF   15  nagf_lapacklin_ztrrfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, triangular matrixforward errorLAPACKlinear equationsZTRRFS
F07UHF   15  nagf_lapacklin_dtprfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorDTPRFSforward errorLAPACKlinear equationsreal, triangular matrix
F07UVF   15  nagf_lapacklin_ztprfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorcomplex, triangular matrixforward errorLAPACKlinear equationsZTPRFS
F07VHF   15  nagf_lapacklin_dtbrfs
Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorDTBRFSforward errorLAPACKlinear equationsmatrix, bandreal, band, triangular matrix
F07VVF   15  nagf_lapacklin_ztbrfs
Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, band, triangular matrixforward errorLAPACKlinear equationsmatrix, bandZTBRFS
error function S15ACF   nagf_specfun_compcdf_normal
Complement of cumulative Normal distribution function Q x
Related keywords: approximations of special functionscomplement of cumulative Normal distributioncumulative Normal distributionfinance
S15ADF   nagf_specfun_erfc_real
Complement of error function erfc x
Related keywords: approximations of special functionscomplement error functionfinance
S15AEF   nagf_specfun_erf_real
Error function erf x
Related keywords: approximations of special functionsfinance
S15AGF   22  nagf_specfun_erfcx_real
Scaled complement of error function, erfcx x
Related keywords: approximations of special functionscomplement error functionfinance
S15DDF   14  nagf_specfun_erfc_complex
Scaled complex complement of error function, exp - z 2 erfc - i z
Related keywords: approximations of special functionscomplement error function
error messages X04AAF   nagf_file_set_unit_error
Return or set unit number for error messages
Related keywords: input utilitiesoutput utilities
error variance ratios G13ACF   nagf_tsa_uni_autocorr_part
Univariate time series, partial autocorrelations from autocorrelations
Related keywords: autocorrelation coefficientsautoregressive parametersbig datadata analyticsfinancepartial autocorrelation coefficientstime seriestime series analysisunivariate time series
estimable function G02DNF   14  nagf_correg_linregm_estfunc
Computes estimable function of a general linear regression model and its standard error
Related keywords: big datacorrelation analysisdata analyticsfinancelinear regressionnonlinear regressionpolynomial regressionregression analysis
G02GNF   14  nagf_correg_glm_estfunc
Computes estimable function of a generalized linear model and its standard error
Related keywords: big datacorrelation analysisdata analyticsfinancegeneralized linear modelnonlinear regressionpolynomial regressionregression analysis
Euclidean norm F06BMF   12  nagf_blas_dnorm
Compute Euclidean norm from scaled form
Related keywords: BLASlinear algebra support routinesnorm, vector
F06EJF   12  nagf_blas_dnrm2
Compute Euclidean norm of real vector
Related keywords: BLASblas, real matricesdnrm2elementary arithmeticfinancelinear algebra support routines
F06FJF   12  nagf_blas_dssq
Update Euclidean norm of real vector in scaled form
Related keywords: BLASlinear algebra support routines
F06FKF   12  nagf_blas_dnrm2w
Compute weighted Euclidean norm of real vector
Related keywords: BLASlinear algebra support routines
F06JJF   12  nagf_blas_dznrm2
Compute Euclidean norm of complex vector
Related keywords: BLASblas, complex matricesdznrm2financelinear algebra support routines
Euler's constant X01ABF   nagf_math_euler
Provides the mathematical constant γ (Euler's constant)
Related keywords: gamma, Euler's constantmathematical constants
Euler equations D03PUF   17  nagf_pde_1d_parab_euler_roe
Roe's approximate Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
Related keywords: PDE, partial differential equationsRiemann solver, PDERoe's method
D03PVF   17  nagf_pde_1d_parab_euler_osher
Osher's approximate Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
Related keywords: Osher's method, Euler equationsPDE, partial differential equationsRiemann solver, PDE
D03PWF   18  nagf_pde_1d_parab_euler_hll
Modified HLL Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
Related keywords: Harten–Lax-van Leer solvermodified HLL solverPDE, partial differential equationsRiemann solver, PDE
D03PXF   18  nagf_pde_1d_parab_euler_exact
Exact Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
Related keywords: PDE, partial differential equationsRiemann solver, PDE
European S30NCF   25  nagf_specfun_opt_heston_term
Heston's model option pricing with term structure
Related keywords: approximations of special functionsfinanceHestonstochastic volatilityterm structure
Everett's formula E01ABF   nagf_interp_1d_everett
Interpolated values, Everett's formula, equally spaced data, one variable
Related keywords: interpolation
exact likelihood G13BEF   11  nagf_tsa_multi_inputmod_estim
Multivariate time series, estimation of multi-input model
Related keywords: ARIMAbig datadata analyticsfinancemarginal likelihoodmultivariate time seriesnonlinear least squarestime seriestime series analysisunivariate time series
exception mode X07CAF   24  nagf_ieee_get_exception_mode
Gets current behaviour of floating-point exceptions
Related keywords: IEEE arithmetic
X07CBF   24  nagf_ieee_set_exception_mode
Sets behaviour of floating-point exceptions
Related keywords: IEEE arithmetic
experimental design G04DAF   17  nagf_anova_contrasts
Computes sum of squares for contrast between means
Related keywords: analysis of variancedesign of experimentssum of squares
G04DBF   17  nagf_anova_confidence
Computes confidence intervals for differences between means computed by G04BBF or G04BCF
Related keywords: analysis of varianceconfidence intervaldesign of experiments
G04EAF   17  nagf_anova_dummyvars
Computes orthogonal polynomials or dummy variables for factor/classification variable
Related keywords: analysis of varianceclassification variabledesign of experimentsfactor variable
explicit blocking F08ABF   25  nagf_lapackeig_dgeqrt
Performs a Q R factorization of real general rectangular matrix, with explicit blocking
Related keywords: DGEQRTeigenproblemLAPACKleast squaresQR factorizationreal, m by n matrixrecursive QR
F08ACF   25  nagf_lapackeig_dgemqrt
Applies the orthogonal transformation determined by F08ABF
Related keywords: DGEMQRTeigenproblemLAPACKleast squaresorthogonal transformationsQR factorizationrecursive QR
F08APF   25  nagf_lapackeig_zgeqrt
Performs a Q R factorization of complex general rectangular matrix using recursive algorithm
Related keywords: complex, m by n matrixeigenproblemLAPACKleast squaresQR factorizationrecursive QRZGEQRT
F08AQF   25  nagf_lapackeig_zgemqrt
Applies the unitary transformation determined by F08APF
Related keywords: eigenproblemLAPACKleast squaresQR factorizationrecursive QRunitary transformationsZGEMQRT
F08BBF   25  nagf_lapackeig_dtpqrt
Q R factorization of real general triangular-pentagonal matrix
Related keywords: DTPQRTeigenproblemLAPACKleast squaresQR factorizationreal, triangular-pentagonal matrixrecursive QR
F08BCF   25  nagf_lapackeig_dtpmqrt
Applies the orthogonal transformation determined by F08BBF
Related keywords: DTPMQRTeigenproblemLAPACKleast squaresorthogonal transformationsQR factorizationrecursive QR
F08BPF   25  nagf_lapackeig_ztpqrt
Q R factorization of complex triangular-pentagonal matrix
Related keywords: complex, triangular-pentagonal matrixeigenproblemLAPACKleast squaresQR factorizationrecursive QRZTPQRT
F08BQF   25  nagf_lapackeig_ztpmqrt
Applies the unitary transformation determined by F08BPF
Related keywords: eigenproblemLAPACKleast squaresQR factorizationrecursive QRunitary transformationsZTPMQRT
exponential S01EAF   14  nagf_specfun_exp_complex
Complex exponential, e z
Related keywords: approximations of special functionscomplex exponential
exponential, matrix F01ECF   22  nagf_matop_real_gen_matrix_exp
Real matrix exponential
Related keywords: inversionmatrix exponentialmatrix operationsreal, nonsymmetric matrix
F01EDF   23  nagf_matop_real_symm_matrix_exp
Real symmetric matrix exponential
Related keywords: financeinversionmatrix exponentialmatrix operationsreal, indefinite, symmetric matrix
F01EKF   24  nagf_matop_real_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm)
Related keywords: cosh, matrixcosine, matrixfunctions, matrixinversionmatrix operationsreal, nonsymmetric matrixsine, matrixsinh, matrix
F01FCF   23  nagf_matop_complex_gen_matrix_exp
Complex matrix exponential
Related keywords: complex, nonsymmetric matrixfinanceinversionmatrix exponentialmatrix operations
F01FDF   23  nagf_matop_complex_herm_matrix_exp
Complex Hermitian matrix exponential
Related keywords: complex, Hermitian, indefinite matrixfinanceinversionmatrix exponentialmatrix operations
F01FKF   24  nagf_matop_complex_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm)
Related keywords: complex, nonsymmetric matrixcosh, matrixcosine, matrixfunctions, matrixinversionmatrix operationssine, matrixsinh, matrix
F01GAF   24  nagf_matop_real_gen_matrix_actexp
Action of a real matrix exponential on a real matrix
Related keywords: inversionmatrix exponentialmatrix operationsproduct, matricesreal, nonsymmetric matrix
F01GBF   24  nagf_matop_real_gen_matrix_actexp_rcomm
Action of a real matrix exponential on a real matrix (reverse communication)
Related keywords: inversionmatrix exponentialmatrix operationsproduct, matricesreal, nonsymmetric matrix
F01HAF   24  nagf_matop_complex_gen_matrix_actexp
Action of a complex matrix exponential on a complex matrix
Related keywords: complex, nonsymmetric matrixinversionmatrix exponentialmatrix operationsproduct, matrices
F01HBF   24  nagf_matop_complex_gen_matrix_actexp_rcomm
Action of a complex matrix exponential on a complex matrix (reverse communication)
Related keywords: complex, nonsymmetric matrixinversionmatrix exponentialmatrix operationsproduct, matrices
F01JAF   24  nagf_matop_real_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix
Related keywords: condition number, matrixcosh, matrixcosine, matrixinversionlogarithm, matrixmatrix operationsreal, nonsymmetric matrixsine, matrixsinh, matrix
F01KAF   24  nagf_matop_complex_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix
Related keywords: complex, nonsymmetric matrixcondition number, matrixcosh, matrixcosine, matrixinversionlogarithm, matrixmatrix operationssine, matrixsinh, matrix
exponential distribution G05SFF   22  nagf_rand_dist_exp
Generates a vector of pseudorandom numbers from an exponential distribution
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
G05SGF   22  nagf_rand_dist_expmix
Generates a vector of pseudorandom numbers from an exponential mix distribution
Related keywords: big datadata analyticsexponential mix distributionfinancerandom number generatorsrandom numbers
G08CLF   23  nagf_nonpar_gofstat_anddar_exp
Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of an unspecified exponential distribution
Related keywords: Anderson–Darling test statisticnonparametric statisticsprobability
exponential GARCH G13FGF   20  nagf_tsa_uni_garch_exp_estim
Univariate time series, parameter estimation for an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsEGARCHfinanceGARCHtime seriestime series analysisunivariate time series
G13FHF   20  nagf_tsa_uni_garch_exp_forecast
Univariate time series, forecast function for an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsEGARCHfinanceforecastingGARCHtime seriestime series analysisunivariate time series
exponential integral S13AAF   nagf_specfun_integral_exp
Exponential integral E 1 x
Related keywords: approximations of special functionsexponential integral, E 1 x finance
exponential integral, E 1 x S13AAF   nagf_specfun_integral_exp
Exponential integral E 1 x
Related keywords: approximations of special functionsexponential integralfinance
exponential mix distribution G05SGF   22  nagf_rand_dist_expmix
Generates a vector of pseudorandom numbers from an exponential mix distribution
Related keywords: big datadata analyticsexponential distributionfinancerandom number generatorsrandom numbers
exponential moving average G13MEF   24  nagf_tsa_inhom_iema
Computes the iterated exponential moving average for a univariate inhomogeneous time series
Related keywords: big datadata analyticsdata streammoving averagestreamingtime seriestime series analysisunivariate time series
G13MFF   24  nagf_tsa_inhom_iema_all
Computes the iterated exponential moving average for a univariate inhomogeneous time series, intermediate results are also returned
Related keywords: big datadata analyticsdata streammoving averagestreamingtime seriestime series analysisunivariate time series
G13MGF   24  nagf_tsa_inhom_ma
Computes the exponential moving average for a univariate inhomogeneous time series
Related keywords: big datadata analyticsdata streammoving averagestreamingtime seriestime series analysisunivariate time series
exponential scores G01DHF   15  nagf_stat_ranks_and_scores
Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores
Related keywords: Blom scoresfinancerank scoresSavage scoresSimple Calculations on Statistical DataTukey scoresvan der Waerden scores
exponential smoothing G05PMF   22  nagf_rand_times_smooth_exp
Generates a realization of a time series from an exponential smoothing model
Related keywords: big datadata analyticsfinancerandom number generatorstime series
G13AMF   22  nagf_tsa_uni_smooth_exp
Univariate time series, exponential smoothing
Related keywords: big dataBrowns Exponentialdata analyticsfinanceHolt WinterLinear Holttime seriestime series analysisunivariate time series
extended precision accumulation X03AAF   nagf_dot_real_prec
Real inner product added to initial value, basic/additional precision
Related keywords: additional precision accumulationdot productinner productinner productsscalar product
X03ABF   nagf_dot_complex_prec
Complex inner product added to initial value, basic/additional precision
Related keywords: additional precision accumulationdot productinner productinner productsscalar product
extract C09EYF   25  nagf_wav_2d_coeff_ext
Two-dimensional discrete wavelet transform coefficient extraction
Related keywords: coefficientstwo-dimensionalwaveletwavelet transforms
C09FYF   25  nagf_wav_3d_coeff_ext
Three-dimensional discrete wavelet transform coefficient extraction
Related keywords: coefficientsthree-dimensionalwaveletwavelet transforms
factor analysis G03BAF   15  nagf_mv_rot_orthomax
Computes orthogonal rotations for loading matrix, generalized orthomax criterion
Related keywords: canonical variate analysismultivariate methodsorthogonal transformationsorthomax criterion
G03CAF   15  nagf_mv_factor
Computes maximum likelihood estimates of the parameters of a factor analysis model, factor loadings, communalities and residual correlations
Related keywords: communalities, maximum likelihoodfactor loadingsmaximum likelihoodmultivariate methodsresidual correlations
G03CCF   15  nagf_mv_factor_score
Computes factor score coefficients (for use after G03CAF)
Related keywords: factor score coefficientsmaximum likelihoodmultivariate methods
factorial design G04CAF   16  nagf_anova_factorial
Analysis of variance, complete factorial design, treatment means and standard errors
Related keywords: analysis of varianceANOVAstandard errorstreatment means
factor loadings G03CAF   15  nagf_mv_factor
Computes maximum likelihood estimates of the parameters of a factor analysis model, factor loadings, communalities and residual correlations
Related keywords: communalities, maximum likelihoodfactor analysismaximum likelihoodmultivariate methodsresidual correlations
factor score coefficients G03CCF   15  nagf_mv_factor_score
Computes factor score coefficients (for use after G03CAF)
Related keywords: factor analysismaximum likelihoodmultivariate methods
factor scores G11SAF   12  nagf_contab_binary
Contingency table, latent variable model for binary data
Related keywords: contingency table analysislatent variable modelscore patternstheta scores
factor variable G04EAF   17  nagf_anova_dummyvars
Computes orthogonal polynomials or dummy variables for factor/classification variable
Related keywords: analysis of varianceclassification variabledesign of experimentsexperimental design
G11BAF   17  nagf_contab_tabulate_stat
Computes multiway table from set of classification factors using selected statistic
Related keywords: classification variablecontingency table analysistable
G11BBF   17  nagf_contab_tabulate_percentile
Computes multiway table from set of classification factors using given percentile/quantile
Related keywords: classification variablecontingency table analysistable
Fast Fourier Transform C06FAF   nagf_sum_fft_real_1d_rfmt
Single one-dimensional real discrete Fourier transform, extra workspace for greater speed
Related keywords: FFTsummation of series
C06FBF   nagf_sum_fft_hermitian_1d_rfmt
Single one-dimensional Hermitian discrete Fourier transform, extra workspace for greater speed
Related keywords: FFTsummation of series
C06FCF   nagf_sum_fft_complex_1d_sep
Single one-dimensional complex discrete Fourier transform, extra workspace for greater speed
Related keywords: FFTsummation of series
C06FFF   11  nagf_sum_fft_complex_multid_1d_sep
One-dimensional complex discrete Fourier transform of multidimensional data
Related keywords: complex Fourier transformFFTsummation of series
C06FJF   11  nagf_sum_fft_complex_multid_sep
Multidimensional complex discrete Fourier transform of multidimensional data
Related keywords: complex Fourier transformFFTsummation of series
C06FKF   11  nagf_sum_convcorr_real
Circular convolution or correlation of two real vectors, no restrictions on n
Related keywords: convolutioncorrelationFFTsummation of series
C06FXF   17  nagf_sum_fft_complex_3d_sep
Three-dimensional complex discrete Fourier transform
Related keywords: complex Fourier transformFFTsummation of series
C06PAF   19  nagf_sum_fft_realherm_1d
Single one-dimensional real and Hermitian complex discrete Fourier transform, using complex storage format for Hermitian sequences
Related keywords: FFTFourier transforms, complexsummation of series
C06PCF   19  nagf_sum_fft_complex_1d
Single one-dimensional complex discrete Fourier transform, complex data type
Related keywords: FFTFourier transforms, complexsummation of series
C06PFF   19  nagf_sum_fft_complex_multid_1d
One-dimensional complex discrete Fourier transform of multidimensional data (using complex data type)
Related keywords: FFTFourier transforms, complexsummation of series
C06PJF   19  nagf_sum_fft_complex_multid
Multidimensional complex discrete Fourier transform of multidimensional data (using complex data type)
Related keywords: FFTFourier transforms, complexsummation of series
C06PPF   19  nagf_sum_fft_realherm_1d_multi_row
Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using row ordered complex storage format for Hermitian sequences
Related keywords: FFTFourier transforms, complexFourier transforms, realsummation of series
C06PQF   19  nagf_sum_fft_realherm_1d_multi_col
Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using column ordered complex storage format for Hermitian sequences
Related keywords: discreteFFTone-dimensionalsummation of series
C06PRF   19  nagf_sum_fft_complex_1d_multi_row
Multiple one-dimensional complex discrete Fourier transforms using complex data type
Related keywords: FFTFourier transforms, complexsummation of series
C06PSF   19  nagf_sum_fft_complex_1d_multi_col
Multiple one-dimensional complex discrete Fourier transforms, complex data type
Related keywords: FFTFourier transforms, complexsummation of series
C06PUF   19  nagf_sum_fft_complex_2d
Two-dimensional complex discrete Fourier transform, complex data type
Related keywords: FFTFourier transforms, complexsummation of series
C06PVF   24  nagf_sum_fft_real_2d
Two-dimensional real-to-complex discrete Fourier transform
Related keywords: FFTFourier transforms, complexsummation of series
C06PWF   24  nagf_sum_fft_hermitian_2d
Two-dimensional complex-to-real discrete Fourier transform
Related keywords: FFTFourier transforms, complexsummation of series
C06PXF   19  nagf_sum_fft_complex_3d
Three-dimensional complex discrete Fourier transform, complex data type
Related keywords: FFTFourier transforms, complexsummation of series
C06PYF   24  nagf_sum_fft_real_3d
Three-dimensional real-to-complex discrete Fourier transform
Related keywords: FFTFourier transforms, complexsummation of series
C06PZF   24  nagf_sum_fft_hermitian_3d
Three-dimensional complex-to-real discrete Fourier transform
Related keywords: FFTsummation of series
C06REF   25  nagf_sum_fft_sine
Multiple discrete sine transforms, simple
Related keywords: Discrete Fourier TransformsFFTFourier Transforms, realsine transformsummation of series
C06RFF   25  nagf_sum_fft_cosine
Multiple discrete cosine transforms, simple
Related keywords: cosine transformDiscrete Fourier TransformsFFTFourier Transforms, realsummation of series
C06RGF   25  nagf_sum_fft_qtrsine
Multiple discrete quarter-wave sine transforms, simple
Related keywords: Discrete Fourier TransformsFFTFourier Transforms, realquarter-wavesine transformsummation of series
C06RHF   25  nagf_sum_fft_qtrcosine
Multiple discrete quarter-wave cosine transforms, simple
Related keywords: cosine transformDiscrete Fourier TransformsFFTFourier Transforms, realquarter-wavesummation of series
D02UDF   23  nagf_ode_bvp_ps_lin_cgl_deriv
Differentiate a function by the FFT using function values on Chebyshev grid
Related keywords: FFTGauss–Lobatto gridODE, ordinary differential equations
Fast Gauss Transform C06SAF   26  nagf_sum_fast_gauss
Multidimensional fast Gauss transform
Related keywords: summation of seriessummation of series
Faure, quasi-random numbers G05YJF   21  nagf_rand_quasi_normal
Generates a Normal quasi-random number sequence
Related keywords: big datadata analyticsGaussian distributionlow-discrepancy sequencesNiederreiter method, quasi-random numbersNormal distributionquasi-random numbersrandom number generatorsrandom numbersSobol, quasi-random numbers
G05YKF   21  nagf_rand_quasi_lognormal
Generates a log-normal quasi-random number sequence
Related keywords: big datadata analyticslog-normal distributionlow-discrepancy sequencesNiederreiter method, quasi-random numbersquasi-random numbersrandom number generatorsrandom numbersSobol, quasi-random numbers
G05YLF   22  nagf_rand_quasi_init
Initializes a quasi-random number generator
Related keywords: big datadata analyticsfinancelow-discrepancy sequencesNiederreiter method, quasi-random numbersquasi-random numbersrandom number generatorsrandom numbersrectangular distributionSobol, quasi-random numbersuniform distribution
Faure–Tezuka G05YNF   22  nagf_rand_quasi_init_scrambled
Initializes a scrambled quasi-random number generator
Related keywords: big datadata analyticsfinanceNiederreiterOwenrandom number generatorsrandom numbersscrambleSobol
F -distribution G01EDF   14  nagf_stat_prob_f
Computes probabilities for F -distribution
Related keywords: CDF, cumulative distribution functionfinancelower tail probabilityprobabilitySimple Calculations on Statistical Dataupper tail probabilityvariance-ratio distribution
G01FDF   14  nagf_stat_inv_cdf_f
Computes deviates for the F -distribution
Related keywords: deviatesfinanceinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01GDF   14  nagf_stat_prob_f_noncentral
Computes probabilities for the non-central F -distribution
Related keywords: financelower tail probabilitySimple Calculations on Statistical Datavariance-ratio distribution
G01SDF   24  nagf_stat_prob_f_vector
Computes a vector of probabilities for F -distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticslower tail probabilitySimple Calculations on Statistical Dataupper tail probabilityvariance-ratio distribution
G01TDF   24  nagf_stat_inv_cdf_f_vector
Computes a vector of deviates for F -distribution
Related keywords: big datadata analyticsdeviatesinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Datavariance-ratio distribution
G05SHF   22  nagf_rand_dist_f
Generates a vector of pseudorandom numbers from an F -distribution
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
FFT C06FAF   nagf_sum_fft_real_1d_rfmt
Single one-dimensional real discrete Fourier transform, extra workspace for greater speed
Related keywords: Fast Fourier Transformsummation of series
C06FBF   nagf_sum_fft_hermitian_1d_rfmt
Single one-dimensional Hermitian discrete Fourier transform, extra workspace for greater speed
Related keywords: Fast Fourier Transformsummation of series
C06FCF   nagf_sum_fft_complex_1d_sep
Single one-dimensional complex discrete Fourier transform, extra workspace for greater speed
Related keywords: Fast Fourier Transformsummation of series
C06FFF   11  nagf_sum_fft_complex_multid_1d_sep
One-dimensional complex discrete Fourier transform of multidimensional data
Related keywords: complex Fourier transformFast Fourier Transformsummation of series
C06FJF   11  nagf_sum_fft_complex_multid_sep
Multidimensional complex discrete Fourier transform of multidimensional data
Related keywords: complex Fourier transformFast Fourier Transformsummation of series
C06FKF   11  nagf_sum_convcorr_real
Circular convolution or correlation of two real vectors, no restrictions on n
Related keywords: convolutioncorrelationFast Fourier Transformsummation of series
C06FXF   17  nagf_sum_fft_complex_3d_sep
Three-dimensional complex discrete Fourier transform
Related keywords: complex Fourier transformFast Fourier Transformsummation of series
C06PAF   19  nagf_sum_fft_realherm_1d
Single one-dimensional real and Hermitian complex discrete Fourier transform, using complex storage format for Hermitian sequences
Related keywords: Fast Fourier TransformFourier transforms, complexsummation of series
C06PCF   19  nagf_sum_fft_complex_1d
Single one-dimensional complex discrete Fourier transform, complex data type
Related keywords: Fast Fourier TransformFourier transforms, complexsummation of series
C06PFF   19  nagf_sum_fft_complex_multid_1d
One-dimensional complex discrete Fourier transform of multidimensional data (using complex data type)
Related keywords: Fast Fourier TransformFourier transforms, complexsummation of series
C06PJF   19  nagf_sum_fft_complex_multid
Multidimensional complex discrete Fourier transform of multidimensional data (using complex data type)
Related keywords: Fast Fourier TransformFourier transforms, complexsummation of series
C06PPF   19  nagf_sum_fft_realherm_1d_multi_row
Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using row ordered complex storage format for Hermitian sequences
Related keywords: Fast Fourier TransformFourier transforms, complexFourier transforms, realsummation of series
C06PQF   19  nagf_sum_fft_realherm_1d_multi_col
Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using column ordered complex storage format for Hermitian sequences
Related keywords: discreteFast Fourier Transformone-dimensionalsummation of series
C06PRF   19  nagf_sum_fft_complex_1d_multi_row
Multiple one-dimensional complex discrete Fourier transforms using complex data type
Related keywords: Fast Fourier TransformFourier transforms, complexsummation of series
C06PSF   19  nagf_sum_fft_complex_1d_multi_col
Multiple one-dimensional complex discrete Fourier transforms, complex data type
Related keywords: Fast Fourier TransformFourier transforms, complexsummation of series
C06PUF   19  nagf_sum_fft_complex_2d
Two-dimensional complex discrete Fourier transform, complex data type
Related keywords: Fast Fourier TransformFourier transforms, complexsummation of series
C06PVF   24  nagf_sum_fft_real_2d
Two-dimensional real-to-complex discrete Fourier transform
Related keywords: Fast Fourier TransformFourier transforms, complexsummation of series
C06PWF   24  nagf_sum_fft_hermitian_2d
Two-dimensional complex-to-real discrete Fourier transform
Related keywords: Fast Fourier TransformFourier transforms, complexsummation of series
C06PXF   19  nagf_sum_fft_complex_3d
Three-dimensional complex discrete Fourier transform, complex data type
Related keywords: Fast Fourier TransformFourier transforms, complexsummation of series
C06PYF   24  nagf_sum_fft_real_3d
Three-dimensional real-to-complex discrete Fourier transform
Related keywords: Fast Fourier TransformFourier transforms, complexsummation of series
C06PZF   24  nagf_sum_fft_hermitian_3d
Three-dimensional complex-to-real discrete Fourier transform
Related keywords: Fast Fourier Transformsummation of series
C06REF   25  nagf_sum_fft_sine
Multiple discrete sine transforms, simple
Related keywords: Discrete Fourier TransformsFast Fourier TransformFourier Transforms, realsine transformsummation of series
C06RFF   25  nagf_sum_fft_cosine
Multiple discrete cosine transforms, simple
Related keywords: cosine transformDiscrete Fourier TransformsFast Fourier TransformFourier Transforms, realsummation of series
C06RGF   25  nagf_sum_fft_qtrsine
Multiple discrete quarter-wave sine transforms, simple
Related keywords: Discrete Fourier TransformsFast Fourier TransformFourier Transforms, realquarter-wavesine transformsummation of series
C06RHF   25  nagf_sum_fft_qtrcosine
Multiple discrete quarter-wave cosine transforms, simple
Related keywords: cosine transformDiscrete Fourier TransformsFast Fourier TransformFourier Transforms, realquarter-wavesummation of series
D02UDF   23  nagf_ode_bvp_ps_lin_cgl_deriv
Differentiate a function by the FFT using function values on Chebyshev grid
Related keywords: Fast Fourier TransformGauss–Lobatto gridODE, ordinary differential equations
file closing X04ADF   19  nagf_file_close
Close file associated with given unit number
Related keywords: close fileinput utilitiesoutput utilities
file opening X04ACF   19  nagf_file_open
Open unit number for reading, writing or appending, and associate unit with named file
Related keywords: input utilitiesopen fileoutput utilities
filter G13EJF   25  nagf_tsa_kalman_unscented_state_revcom
Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise (reverse communication)
Related keywords: big datadata analyticstime seriestime series analysistransformUKFunscentedUT
G13EKF   25  nagf_tsa_kalman_unscented_state
Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise
Related keywords: big datadata analyticstime seriestime series analysisUKFunscented
filtering G13BAF   10  nagf_tsa_multi_filter_arima
Multivariate time series, filtering (pre-whitening) by an ARIMA model
Related keywords: ARIMAbig datadata analyticsfinancemultivariate time seriespre-whitening, filteringtime seriestime series analysis
G13BBF   11  nagf_tsa_multi_filter_transf
Multivariate time series, filtering by a transfer function model
Related keywords: big datadata analyticsfinancemultivariate time seriestime seriestime series analysis
finance C05AUF   23  nagf_roots_contfn_brent_interval
Zero of continuous function, Brent algorithm, from a given starting value, binary search for interval
Related keywords: Brent algorithmroot-findingroots of transcendental equationszeros of transcendental functions
C05AVF   nagf_roots_contfn_interval_rcomm
Binary search for interval containing zero of continuous function (reverse communication)
Related keywords: root-findingroots of transcendental equationszeros of transcendental functions
C05AWF   23  nagf_roots_contfn_cntin
Zero of continuous function, continuation method, from a given starting value
Related keywords: root-findingroots of transcendental equationszeros of transcendental functions
C05AXF   nagf_roots_contfn_cntin_rcomm
Zero of continuous function, continuation method, from a given starting value (reverse communication)
Related keywords: root-findingroots of transcendental equationszeros of transcendental functions
C05AYF   23  nagf_roots_contfn_brent
Zero of continuous function in a given interval, Brent algorithm
Related keywords: Brent algorithmroot-findingroots of transcendental equationszeros of transcendental functions
C05AZF   nagf_roots_contfn_brent_rcomm
Zero of continuous function in a given interval, Brent algorithm (reverse communication)
Related keywords: Brent algorithmroot-findingroots of transcendental equationszeros of transcendental functions
C05QBF   23  nagf_roots_sys_func_easy
Solution of a system of nonlinear equations using function values only (easy-to-use)
Related keywords: root-findingroots of transcendental equationszeros of transcendental functions
C05QCF   23  nagf_roots_sys_func_expert
Solution of a system of nonlinear equations using function values only (comprehensive)
Related keywords: root-findingroots of transcendental equationszeros of transcendental functions
C05QDF   23  nagf_roots_sys_func_rcomm
Solution of a system of nonlinear equations using function values only (reverse communication)
Related keywords: root-findingroots of transcendental equationszeros of transcendental functions
C05RBF   23  nagf_roots_sys_deriv_easy
Solution of a system of nonlinear equations using first derivatives (easy-to-use)
Related keywords: root-findingroots of transcendental equationszeros of transcendental functions
C05RCF   23  nagf_roots_sys_deriv_expert
Solution of a system of nonlinear equations using first derivatives (comprehensive)
Related keywords: root-findingroots of transcendental equationszeros of transcendental functions
C05RDF   23  nagf_roots_sys_deriv_rcomm
Solution of a system of nonlinear equations using first derivatives (reverse communication)
Related keywords: root-findingroots of transcendental equationszeros of transcendental functions
C05ZDF   23  nagf_roots_sys_deriv_check
Check user's routine for calculating first derivatives of a set of nonlinear functions of several variables
Related keywords: check derivativeroots of transcendental equations
C09CAF   22  nagf_wav_1d_sngl_fwd
One-dimensional discrete wavelet transform
Related keywords: discrete transformwaveletswavelets, one-dimensionalwavelet transforms
C09CBF   22  nagf_wav_1d_sngl_inv
One-dimensional inverse discrete wavelet transform
Related keywords: discrete transformwaveletswavelets, one-dimensionalwavelet transforms
C09CCF   22  nagf_wav_1d_multi_fwd
One-dimensional multi-level discrete wavelet transform
Related keywords: multi-level discrete transformwaveletswavelets, one-dimensionalwavelet transforms
C09CDF   22  nagf_wav_1d_multi_inv
One-dimensional inverse multi-level discrete wavelet transform
Related keywords: multi-level discrete transformwaveletswavelets, one-dimensionalwavelet transforms
D01AHF   nagf_quad_1d_fin_well
One-dimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands
Related keywords: integration, adaptivequadraturequadrature, adaptive
D01AJF   nagf_quad_1d_fin_bad
One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands
Related keywords: Gauss–Kronrod quadratureintegration, adaptiveQAGSQUADPACKquadraturequadrature, adaptive
D01AKF   nagf_quad_1d_fin_osc
One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions
Related keywords: Gauss–Kronrod quadratureintegration, adaptiveQAGQUADPACKquadraturequadrature, adaptive
D01ALF   nagf_quad_1d_fin_sing
One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points
Related keywords: Gauss–Kronrod quadratureintegration, adaptiveQAGPQUADPACKquadraturequadrature, adaptive
D01AMF   nagf_quad_1d_inf
One-dimensional quadrature, adaptive, infinite or semi-infinite interval
Related keywords: Gauss–Kronrod quadratureintegration, adaptiveintegration, infinite intervalQAGIQUADPACKquadraturequadrature, adaptive
D01ANF   nagf_quad_1d_fin_wtrig
One-dimensional quadrature, adaptive, finite interval, weight function cos ω x or sin ω x
Related keywords: Gauss–Kronrod quadratureintegration, adaptiveQFOURQUADPACKquadraturequadrature, adaptive
D01APF   nagf_quad_1d_fin_wsing
One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type
Related keywords: Gauss–Kronrod quadratureintegration, adaptiveQAWSEQUADPACKquadraturequadrature, adaptive
D01AQF   nagf_quad_1d_fin_wcauchy
One-dimensional quadrature, adaptive, finite interval, weight function 1 / x - c , Cauchy principal value (Hilbert transform)
Related keywords: Cauchy principal valueGauss–Kronrod quadratureHilbert transformintegration, adaptiveQAWCQUADPACKquadraturequadrature, adaptive
D01ARF   10  nagf_quad_1d_indef
One-dimensional quadrature, non-adaptive, finite interval with provision for indefinite integrals
Related keywords: quadraturequadrature non-adaptive
D01ASF   13  nagf_quad_1d_inf_wtrig
One-dimensional quadrature, adaptive, semi-infinite interval, weight function cos ω x or sin ω x
Related keywords: Gauss–Kronrod quadratureintegration, adaptiveintegration, infinite intervalQAWFEQUADPACKquadraturequadrature, adaptivevectorized quadrature
D01AUF   13  nagf_quad_1d_fin_osc_vec
One-dimensional quadrature, adaptive, finite interval, variant of D01AKF efficient on vector machines
Related keywords: integration, adaptivequadraturequadrature, adaptive
D01BCF   nagf_quad_1d_gauss_wgen
Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule
Related keywords: abscissaecubatureintegration, non-adaptivequadratureweights and abscissae
D01BDF   nagf_quad_1d_fin_smooth
One-dimensional quadrature, non-adaptive, finite interval
Related keywords: integration, non-adaptivequadraturequadrature non-adaptive
D01DAF   nagf_quad_2d_fin
Two-dimensional quadrature, finite region
Related keywords: integration, multidimensionalquadraturequadrature, adaptive
D01FBF   nagf_quad_md_gauss
Multidimensional Gaussian quadrature over hyper-rectangle
Related keywords: integration, multidimensionalintegration, non-adaptivequadraturequadrature non-adaptive
D01FCF   nagf_quad_md_adapt
Multidimensional adaptive quadrature over hyper-rectangle
Related keywords: integration, adaptiveintegration, multidimensionalquadraturequadrature, adaptive
D01GAF   nagf_quad_1d_data
One-dimensional quadrature, integration of function defined by data values, Gill–Miller method
Related keywords: Gill–Miller quadratureintegration, non-adaptivequadraturequadrature non-adaptive
D01GDF   14  nagf_quad_md_numth_vec
Multidimensional quadrature, general product region, number-theoretic method, variant of D01GCF efficient on vector machines
Related keywords: integration, multidimensionalquadraturequadrature non-adaptive
D01GYF   10  nagf_quad_md_numth_coeff_prime
Korobov optimal coefficients for use in D01GCF or D01GDF, when number of points is prime
Related keywords: Korobov–Conroy method, numerical integrationquadrature
D01GZF   10  nagf_quad_md_numth_coeff_2prime
Korobov optimal coefficients for use in D01GCF or D01GDF, when number of points is product of two primes
Related keywords: Korobov–Conroy method, numerical integrationquadrature
D01JAF   10  nagf_quad_md_sphere_bad
Multidimensional quadrature over an n -sphere, allowing for badly behaved integrands
Related keywords: integration, multidimensionalquadraturequadrature non-adaptive
D01PAF   10  nagf_quad_md_simplex
Multidimensional quadrature over an n -simplex
Related keywords: integration, multidimensionalquadraturequadrature non-adaptive
D01RGF   24  nagf_quad_1d_fin_gonnet_vec
One-dimensional quadrature, adaptive, finite interval, strategy due to Gonnet, allowing for badly behaved integrands
Related keywords: Gonnet method, quadratureintegration, adaptivequadraturequadrature, adaptive
E01AAF   nagf_interp_1d_aitken
Interpolated values, Aitken's technique, unequally spaced data, one variable
Related keywords: Aitken's methodinterpolation
E01BAF   nagf_interp_1d_spline
Interpolating functions, cubic spline interpolant, one variable
Related keywords: cubic splineinterpolationone-dimensional
E01BEF   13  nagf_interp_1d_monotonic
Interpolating functions, monotonicity-preserving, piecewise cubic Hermite, one variable
Related keywords: cubic spline interpolationHermite interpolationinterpolationmonotonicity-preserving spline
E01BFF   13  nagf_interp_1d_monotonic_eval
Interpolated values, interpolant computed by E01BEF, function only, one variable
Related keywords: Hermite interpolationinterpolationmonotonicity-preserving spline
E01BGF   13  nagf_interp_1d_monotonic_deriv
Interpolated values, interpolant computed by E01BEF, function and first derivative, one variable
Related keywords: Hermite interpolationinterpolationmonotonicity-preserving spline
E01BHF   13  nagf_interp_1d_monotonic_intg
Interpolated values, interpolant computed by E01BEF, definite integral, one variable
Related keywords: Hermite interpolationinterpolationmonotonicity-preserving spline
E01DAF   14  nagf_interp_2d_spline_grid
Interpolating functions, fitting bicubic spline, data on rectangular grid
Related keywords: bicubic splineinterpolationtwo-dimensional
E01EBF   25  nagf_interp_2d_triang_bary_eval
Barycentric interpolation on function values provided on a two-dimensional scattered grid
Related keywords: Barycentric interpolationBilinear interpolationinterpolationInterpolationRenka and Cline methodScattered dataScattered data interpolationTriangulation
E02BBF   nagf_fit_1dspline_eval
Evaluation of fitted cubic spline, function only
Related keywords: B-splinescubic splinescurve and surface fitting
E02BCF   nagf_fit_1dspline_deriv
Evaluation of fitted cubic spline, function and derivatives
Related keywords: b-splines, derivativecubic splinescurve and surface fitting
E02DEF   14  nagf_fit_2dspline_evalv
Evaluation of fitted bicubic spline at a vector of points
Related keywords: bicubic splinesB-splinescurve and surface fitting
E02DFF   14  nagf_fit_2dspline_evalm
Evaluation of fitted bicubic spline at a mesh of points
Related keywords: bicubic splinesB-splinescurve and surface fittinggridded data
E04ABF   nagf_opt_one_var_func_old
Minimum, function of one variable, using function values only
Related keywords: derivative-free minimizationmaximizing a functionminimization, unconstrainedminimizing a functionNLPnonlinear programmingone-dimensional quadratic interpolationoptimizationunivariate minimization
E04BBF   nagf_opt_one_var_deriv_old
Minimum, function of one variable, using first derivative
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingone-dimensional cubic interpolationoptimization
E04CBF   22  nagf_opt_uncon_simplex
Unconstrained minimum, Nelder–Mead simplex algorithm, using function values only
Related keywords: derivative-free minimizationmaximizing a functionminimization, unconstrainedminimizing a functionNelder–Mead algorithmNLPnonlinear programmingoptimizationsimplex algorithm
E04DGF   12  nagf_opt_uncon_conjgrd_comp_old
Unconstrained minimum, preconditioned conjugate gradient algorithm, using first derivatives (comprehensive)
Related keywords: conjugate gradient methodmaximizing a functionminimization, unconstrainedminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton
E04FCF   nagf_opt_lsq_uncon_mod_func_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (comprehensive)
Related keywords: data fittingderivative-free minimizationGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04FYF   18  nagf_opt_lsq_uncon_mod_func_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (easy-to-use)
Related keywords: data fittingderivative-free minimizationGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04GBF   nagf_opt_lsq_uncon_quasi_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (comprehensive)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmdata fittingGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationquasi-Newton algorithmsum-of-squares minimization
E04GDF   nagf_opt_lsq_uncon_mod_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (comprehensive)
Related keywords: data fittingGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04GYF   18  nagf_opt_lsq_uncon_quasi_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmdata fittingGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationquasi-Newton algorithmsum-of-squares minimization
E04GZF   18  nagf_opt_lsq_uncon_mod_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (easy-to-use)
Related keywords: data fittingGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04HCF   nagf_opt_check_deriv
Check user's routine for calculating first derivatives of function
Related keywords: check derivativemaximizing a functionminimization, unconstrainedminimizing a functionoptimizationservice routine
E04HDF   nagf_opt_check_deriv2
Check user's routine for calculating second derivatives of function
Related keywords: check derivativemaximizing a functionminimization, unconstrainedminimizing a functionoptimizationservice routine
E04HEF   nagf_opt_lsq_uncon_mod_deriv2_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive)
Related keywords: data fittingGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04HYF   18  nagf_opt_lsq_uncon_mod_deriv2_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use)
Related keywords: data fittingGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04JCF   23  nagf_opt_bounds_bobyqa_func
Bound constrained minimum, model-based algorithm, using function values only
Related keywords: BOBYQA methodmaximizing a functionminimization, simple bound constraintsminimizing a functionNLPnonlinear programmingoptimization
E04JYF   18  nagf_opt_bounds_quasi_func_easy
Bound constrained minimum, quasi-Newton algorithm, using function values only (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmmaximizing a functionminimization, simple bound constraintsminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton algorithm
E04KDF   nagf_opt_bounds_mod_deriv_comp
Bound constrained minimum, modified Newton algorithm, using first derivatives (comprehensive)
Related keywords: maximizing a functionminimization, simple bound constraintsminimizing a functionNewton algorithmNLPnonlinear programmingoptimization
E04KYF   18  nagf_opt_bounds_quasi_deriv_easy
Bound constrained minimum, quasi-Newton algorithm, using first derivatives (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmmaximizing a functionminimization, simple bound constraintsminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton algorithm
E04KZF   18  nagf_opt_bounds_mod_deriv_easy
Bound constrained minimum, modified Newton algorithm, using first derivatives (easy-to-use)
Related keywords: maximizing a functionminimization, simple bound constraintsminimizing a functionNewton algorithmNLPnonlinear programmingoptimization
E04LBF   nagf_opt_bounds_mod_deriv2_comp
Bound constrained minimum, modified Newton algorithm, using first and second derivatives (comprehensive)
Related keywords: maximizing a functionminimization, simple bound constraintsminimizing a functionNewton algorithmNLPnonlinear programmingoptimization
E04LYF   18  nagf_opt_bounds_mod_deriv2_easy
Bound constrained minimum, modified Newton algorithm, using first and second derivatives (easy-to-use)
Related keywords: maximizing a functionminimization, simple bound constraintsminimizing a functionNewton algorithmNLPnonlinear programmingoptimization
E04MFF   16  nagf_opt_lp_solve_old
Linear programming (LP), dense, active-set method
Related keywords: active-set methodLP, linear programmingmaximizing a functionminimizing a functionoptimization
E04NCF   12  nagf_opt_lsq_lincon_solve_old
Linear programming (LP) convex quadratic programming (QP) or linearly-constrained linear least squares problem, dense
Related keywords: active-setconvex optimizationdata fittingleast squaresmaximizing a functionminimizing a functionnonlinear least squaresoptimizationQP, quadratic programming
E04NFF   16  nagf_opt_qp_dense_solve_old
General (possibly non-convex) quadratic programming (QP), dense, active-set method
Related keywords: active-set methodmaximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04NKF   18  nagf_opt_qpconvex1_sparse_solve_old
Linear programming (LP) or convex quadratic programming (QP), sparse, active-set method
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programmingservice routine
E04NQF   21  nagf_opt_qpconvex2_sparse_solve
Linear programming (LP) or convex quadratic programming (QP), sparse, active-set method, recommended
Related keywords: active-set methodLP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programmingservice routinesparse convex QP prolem
E04PCF   24  nagf_opt_bnd_lin_lsq
Computes the least squares solution to a set of linear equations subject to fixed upper and lower bounds on the variables. An option is provided to return a minimal length solution if a solution is not unique
Related keywords: BVLS, bounded variable least squaresdata fittingmaximizing a functionminimizing a functionNNLS, non-negative least squaresnonlinear least squaresnon-negative least squaresoptimization
E04UCF   12  nagf_opt_nlp1_solve_old
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: densemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationsequential QP methodSQP
E04UFF   18  nagf_opt_nlp1_rcomm_old
Nonlinear programming (NLP), dense, active-set, SQP method, using function values and optionally first derivatives (reverse communication, comprehensive)
Related keywords: densemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationsequential QP methodSQP
E04UGF   19  nagf_opt_nlp1_sparse_solve_old
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationsequential QP methodSQP
E04USF   14  nagf_opt_lsq_gencon_deriv_old
Minimum of a sum of squares, nonlinear constraints, dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: data fittingmaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear least squaresnonlinear programmingoptimizationquasi-Newton approximationsequential QP methodsum of squares
E04VHF   21  nagf_opt_nlp2_sparse_solve
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: LP, linear programmingmaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton algorithmsequential QP methodsimplex algorithmSQP
E04VJF   21  nagf_opt_nlp2_sparse_jacobian
Determine the pattern of nonzeros in the Jacobian matrix for E04VHF
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationsparsity structureSQP
E04WDF   21  nagf_opt_nlp2_solve
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: densemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationsequential QP methodSQP
E04XAF   12  nagf_opt_estimate_deriv_old
Estimate (using numerical differentiation) gradient and/or Hessian of a function
Related keywords: Hessian estimationJacobian estimationmaximizing a functionminimizing a functionoptimization
E04YAF   nagf_opt_lsq_check_deriv
Check user's routine for calculating Jacobian of first derivatives
Related keywords: Jacobian estimationmaximizing a functionminimizing a functionoptimizationservice routine
E04YBF   nagf_opt_lsq_check_hessian
Check user's routine for calculating Hessian of a sum of squares
Related keywords: Hessian estimationmaximizing a functionminimizing a functionoptimizationservice routine
E05JBF   22  nagf_glopt_bnd_mcs_solve
Global optimization by multi-level coordinate search, simple bounds, using function values only
Related keywords: global optimizationminimization, simple bound constraintsmulti-level coordinate searchoptions, computational
E05UCF   24  nagf_glopt_nlp_multistart_sqp
Global optimization using multi-start, nonlinear constraints
Related keywords: global optimizationminimization, nonlinear constraintsmulti-start algorithmsequential QP method
E05USF   24  nagf_glopt_nlp_multistart_sqp_lsq
Global optimization of a sum of squares problem using multi-start, nonlinear constraints
Related keywords: global optimizationmulti-start algorithmsequential QP methodsum of squares
F01EDF   23  nagf_matop_real_symm_matrix_exp
Real symmetric matrix exponential
Related keywords: exponential, matrixinversionmatrix exponentialmatrix operationsreal, indefinite, symmetric matrix
F01EFF   23  nagf_matop_real_symm_matrix_fun
Function of a real symmetric matrix
Related keywords: functions, matrixinversionmatrix functionsmatrix operationsreal, indefinite, symmetric matrix
F01FCF   23  nagf_matop_complex_gen_matrix_exp
Complex matrix exponential
Related keywords: complex, nonsymmetric matrixexponential, matrixinversionmatrix exponentialmatrix operations
F01FDF   23  nagf_matop_complex_herm_matrix_exp
Complex Hermitian matrix exponential
Related keywords: complex, Hermitian, indefinite matrixexponential, matrixinversionmatrix exponentialmatrix operations
F01FFF   23  nagf_matop_complex_herm_matrix_fun
Function of a complex Hermitian matrix
Related keywords: complex, Hermitian, indefinite matrixfunctions, matrixinversionmatrix functionsmatrix operations
F01VAF   23  nagf_matop_dtrttp
Copies a real triangular matrix from full format to packed format
Related keywords: DTRTTPinversionLAPACKmatrix operationsreal, triangular matrix
F01VBF   23  nagf_matop_ztrttp
Copies a complex triangular matrix from full format to packed format
Related keywords: complex, triangular matrixinversionLAPACKmatrix operationsZTRTTP
F01VCF   23  nagf_matop_dtpttr
Copies a real triangular matrix from packed format to full format
Related keywords: DTPTTRinversionLAPACKmatrix operationsreal, triangular matrix
F01VDF   23  nagf_matop_ztpttr
Copies a complex triangular matrix from packed format to full format
Related keywords: complex, triangular matrixinversionLAPACKmatrix operationsZTPTTR
F01VEF   23  nagf_matop_dtrttf
Copies a real triangular matrix from full format to Rectangular Full Packed format
Related keywords: DTRTTPinversionLAPACKmatrix operationsreal, triangular matrix
F01VFF   23  nagf_matop_ztrttf
Copies a complex triangular matrix from full format to Rectangular Full Packed format
Related keywords: complex, triangular matrixinversionLAPACKmatrix operationsZTRTTF
F01VGF   23  nagf_matop_dtfttr
Copies a real triangular matrix from Rectangular Full Packed format to full format
Related keywords: DTFTTRinversionLAPACKmatrix operationsreal, triangular matrix
F01VHF   23  nagf_matop_ztfttr
Copies a complex triangular matrix from Rectangular Full Packed format to full format
Related keywords: complex, triangular matrixinversionLAPACKmatrix operationsZTFTTR
F01VJF   23  nagf_matop_dtpttf
Copies a real triangular matrix from packed format to Rectangular Full Packed format
Related keywords: DTPTTFinversionLAPACKmatrix operationsreal, triangular matrix
F01VKF   23  nagf_matop_ztpttf
Copies a complex triangular matrix from packed format to Rectangular Full Packed format
Related keywords: complex, triangular matrixinversionLAPACKmatrix operationsZTPTTF
F01VLF   23  nagf_matop_dtfttp
Copies a real triangular matrix from Rectangular Full Packed format to packed format
Related keywords: DTFTTPinversionLAPACKmatrix operationsreal, triangular matrix
F01VMF   23  nagf_matop_ztfttp
Copies a complex triangular matrix from Rectangular Full Packed format to packed format
Related keywords: complex, triangular matrixinversionLAPACKmatrix operationsZTFTTP
F06BNF   12  nagf_blas_dpyth
Compute square root of a 2 + b 2 , real a and b
Related keywords: BLASelementary arithmeticlinear algebra support routines
F06DBF   12  nagf_blas_iload
Broadcast scalar into integer vector
Related keywords: BLASelementary arithmeticlinear algebra support routines
F06EAF   12  nagf_blas_ddot
Dot product of two real vectors
Related keywords: BLASblas, real matricesddotinner productlinear algebra support routines
F06EFF   12  nagf_blas_dcopy
Copy real vector
Related keywords: BLASblas, real matricesdcopyelementary arithmeticlinear algebra support routines
F06EJF   12  nagf_blas_dnrm2
Compute Euclidean norm of real vector
Related keywords: BLASblas, real matricesdnrm2elementary arithmeticEuclidean normlinear algebra support routines
F06FDF   12  nagf_blas_axpzy
Multiply real vector by scalar, preserving input vector
Related keywords: BLASelementary arithmeticlinear algebra support routines
F06JJF   12  nagf_blas_dznrm2
Compute Euclidean norm of complex vector
Related keywords: BLASblas, complex matricesdznrm2Euclidean normlinear algebra support routines
F06PAF   12  nagf_blas_dgemv
Matrix-vector product, real rectangular matrix
Related keywords: BLASblas, real matricesdgemvlinear algebra support routinesmultiply, matrixreal, m by n matrix
F06PJF   12  nagf_blas_dtrsv
System of equations, real triangular matrix
Related keywords: BLASblas, real matricesdtrsvlinear algebra support routineslinear equationsreal, triangular matrix
F06QFF   13  nagf_blas_dmcopy
Matrix copy, real rectangular or trapezoidal matrix
Related keywords: BLAScopy, vectors and matriceselementary arithmeticlinear algebra support routinesreal, m by n matrixreal, trapezoidal matrix
F06QHF   13  nagf_blas_dmload
Matrix initialization, real rectangular matrix
Related keywords: BLASelementary arithmeticlinear algebra support routinesreal, m by n matrix
F06YAF   14  nagf_blas_dgemm
Matrix-matrix product, two real rectangular matrices
Related keywords: BLASblas, real matricesdgemmlinear algebra support routinesmultiply, matrixreal, m by n matrix
F06YJF   14  nagf_blas_dtrsm
Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix
Related keywords: BLASblas, real matriceslinear algebra support routineslinear equationsreal, triangular matrix
F07AAF   21  nagf_lapacklin_dgesv
Computes the solution to a real system of linear equations
Related keywords: DGESVLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
F07ABF   21  nagf_lapacklin_dgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
Related keywords: backward errorcondition number, matrixDGESVXerror bound, matrixforward errorLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
F07ADF   15  nagf_lapacklin_dgetrf
L U factorization of real m by n matrix
Related keywords: DGETRFLAPACKlinear equations L U decompositionreal, m by n matrix
F07AJF   15  nagf_lapacklin_dgetri
Inverse of real matrix, matrix already factorized by F07ADF
Related keywords: DGETRIinverse, matrixLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
F07APF   21  nagf_lapacklin_zgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
Related keywords: backward errorcomplex, nonsymmetric matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equations L U decompositionZGESVX
F07ARF   15  nagf_lapacklin_zgetrf
L U factorization of complex m by n matrix
Related keywords: complex, m by n matrixLAPACKlinear equations L U decompositionZGETRF
F07ASF   15  nagf_lapacklin_zgetrs
Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by F07ARF
Related keywords: complex, nonsymmetric matrixLAPACKlinear equations L U decompositionZGETRS
F07CAF   21  nagf_lapacklin_dgtsv
Computes the solution to a real tridiagonal system of linear equations
Related keywords: DGTSVLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
F07CDF   22  nagf_lapacklin_dgttrf
L U factorization of real tridiagonal matrix
Related keywords: DGTTRFLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
F07CEF   22  nagf_lapacklin_dgttrs
Solves a real tridiagonal system of linear equations using the L U factorization computed by F07CDF
Related keywords: DGTTRSLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
F07FAF   21  nagf_lapacklin_dposv
Computes the solution to a real symmetric positive definite system of linear equations
Related keywords: Cholesky decompositionDPOSVLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FBF   21  nagf_lapacklin_dposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixDPOSVXerror bound, matrixforward errorLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FDF   15  nagf_lapacklin_dpotrf
Cholesky factorization of real symmetric positive definite matrix
Related keywords: Cholesky decompositionDPOTRFLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FEF   15  nagf_lapacklin_dpotrs
Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FDF
Related keywords: Cholesky decompositionDPOTRSLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FJF   15  nagf_lapacklin_dpotri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07FDF
Related keywords: Cholesky decompositionDPOTRIinverse, matrixLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FPF   21  nagf_lapacklin_zposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsZPOSVX
F07HDF   15  nagf_lapacklin_dpbtrf
Cholesky factorization of real symmetric positive definite band matrix
Related keywords: Cholesky decompositionDPBTRFLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
F07HEF   15  nagf_lapacklin_dpbtrs
Solution of real symmetric positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HDF
Related keywords: Cholesky decompositionDPBTRSLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
F07TEF   15  nagf_lapacklin_dtrtrs
Solution of real triangular system of linear equations, multiple right-hand sides
Related keywords: DTRTRSLAPACKlinear equationsreal, triangular matrix
F07THF   15  nagf_lapacklin_dtrrfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorDTRRFSerror bound, matrixforward errorLAPACKlinear equationsreal, triangular matrix
F07TJF   15  nagf_lapacklin_dtrtri
Inverse of real triangular matrix
Related keywords: DTRTRIinverse, matrixLAPACKlinear equationsreal, triangular matrix
F08AAF   21  nagf_lapackeig_dgels
Solves a real linear least squares problem of full rank
Related keywords: DGELSeigenproblemLAPACKLAPACKleast squareslinear least squares LQ decompositionoverdetermined linear equations QR factorizationreal, m by n matrixunderdetermined linear system
F08AEF   16  nagf_lapackeig_dgeqrf
Performs a Q R factorization of real general rectangular matrix
Related keywords: DGEQRFeigenproblemLAPACKLAPACKleast squares QR factorizationreal, m by n matrix
F08AGF   16  nagf_lapackeig_dormqr
Applies an orthogonal transformation determined by F08AEF F08BEF F08BFF
Related keywords: DORMQReigenproblemLAPACKLAPACKleast squaresorthogonal transformations QR factorization
F08ANF   21  nagf_lapackeig_zgels
Solves a complex linear least problem of full rank
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squareslinear least squares LQ decompositionoverdetermined linear equations QR factorizationunderdetermined linear systemZGELS
F08BAF   21  nagf_lapackeig_dgelsy
Computes the minimum-norm solution to a real linear least squares problem
Related keywords: DGELSYeigenproblemLAPACKLAPACKleast squareslinear least squaresminimal least squaresreal, m by n matrix
F08BEF   16  nagf_lapackeig_dgeqpf
Q R factorization, with column pivoting, of real general rectangular matrix
Related keywords: DGEQPFeigenproblemLAPACKLAPACKleast squaresorthogonal transformations QR factorizationreal, m by n matrix
F08BFF   22  nagf_lapackeig_dgeqp3
Q R factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
Related keywords: DGEQP3eigenproblemLAPACKLAPACKleast squaresorthogonal transformations QR factorizationreal, m by n matrix
F08FAF   21  nagf_lapackeig_dsyev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Related keywords: DSYEVeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08FBF   21  nagf_lapackeig_dsyevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Related keywords: DSYEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08FCF   19  nagf_lapackeig_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
Related keywords: divide-and-conquer methodDSYEVDeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08FLF   22  nagf_lapackeig_ddisna
Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix
Related keywords: complex, Hermitian, indefinite matrixcondition number, matrixDDISNAeigenproblemeigenvectorsLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08FPF   21  nagf_lapackeig_zheevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresZHEEVX
F08FQF   19  nagf_lapackeig_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
Related keywords: complex, Hermitian, indefinite matrixdivide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresZHEEVD
F08KBF   21  nagf_lapackeig_dgesvd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
Related keywords: DGESVDeigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrixSVD, singular value decomposition
F08KCF   21  nagf_lapackeig_dgelsd
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
Related keywords: DGELSDdivide-and-conquer methodeigenproblemLAPACKLAPACKleast squareslinear least squaresminimal least squaresreal, m by n matrixSVD, singular value decomposition
F08KDF   21  nagf_lapackeig_dgesdd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
Related keywords: DGESDDdivide-and-conquer methodeigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrixSVD, singular value decomposition
F08KPF   21  nagf_lapackeig_zgesvd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
Related keywords: complex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresSVD, singular value decompositionZGESVD
F08NBF   21  nagf_lapackeig_dgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGEEVXeigenproblemeigenvalueseigenvectorsforward errorLAPACKLAPACKleast squaresorthogonal transformations QR algorithmreal, nonsymmetric matrix
F08NPF   21  nagf_lapackeig_zgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixcondition number, matrixDGEEVeigenproblemeigenvalueseigenvectorsforward errorLAPACKLAPACKleast squares
F08WBF   21  nagf_lapackeig_dggevx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGGEVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsforward errorgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WPF   21  nagf_lapackeig_zggevx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixcondition number, matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsforward errorgeneralized eigenproblemLAPACKLAPACKleast squaresZGGEVX
G01ADF   nagf_stat_summary_freq
Mean, variance, skewness, kurtosis, etc., one variable, from frequency table
Related keywords: kurtosismeanSimple Calculations on Statistical Dataskewnessstandard deviation
G01AEF   nagf_stat_frequency_table
Frequency table from raw data
Related keywords: frequency distributionfrequency tableSimple Calculations on Statistical Data
G01AFF   nagf_stat_contingency_table
Two-way contingency table analysis, with χ 2 /Fisher's exact test
Related keywords: chi-squared distributioncontingency tableFisher's exact testSimple Calculations on Statistical Datatwo-way contingency tableYates' correction
G01ALF   14  nagf_stat_5pt_summary
Computes a five-point summary (median, hinges and extremes)
Related keywords: five-point summaryhingesmaximum valuemedianminimum valueSimple Calculations on Statistical Data
G01AMF   22  nagf_stat_quantiles
Find quantiles of an unordered vector, real numbers
Related keywords: quantilesSimple Calculations on Statistical Data
G01BJF   13  nagf_stat_prob_binomial
Binomial distribution function
Related keywords: binomial distributionCDF, cumulative distribution functionSimple Calculations on Statistical Data
G01BKF   13  nagf_stat_prob_poisson
Poisson distribution function
Related keywords: CDF, cumulative distribution functionPoisson distributionSimple Calculations on Statistical Data
G01BLF   13  nagf_stat_prob_hypergeom
Hypergeometric distribution function
Related keywords: CDF, cumulative distribution functionhypergeometric distributionSimple Calculations on Statistical Data
G01DAF   nagf_stat_normal_scores_exact
Normal scores, accurate values
Related keywords: Normal scoresSimple Calculations on Statistical Data
G01DBF   12  nagf_stat_normal_scores_approx
Normal scores, approximate values
Related keywords: Normal scoresSimple Calculations on Statistical Data
G01DCF   12  nagf_stat_normal_scores_var
Normal scores, approximate variance-covariance matrix
Related keywords: covariance matrixNormal scoresSimple Calculations on Statistical Datavariance-covariance matrix
G01DDF   12  nagf_stat_test_shapiro_wilk
Shapiro and Wilk's W test for Normality
Related keywords: Shapiro and Wilk's W test for NormalitySimple Calculations on Statistical DataW test for Normality
G01DHF   15  nagf_stat_ranks_and_scores
Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores
Related keywords: Blom scoresexponential scoresrank scoresSavage scoresSimple Calculations on Statistical DataTukey scoresvan der Waerden scores
G01EAF   15  nagf_stat_prob_normal
Computes probabilities for the standard Normal distribution
Related keywords: CDF, cumulative distribution functionlower tail probabilityNormal distributionprobabilitySimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01EBF   14  nagf_stat_prob_students_t
Computes probabilities for Student's t -distribution
Related keywords: CDF, cumulative distribution functionlower tail probabilityprobabilitySimple Calculations on Statistical DataStudent's t -distributiontwo-tail probabilityupper tail probability
G01ECF   14  nagf_stat_prob_chisq
Computes probabilities for χ 2 distribution
Related keywords: CDF, cumulative distribution functionchi-squared distributionlower tail probabilityprobabilitySimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01EDF   14  nagf_stat_prob_f
Computes probabilities for F -distribution
Related keywords: CDF, cumulative distribution function F -distributionlower tail probabilityprobabilitySimple Calculations on Statistical Dataupper tail probabilityvariance-ratio distribution
G01EEF   14  nagf_stat_prob_beta
Computes upper and lower tail probabilities and probability density function for the beta distribution
Related keywords: beta distributionCDF, cumulative distribution functionlower tail probabilityprobabilitySimple Calculations on Statistical Dataupper tail probability
G01EFF   14  nagf_stat_prob_gamma
Computes probabilities for the gamma distribution
Related keywords: CDF, cumulative distribution functiongamma distributionlower tail probabilityprobabilitySimple Calculations on Statistical Dataupper tail probability
G01EMF   15  nagf_stat_prob_studentized_range
Computes probability for the Studentized range statistic
Related keywords: CDF, cumulative distribution functionprobabilitySimple Calculations on Statistical DataStudentized range statistic
G01EPF   15  nagf_stat_prob_durbin_watson
Computes bounds for the significance of a Durbin–Watson statistic
Related keywords: CDF, cumulative distribution functionDurbin–Watson statisticsignificanceSimple Calculations on Statistical Data
G01ERF   16  nagf_stat_prob_vonmises
Computes probability for von Mises distribution
Related keywords: CDF, cumulative distribution functionlower tail probabilitySimple Calculations on Statistical Datavon Mises distribution
G01ETF   21  nagf_stat_prob_landau
Landau distribution function
Related keywords: Landau distributionSimple Calculations on Statistical Data
G01EUF   21  nagf_stat_prob_vavilov
Vavilov distribution function
Related keywords: Simple Calculations on Statistical DataVavilov distribution
G01EYF   14  nagf_stat_prob_kolmogorov1
Computes probabilities for the one-sample Kolmogorov–Smirnov distribution
Related keywords: Kolmogorov–Smirnov distributionSimple Calculations on Statistical Dataupper tail probability
G01EZF   14  nagf_stat_prob_kolmogorov2
Computes probabilities for the two-sample Kolmogorov–Smirnov distribution
Related keywords: Kolmogorov–Smirnov distributionSimple Calculations on Statistical Dataupper tail probability
G01FAF   15  nagf_stat_inv_cdf_normal
Computes deviates for the standard Normal distribution
Related keywords: deviatesinverse CDFinverse cumulative distribution functionNormal distributionSimple Calculations on Statistical Data
G01FBF   14  nagf_stat_inv_cdf_students_t
Computes deviates for Student's t -distribution
Related keywords: deviatesinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical DataStudent's t -distribution
G01FCF   14  nagf_stat_inv_cdf_chisq
Computes deviates for the χ 2 distribution
Related keywords: chi-squared distributiondeviatesinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01FDF   14  nagf_stat_inv_cdf_f
Computes deviates for the F -distribution
Related keywords: deviates F -distributioninverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01FEF   14  nagf_stat_inv_cdf_beta
Computes deviates for the beta distribution
Related keywords: beta distributiondeviatesinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01FFF   14  nagf_stat_inv_cdf_gamma
Computes deviates for the gamma distribution
Related keywords: deviatesgamma distributioninverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01FMF   15  nagf_stat_inv_cdf_studentized_range
Computes deviates for the Studentized range statistic
Related keywords: deviatesinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical DataStudentized range statistic
G01FTF   21  nagf_stat_inv_cdf_landau
Landau inverse function Ψ x
Related keywords: inverse Landau functionLandau distributionSimple Calculations on Statistical Data
G01GBF   14  nagf_stat_prob_students_t_noncentral
Computes probabilities for the non-central Student's t -distribution
Related keywords: lower tail probabilitySimple Calculations on Statistical DataStudent's t -distribution
G01GCF   14  nagf_stat_prob_chisq_noncentral
Computes probabilities for the non-central χ 2 distribution
Related keywords: chi-squared distributionlower tail probabilitySimple Calculations on Statistical Data
G01GDF   14  nagf_stat_prob_f_noncentral
Computes probabilities for the non-central F -distribution
Related keywords: F -distributionlower tail probabilitySimple Calculations on Statistical Datavariance-ratio distribution
G01GEF   14  nagf_stat_prob_beta_noncentral
Computes probabilities for the non-central beta distribution
Related keywords: beta distributionlower tail probabilitySimple Calculations on Statistical Data
G01HAF   14  nagf_stat_prob_bivariate_normal
Computes probability for the bivariate Normal distribution
Related keywords: bivariate Normal distributionlower tail probabilityNormal distributionSimple Calculations on Statistical Data
G01HBF   15  nagf_stat_prob_multi_normal
Computes probabilities for the multivariate Normal distribution
Related keywords: central probabilitylower tail probabilitymultivariate Normal distributionNormal distributionSimple Calculations on Statistical Dataupper tail probability
G01JCF   14  nagf_stat_prob_chisq_noncentral_lincomb
Computes probability for a positive linear combination of χ 2 variables
Related keywords: chi-squared distributionlower tail probabilitySimple Calculations on Statistical Data
G01JDF   15  nagf_stat_prob_chisq_lincomb
Computes lower tail probability for a linear combination of (central) χ 2 variables
Related keywords: chi-squared distributionImhof's methodlower tail probabilityPan's methodSimple Calculations on Statistical Data
G01MBF   15  nagf_stat_mills_ratio
Computes reciprocal of Mills' Ratio
Related keywords: hazard rateMills' RatioSimple Calculations on Statistical Data
G01MTF   21  nagf_stat_pdf_landau
Landau density function ϕ λ
Related keywords: Landau density functionSimple Calculations on Statistical Data
G01MUF   21  nagf_stat_pdf_vavilov
Vavilov density function ϕ V λ ; κ , β 2
Related keywords: Simple Calculations on Statistical DataVavilov density function
G01NAF   16  nagf_stat_moments_quad_form
Cumulants and moments of quadratic forms in Normal variables
Related keywords: cumulantGaussian distributionmoments quadratic formmultivariate Normal distributionNormal distributionSimple Calculations on Statistical Data
G01NBF   16  nagf_stat_moments_ratio_quad_forms
Moments of ratios of quadratic forms in Normal variables, and related statistics
Related keywords: Gaussian distributionmoments quadratic formmultivariate Normal distributionNormal distributionSimple Calculations on Statistical Data
G01PTF   21  nagf_stat_pdf_landau_moment1
Landau first moment function Φ 1 x
Related keywords: Landau moment functionSimple Calculations on Statistical Data
G01QTF   21  nagf_stat_pdf_landau_moment2
Landau second moment function Φ 2 x
Related keywords: Landau moment functionSimple Calculations on Statistical Data
G01RTF   21  nagf_stat_pdf_landau_deriv
Landau derivative function ϕ λ
Related keywords: derivative, Landau density functionLandau density functionSimple Calculations on Statistical Data
G01ZUF   21  nagf_stat_init_vavilov
Initialization routine for G01MUF and G01EUF
Related keywords: Simple Calculations on Statistical DataVavilov density function
G02AAF   22  nagf_correg_corrmat_nearest
Computes the nearest correlation matrix to a real square matrix, using the method of Qi and Sun
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsnearest correlation matrixnonlinear regressionpolynomial regressionQi and Sun algorithmregression analysis
G02ABF   23  nagf_correg_corrmat_nearest_bounded
Computes the nearest correlation matrix to a real square matrix, augmenting G02AAF to incorporate weights and bounds
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsnearest correlation matrixnonlinear regressionpolynomial regressionQi and Sun algorithmregression analysis
G02AEF   23  nagf_correg_corrmat_nearest_kfactor
Computes the nearest correlation matrix with k -factor structure to a real square matrix
Related keywords: big datacorrelation analysiscorrelation matrixdata analytics k -factor structurenearest correlation matrixnonlinear regressionpolynomial regressionQi and Sun algorithmregression analysis
G02BAF   nagf_correg_coeffs_pearson
Pearson product-moment correlation coefficients, all variables, no missing values
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsnonlinear regressionPearson product moment correlationpolynomial regressionregression analysis
G02BBF   nagf_correg_coeffs_pearson_miss_case
Pearson product-moment correlation coefficients, all variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsmissing valuesnonlinear regressionPearson product moment correlationpolynomial regressionregression analysis
G02BCF   nagf_correg_coeffs_pearson_miss_pair
Pearson product-moment correlation coefficients, all variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsmissing valuesnonlinear regressionPearson product moment correlationpolynomial regressionregression analysis
G02BDF   nagf_correg_coeffs_zero
Correlation-like coefficients (about zero), all variables, no missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsmeannonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BEF   nagf_correg_coeffs_zero_miss_case
Correlation-like coefficients (about zero), all variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsmeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BFF   nagf_correg_coeffs_zero_miss_pair
Correlation-like coefficients (about zero), all variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsmeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BGF   nagf_correg_coeffs_pearson_subset
Pearson product-moment correlation coefficients, subset of variables, no missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsmeannonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviationsum of squares
G02BHF   nagf_correg_coeffs_pearson_subset_miss_case
Pearson product-moment correlation coefficients, subset of variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsmeanmissing valuesnonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviationsum of squares
G02BJF   nagf_correg_coeffs_pearson_subset_miss_pair
Pearson product-moment correlation coefficients, subset of variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsmeanmissing valuesnonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviationsum of squares
G02BKF   nagf_correg_coeffs_zero_subset
Correlation-like coefficients (about zero), subset of variables, no missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsmeannonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BLF   nagf_correg_coeffs_zero_subset_miss_case
Correlation-like coefficients (about zero), subset of variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsmeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BMF   nagf_correg_coeffs_zero_subset_miss_pair
Correlation-like coefficients (about zero), subset of variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsmeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BNF   nagf_correg_coeffs_kspearman_overwrite
Kendall/Spearman non-parametric rank correlation coefficients, no missing values, overwriting input data
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsKendall's tau correlation coefficientnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02BPF   nagf_correg_coeffs_kspearman_miss_case_overwrite
Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsKendall's tau correlation coefficientmissing valuesnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02BQF   nagf_correg_coeffs_kspearman
Kendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsKendall's tau correlation coefficientnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02BRF   nagf_correg_coeffs_kspearman_miss_case
Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsKendall's tau correlation coefficientmissing valuesnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02BSF   nagf_correg_coeffs_kspearman_miss_pair
Kendall/Spearman non-parametric rank correlation coefficients, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsKendall's tau correlation coefficientmissing valuesnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02BTF   14  nagf_correg_ssqmat_update
Update a weighted sum of squares matrix with a new observation
Related keywords: big datacorrelation analysiscross-productsdata analyticsmeannonlinear regressionpolynomial regressionregression analysissum of squares
G02BUF   14  nagf_correg_ssqmat
Computes a weighted sum of squares matrix
Related keywords: big datacorrelation analysiscross-productsdata analyticsmeannonlinear regressionpolynomial regressionregression analysissum of squaresWest's WV2 algorithm
G02BWF   14  nagf_correg_ssqmat_to_corrmat
Computes a correlation matrix from a sum of squares matrix
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionPearson product moment correlationpolynomial regressionregression analysis
G02BXF   14  nagf_correg_corrmat
Computes (optionally weighted) correlation and covariance matrices
Related keywords: big datacorrelation analysisdata analyticsmeannonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviationvariance-covariance matrix
G02BYF   17  nagf_correg_corrmat_partial
Computes partial correlation/variance-covariance matrix from correlation/variance-covariance matrix computed by G02BXF
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionpartial correlationpolynomial regressionregression analysis
G02CAF   nagf_correg_linregs_const
Simple linear regression with constant term, no missing values
Related keywords: big datacorrelation analysisdata analyticslinear regressionnonlinear regressionpolynomial regressionregressionregression analysis
G02CBF   nagf_correg_linregs_noconst
Simple linear regression without constant term, no missing values
Related keywords: big datacorrelation analysisdata analyticslinear regressionnonlinear regressionpolynomial regressionregressionregression analysis
G02CCF   nagf_correg_linregs_const_miss
Simple linear regression with constant term, missing values
Related keywords: big datacorrelation analysisdata analyticslinear regressionmissing valuesnonlinear regressionpolynomial regressionregressionregression analysis
G02CDF   nagf_correg_linregs_noconst_miss
Simple linear regression without constant term, missing values
Related keywords: big datacorrelation analysisdata analyticslinear regressionmissing valuesnonlinear regressionpolynomial regressionregressionregression analysis
G02CEF   nagf_correg_linregm_service_select
Service routine for multiple linear regression, select elements from vectors and matrices
Related keywords: big datacorrelation analysisdata analyticslinear regressionnonlinear regressionpolynomial regressionregression analysis
G02CFF   nagf_correg_linregm_service_reorder
Service routine for multiple linear regression, reorder elements of vectors and matrices
Related keywords: big datacorrelation analysisdata analyticslinear regressionnonlinear regressionpolynomial regressionregression analysis
G02CGF   nagf_correg_linregm_coeffs_const
Multiple linear regression, from correlation coefficients, with constant term
Related keywords: big datacorrelation analysisdata analyticsmultiple linear regressionnonlinear regressionpolynomial regressionregression analysis
G02CHF   nagf_correg_linregm_coeffs_noconst
Multiple linear regression, from correlation-like coefficients, without constant term
Related keywords: big datacorrelation analysisdata analyticsmultiple linear regressionnonlinear regressionpolynomial regressionregression analysis
G02DAF   14  nagf_correg_linregm_fit
Fits a general (multiple) linear regression model
Related keywords: big datacorrelation analysisdata analyticsmultiple linear regressionnonlinear regressionpolynomial regressionregression analysis
G02DCF   14  nagf_correg_linregm_obs_edit
Add/delete an observation to/from a general linear regression model
Related keywords: big datacorrelation analysisdata analyticslinear regressionnonlinear regressionpolynomial regressionregressionregression analysisstandard errorsvariance-covariance matrix
G02DDF   14  nagf_correg_linregm_update
Estimates of linear parameters and general linear regression model from updated model
Related keywords: big datacorrelation analysisdata analyticslinear regressionnonlinear regressionpolynomial regressionregressionregression analysis
G02DEF   14  nagf_correg_linregm_var_add
Add a new independent variable to a general linear regression model
Related keywords: big datacorrelation analysisdata analyticslinear regressionnonlinear regressionpolynomial regressionregression analysis
G02DFF   14  nagf_correg_linregm_var_del
Delete an independent variable from a general linear regression model
Related keywords: big datacorrelation analysisdata analyticslinear regressionnonlinear regressionpolynomial regressionregression analysis
G02DGF   14  nagf_correg_linregm_fit_newvar
Fits a general linear regression model to new dependent variable
Related keywords: big datacorrelation analysisdata analyticslinear regressionnonlinear regressionpolynomial regressionregression analysis
G02DKF   14  nagf_correg_linregm_constrain
Estimates and standard errors of parameters of a general linear regression model for given constraints
Related keywords: big datacorrelation analysisdata analyticslinear regressionnonlinear regressionpolynomial regressionregression analysisstandard errors
G02DNF   14  nagf_correg_linregm_estfunc
Computes estimable function of a general linear regression model and its standard error
Related keywords: big datacorrelation analysisdata analyticsestimable functionlinear regressionnonlinear regressionpolynomial regressionregression analysis
G02EFF   21  nagf_correg_linregm_fit_stepwise
Stepwise linear regression
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionpolynomial regressionregression analysisstepwise linear regression
G02FAF   14  nagf_correg_linregm_stat_resinf
Calculates standardized residuals and influence statistics
Related keywords: big datacorrelation analysisdata analyticsinfluence statisticsnonlinear regressionpolynomial regressionregression analysisstandardized residuals
G02FCF   15  nagf_correg_linregm_stat_durbwat
Computes Durbin–Watson test statistic
Related keywords: big datacorrelation analysisdata analyticsDurbin–Watson statisticnonlinear regressionpolynomial regressionregression analysissignificance
G02GAF   14  nagf_correg_glm_normal
Fits a generalized linear model with Normal errors
Related keywords: big datacorrelation analysisdata analyticsgeneralized linear modelnonlinear regressionpolynomial regressionregression analysis
G02GBF   14  nagf_correg_glm_binomial
Fits a generalized linear model with binomial errors
Related keywords: big datacorrelation analysisdata analyticsgeneralized linear modellogistic regressionlogitnonlinear regressionpolynomial regressionprobitregression analysis
G02GCF   14  nagf_correg_glm_poisson
Fits a generalized linear model with Poisson errors
Related keywords: big datacorrelation analysisdata analyticsgeneralized linear modelnonlinear regressionpolynomial regressionregression analysis
G02GDF   14  nagf_correg_glm_gamma
Fits a generalized linear model with gamma errors
Related keywords: big datacorrelation analysisdata analyticsgeneralized linear modelnonlinear regressionpolynomial regressionregression analysis
G02GKF   14  nagf_correg_glm_constrain
Estimates and standard errors of parameters of a general linear model for given constraints
Related keywords: big datacorrelation analysisdata analyticsgeneralized linear modelnonlinear regressionpolynomial regressionregression analysisstandard errors
G02GNF   14  nagf_correg_glm_estfunc
Computes estimable function of a generalized linear model and its standard error
Related keywords: big datacorrelation analysisdata analyticsestimable functiongeneralized linear modelnonlinear regressionpolynomial regressionregression analysis
G02GPF   22  nagf_correg_glm_predict
Computes a predicted value and its associated standard error based on a previously fitted generalized linear model
Related keywords: big datacorrelation analysisdata analyticsgeneralized linear modelnonlinear regressionpolynomial regressionpredicted valueregression analysisstandard errors
G02HAF   13  nagf_correg_robustm
Robust regression, standard M -estimates
Related keywords: Andrew's sine wavebig datacorrelation analysisdata analyticsHampel's piecewise linear functionHuber type regressionKrasker–Welsch weightsMallows type regressionMaronna's weights M -estimatesnonlinear regressionpolynomial regressionregressionregression analysisrobust regressionScheppe type regressionTukey's bi-weight
G02HBF   13  nagf_correg_robustm_wts
Robust regression, compute weights for use with G02HDF
Related keywords: big databounded influencecorrelation analysisdata analyticsnonlinear regressionpolynomial regressionregression analysisrobust regression
G02HDF   13  nagf_correg_robustm_user
Robust regression, compute regression with user-supplied functions and weights
Related keywords: big databounded influencecorrelation analysisdata analyticsiterative weighted least squares M -estimatesnonlinear regressionpolynomial regressionregression analysisrobust regression
G02HFF   13  nagf_correg_robustm_user_varmat
Robust regression, variance-covariance matrix following G02HDF
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionpolynomial regressionregression analysisrobust regressionvariance-covariance matrix
G02HKF   14  nagf_correg_robustm_corr_huber
Calculates a robust estimation of a covariance matrix, Huber's weight function
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsHuber's weight functionnonlinear regressionpolynomial regressionregression analysis
G02HLF   14  nagf_correg_robustm_corr_user_deriv
Calculates a robust estimation of a covariance matrix, user-supplied weight function plus derivatives
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsnonlinear regressionpolynomial regressionregression analysisrobust estimation
G02HMF   14  nagf_correg_robustm_corr_user
Calculates a robust estimation of a covariance matrix, user-supplied weight function
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsnonlinear regressionpolynomial regressionregression analysisrobust estimation
G02JAF   21  nagf_correg_mixeff_reml
Linear mixed effects regression using Restricted Maximum Likelihood (REML)
Related keywords: big datacorrelation analysisdata analyticsmaximum likelihoodmixed effects regressionnonlinear regressionpolynomial regressionregression analysisREML, Restricted Maximum Likelihood
G02JBF   21  nagf_correg_mixeff_ml
Linear mixed effects regression using Maximum Likelihood (ML)
Related keywords: big datacorrelation analysisdata analyticsmaximum likelihoodmixed effects regressionnonlinear regressionpolynomial regressionregression analysis
G02KAF   22  nagf_correg_ridge_opt
Ridge regression, optimizing a ridge regression parameter
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionpolynomial regressionregression analysisridge regression
G02KBF   22  nagf_correg_ridge
Ridge regression using a number of supplied ridge regression parameters
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionpolynomial regressionregression analysisridge regression
G02LAF   22  nagf_correg_pls_svd
Partial least squares (PLS) regression using singular value decomposition
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionpartial least squares regressionpolynomial regressionregression analysis
G02LBF   22  nagf_correg_pls_wold
Partial least squares (PLS) regression using Wold's iterative method
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionpartial least squares regressionpolynomial regressionregression analysisWold's iterative method
G02LCF   22  nagf_correg_pls_fit
PLS parameter estimates following partial least squares regression by G02LAF G02LBF
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionpartial least squares regressionpolynomial regressionregression analysis
G02LDF   22  nagf_correg_pls_pred
PLS predictions based on parameter estimates from G02LCF
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionpartial least squares regressionpolynomial regressionregression analysis
G02QFF   23  nagf_correg_quantile_linreg_easy
Linear quantile regression, simple interface, independent, identically distributed (IID) errors
Related keywords: big datacorrelation analysisdata analyticslinear quantile regressionnonlinear regressionpolynomial regressionquantile regressionregression analysis
G02QGF   23  nagf_correg_quantile_linreg
Linear quantile regression, comprehensive interface
Related keywords: big datacorrelation analysisdata analyticslinear quantile regressionnonlinear regressionpolynomial regressionquantile regressionregression analysis
G03AAF   14  nagf_mv_prin_comp
Performs principal component analysis
Related keywords: big datadata analyticsmultivariate methodsprincipal component analysis
G05KHF   22  nagf_rand_init_leapfrog
Primes a pseudorandom number generator for generating multiple streams using leap-frog
Related keywords: big datadata analyticsoptions, computationalrandom number generatorsrandom numbers
G05KJF   22  nagf_rand_init_skipahead
Primes a pseudorandom number generator for generating multiple streams using skip-ahead
Related keywords: big datadata analyticsoptions, computationalrandom number generatorsrandom numbers
G05KKF   23  nagf_rand_init_skipahead_power2
Primes a pseudorandom number generator for generating multiple streams using skip-ahead, skipping ahead a power of 2
Related keywords: big datadata analyticsoptions, computationalrandom number generatorsrandom numbers
G05NCF   22  nagf_rand_permute
Pseudorandom permutation of an integer vector
Related keywords: big datadata analyticspermutationrandom number generatorsrandom permutation
G05NDF   22  nagf_rand_sample
Pseudorandom sample from an integer vector
Related keywords: big datadata analyticsrandom number generatorsrandom samplesample, random
G05PDF   22  nagf_rand_times_garch_asym1
Generates a realization of a time series from a GARCH process with asymmetry of the form ε t - 1 + γ 2
Related keywords: big datadata analyticsGARCHrandom number generatorstime series
G05PEF   22  nagf_rand_times_garch_asym2
Generates a realization of a time series from a GARCH process with asymmetry of the form ε t - 1 + γ ε t - 1 2
Related keywords: big datadata analyticsGARCHrandom number generatorstime series
G05PFF   22  nagf_rand_times_garch_gjr
Generates a realization of a time series from an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsGARCHrandom number generatorstime series
G05PGF   22  nagf_rand_times_garch_exp
Generates a realization of a time series from an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsEGARCHrandom number generatorstime series
G05PHF   22  nagf_rand_times_arma
Generates a realization of a time series from an ARMA model
Related keywords: ARMAbig datadata analyticsrandom number generatorstime series
G05PJF   22  nagf_rand_times_mv_varma
Generates a realization of a multivariate time series from a VARMA model
Related keywords: big datadata analyticsrandom number generatorstime seriesVARMA, vector autoregressive moving average model
G05PMF   22  nagf_rand_times_smooth_exp
Generates a realization of a time series from an exponential smoothing model
Related keywords: big datadata analyticsexponential smoothingrandom number generatorstime series
G05PXF   22  nagf_rand_matrix_orthog
Generates a random orthogonal matrix
Related keywords: big datadata analyticsrandom number generatorsrandom orthogonal matrix
G05PYF   22  nagf_rand_matrix_corr
Generates a random correlation matrix
Related keywords: big datadata analyticsrandom correlation matrixrandom number generators
G05PZF   22  nagf_rand_matrix_2waytable
Generates a random two-way table
Related keywords: big datadata analyticsrandom number generatorsrandom two-way tabletwo-way contingency table
G05RCF   22  nagf_rand_copula_students_t
Generates a matrix of pseudorandom numbers from a Student's t -copula
Related keywords: big datacopuladata analyticsrandom number generatorsrandom numbersstudent's t-copula
G05RDF   22  nagf_rand_copula_normal
Generates a matrix of pseudorandom numbers from a Gaussian copula
Related keywords: big datacopuladata analyticsGaussian copularandom number generatorsrandom numbers
G05RYF   22  nagf_rand_multivar_students_t
Generates a matrix of pseudorandom numbers from a multivariate Student's t -distribution
Related keywords: big datadata analyticsmultivariate Student's t -distributionrandom number generatorsrandom numbersStudent's t -distribution
G05RZF   22  nagf_rand_multivar_normal
Generates a matrix of pseudorandom numbers from a multivariate Normal distribution
Related keywords: big datadata analyticsGaussian distributionmultivariate Normal distributionNormal distributionrandom number generatorsrandom numbers
G05SAF   22  nagf_rand_dist_uniform01
Generates a vector of pseudorandom numbers from a uniform distribution over 0 , 1
Related keywords: big datadata analyticsrandom number generatorsrandom numbersrectangular distributionuniform distribution
G05SBF   22  nagf_rand_dist_beta
Generates a vector of pseudorandom numbers from a beta distribution
Related keywords: beta distributionbig datadata analyticsrandom number generatorsrandom numbers
G05SCF   22  nagf_rand_dist_cauchy
Generates a vector of pseudorandom numbers from a Cauchy distribution
Related keywords: big dataCauchy distributiondata analyticsrandom number generatorsrandom numbers
G05SDF   22  nagf_rand_dist_chisq
Generates a vector of pseudorandom numbers from a χ 2 distribution
Related keywords: big datachi-squared distributiondata analyticsrandom number generatorsrandom numbers
G05SEF   22  nagf_rand_dist_dirichlet
Generates a vector of pseudorandom numbers from a Dirichlet distribution
Related keywords: big datadata analyticsDirichlet distributionrandom number generatorsrandom numbers
G05SFF   22  nagf_rand_dist_exp
Generates a vector of pseudorandom numbers from an exponential distribution
Related keywords: big datadata analyticsexponential distributionrandom number generatorsrandom numbers
G05SGF   22  nagf_rand_dist_expmix
Generates a vector of pseudorandom numbers from an exponential mix distribution
Related keywords: big datadata analyticsexponential distributionexponential mix distributionrandom number generatorsrandom numbers
G05SHF   22  nagf_rand_dist_f
Generates a vector of pseudorandom numbers from an F -distribution
Related keywords: big datadata analytics F -distributionrandom number generatorsrandom numbers
G05SJF   22  nagf_rand_dist_gamma
Generates a vector of pseudorandom numbers from a gamma distribution
Related keywords: big datadata analyticsgamma distributionrandom number generatorsrandom numbers
G05SKF   22  nagf_rand_dist_normal
Generates a vector of pseudorandom numbers from a Normal distribution
Related keywords: big datadata analyticsGaussian distributionNormal distributionrandom number generatorsrandom numbers
G05SLF   22  nagf_rand_dist_logistic
Generates a vector of pseudorandom numbers from a logistic distribution
Related keywords: big datadata analyticslogistic distributionrandom number generatorsrandom numbers
G05SMF   22  nagf_rand_dist_lognormal
Generates a vector of pseudorandom numbers from a log-normal distribution
Related keywords: big datadata analyticslog-normal distributionrandom number generatorsrandom numbers
G05SNF   22  nagf_rand_dist_students_t
Generates a vector of pseudorandom numbers from a Student's t -distribution
Related keywords: big datadata analyticsrandom number generatorsrandom numbersStudent's t -distribution
G05SPF   22  nagf_rand_dist_triangular
Generates a vector of pseudorandom numbers from a triangular distribution
Related keywords: big datadata analyticsrandom number generatorsrandom numberstriangular distribution
G05SQF   22  nagf_rand_dist_uniform
Generates a vector of pseudorandom numbers from a uniform distribution over a , b
Related keywords: big datadata analyticsrandom number generatorsrandom numbersrectangular distributionuniform distribution
G05SRF   22  nagf_rand_dist_vonmises
Generates a vector of pseudorandom numbers from a von Mises distribution
Related keywords: big datadata analyticsrandom number generatorsrandom numbersvon Mises distribution
G05SSF   22  nagf_rand_dist_weibull
Generates a vector of pseudorandom numbers from a Weibull distribution
Related keywords: big datadata analyticsrandom number generatorsrandom numbersWeibull distribution
G05TAF   22  nagf_rand_int_binomial
Generates a vector of pseudorandom integers from a binomial distribution
Related keywords: big databinomial distributiondata analyticsrandom integersrandom number generators
G05TBF   22  nagf_rand_logical
Generates a vector of pseudorandom logical values
Related keywords: big datadata analyticsprobabilityrandom logicalsrandom number generators
G05TCF   22  nagf_rand_int_geom
Generates a vector of pseudorandom integers from a geometric distribution
Related keywords: big datadata analyticsgeometric distributionrandom integersrandom number generators
G05TDF   22  nagf_rand_int_general
Generates a vector of pseudorandom integers from a general discrete distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticsdistribution functionrandom integersrandom number generators
G05TEF   22  nagf_rand_int_hypergeom
Generates a vector of pseudorandom integers from a hypergeometric distribution
Related keywords: big datadata analyticshypergeometric distributionrandom integersrandom number generators
G05TFF   22  nagf_rand_int_log
Generates a vector of pseudorandom integers from a logarithmic distribution
Related keywords: big datadata analyticslogarithmic distributionrandom integersrandom number generators
G05TGF   22  nagf_rand_int_multinomial
Generates a vector of pseudorandom integers from a multinomial distribution
Related keywords: big datadata analyticsmultinomial distributionrandom integersrandom number generators
G05THF   22  nagf_rand_int_negbin
Generates a vector of pseudorandom integers from a negative binomial distribution
Related keywords: big datadata analyticsnegative binomial distributionPascal distributionPolya distributionrandom integersrandom number generators
G05TJF   22  nagf_rand_int_poisson
Generates a vector of pseudorandom integers from a Poisson distribution
Related keywords: big datadata analyticsPoisson distributionrandom integersrandom number generators
G05TKF   22  nagf_rand_int_poisson_varmean
Generates a vector of pseudorandom integers from a Poisson distribution with varying mean
Related keywords: big datadata analyticsPoisson distributionrandom integersrandom number generators
G05TLF   22  nagf_rand_int_uniform
Generates a vector of pseudorandom integers from a uniform distribution
Related keywords: big datadata analyticsrandom integersrandom number generatorsrectangular distributionuniform distribution
G05YLF   22  nagf_rand_quasi_init
Initializes a quasi-random number generator
Related keywords: big datadata analyticsFaure, quasi-random numberslow-discrepancy sequencesNiederreiter method, quasi-random numbersquasi-random numbersrandom number generatorsrandom numbersrectangular distributionSobol, quasi-random numbersuniform distribution
G05YMF   22  nagf_rand_quasi_uniform
Generates a uniform quasi-random number sequence
Related keywords: big datadata analyticslow-discrepancy sequencesoptions, computationalquasi-random numbersrandom number generatorsrandom numbers
G05YNF   22  nagf_rand_quasi_init_scrambled
Initializes a scrambled quasi-random number generator
Related keywords: big datadata analyticsFaure–TezukaNiederreiterOwenrandom number generatorsrandom numbersscrambleSobol
G07GAF   23  nagf_univar_outlier_peirce_1var
Outlier detection using method of Peirce, raw data or single variance supplied
Related keywords: outlier detectionPeirce outlier detectionunivariate estimation
G07GBF   23  nagf_univar_outlier_peirce_2var
Outlier detection using method of Peirce, two variances supplied
Related keywords: outlier detectionPeirce outlier detectionunivariate estimation
G13AAF   nagf_tsa_uni_diff
Univariate time series, seasonal and non-seasonal differencing
Related keywords: big datadata analyticsdifferencing, time seriesnon-seasonal differencingseasonal differencingtime seriestime series analysisunivariate time series
G13ABF   nagf_tsa_uni_autocorr
Univariate time series, sample autocorrelation function
Related keywords: autocorrelation coefficientsbig datadata analyticsmeantest statistictime seriestime series analysisunivariate time seriesvariance
G13ACF   nagf_tsa_uni_autocorr_part
Univariate time series, partial autocorrelations from autocorrelations
Related keywords: autocorrelation coefficientsautoregressive parametersbig datadata analyticserror variance ratiospartial autocorrelation coefficientstime seriestime series analysisunivariate time series
G13ADF   nagf_tsa_uni_arima_prelim
Univariate time series, preliminary estimation, seasonal ARIMA model
Related keywords: ARIMAbig datadata analyticstime seriestime series analysisunivariate time series
G13AFF   nagf_tsa_uni_arima_estim_easy
Univariate time series, estimation, seasonal ARIMA model (easy-to-use)
Related keywords: ARIMAbig datadata analyticstime seriestime series analysisunivariate time series
G13AGF   nagf_tsa_uni_arima_update
Univariate time series, update state set for forecasting
Related keywords: big datadata analyticsforecastingtime seriestime series analysisunivariate time series
G13AHF   nagf_tsa_uni_arima_forecast_state
Univariate time series, forecasting from state set
Related keywords: big datadata analyticsforecastingtime seriestime series analysisunivariate time series
G13AJF   10  nagf_tsa_uni_arima_forcecast
Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model
Related keywords: big datadata analyticsforecastingstandard deviationtime seriestime series analysisunivariate time series
G13AMF   22  nagf_tsa_uni_smooth_exp
Univariate time series, exponential smoothing
Related keywords: big dataBrowns Exponentialdata analyticsexponential smoothingHolt WinterLinear Holttime seriestime series analysisunivariate time series
G13ASF   13  nagf_tsa_uni_arima_resid
Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF
Related keywords: ARMAautocorrelation functionbig dataBox–Jenkins modelsBox–Ljung portmanteau statisticdata analyticssignificancestandard errorstime seriestime series analysisunivariate time series
G13AUF   14  nagf_tsa_uni_means
Computes quantities needed for range-mean or standard deviation-mean plot
Related keywords: big datadata analyticsmeanrangerange-mean plotstandard deviationtime seriestime series analysis
G13BAF   10  nagf_tsa_multi_filter_arima
Multivariate time series, filtering (pre-whitening) by an ARIMA model
Related keywords: ARIMAbig datadata analyticsfilteringmultivariate time seriespre-whitening, filteringtime seriestime series analysis
G13BBF   11  nagf_tsa_multi_filter_transf
Multivariate time series, filtering by a transfer function model
Related keywords: big datadata analyticsfilteringmultivariate time seriestime seriestime series analysis
G13BCF   10  nagf_tsa_multi_xcorr
Multivariate time series, cross-correlations
Related keywords: big datacross-correlationdata analyticsmultivariate time seriestime seriestime series analysis
G13BDF   11  nagf_tsa_multi_transf_prelim
Multivariate time series, preliminary estimation of transfer function model
Related keywords: big datadata analyticsmultivariate time seriestime seriestime series analysis
G13BEF   11  nagf_tsa_multi_inputmod_estim
Multivariate time series, estimation of multi-input model
Related keywords: ARIMAbig datadata analyticsexact likelihoodmarginal likelihoodmultivariate time seriesnonlinear least squarestime seriestime series analysisunivariate time series
G13BGF   11  nagf_tsa_multi_inputmod_update
Multivariate time series, update state set for forecasting from multi-input model
Related keywords: big datadata analyticsforecastingmultivariate time seriestime seriestime series analysis
G13BJF   11  nagf_tsa_multi_inputmod_forecast
Multivariate time series, state set and forecasts from fully specified multi-input model
Related keywords: big datadata analyticsforecastingmultivariate time seriestime seriestime series analysis
G13CAF   10  nagf_tsa_uni_spectrum_lag
Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: Bartlett lag windowbig datadata analyticsParzen lag windowrectangular lag windowsmoothingtime seriestime series analysisTukey lag windowunivariate time series
G13CBF   10  nagf_tsa_uni_spectrum_daniell
Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window
Related keywords: big dataDaniell windowdata analyticssmoothingspectral smoothingtime seriestime series analysistrapezium frequency windowunivariate time series
G13CCF   10  nagf_tsa_multi_spectrum_lag
Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: Bartlett lag windowbig datacross-spectrumdata analyticsmultivariate time seriesParzen lag windowrectangular lag windowsmoothingtime seriestime series analysisTukey lag window
G13CDF   10  nagf_tsa_multi_spectrum_daniell
Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window
Related keywords: big datacross-spectrumDaniell windowdata analyticsmultivariate time seriessmoothingspectral smoothingtime seriestime series analysistrapezium frequency window
G13CEF   10  nagf_tsa_multi_spectrum_bivar
Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra
Related keywords: big databivariate spectracoherency, squared, time seriescross amplitude spectrumdata analyticsmultivariate time seriessquared coherencytime seriestime series analysis
G13CFF   10  nagf_tsa_multi_gain_bivar
Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra
Related keywords: big databivariate time seriescross-spectrumdata analyticsgain, time seriesmultivariate time seriesphase, time seriestime seriestime series analysis
G13CGF   10  nagf_tsa_multi_noise_bivar
Multivariate time series, noise spectrum, bounds, impulse response function and its standard error
Related keywords: big datadata analyticsimpulse response functionmultivariate time seriesnoise spectrumstandard errorstime seriestime series analysis
G13DDF   22  nagf_tsa_multi_varma_estimate
Multivariate time series, estimation of VARMA model
Related keywords: big datacorrelation matrixdata analyticsmaximum likelihoodmultivariate time seriesstandard errorstime seriestime series analysisVARMA, vector autoregressive moving average model
G13DJF   15  nagf_tsa_multi_varma_forecast
Multivariate time series, forecasts and their standard errors
Related keywords: big datadata analyticsforecastingmultivariate time seriesstandard errorstime seriestime series analysis
G13DKF   15  nagf_tsa_multi_varma_update
Multivariate time series, updates forecasts and their standard errors
Related keywords: big datadata analyticsforecastingmultivariate time seriesstandard errorstime seriestime series analysis
G13DLF   15  nagf_tsa_multi_diff
Multivariate time series, differences and/or transforms
Related keywords: big datadata analyticsmultivariate time seriestime seriestime series analysisVARMA, vector autoregressive moving average model
G13DXF   15  nagf_tsa_uni_arma_roots
Calculates the zeros of a vector autoregressive (or moving average) operator
Related keywords: big datadata analyticstime seriestime series analysisVARMA, vector autoregressive moving average model
G13FAF   20  nagf_tsa_uni_garch_asym1_estim
Univariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the form ε t - 1 + γ 2
Related keywords: big datadata analyticsGARCHtime seriestime series analysisunivariate time series
G13FBF   20  nagf_tsa_uni_garch_asym1_forecast
Univariate time series, forecast function for either a symmetric GARCH process or a GARCH process with asymmetry of the form ε t - 1 + γ 2
Related keywords: big datadata analyticsforecastingGARCHtime seriestime series analysisunivariate time series
G13FCF   20  nagf_tsa_uni_garch_asym2_estim
Univariate time series, parameter estimation for a GARCH process with asymmetry of the form ε t - 1 + γ ε t - 1 2
Related keywords: big datadata analyticsGARCHtime seriestime series analysisunivariate time series
G13FDF   20  nagf_tsa_uni_garch_asym2_forecast
Univariate time series, forecast function for a GARCH process with asymmetry of the form ε t - 1 + γ ε t - 1 2
Related keywords: big datadata analyticsforecastingGARCHtime seriestime series analysisunivariate time series
G13FEF   20  nagf_tsa_uni_garch_gjr_estim
Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsGARCHGJR GARCH processGlosten, Jagannathan and Runkle processtime seriestime series analysisunivariate time series
G13FFF   20  nagf_tsa_uni_garch_gjr_forecast
Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsforecastingGARCHGJR GARCH processGlosten, Jagannathan and Runkle processtime seriestime series analysisunivariate time series
G13FGF   20  nagf_tsa_uni_garch_exp_estim
Univariate time series, parameter estimation for an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsEGARCHexponential GARCHGARCHtime seriestime series analysisunivariate time series
G13FHF   20  nagf_tsa_uni_garch_exp_forecast
Univariate time series, forecast function for an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsEGARCHexponential GARCHforecastingGARCHtime seriestime series analysisunivariate time series
H02BBF   14  nagf_mip_ilp_dense
Integer LP problem (dense)
Related keywords: branch and boundinteger programmingmixed integer programmingoperations research
H02CBF   19  nagf_mip_iqp_dense
Integer QP problem (dense)
Related keywords: branch and boundinteger programminginteger quadratic programmixed integer programmingoperations researchQP, quadratic programming
H02CEF   19  nagf_mip_iqp_sparse
Integer LP or QP problem (sparse), using E04NKF
Related keywords: branch and boundinteger programminginteger quadratic programmixed integer programmingoperations researchQP, quadratic programming
S01BAF   14  nagf_specfun_log_shifted
ln 1 + x
Related keywords: approximations of special functionslogarithmic functionshifted logarithmic function
S07AAF   nagf_specfun_tan
tan x
Related keywords: approximations of special functionscircular tangenttangent, circular tan x
S09AAF   nagf_specfun_arcsin
arcsin x
Related keywords: approximations of special functionsarcsineinverse circular sine
S09ABF   nagf_specfun_arccos
arccos x
Related keywords: approximations of special functionsarccosinverse circular cosine
S10AAF   nagf_specfun_tanh
tanh x
Related keywords: approximations of special functionshyperbolic tangent tanh x
S10ABF   nagf_specfun_sinh
sinh x
Related keywords: approximations of special functionshyperbolic sine
S10ACF   nagf_specfun_cosh
cosh x
Related keywords: approximations of special functionshyperbolic cosine cosh x
S11AAF   nagf_specfun_arctanh
arctanh x
Related keywords: approximations of special functionsinverse hyperbolic tangent
S11ABF   nagf_specfun_arcsinh
arcsinh x
Related keywords: approximations of special functionsinverse hyperbolic sine
S11ACF   nagf_specfun_arccosh
arccosh x
Related keywords: approximations of special functionsinverse hyperbolic cosine
S13AAF   nagf_specfun_integral_exp
Exponential integral E 1 x
Related keywords: approximations of special functionsexponential integralexponential integral, E 1 x
S13ACF   nagf_specfun_integral_cos
Cosine integral Ci x
Related keywords: approximations of special functionscosine integral, Ci x
S13ADF   nagf_specfun_integral_sin
Sine integral Si x
Related keywords: approximations of special functionssine integralsine integral, Si x
S14AAF   nagf_specfun_gamma
Gamma function
Related keywords: approximations of special functionsgamma function
S14ABF   nagf_specfun_gamma_log_real
Log gamma function, real argument
Related keywords: approximations of special functionslog gamma function
S14ACF   14  nagf_specfun_polygamma
ψ x - ln x
Related keywords: approximations of special functionspsi function
S14ADF   14  nagf_specfun_polygamma_deriv
Scaled derivatives of ψ x
Related keywords: approximations of special functionsderivatives, psi functionpsi function
S14AEF   20  nagf_specfun_psi_deriv_real
Polygamma function ψ n x for real x
Related keywords: approximations of special functionsderivatives, psi functionpsi function
S14BAF   14  nagf_specfun_gamma_incomplete
Incomplete gamma functions P a , x and Q a , x
Related keywords: approximations of special functionsincomplete gamma function
S15ABF   nagf_specfun_cdf_normal
Cumulative Normal distribution function P x
Related keywords: approximations of special functionscumulative Normal distributionGaussian distributionNormal distribution
S15ACF   nagf_specfun_compcdf_normal
Complement of cumulative Normal distribution function Q x
Related keywords: approximations of special functionscomplement of cumulative Normal distributioncumulative Normal distributionerror function
S15ADF   nagf_specfun_erfc_real
Complement of error function erfc x
Related keywords: approximations of special functionscomplement error functionerror function
S15AEF   nagf_specfun_erf_real
Error function erf x
Related keywords: approximations of special functionserror function
S15AFF   nagf_specfun_dawson
Dawson's integral
Related keywords: approximations of special functionsDawson's integral
S15AGF   22  nagf_specfun_erfcx_real
Scaled complement of error function, erfcx x
Related keywords: approximations of special functionscomplement error functionerror function
S17ACF   nagf_specfun_bessel_y0_real
Bessel function Y 0 x
Related keywords: approximations of special functionsBessel function Y 0 x , Bessel function
S17ADF   nagf_specfun_bessel_y1_real
Bessel function Y 1 x
Related keywords: approximations of special functionsBessel function Y 1 x , Bessel function
S17AEF   nagf_specfun_bessel_j0_real
Bessel function J 0 x
Related keywords: approximations of special functionsBessel function J 0 , Bessel function
S17AFF   nagf_specfun_bessel_j1_real
Bessel function J 1 x
Related keywords: approximations of special functionsBessel function J 1 , Bessel function
S17AGF   nagf_specfun_airy_ai_real
Airy function Ai x
Related keywords: Ai , Airy functionAiry functionapproximations of special functions
S17AHF   nagf_specfun_airy_bi_real
Airy function Bi x
Related keywords: Airy functionapproximations of special functions Bi , Airy function
S17AJF   nagf_specfun_airy_ai_deriv
Airy function Ai x
Related keywords: Airy function Ai , derivative Airy functionapproximations of special functions
S17AKF   nagf_specfun_airy_bi_deriv
Airy function Bi x
Related keywords: Airy functionapproximations of special functions Bi , derivative Airy function
S17ALF   20  nagf_specfun_bessel_zeros
Zeros of Bessel functions J α x , J α x , Y α x or Y α x
Related keywords: approximations of special functionsBessel functionzeros of bessel functions
S17DGF   13  nagf_specfun_airy_ai_complex
Airy functions Ai z and Ai z , complex z
Related keywords: Ai , Airy functionAiry function Ai , derivative Airy functionapproximations of special functions
S17DHF   13  nagf_specfun_airy_bi_complex
Airy functions Bi z and Bi z , complex z
Related keywords: Airy functionapproximations of special functions Bi , Airy function Bi , derivative Airy function
S18ACF   nagf_specfun_bessel_k0_real
Modified Bessel function K 0 x
Related keywords: approximations of special functions K 0 , modified Bessel functionmodified Bessel function
S18ADF   nagf_specfun_bessel_k1_real
Modified Bessel function K 1 x
Related keywords: approximations of special functions K 1 , modified Bessel functionmodified Bessel function
S18AEF   nagf_specfun_bessel_i0_real
Modified Bessel function I 0 x
Related keywords: approximations of special functions I 0 , modified Bessel functionmodified Bessel function
S18AFF   nagf_specfun_bessel_i1_real
Modified Bessel function I 1 x
Related keywords: approximations of special functions I 1 , modified Bessel functionmodified Bessel function
S18CCF   10  nagf_specfun_bessel_k0_scaled
Scaled modified Bessel function e x K 0 x
Related keywords: approximations of special functions K 0 , modified Bessel functionmodified Bessel function
S18CDF   10  nagf_specfun_bessel_k1_scaled
Scaled modified Bessel function e x K 1 x
Related keywords: approximations of special functions K 1 , modified Bessel functionmodified Bessel function
S18CEF   10  nagf_specfun_bessel_i0_scaled
Scaled modified Bessel function e - x I 0 x
Related keywords: approximations of special functions I 0 , modified Bessel functionmodified Bessel function
S18CFF   10  nagf_specfun_bessel_i1_scaled
Scaled modified Bessel function e - x I 1 x
Related keywords: approximations of special functions I 1 , modified Bessel functionmodified Bessel function
S19AAF   11  nagf_specfun_kelvin_ber
Kelvin function ber x
Related keywords: approximations of special functionsKelvin functions ber x , Kelvin function
S19ABF   11  nagf_specfun_kelvin_bei
Kelvin function bei x
Related keywords: approximations of special functionsKelvin functions bei x , Kelvin function
S19ACF   11  nagf_specfun_kelvin_ker
Kelvin function ker x
Related keywords: approximations of special functionsKelvin functions ker x , Kelvin function
S19ADF   11  nagf_specfun_kelvin_kei
Kelvin function kei x
Related keywords: approximations of special functionsKelvin functions kei x , Kelvin function
S20ACF   nagf_specfun_fresnel_s
Fresnel integral S x
Related keywords: approximations of special functionsFresnel integral S x , Fresnel Integral
S20ADF   nagf_specfun_fresnel_c
Fresnel integral C x
Related keywords: approximations of special functions C x , Fresnel IntegralFresnel integral
S21BAF   nagf_specfun_ellipint_symm_1_degen
Degenerate symmetrised elliptic integral of 1st kind R C x , y
Related keywords: approximations of special functionselliptic integral
S21BBF   nagf_specfun_ellipint_symm_1
Symmetrised elliptic integral of 1st kind R F x , y , z
Related keywords: approximations of special functionselliptic integral
S21BCF   nagf_specfun_ellipint_symm_2
Symmetrised elliptic integral of 2nd kind R D x , y , z
Related keywords: approximations of special functionselliptic integral
S21BDF   nagf_specfun_ellipint_symm_3
Symmetrised elliptic integral of 3rd kind R J x , y , z , r
Related keywords: approximations of special functionselliptic integral
S21BEF   22  nagf_specfun_ellipint_legendre_1
Elliptic integral of 1st kind, Legendre form, F ϕ m
Related keywords: approximations of special functionselliptic integral
S21BFF   22  nagf_specfun_ellipint_legendre_2
Elliptic integral of 2nd kind, Legendre form, E ϕ m
Related keywords: approximations of special functionselliptic integral
S21BGF   22  nagf_specfun_ellipint_legendre_3
Elliptic integral of 3rd kind, Legendre form, Π n ; ϕ m
Related keywords: approximations of special functionselliptic integral
S21BHF   22  nagf_specfun_ellipint_complete_1
Complete elliptic integral of 1st kind, Legendre form, K m
Related keywords: approximations of special functionselliptic integral
S21BJF   22  nagf_specfun_ellipint_complete_2
Complete elliptic integral of 2nd kind, Legendre form, E m
Related keywords: approximations of special functionselliptic integral
S21CAF   15  nagf_specfun_jacellip_real
Jacobian elliptic functions sn, cn and dn of real argument
Related keywords: approximations of special functionscn, Jacobian elliptic functiondn, Jacobian elliptic functionelliptic functionsJacobian elliptic functionssn, Jacobian elliptic functions
S21CBF   20  nagf_specfun_jacellip_complex
Jacobian elliptic functions sn, cn and dn of complex argument
Related keywords: approximations of special functionscn, Jacobian elliptic functiondn, Jacobian elliptic functionelliptic functionsJacobian elliptic functionssn, Jacobian elliptic functions
S21CCF   20  nagf_specfun_jactheta_real
Jacobian theta functions θ k x , q of real argument
Related keywords: approximations of special functionsJacobian theta functionstheta, Jacobian theta functions
S22AAF   20  nagf_specfun_legendre_p
Legendre functions of 1st kind P n m x or P n m ¯ x
Related keywords: approximations of special functionsLegendre functions
S30AAF   22  nagf_specfun_opt_bsm_price
Black–Scholes–Merton option pricing formula
Related keywords: approximations of special functionsBlack–Scholes option pricingderivative, optionsoption pricing
S30ABF   22  nagf_specfun_opt_bsm_greeks
Black–Scholes–Merton option pricing formula with Greeks
Related keywords: approximations of special functionsBlack–Scholes option pricingderivative, optionsGreeks, optionsoption pricing
S30BAF   22  nagf_specfun_opt_lookback_fls_price
Floating-strike lookback option pricing formula in the Black-Scholes-Merton model
Related keywords: approximations of special functionsderivative, optionsfloating-strike lookback optionoption pricing
S30BBF   22  nagf_specfun_opt_lookback_fls_greeks
Floating-strike lookback option pricing formula with Greeks in the Black-Scholes-Merton model
Related keywords: approximations of special functionsderivative, optionsfloating-strike lookback optionGreeks, optionsoption pricing
S30CAF   22  nagf_specfun_opt_binary_con_price
Binary option, cash-or-nothing pricing formula
Related keywords: approximations of special functionsbinary optioncash-or-nothing optionderivative, optionsoption pricing
S30CBF   22  nagf_specfun_opt_binary_con_greeks
Binary option, cash-or-nothing pricing formula with Greeks
Related keywords: approximations of special functionsbinary optioncash-or-nothing optionderivative, optionsGreeks, optionsoption pricing
S30CCF   22  nagf_specfun_opt_binary_aon_price
Binary option, asset-or-nothing pricing formula
Related keywords: approximations of special functionsbinary optioncash-or-nothing optionderivative, optionsoption pricing
S30CDF   22  nagf_specfun_opt_binary_aon_greeks
Binary option, asset-or-nothing pricing formula with Greeks
Related keywords: approximations of special functionsbinary optioncash-or-nothing optionderivative, optionsGreeks, optionsoption pricing
S30FAF   22  nagf_specfun_opt_barrier_std_price
Standard barrier option pricing formula
Related keywords: approximations of special functionsbarrier optionderivative, optionsoption pricing
S30JAF   22  nagf_specfun_opt_jumpdiff_merton_price
Jump-diffusion, Merton's model, option pricing formula
Related keywords: approximations of special functionsderivative, optionsjump-diffusion model, option pricingMerton model, option pricingoption pricing
S30JBF   22  nagf_specfun_opt_jumpdiff_merton_greeks
Jump-diffusion, Merton's model, option pricing formula with Greeks
Related keywords: approximations of special functionsderivative, optionsGreeks, optionsjump-diffusion model, option pricingMerton model, option pricingoption pricing
S30NAF   22  nagf_specfun_opt_heston_price
Heston's model option pricing formula
Related keywords: approximations of special functionsderivative, optionsHeston model, optionsoption pricing
S30NBF   23  nagf_specfun_opt_heston_greeks
Heston's model option pricing formula with Greeks
Related keywords: approximations of special functionsderivative, optionsGreeks, optionsHeston model, optionsoption pricing
S30NCF   25  nagf_specfun_opt_heston_term
Heston's model option pricing with term structure
Related keywords: approximations of special functionsEuropeanHestonstochastic volatilityterm structure
S30QCF   22  nagf_specfun_opt_amer_bs_price
American option, Bjerksund and Stensland pricing formula
Related keywords: American optionsapproximations of special functionsBjerksund and Stensland pricing formula
S30SAF   22  nagf_specfun_opt_asian_geom_price
Asian option, geometric continuous average rate pricing formula
Related keywords: approximations of special functionsAsian optionderivative, optionsoption pricing
S30SBF   22  nagf_specfun_opt_asian_geom_greeks
Asian option, geometric continuous average rate pricing formula with Greeks
Related keywords: approximations of special functionsAsian optionderivative, optionsGreeks, optionsoption pricing
finite X07AAF   24  nagf_ieee_is_finite
Determines whether its argument has a finite value
Related keywords: IEEE arithmetic
finite difference discretization D03PHF   15  nagf_pde_1d_parab_dae_fd_old
General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable
Related keywords: DAE, differential algebraic equationsmethod of linesparabolic partial differential equationpartial differential equationsPDE, partial differential equations
finite difference method, ODE D02GAF   nagf_ode_bvp_fd_nonlin_fixedbc
Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem
Related keywords: boundary value problemBVPODE, ordinary differential equations
D02GBF   nagf_ode_bvp_fd_lin_gen
Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, general linear problem
Related keywords: boundary value problemBVPODE, ordinary differential equations
D02RAF   nagf_ode_bvp_fd_nonlin_gen
Ordinary differential equations, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility
Related keywords: BVP, boundary value problemODE, ordinary differential equations
finite element D06CBF   20  nagf_mesh_2d_sparsity
Generates a sparsity pattern of a Finite Element matrix associated with a given mesh
Related keywords: mesh generationsparsity pattern
first-order system D02CJF   13  nagf_ode_ivp_adams_zero_simple
Ordinary differential equations, initial value problem, Adams' method, until function of solution is zero, intermediate output (simple driver)
Related keywords: Adams' methodinitial value problemIVP, initial value problemNonstiffODE, ordinary differential equationsstop at roots
D02PEF   24  nagf_ode_ivp_rkts_range
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output
Related keywords: IVP, initial value problemNonstiffODE, ordinary differential equationsRK23RK45RK78Runge–Kutta–Merson
D02PFF   24  nagf_ode_ivp_rkts_onestep
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step
Related keywords: IVP, initial value problemNonstiffODE, ordinary differential equationsRK23RK45RK78Runge–Kutta–Merson
D02PHF   26  nagf_ode_ivp_rk_interp_setup
Set up interpolant by reverse communication for solution and derivative evaluations at points within the range of the last integration step taken by D02PGF
Related keywords: interpolationIVP, initial value problemNonstiffODE, ordinary differential equationsRunge–Kutta–Merson
Fisher's exact test G01AFF   nagf_stat_contingency_table
Two-way contingency table analysis, with χ 2 /Fisher's exact test
Related keywords: chi-squared distributioncontingency tablefinanceSimple Calculations on Statistical Datatwo-way contingency tableYates' correction
five-point stencil D03UAF   nagf_pde_2d_ellip_fd_iter
Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, one iteration
Related keywords: elliptic partial differential equationsPDE, partial differential equationsStone's strongly implicit procedure
five-point summary G01ALF   14  nagf_stat_5pt_summary
Computes a five-point summary (median, hinges and extremes)
Related keywords: financehingesmaximum valuemedianminimum valueSimple Calculations on Statistical Data
floating-point complex safe range X02ANF   15  nagf_machine_complex_safe
The safe range parameter for complex floating-point arithmetic
Related keywords: machine constants
floating-point model X02BHF   12  nagf_machine_model_base
The floating-point model parameter, b
Related keywords: basemachine constants
X02BJF   12  nagf_machine_model_digits
The floating-point model parameter, p
Related keywords: machine constantsprecision
X02BKF   12  nagf_machine_model_minexp
The floating-point model parameter e min
Related keywords: machine constantsminimum exponent
X02BLF   12  nagf_machine_model_maxexp
The floating-point model parameter e max
Related keywords: machine constantsmaximum exponent
floating-point safe range X02AMF   12  nagf_machine_real_safe
The safe range parameter
Related keywords: machine constants
floating-strike lookback option S30BAF   22  nagf_specfun_opt_lookback_fls_price
Floating-strike lookback option pricing formula in the Black-Scholes-Merton model
Related keywords: approximations of special functionsderivative, optionsfinanceoption pricing
S30BBF   22  nagf_specfun_opt_lookback_fls_greeks
Floating-strike lookback option pricing formula with Greeks in the Black-Scholes-Merton model
Related keywords: approximations of special functionsderivative, optionsfinanceGreeks, optionsoption pricing
forecasting G13AGF   nagf_tsa_uni_arima_update
Univariate time series, update state set for forecasting
Related keywords: big datadata analyticsfinancetime seriestime series analysisunivariate time series
G13AHF   nagf_tsa_uni_arima_forecast_state
Univariate time series, forecasting from state set
Related keywords: big datadata analyticsfinancetime seriestime series analysisunivariate time series
G13AJF   10  nagf_tsa_uni_arima_forcecast
Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model
Related keywords: big datadata analyticsfinancestandard deviationtime seriestime series analysisunivariate time series
G13BGF   11  nagf_tsa_multi_inputmod_update
Multivariate time series, update state set for forecasting from multi-input model
Related keywords: big datadata analyticsfinancemultivariate time seriestime seriestime series analysis
G13BHF   11  nagf_tsa_multi_inputmod_forecast_state
Multivariate time series, forecasting from state set of multi-input model
Related keywords: big datadata analyticsmultivariate time seriestime seriestime series analysis
G13BJF   11  nagf_tsa_multi_inputmod_forecast
Multivariate time series, state set and forecasts from fully specified multi-input model
Related keywords: big datadata analyticsfinancemultivariate time seriestime seriestime series analysis
G13DJF   15  nagf_tsa_multi_varma_forecast
Multivariate time series, forecasts and their standard errors
Related keywords: big datadata analyticsfinancemultivariate time seriesstandard errorstime seriestime series analysis
G13DKF   15  nagf_tsa_multi_varma_update
Multivariate time series, updates forecasts and their standard errors
Related keywords: big datadata analyticsfinancemultivariate time seriesstandard errorstime seriestime series analysis
G13FBF   20  nagf_tsa_uni_garch_asym1_forecast
Univariate time series, forecast function for either a symmetric GARCH process or a GARCH process with asymmetry of the form ε t - 1 + γ 2
Related keywords: big datadata analyticsfinanceGARCHtime seriestime series analysisunivariate time series
G13FDF   20  nagf_tsa_uni_garch_asym2_forecast
Univariate time series, forecast function for a GARCH process with asymmetry of the form ε t - 1 + γ ε t - 1 2
Related keywords: big datadata analyticsfinanceGARCHtime seriestime series analysisunivariate time series
G13FFF   20  nagf_tsa_uni_garch_gjr_forecast
Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsfinanceGARCHGJR GARCH processGlosten, Jagannathan and Runkle processtime seriestime series analysisunivariate time series
G13FHF   20  nagf_tsa_uni_garch_exp_forecast
Univariate time series, forecast function for an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsEGARCHexponential GARCHfinanceGARCHtime seriestime series analysisunivariate time series
forward error F04BAF   21  nagf_linsys_real_square_solve
Computes the solution, estimated condition number and error-bound to a real system of linear equations
Related keywords: big datadata analyticslinear equationsreal, nonsymmetric matrixsimultaneous linear equations
F04BBF   21  nagf_linsys_real_band_solve
Computes the solution, estimated condition number and error-bound to a real banded system of linear equations
Related keywords: big datadata analyticslinear equationsmatrix, bandreal, band matrixsimultaneous linear equations
F04BCF   21  nagf_linsys_real_tridiag_solve
Computes the solution, estimated condition number and error-bound to a real tridiagonal system of linear equations
Related keywords: big datadata analyticslinear equationsmatrix, bandreal, tridiagonal matrixsimultaneous linear equations
F04BDF   21  nagf_linsys_real_posdef_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite system of linear equations
Related keywords: big datadata analyticslinear equationsreal, positive-definite, symmetric matrixsimultaneous linear equations
F04BEF   21  nagf_linsys_real_posdef_packed_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite system of linear equations, packed storage
Related keywords: big datadata analyticslinear equationsreal, positive-definite, symmetric matrixsimultaneous linear equations
F04BFF   21  nagf_linsys_real_posdef_band_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite banded system of linear equations
Related keywords: big datadata analyticslinear equationsreal, band, positive-definite, symmetric matrixsimultaneous linear equations
F04BGF   21  nagf_linsys_real_posdef_tridiag_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite tridiagonal system of linear equations
Related keywords: big datadata analyticslinear equationsreal, positive-definite, symmetric, tridiagonal matrixsimultaneous linear equations
F04BHF   21  nagf_linsys_real_symm_solve
Computes the solution, estimated condition number and error-bound to a real symmetric system of linear equations
Related keywords: big datadata analyticslinear equationsreal, indefinite, symmetric matrixsimultaneous linear equations
F04BJF   21  nagf_linsys_real_symm_packed_solve
Computes the solution, estimated condition number and error-bound to a real symmetric system of linear equations, packed storage
Related keywords: big datadata analyticslinear equationsreal, indefinite, symmetric matrixsimultaneous linear equations
F04CAF   21  nagf_linsys_complex_square_solve
Computes the solution, estimated condition number and error-bound to a complex system of linear equations
Related keywords: big datacomplex, nonsymmetric matrixdata analyticslinear equationssimultaneous linear equations
F04CBF   21  nagf_linsys_complex_band_solve
Computes the solution, estimated condition number and error-bound to a complex banded system of linear equations
Related keywords: big datacomplex, band matrixdata analyticslinear equationsmatrix, bandsimultaneous linear equations
F04CCF   21  nagf_linsys_complex_tridiag_solve
Computes the solution, estimated condition number and error-bound to a complex tridiagonal system of linear equations
Related keywords: big datacomplex, tridiagonal matrixdata analyticslinear equationsmatrix, bandsimultaneous linear equations
F04CDF   21  nagf_linsys_complex_posdef_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite system of linear equations
Related keywords: big datacomplex, Hermitian, positive-definite matrixdata analyticslinear equationssimultaneous linear equations
F04CEF   21  nagf_linsys_complex_posdef_packed_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite system of linear equations, packed storage
Related keywords: big datacomplex, Hermitian, positive-definite matrixdata analyticslinear equationssimultaneous linear equations
F04CFF   21  nagf_linsys_complex_posdef_band_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite banded system of linear equations
Related keywords: big datacomplex, band, Hermitian, positive-definite matrixdata analyticslinear equationsmatrix, bandsimultaneous linear equations
F04CGF   21  nagf_linsys_complex_posdef_tridiag_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: big datacomplex, Hermitian, positive-definite, tridiagonal matrixdata analyticslinear equationsmatrix, bandsimultaneous linear equations
F04CHF   21  nagf_linsys_complex_herm_solve
Computes the solution and error-bound to a complex Hermitian system of linear equations
Related keywords: big datacomplex, Hermitian, indefinite matrixdata analyticslinear equationssimultaneous linear equations
F04CJF   21  nagf_linsys_complex_herm_packed_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian system of linear equations, packed storage
Related keywords: big datacomplex, Hermitian, indefinite matrixdata analyticslinear equationssimultaneous linear equations
F04DHF   21  nagf_linsys_complex_symm_solve
Computes the solution, estimated condition number and error-bound to a complex symmetric system of linear equations
Related keywords: big datacomplex, symmetric matrixdata analyticslinear equationssimultaneous linear equations
F04DJF   21  nagf_linsys_complex_symm_packed_solve
Computes the solution, estimated condition number and error-bound to a complex symmetric system of linear equations, packed storage
Related keywords: big datacomplex, symmetric matrixdata analyticslinear equationssimultaneous linear equations
F07ABF   21  nagf_lapacklin_dgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
Related keywords: backward errorcondition number, matrixDGESVXerror bound, matrixfinanceLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
F07AHF   15  nagf_lapacklin_dgerfs
Refined solution with error bounds of real system of linear equations, multiple right-hand sides
Related keywords: backward errorDGERFSerror bound, matrixLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
F07APF   21  nagf_lapacklin_zgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
Related keywords: backward errorcomplex, nonsymmetric matrixcondition number, matrixerror bound, matrixfinanceLAPACKlinear equations L U decompositionZGESVX
F07AVF   15  nagf_lapacklin_zgerfs
Refined solution with error bounds of complex system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, nonsymmetric matrixLAPACKlinear equationsZGERFS
F07BBF   21  nagf_lapacklin_dgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
Related keywords: backward errorcondition number, matrixDGBSVXerror bound, matrixLAPACKlinear equations L U decompositionmatrix, bandreal, band matrix
F07BHF   15  nagf_lapacklin_dgbrfs
Refined solution with error bounds of real band system of linear equations, multiple right-hand sides
Related keywords: backward errorDGBRFSLAPACKlinear equations L U decompositionmatrix, bandreal, band matrix
F07BPF   21  nagf_lapacklin_zgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
Related keywords: backward errorcomplex, band matrixcondition number, matrixerror bound, matrixLAPACKlinear equations L U decompositionmatrix, bandZGBSVX
F07BVF   15  nagf_lapacklin_zgbrfs
Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, band matrixerror bound, matrixLAPACKlinear equationsmatrix, bandZGBRFS
F07CBF   21  nagf_lapacklin_dgtsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
Related keywords: backward errorcondition number, matrixDGTSVXerror bound, matrixLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
F07CHF   22  nagf_lapacklin_dgtrfs
Refined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorDGTCONLAPACKlinear equations L U decompositionmatrix, bandreal, tridiagonal matrix
F07CPF   21  nagf_lapacklin_zgtsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations
Related keywords: backward errorcomplex, tridiagonal matrixLAPACKlinear equations L U decompositionmatrix, bandZGTSVX
F07CVF   22  nagf_lapacklin_zgtrfs
Refined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, tridiagonal matrixLAPACKlinear equations L U decompositionmatrix, bandZGTRFS
F07FBF   21  nagf_lapacklin_dposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixDPOSVXerror bound, matrixfinanceLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FHF   15  nagf_lapacklin_dporfs
Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositionDPORFSLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FPF   21  nagf_lapacklin_zposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite matrixcondition number, matrixerror bound, matrixfinanceLAPACKlinear equationsZPOSVX
F07FVF   15  nagf_lapacklin_zporfs
Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite matrixerror bound, matrixLAPACKlinear equationsZPORFS
F07GBF   21  nagf_lapacklin_dppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations, packed storage
Related keywords: backward errorCholesky decompositioncondition number, matrixDPPSVXerror bound, matrixLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GHF   15  nagf_lapacklin_dpprfs
Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorCholesky decompositionDPPRFSLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GPF   21  nagf_lapacklin_zppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations, packed storage
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite matrixcondition number, matrixerror bound, matrixLAPACKlinear equationsZPPSVX
F07GVF   15  nagf_lapacklin_zpprfs
Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite matrixerror bound, matrixLAPACKlinear equationsZPPRFS
F07HBF   21  nagf_lapacklin_dpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite banded system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixDPBSVXerror bound, matrixLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
F07HHF   15  nagf_lapacklin_dpbrfs
Refined solution with error bounds of real symmetric positive definite band system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositionDPBRFSLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
F07HPF   21  nagf_lapacklin_zpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite banded system of linear equations
Related keywords: backward errorCholesky decompositioncomplex, band, Hermitian, positive-definite matrixcondition number, matrixerror bound, matrixLAPACKlinear equationsmatrix, bandZPBSVX
F07HVF   15  nagf_lapacklin_zpbrfs
Refined solution with error bounds of complex Hermitian positive definite band system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositioncomplex, band, Hermitian, positive-definite matrixerror bound, matrixLAPACKlinear equationsmatrix, bandZPBRFS
F07JBF   21  nagf_lapacklin_dptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixDPTSVXerror bound, matrixLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
F07JHF   22  nagf_lapacklin_dptrfs
Refined solution with error bounds of real symmetric positive definite tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositionDPTRFSLAPACKlinear equationsmatrix, bandreal, positive-definite, symmetric, tridiagonal matrix
F07JPF   21  nagf_lapacklin_zptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixcondition number, matrixerror bound, matrixLAPACKlinear equationsmatrix, bandZPTSVX
F07JVF   22  nagf_lapacklin_zptrfs
Refined solution with error bounds of complex Hermitian positive definite tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixLAPACKlinear equationsmatrix, bandZPTRFS
F07MBF   21  nagf_lapacklin_dsysvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations
Related keywords: backward errordiagonal pivoting methodDSYSVXLAPACKLDLT decompositionlinear equationsreal, indefinite, symmetric matrix UDU T decompositiuon
F07MHF   15  nagf_lapacklin_dsyrfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides
Related keywords: backward errorBunch–Kaufman factorizationdiagonal pivoting methodDSYRFSLAPACKlinear equationsreal, indefinite, symmetric matrix
F07MPF   21  nagf_lapacklin_zhesvx
Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations
Related keywords: backward errorcomplex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACK LDL H decompositionlinear equations UDU H decompositionZHESVX
F07MVF   15  nagf_lapacklin_zherfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
Related keywords: backward errorBunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methoderror bound, matrixLAPACKlinear equationsZHERFS
F07NPF   21  nagf_lapacklin_zsysvx
Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations
Related keywords: backward errorcomplex, symmetric matrixdiagonal pivoting methodLAPACK LDL H decompositionlinear equations UDU H decompositionZSYSVX
F07NVF   15  nagf_lapacklin_zsyrfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
Related keywords: backward errorBunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methoderror bound, matrixLAPACKlinear equationsZSYRFS
F07PBF   21  nagf_lapacklin_dspsvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage. Error bounds and a condition estimate are also computed
Related keywords: backward errorcondition number, matrixdiagonal pivoting methodDSPSVXerror bound, matrixLAPACK LDL H decompositionlinear equationsreal, indefinite, symmetric matrix UDU H decomposition
F07PHF   15  nagf_lapacklin_dsprfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorBunch–Kaufman factorizationdiagonal pivoting methodDSPRFSLAPACKlinear equationsreal, indefinite, symmetric matrix
F07PPF   21  nagf_lapacklin_zhpsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, Hermitian, system of linear equations, error bounds and condition estimates. Packed storage
Related keywords: backward errorcomplex, Hermitian, indefinite matrixdiagonal pivoting methodinverse, matrixLAPACK LDL H decompositionlinear equations UDU H decompositionZHPSVX
F07PVF   15  nagf_lapacklin_zhprfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorBunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methoderror bound, matrixLAPACKlinear equationsZHPRFS
F07QPF   21  nagf_lapacklin_zspsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, symmetric, system of linear equations, error bounds and condition estimates. Packed storage
Related keywords: backward errorcomplex, symmetric matrixdiagonal pivoting methodLAPACK LDL T decompositionlinear equations UDU T decompositionZSPSVX
F07QVF   15  nagf_lapacklin_zsprfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorBunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methoderror bound, matrixLAPACKlinear equationsZSPRFS
F07THF   15  nagf_lapacklin_dtrrfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorDTRRFSerror bound, matrixfinanceLAPACKlinear equationsreal, triangular matrix
F07TVF   15  nagf_lapacklin_ztrrfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, triangular matrixerror bound, matrixLAPACKlinear equationsZTRRFS
F07UHF   15  nagf_lapacklin_dtprfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorDTPRFSerror bound, matrixLAPACKlinear equationsreal, triangular matrix
F07UVF   15  nagf_lapacklin_ztprfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorcomplex, triangular matrixerror bound, matrixLAPACKlinear equationsZTPRFS
F07VHF   15  nagf_lapacklin_dtbrfs
Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorDTBRFSerror bound, matrixLAPACKlinear equationsmatrix, bandreal, band, triangular matrix
F07VVF   15  nagf_lapacklin_ztbrfs
Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, band, triangular matrixerror bound, matrixLAPACKlinear equationsmatrix, bandZTBRFS
F08NBF   21  nagf_lapackeig_dgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGEEVXeigenproblemeigenvalueseigenvectorsfinanceLAPACKLAPACKleast squaresorthogonal transformations QR algorithmreal, nonsymmetric matrix
F08NPF   21  nagf_lapackeig_zgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixcondition number, matrixDGEEVeigenproblemeigenvalueseigenvectorsfinanceLAPACKLAPACKleast squares
F08WBF   21  nagf_lapackeig_dggevx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGGEVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsfinancegeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WPF   21  nagf_lapackeig_zggevx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixcondition number, matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsfinancegeneralized eigenproblemLAPACKLAPACKleast squaresZGGEVX
F11MHF   21  nagf_sparse_direct_real_gen_refine
Refined solution with error bounds of real system of linear equations, multiple right-hand sides
Related keywords: backward errorbig datadata analyticslarge scale linear systemslinear equationsreal, sparse matrix
forward stagewise G02MAF   25  nagf_correg_lars
Least angle regression (LARS), least absolute shrinkage and selection operator (LASSO) and forward stagewise regression
Related keywords: big datacorrelation analysisdata analyticsLARSLASSOleast angle regressionmodel selectionnonlinear regressionpolynomial regressionregression analysis
G02MBF   25  nagf_correg_lars_xtx
Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) and forward stagewise regression using the cross-products matrix
Related keywords: big datacorrelation analysiscross-productdata analyticsLARSLASSOleast angle regressionmodel selectionnonlinear regressionpolynomial regressionregression analysis
G02MCF   25  nagf_correg_lars_param
Calculates additional parameter estimates following Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) or forward stagewise regression
Related keywords: big datacorrelation analysisdata analyticsLARSLASSOleast angle regressionnonlinear regressionpolynomial regressionregression analysis
Fourier transforms, complex C06PAF   19  nagf_sum_fft_realherm_1d
Single one-dimensional real and Hermitian complex discrete Fourier transform, using complex storage format for Hermitian sequences
Related keywords: Fast Fourier TransformFFTsummation of series
C06PCF   19  nagf_sum_fft_complex_1d
Single one-dimensional complex discrete Fourier transform, complex data type
Related keywords: Fast Fourier TransformFFTsummation of series
C06PFF   19  nagf_sum_fft_complex_multid_1d
One-dimensional complex discrete Fourier transform of multidimensional data (using complex data type)
Related keywords: Fast Fourier TransformFFTsummation of series
C06PJF   19  nagf_sum_fft_complex_multid
Multidimensional complex discrete Fourier transform of multidimensional data (using complex data type)
Related keywords: Fast Fourier TransformFFTsummation of series
C06PPF   19  nagf_sum_fft_realherm_1d_multi_row
Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using row ordered complex storage format for Hermitian sequences
Related keywords: Fast Fourier TransformFFTFourier transforms, realsummation of series
C06PRF   19  nagf_sum_fft_complex_1d_multi_row
Multiple one-dimensional complex discrete Fourier transforms using complex data type
Related keywords: Fast Fourier TransformFFTsummation of series
C06PSF   19  nagf_sum_fft_complex_1d_multi_col
Multiple one-dimensional complex discrete Fourier transforms, complex data type
Related keywords: Fast Fourier TransformFFTsummation of series
C06PUF   19  nagf_sum_fft_complex_2d
Two-dimensional complex discrete Fourier transform, complex data type
Related keywords: Fast Fourier TransformFFTsummation of series
C06PVF   24  nagf_sum_fft_real_2d
Two-dimensional real-to-complex discrete Fourier transform
Related keywords: Fast Fourier TransformFFTsummation of series
C06PWF   24  nagf_sum_fft_hermitian_2d
Two-dimensional complex-to-real discrete Fourier transform
Related keywords: Fast Fourier TransformFFTsummation of series
C06PXF   19  nagf_sum_fft_complex_3d
Three-dimensional complex discrete Fourier transform, complex data type
Related keywords: Fast Fourier TransformFFTsummation of series
C06PYF   24  nagf_sum_fft_real_3d
Three-dimensional real-to-complex discrete Fourier transform
Related keywords: Fast Fourier TransformFFTsummation of series
Fourier transforms, real C06PPF   19  nagf_sum_fft_realherm_1d_multi_row
Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using row ordered complex storage format for Hermitian sequences
Related keywords: Fast Fourier TransformFFTFourier transforms, complexsummation of series
Fourier Transforms, real C06REF   25  nagf_sum_fft_sine
Multiple discrete sine transforms, simple
Related keywords: Discrete Fourier TransformsFast Fourier TransformFFTsine transformsummation of series
C06RFF   25  nagf_sum_fft_cosine
Multiple discrete cosine transforms, simple
Related keywords: cosine transformDiscrete Fourier TransformsFast Fourier TransformFFTsummation of series
C06RGF   25  nagf_sum_fft_qtrsine
Multiple discrete quarter-wave sine transforms, simple
Related keywords: Discrete Fourier TransformsFast Fourier TransformFFTquarter-wavesine transformsummation of series
C06RHF   25  nagf_sum_fft_qtrcosine
Multiple discrete quarter-wave cosine transforms, simple
Related keywords: cosine transformDiscrete Fourier TransformsFast Fourier TransformFFTquarter-wavesummation of series
fractional Brownian motion G05ZTF   24  nagf_rand_field_fracbm_generate
Generates realizations of fractional Brownian motion
Related keywords: big dataBrownian motiondata analyticsrandom number generators
Frank copula G05RFF   23  nagf_rand_copula_frank_bivar
Generates a matrix of pseudorandom numbers from a bivariate Frank copula
Related keywords: big datacopuladata analyticsrandom number generatorsrandom numbers
G05RJF   23  nagf_rand_copula_frank
Generates a matrix of pseudorandom numbers from a multivariate Frank copula
Related keywords: big datacopuladata analyticsrandom number generatorsrandom numbers
Fréchet derivative F01JFF   25  nagf_matop_real_gen_matrix_frcht_pow
Fréchet derivative of real matrix power
Related keywords: inversionmatrix operationsmatrix operations including inversion
F01JHF   25  nagf_matop_real_gen_matrix_frcht_exp
Fréchet derivative of real matrix exponential
Related keywords: inversionmatrix operationsreal, nonsymmetric matrix
F01JKF   25  nagf_matop_real_gen_matrix_frcht_log
Fréchet derivative of real matrix logarithm
Related keywords: inversionmatrix operationsreal, nonsymmetric matrix
F01KFF   25  nagf_matop_complex_gen_matrix_frcht_pow
Fréchet derivative of complex matrix power
Related keywords: eigenvalues and eigenvectorsinversionmatrix operationsmatrix operations including inversion
F01KHF   25  nagf_matop_complex_gen_matrix_frcht_exp
Fréchet derivative of complex matrix exponential
Related keywords: complex, nonsymmetric matrixinversionmatrix operations
F01KKF   25  nagf_matop_complex_gen_matrix_frcht_log
Fréchet derivative of complex matrix logarithm
Related keywords: complex, nonsymmetric matrixinversionmatrix operations
Fredholm integral equations D05AAF   nagf_inteq_fredholm2_split
Linear nonsingular Fredholm integral equation, second kind, split kernel
Related keywords: integral equations
D05ABF   nagf_inteq_fredholm2_smooth
Linear nonsingular Fredholm integral equation, second kind, smooth kernel
Related keywords: integral equations
free E04RZF   26  nagf_opt_handle_free
Destroy the problem handle initialized by E04RAF and deallocate all the memory used
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
G22ZAF   26  nagf_blgm_handle_free
Destroy a and deallocate all the memory used
Related keywords: destroyhandle
frequency distribution G01AEF   nagf_stat_frequency_table
Frequency table from raw data
Related keywords: financefrequency tableSimple Calculations on Statistical Data
G11SBF   12  nagf_contab_binary_service
Frequency count for G11SAF
Related keywords: contingency table analysis
frequency table G01AEF   nagf_stat_frequency_table
Frequency table from raw data
Related keywords: financefrequency distributionSimple Calculations on Statistical Data
Fresnel integral S20ACF   nagf_specfun_fresnel_s
Fresnel integral S x
Related keywords: approximations of special functionsfinance S x , Fresnel Integral
S20ADF   nagf_specfun_fresnel_c
Fresnel integral C x
Related keywords: approximations of special functions C x , Fresnel Integralfinance
S20AQF   24  nagf_specfun_fresnel_s_vector
Fresnel integral vectorized S x
Related keywords: approximations of special functions S x , Fresnel Integral
S20ARF   24  nagf_specfun_fresnel_c_vector
Fresnel integral vectorized C x
Related keywords: approximations of special functions C x , Fresnel Integral
Friedman two-way analysis of variance G08AEF   nagf_nonpar_test_friedman
Friedman two-way analysis of variance on k matched samples
Related keywords: ANOVAnonparametric statistics
Frobenius norm F06RAF   15  nagf_blas_dlange
1 -norm, -norm, Frobenius norm, largest absolute element, real general matrix
Related keywords: 1-normBLASinfinity-normlinear algebra support routinesnorm, matrixreal, m by n matrix
F06RBF   15  nagf_blas_dlangb
1 -norm, -norm, Frobenius norm, largest absolute element, real band matrix
Related keywords: 1-normBLASinfinity-normlinear algebra support routinesmatrix, bandnorm, matrixreal, band, m by n matrix
F06RCF   15  nagf_blas_dlansy
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix
Related keywords: 1-normBLASinfinity-normlinear algebra support routinesnorm, matrixreal, indefinite, symmetric matrix
F06RDF   15  nagf_blas_dlansp
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage
Related keywords: 1-normBLASinfinity-normlinear algebra support routinesnorm, matrixreal, indefinite, symmetric matrix
F06REF   15  nagf_blas_dlansb
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric band matrix
Related keywords: 1-normBLASinfinity-normlinear algebra support routinesmatrix, bandnorm, matrixreal, band, symmetric matrix
F06RJF   15  nagf_blas_dlantr
1 -norm, -norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix
Related keywords: 1-normBLASinfinity-normlinear algebra support routinesnorm, matrixreal, trapezoidal matrixreal, triangular matrix
F06RKF   15  nagf_blas_dlantp
1 -norm, -norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage
Related keywords: 1-normBLASinfinity-normlinear algebra support routinesnorm, matrixreal, triangular matrix
F06RLF   15  nagf_blas_dlantb
1 -norm, -norm, Frobenius norm, largest absolute element, real triangular band matrix
Related keywords: 1-normBLASinfinity-normlinear algebra support routinesnorm, matrixreal, band, triangular matrix
F06RMF   15  nagf_blas_dlanhs
1 -norm, -norm, Frobenius norm, largest absolute element, real upper Hessenberg matrix
Related keywords: 1-normBLASinfinity-normlinear algebra support routinesnorm, matrixreal, Hessenberg matrix
F06RNF   21  nagf_blas_dlangt
1 -norm, -norm, Frobenius norm, largest absolute element, real tridiagonal matrix
Related keywords: 1-normBLASinfinity-normlinear algebra support routinesmatrix, bandnorm, matrixreal, tridiagonal matrix
F06RPF   21  nagf_blas_dlanst
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix
Related keywords: 1-normBLASinfinity-normlinear algebra support routinesmatrix, bandnorm, matrixreal, symmetric, tridiagonal matrix
F06UAF   15  nagf_blas_zlange
1 -norm, -norm, Frobenius norm, largest absolute element, complex general matrix
Related keywords: 1-normBLAScomplex, m by n matrixinfinity-normlinear algebra support routines
F06UBF   15  nagf_blas_zlangb
1 -norm, -norm, Frobenius norm, largest absolute element, complex band matrix
Related keywords: 1-normBLAScomplex, band matrixinfinity-normlinear algebra support routinesmatrix, band
F06UCF   15  nagf_blas_zlanhe
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix
Related keywords: 1-normBLAScomplex, band matrixinfinity-normlinear algebra support routines
F06UDF   15  nagf_blas_zlanhp
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage
Related keywords: 1-normBLAScomplex, Hermitian matrixinfinity-normlinear algebra support routines
F06UEF   15  nagf_blas_zlanhb
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian band matrix
Related keywords: 1-normBLAScomplex, band, Hermitian matrixinfinity-normlinear algebra support routinesmatrix, band
F06UFF   15  nagf_blas_zlansy
1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix
Related keywords: 1-normBLAScomplex, symmetric matrixinfinity-normlinear algebra support routines
F06UGF   15  nagf_blas_zlansp
1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage
Related keywords: 1-normBLAScomplex, symmetric matrixinfinity-normlinear algebra support routines
F06UHF   15  nagf_blas_zlansb
1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric band matrix
Related keywords: 1-normBLAScomplex, band, symmetric matrixinfinity-normlinear algebra support routinesmatrix, band
F06UJF   15  nagf_blas_zlantr
1 -norm, -norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix
Related keywords: 1-normBLAScomplex, trapezoidal matrixcomplex, triangular matrixinfinity-normlinear algebra support routines
F06UKF   15  nagf_blas_zlantp
1 -norm, -norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage
Related keywords: 1-normBLAScomplex, triangular matrixinfinity-normlinear algebra support routines
F06ULF   15  nagf_blas_zlantb
1 -norm, -norm, Frobenius norm, largest absolute element, complex triangular band matrix
Related keywords: 1-normBLAScomplex, band, triangular matrixinfinity-normlinear algebra support routinesmatrix, band
F06UMF   15  nagf_blas_zlanhs
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hessenberg matrix
Related keywords: 1-normBLAScomplex, Hessenberg matrixinfinity-normlinear algebra support routines
F06UNF   21  nagf_blas_zlangt
1 -norm, -norm, Frobenius norm, largest absolute element, complex tridiagonal matrix
Related keywords: 1-normBLAScomplex, triangular matrixinfinity-normlinear algebra support routinesmatrix, band
F06UPF   21  nagf_blas_zlanht
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian tridiagonal matrix
Related keywords: 1-normBLAScomplex, Hermitian, tridiagonal matrixinfinity-normlinear algebra support routinesmatrix, band
F06WAF   23  nagf_blas_dlansf
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format
Related keywords: 1-normBLASBLASblas, real matricesdlansfinfinity-normlinear algebra support routineslinear algebra support routines;real, symmetric matrix
F06WNF   23  nagf_blas_zlanhf
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format
Related keywords: 1-normBLASBLASblas, complex matricescomplex, Hermitian matrixinfinity-normlinear algebra support routineslinear algebra support routines;zlanhf
F16RBF   23  nagf_blast_dgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, real band matrix
Related keywords: 1-normabsolute valueabsolute valuebanded matrixfurther linear algebra support routinesinfinity-normmatrix, bandnorm, matrixreal, band, m by n matrix
F16UBF   23  nagf_blast_zgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, complex band matrix
Related keywords: 1-normabsolute valuebanded matrixcomplex, band matrixfurther linear algebra support routinesinfinity-normmatrix, bandnorm, matrix
functions, matrix F01EFF   23  nagf_matop_real_symm_matrix_fun
Function of a real symmetric matrix
Related keywords: financeinversionmatrix functionsmatrix operationsreal, indefinite, symmetric matrix
F01EKF   24  nagf_matop_real_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm)
Related keywords: cosh, matrixcosine, matrixexponential, matrixinversionmatrix operationsreal, nonsymmetric matrixsine, matrixsinh, matrix
F01ELF   24  nagf_matop_real_gen_matrix_fun_num
Function of a real matrix (using numerical differentiation)
Related keywords: inversionmatrix functionsmatrix operationsreal, nonsymmetric matrix
F01EMF   24  nagf_matop_real_gen_matrix_fun_usd
Function of a real matrix (using user-supplied derivatives)
Related keywords: inversionmatrix functionsmatrix operationsreal, nonsymmetric matrix
F01FFF   23  nagf_matop_complex_herm_matrix_fun
Function of a complex Hermitian matrix
Related keywords: complex, Hermitian, indefinite matrixfinanceinversionmatrix functionsmatrix operations
F01FKF   24  nagf_matop_complex_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm)
Related keywords: complex, nonsymmetric matrixcosh, matrixcosine, matrixexponential, matrixinversionmatrix operationssine, matrixsinh, matrix
F01FLF   24  nagf_matop_complex_gen_matrix_fun_num
Function of a complex matrix (using numerical differentiation)
Related keywords: complex, nonsymmetric matrixinversionmatrix functionsmatrix operations
F01FMF   24  nagf_matop_complex_gen_matrix_fun_usd
Function of a complex matrix (using user-supplied derivatives)
Related keywords: complex, nonsymmetric matrixinversionmatrix functionsmatrix operations
further linear algebra support routines F16 Chapter Introduction     Further Linear Algebra Support Routines
gain, time series G13CFF   10  nagf_tsa_multi_gain_bivar
Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra
Related keywords: big databivariate time seriescross-spectrumdata analyticsfinancemultivariate time seriesphase, time seriestime seriestime series analysis
gamma, Euler's constant X01ABF   nagf_math_euler
Provides the mathematical constant γ (Euler's constant)
Related keywords: Euler's constantmathematical constants
gamma distribution G01EFF   14  nagf_stat_prob_gamma
Computes probabilities for the gamma distribution
Related keywords: CDF, cumulative distribution functionfinancelower tail probabilityprobabilitySimple Calculations on Statistical Dataupper tail probability
G01FFF   14  nagf_stat_inv_cdf_gamma
Computes deviates for the gamma distribution
Related keywords: deviatesfinanceinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01KFF   23  nagf_stat_pdf_gamma
Calculates the value for the probability density function of the gamma distribution at a chosen point
Related keywords: pdfprobability density functionSimple Calculations on Statistical Data
G01KKF   24  nagf_stat_pdf_gamma_vector
Computes a vector of values for the probability density function of the gamma distribution
Related keywords: pdfprobability density functionSimple Calculations on Statistical Data
G01SFF   24  nagf_stat_prob_gamma_vector
Computes a vector of probabilities for the gamma distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticslower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01TFF   24  nagf_stat_inv_cdf_gamma_vector
Computes a vector of deviates for the gamma distribution
Related keywords: big datadata analyticsdeviatesinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G05SJF   22  nagf_rand_dist_gamma
Generates a vector of pseudorandom numbers from a gamma distribution
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
gamma function S14AAF   nagf_specfun_gamma
Gamma function
Related keywords: approximations of special functionsfinance
gaps test for randomness G08EDF   14  nagf_nonpar_randtest_gaps
Performs the gaps test for randomness
Related keywords: nonparametric statisticsrandomness, tests for
GARCH G05PDF   22  nagf_rand_times_garch_asym1
Generates a realization of a time series from a GARCH process with asymmetry of the form ε t - 1 + γ 2
Related keywords: big datadata analyticsfinancerandom number generatorstime series
G05PEF   22  nagf_rand_times_garch_asym2
Generates a realization of a time series from a GARCH process with asymmetry of the form ε t - 1 + γ ε t - 1 2
Related keywords: big datadata analyticsfinancerandom number generatorstime series
G05PFF   22  nagf_rand_times_garch_gjr
Generates a realization of a time series from an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsfinancerandom number generatorstime series
G13FAF   20  nagf_tsa_uni_garch_asym1_estim
Univariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the form ε t - 1 + γ 2
Related keywords: big datadata analyticsfinancetime seriestime series analysisunivariate time series
G13FBF   20  nagf_tsa_uni_garch_asym1_forecast
Univariate time series, forecast function for either a symmetric GARCH process or a GARCH process with asymmetry of the form ε t - 1 + γ 2
Related keywords: big datadata analyticsfinanceforecastingtime seriestime series analysisunivariate time series
G13FCF   20  nagf_tsa_uni_garch_asym2_estim
Univariate time series, parameter estimation for a GARCH process with asymmetry of the form ε t - 1 + γ ε t - 1 2
Related keywords: big datadata analyticsfinancetime seriestime series analysisunivariate time series
G13FDF   20  nagf_tsa_uni_garch_asym2_forecast
Univariate time series, forecast function for a GARCH process with asymmetry of the form ε t - 1 + γ ε t - 1 2
Related keywords: big datadata analyticsfinanceforecastingtime seriestime series analysisunivariate time series
G13FEF   20  nagf_tsa_uni_garch_gjr_estim
Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsfinanceGJR GARCH processGlosten, Jagannathan and Runkle processtime seriestime series analysisunivariate time series
G13FFF   20  nagf_tsa_uni_garch_gjr_forecast
Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsfinanceforecastingGJR GARCH processGlosten, Jagannathan and Runkle processtime seriestime series analysisunivariate time series
G13FGF   20  nagf_tsa_uni_garch_exp_estim
Univariate time series, parameter estimation for an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsEGARCHexponential GARCHfinancetime seriestime series analysisunivariate time series
G13FHF   20  nagf_tsa_uni_garch_exp_forecast
Univariate time series, forecast function for an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsEGARCHexponential GARCHfinanceforecastingtime seriestime series analysisunivariate time series
Gauss hypergeometric function S22BEF   25  nagf_specfun_2f1_real
Real Gauss hypergeometric function F 1 2 a , b ; c ; x
Related keywords: 2 F 1 , hypergeometric functionapproximations of special functionshypergeometric function
S22BFF   25  nagf_specfun_2f1_real_scaled
Real Gauss hypergeometric function F 1 2 a , b ; c ; x in scaled form
Related keywords: 2 F 1 , hypergeometric functionapproximations of special functionshypergeometric function
Gaussian D01TDF   26  nagf_quad_1d_gauss_wrec
Calculation of weights and abscissae for Gaussian quadrature rules, method of Golub and Welsch
Related keywords: abscissaecubatureGolubGolub and Welschintegrationnon-adaptivequadratureweights and abscissaeWelsch
D01TEF   26  nagf_quad_1d_gauss_recm
Generates recursion coefficients needed by D01TDF to calculate a Gaussian quadrature rule
Related keywords: abscissaecubatureGolubGolub and Welschintegrationnon-adaptivequadraturerecursion coefficientsWelsch
Gaussian copula G05RDF   22  nagf_rand_copula_normal
Generates a matrix of pseudorandom numbers from a Gaussian copula
Related keywords: big datacopuladata analyticsfinancerandom number generatorsrandom numbers
Gaussian distribution G01KAF   23  nagf_stat_pdf_normal
Calculates the value for the probability density function of the Normal distribution at a chosen point
Related keywords: Normal distributionpdfprobability density functionSimple Calculations on Statistical Data
G01KQF   24  nagf_stat_pdf_normal_vector
Computes a vector of values for the probability density function of the Normal distribution
Related keywords: logarithm, pdfNormal distributionpdfprobability density functionSimple Calculations on Statistical Data
G01LBF   24  nagf_stat_pdf_multi_normal_vector
Computes a vector of values for the probability density function of the multivariate Normal distribution
Related keywords: logarithm, pdfmultivariate Normal distributionNormal distributionpdfprobability density functionSimple Calculations on Statistical Data
G01NAF   16  nagf_stat_moments_quad_form
Cumulants and moments of quadratic forms in Normal variables
Related keywords: cumulantfinancemoments quadratic formmultivariate Normal distributionNormal distributionSimple Calculations on Statistical Data
G01NBF   16  nagf_stat_moments_ratio_quad_forms
Moments of ratios of quadratic forms in Normal variables, and related statistics
Related keywords: financemoments quadratic formmultivariate Normal distributionNormal distributionSimple Calculations on Statistical Data
G01SAF   24  nagf_stat_prob_normal_vector
Computes a vector of probabilities for the standard Normal distribution
Related keywords: big dataCDF, cumulative distribution functionconfidence intervaldata analyticslower tail probabilityNormal distributionsignificanceSimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01TAF   24  nagf_stat_inv_cdf_normal_vector
Computes a vector of deviates for the standard Normal distribution
Related keywords: big datadata analyticsdeviatesinverse CDFinverse cumulative distribution functionNormal distributionSimple Calculations on Statistical Data
G05RZF   22  nagf_rand_multivar_normal
Generates a matrix of pseudorandom numbers from a multivariate Normal distribution
Related keywords: big datadata analyticsfinancemultivariate Normal distributionNormal distributionrandom number generatorsrandom numbers
G05SKF   22  nagf_rand_dist_normal
Generates a vector of pseudorandom numbers from a Normal distribution
Related keywords: big datadata analyticsfinanceNormal distributionrandom number generatorsrandom numbers
G05YJF   21  nagf_rand_quasi_normal
Generates a Normal quasi-random number sequence
Related keywords: big datadata analyticsFaure, quasi-random numberslow-discrepancy sequencesNiederreiter method, quasi-random numbersNormal distributionquasi-random numbersrandom number generatorsrandom numbersSobol, quasi-random numbers
G07BBF   15  nagf_univar_estim_normal
Computes maximum likelihood estimates for parameters of the Normal distribution from grouped and/or censored data
Related keywords: censored datagrouping datamaximum likelihoodNormal distributionunivariate estimation
G07CAF   15  nagf_univar_ttest_2normal
Computes t -test statistic for a difference in means between two Normal populations, confidence interval
Related keywords: confidence intervalNormal distributiont-test statisticunivariate estimation
G08CKF   23  nagf_nonpar_gofstat_anddar_normal
Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of a fully-unspecified Normal distribution
Related keywords: Anderson–Darling test statisticnonparametric statisticsNormal distributionprobability
S15ABF   nagf_specfun_cdf_normal
Cumulative Normal distribution function P x
Related keywords: approximations of special functionscumulative Normal distributionfinanceNormal distribution
Gaussian mixture model G03GAF   24  nagf_mv_gaussian_mixture
Fits a Gaussian mixture model
Related keywords: cluster analysismultivariate methods
Gauss–Kronrod quadrature D01AJF   nagf_quad_1d_fin_bad
One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands
Related keywords: financeintegration, adaptiveQAGSQUADPACKquadraturequadrature, adaptive
D01AKF   nagf_quad_1d_fin_osc
One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions
Related keywords: financeintegration, adaptiveQAGQUADPACKquadraturequadrature, adaptive
D01ALF   nagf_quad_1d_fin_sing
One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points
Related keywords: financeintegration, adaptiveQAGPQUADPACKquadraturequadrature, adaptive
D01AMF   nagf_quad_1d_inf
One-dimensional quadrature, adaptive, infinite or semi-infinite interval
Related keywords: financeintegration, adaptiveintegration, infinite intervalQAGIQUADPACKquadraturequadrature, adaptive
D01ANF   nagf_quad_1d_fin_wtrig
One-dimensional quadrature, adaptive, finite interval, weight function cos ω x or sin ω x
Related keywords: financeintegration, adaptiveQFOURQUADPACKquadraturequadrature, adaptive
D01APF   nagf_quad_1d_fin_wsing
One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type
Related keywords: financeintegration, adaptiveQAWSEQUADPACKquadraturequadrature, adaptive
D01AQF   nagf_quad_1d_fin_wcauchy
One-dimensional quadrature, adaptive, finite interval, weight function 1 / x - c , Cauchy principal value (Hilbert transform)
Related keywords: Cauchy principal valuefinanceHilbert transformintegration, adaptiveQAWCQUADPACKquadraturequadrature, adaptive
D01ASF   13  nagf_quad_1d_inf_wtrig
One-dimensional quadrature, adaptive, semi-infinite interval, weight function cos ω x or sin ω x
Related keywords: financeintegration, adaptiveintegration, infinite intervalQAWFEQUADPACKquadraturequadrature, adaptivevectorized quadrature
D01ATF   13  nagf_quad_1d_fin_bad_vec
One-dimensional quadrature, adaptive, finite interval, variant of D01AJF efficient on vector machines
Related keywords: integration, adaptiveQAGQAGSQUADPACKquadraturequadrature, adaptivevectorized quadrature
Gauss–Lobatto grid D02UAF   23  nagf_ode_bvp_ps_lin_coeffs
Coefficients of Chebyshev interpolating polynomial from function values on Chebyshev grid
Related keywords: Chebyshev polynomial interpolationinterpolationODE, ordinary differential equations
D02UBF   23  nagf_ode_bvp_ps_lin_cgl_vals
Function or low-order-derivative values on Chebyshev grid from coefficients of Chebyshev interpolating polynomial
Related keywords: Chebyshev polynomial interpolationChebyshev series, solutioninterpolationODE, ordinary differential equations
D02UCF   23  nagf_ode_bvp_ps_lin_cgl_grid
Chebyshev Gauss–Lobatto grid generation
Related keywords: ODE, ordinary differential equations
D02UDF   23  nagf_ode_bvp_ps_lin_cgl_deriv
Differentiate a function by the FFT using function values on Chebyshev grid
Related keywords: Fast Fourier TransformFFTODE, ordinary differential equations
D02UEF   23  nagf_ode_bvp_ps_lin_solve
Solve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation
Related keywords: boundary value problemBVPODE, ordinary differential equationspseudo-spectral method
D02UWF   23  nagf_ode_bvp_ps_lin_grid_vals
Interpolate a function from Chebyshev grid to uniform grid using barycentric Lagrange interpolation
Related keywords: barycentric Lagrange interpolationinterpolationODE, ordinary differential equations
Gauss–Markov linear model F08ZBF   21  nagf_lapackeig_dggglm
Solves a real general Gauss–Markov linear model (GLM) problem
Related keywords: DGGGLMeigenproblemLAPACKLAPACKleast squares QR factorizationreal, m by n matrix
F08ZPF   21  nagf_lapackeig_zggglm
Solves a complex general Gauss–Markov linear model (GLM) problem
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresZGGGLM
Gauss–Newton optimization E04FCF   nagf_opt_lsq_uncon_mod_func_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (comprehensive)
Related keywords: data fittingderivative-free minimizationfinancemaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04FYF   18  nagf_opt_lsq_uncon_mod_func_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (easy-to-use)
Related keywords: data fittingderivative-free minimizationfinancemaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04GBF   nagf_opt_lsq_uncon_quasi_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (comprehensive)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmdata fittingfinancemaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationquasi-Newton algorithmsum-of-squares minimization
E04GDF   nagf_opt_lsq_uncon_mod_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (comprehensive)
Related keywords: data fittingfinancemaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04GYF   18  nagf_opt_lsq_uncon_quasi_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmdata fittingfinancemaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationquasi-Newton algorithmsum-of-squares minimization
E04GZF   18  nagf_opt_lsq_uncon_mod_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (easy-to-use)
Related keywords: data fittingfinancemaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04HEF   nagf_opt_lsq_uncon_mod_deriv2_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive)
Related keywords: data fittingfinancemaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04HYF   18  nagf_opt_lsq_uncon_mod_deriv2_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use)
Related keywords: data fittingfinancemaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
general D02KDF   nagf_ode_sl2_breaks_vals
Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points
Related keywords: boundary value problemBVPeigenproblemODE, ordinary differential equationsSturm–Liouville equations
generalized augmented Lagrangian method E04SVF   26  nagf_opt_handle_solve_pennon
Run the Pennon solver on a compatible problem initialized by E04RAF and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI)
Related keywords: bilinear matrix inequalityBMILagrangianleast squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionmonitoring informationoptimizationoptimizationSDPsemidefinite programming
generalized eigenproblem F01BVF   nagf_matop_real_symm_posdef_geneig
Reduction to standard form, generalized real symmetric-definite banded eigenproblem
Related keywords: eigenproblem, generalizedinversionmatrix, bandmatrix operationsreal, band, positive-definite, symmetric matrix
F08SAF   21  nagf_lapackeig_dsygv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Related keywords: DSYGVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08SBF   21  nagf_lapackeig_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Related keywords: DSYGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08SCF   21  nagf_lapackeig_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodDSYGVDeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08SEF   16  nagf_lapackeig_dsygst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , B factorized by F07FDF
Related keywords: DSYGSTeigenproblemeigenproblem, generalizedLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08SNF   21  nagf_lapackeig_zhegv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresZHEGV
F08SPF   21  nagf_lapackeig_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresZHEGVX
F08SQF   21  nagf_lapackeig_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: complex, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresZHEGVD
F08SSF   16  nagf_lapackeig_zhegst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , B factorized by F07FRF
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedLAPACKLAPACKleast squaresZHEGST
F08TAF   21  nagf_lapackeig_dspgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Related keywords: DSPGVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TBF   21  nagf_lapackeig_dspgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Related keywords: DSPGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TCF   21  nagf_lapackeig_dspgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: divide-and-conquer methodDSPGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TEF   16  nagf_lapackeig_dspgst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , packed storage, B factorized by F07GDF
Related keywords: DSPGVXeigenproblemeigenproblem, generalizedLAPACKLAPACKleast squaresreal, positive-definite, symmetric matrix
F08TNF   21  nagf_lapackeig_zhpgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresZHPGV
F08TPF   21  nagf_lapackeig_zhpgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresZHPGVX
F08TQF   21  nagf_lapackeig_zhpgvd
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: complex, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresZHPGVD
F08TSF   16  nagf_lapackeig_zhpgst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , packed storage, B factorized by F07GRF
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedLAPACKLAPACKleast squaresZHPGVD
F08UAF   21  nagf_lapackeig_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: DSBGVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UBF   21  nagf_lapackeig_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: DSBGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UCF   21  nagf_lapackeig_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodDSBGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UEF   19  nagf_lapackeig_dsbgst
Performs a reduction of real symmetric-definite banded generalized eigenproblem A x = λ B x to standard form C y = λ y , such that C has the same bandwidth as A
Related keywords: DSBGSTeigenproblemeigenproblem, generalizedLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UFF   19  nagf_lapackeig_dpbstf
Computes a split Cholesky factorization of real symmetric positive definite band matrix A
Related keywords: Cholesky decompositionDPBSTFDSBGSTeigenproblemeigenproblem, generalizedLAPACKLAPACKleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UNF   21  nagf_lapackeig_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandZHBGV
F08UPF   21  nagf_lapackeig_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandZHBGVX
F08UQF   21  nagf_lapackeig_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: complex, band, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandZHBGVD
F08USF   19  nagf_lapackeig_zhbgst
Performs a reduction of complex Hermitian-definite banded generalized eigenproblem A x = λ B x to standard form C y = λ y , such that C has the same bandwidth as A
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedLAPACKLAPACKleast squaresmatrix, bandZHBGST
F08UTF   19  nagf_lapackeig_zpbstf
Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedLAPACKLAPACKleast squaresmatrix, bandSplit Cholesky factorizationZPBSTF
F08WAF   21  nagf_lapackeig_dggev
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: DGGEVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WBF   21  nagf_lapackeig_dggevx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGGEVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsfinanceforward errorLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WCF   26  nagf_lapackeig_dggev3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: DGGEVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WEF   20  nagf_lapackeig_dgghrd
Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Related keywords: DGGHRDeigenproblemeigenproblem, generalizedLAPACKLAPACKleast squaresorthogonal transformationsreal, nonsymmetric matrix
F08WFF   26  nagf_lapackeig_dgghd3
Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Related keywords: DGGHD3eigenproblemeigenproblem, generalizedLAPACKLAPACKleast squaresorthogonal transformationsreal, nonsymmetric matrix
F08WHF   20  nagf_lapackeig_dggbal
Balances a pair of real, square, matrices
Related keywords: balancingDGGHRDeigenproblemeigenproblem, generalizedLAPACKLAPACKleast squares
F08WJF   20  nagf_lapackeig_dggbak
Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF
Related keywords: balancingDGGBAKeigenproblemeigenproblem, generalizedeigenvectorsLAPACKLAPACKleast squares
F08WNF   21  nagf_lapackeig_zggev
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresZGGEV
F08WPF   21  nagf_lapackeig_zggevx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixcondition number, matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsfinanceforward errorLAPACKLAPACKleast squaresZGGEVX
F08WQF   26  nagf_lapackeig_zggev3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsLAPACKLAPACKleast squaresZGGEV3
F08XNF   21  nagf_lapackeig_zgges
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresSchur vectorsZGGES
F08XPF   21  nagf_lapackeig_zggesx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresSchur vectorsZGGES
F08XQF   26  nagf_lapackeig_zgges3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresSchur vectorsZGGES3
F08XSF   20  nagf_lapackeig_zhgeqz
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresQZ algorithmZHGEQZ
generalized linear model G02GAF   14  nagf_correg_glm_normal
Fits a generalized linear model with Normal errors
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02GBF   14  nagf_correg_glm_binomial
Fits a generalized linear model with binomial errors
Related keywords: big datacorrelation analysisdata analyticsfinancelogistic regressionlogitnonlinear regressionpolynomial regressionprobitregression analysis
G02GCF   14  nagf_correg_glm_poisson
Fits a generalized linear model with Poisson errors
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02GDF   14  nagf_correg_glm_gamma
Fits a generalized linear model with gamma errors
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02GKF   14  nagf_correg_glm_constrain
Estimates and standard errors of parameters of a general linear model for given constraints
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysisstandard errors
G02GNF   14  nagf_correg_glm_estfunc
Computes estimable function of a generalized linear model and its standard error
Related keywords: big datacorrelation analysisdata analyticsestimable functionfinancenonlinear regressionpolynomial regressionregression analysis
G02GPF   22  nagf_correg_glm_predict
Computes a predicted value and its associated standard error based on a previously fitted generalized linear model
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionpredicted valueregression analysisstandard errors
generalized Schur form F08XAF   21  nagf_lapackeig_dgges
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: DGGESeigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form, generalizedSchur vectors
F08XBF   21  nagf_lapackeig_dggesx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: condition number, matrixDGGESXeigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form, generalizedSchur vectors
F08XCF   26  nagf_lapackeig_dgges3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: DGGES3eigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form, generalizedSchur vectors
F08XEF   20  nagf_lapackeig_dhgeqz
Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
Related keywords: DHGEQZeigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, Hessenberg matrix
F08XNF   21  nagf_lapackeig_zgges
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresSchur vectorsZGGES
F08XPF   21  nagf_lapackeig_zggesx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresSchur vectorsZGGES
F08XQF   26  nagf_lapackeig_zgges3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresSchur vectorsZGGES3
F08XSF   20  nagf_lapackeig_zhgeqz
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemLAPACKLAPACKleast squaresQZ algorithmZHGEQZ
F08YFF   22  nagf_lapackeig_dtgexc
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
Related keywords: DTGEXCeigenproblemLAPACKLAPACKleast squaresorthogonal transformations
F08YGF   22  nagf_lapackeig_dtgsen
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Related keywords: condition number, matrixDTGSENeigenproblemeigenvaluesLAPACKLAPACKleast squaresorthogonal transformationsreal, nonsymmetric matrix
F08YKF   20  nagf_lapackeig_dtgevc
Computes right and left generalized eigenvectors of the matrix pair A , B which is assumed to be in generalized upper Schur form
Related keywords: DTGEVCeigenproblemeigenvectorsLAPACKLAPACKleast squares
F08YLF   22  nagf_lapackeig_dtgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
Related keywords: condition number, matrixDTGSNAeigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08YTF   22  nagf_lapackeig_ztgexc
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
Related keywords: complex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresunitary transformationsZTGEXC
F08YUF   22  nagf_lapackeig_ztgsen
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemeigenvaluesLAPACKLAPACKleast squaresunitary transformationsZTGEXC
F08YXF   20  nagf_lapackeig_ztgevc
Computes left and right eigenvectors of a pair of complex upper triangular matrices
Related keywords: complex, triangular matrixeigenproblemeigenvectorsLAPACKLAPACKleast squaresZTGEVC
F08YYF   22  nagf_lapackeig_ztgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemLAPACKLAPACKleast squaresZTGSNA
general power F01EQF   25  nagf_matop_real_gen_matrix_pow
General power of a real matrix
Related keywords: inversionmatrix operationsmatrix operations including inversion
F01FQF   25  nagf_matop_complex_gen_matrix_pow
General power of a complex matrix
Related keywords: eigenvalues and eigenvectorsinversionmatrix operationsmatrix operations including inversion
geometric distribution G05TCF   22  nagf_rand_int_geom
Generates a vector of pseudorandom integers from a geometric distribution
Related keywords: big datadata analyticsfinancerandom integersrandom number generators
get X10ADF   26 
Get the algorithmic mode
Related keywords: adjoint derivativesAD utility operationsalgorithmic modeautomatic differentiation
X10BDF   26 
Get the callback algorithmic mode
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationcallback algorithmic mode
get information E04RXF   26  nagf_opt_handle_set_get_real
Retrieve or write a piece of information in a problem handle initialized by E04RAF
Related keywords: maximizing a functionminimizing a functionoptimizationset information
Gibbs method D06CCF   20  nagf_mesh_2d_renumber
Renumbers a given mesh using Gibbs method
Related keywords: mesh generationmesh renumbering
Gill–Miller quadrature D01GAF   nagf_quad_1d_data
One-dimensional quadrature, integration of function defined by data values, Gill–Miller method
Related keywords: financeintegration, non-adaptivequadraturequadrature non-adaptive
Givens rotations F08LEF   19  nagf_lapackeig_dgbbrd
Performs a reduction of real rectangular band matrix to upper bidiagonal form
Related keywords: DGBBRDeigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, m by n matrix
F08LSF   19  nagf_lapackeig_zgbbrd
Reduction of complex rectangular band matrix to upper bidiagonal form
Related keywords: eigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, m by n matrixZGBBRD
GJR GARCH process G13FEF   20  nagf_tsa_uni_garch_gjr_estim
Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsfinanceGARCHGlosten, Jagannathan and Runkle processtime seriestime series analysisunivariate time series
G13FFF   20  nagf_tsa_uni_garch_gjr_forecast
Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsfinanceforecastingGARCHGlosten, Jagannathan and Runkle processtime seriestime series analysisunivariate time series
global optimization E05 Chapter Introduction   22  Global Optimization of a Function
Glosten, Jagannathan and Runkle process G13FEF   20  nagf_tsa_uni_garch_gjr_estim
Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsfinanceGARCHGJR GARCH processtime seriestime series analysisunivariate time series
G13FFF   20  nagf_tsa_uni_garch_gjr_forecast
Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsfinanceforecastingGARCHGJR GARCH processtime seriestime series analysisunivariate time series
Golub D01TDF   26  nagf_quad_1d_gauss_wrec
Calculation of weights and abscissae for Gaussian quadrature rules, method of Golub and Welsch
Related keywords: abscissaecubatureGaussianGolub and Welschintegrationnon-adaptivequadratureweights and abscissaeWelsch
D01TEF   26  nagf_quad_1d_gauss_recm
Generates recursion coefficients needed by D01TDF to calculate a Gaussian quadrature rule
Related keywords: abscissaecubatureGaussianGolub and Welschintegrationnon-adaptivequadraturerecursion coefficientsWelsch
Golub and Welsch D01TDF   26  nagf_quad_1d_gauss_wrec
Calculation of weights and abscissae for Gaussian quadrature rules, method of Golub and Welsch
Related keywords: abscissaecubatureGaussianGolubintegrationnon-adaptivequadratureweights and abscissaeWelsch
D01TEF   26  nagf_quad_1d_gauss_recm
Generates recursion coefficients needed by D01TDF to calculate a Gaussian quadrature rule
Related keywords: abscissaecubatureGaussianGolubintegrationnon-adaptivequadraturerecursion coefficientsWelsch
Gonnet method, quadrature D01RGF   24  nagf_quad_1d_fin_gonnet_vec
One-dimensional quadrature, adaptive, finite interval, strategy due to Gonnet, allowing for badly behaved integrands
Related keywords: financeintegration, adaptivequadraturequadrature, adaptive
Gram–Schmidt orthogonalization F05AAF   nagf_orthog_real_gram_schmidt
Gram–Schmidt orthogonalization of n vectors of order m
Related keywords: orthogonalization
Greeks, options S30ABF   22  nagf_specfun_opt_bsm_greeks
Black–Scholes–Merton option pricing formula with Greeks
Related keywords: approximations of special functionsBlack–Scholes option pricingderivative, optionsfinanceoption pricing
S30BBF   22  nagf_specfun_opt_lookback_fls_greeks
Floating-strike lookback option pricing formula with Greeks in the Black-Scholes-Merton model
Related keywords: approximations of special functionsderivative, optionsfinancefloating-strike lookback optionoption pricing
S30CBF   22  nagf_specfun_opt_binary_con_greeks
Binary option, cash-or-nothing pricing formula with Greeks
Related keywords: approximations of special functionsbinary optioncash-or-nothing optionderivative, optionsfinanceoption pricing
S30CDF   22  nagf_specfun_opt_binary_aon_greeks
Binary option, asset-or-nothing pricing formula with Greeks
Related keywords: approximations of special functionsbinary optioncash-or-nothing optionderivative, optionsfinanceoption pricing
S30JBF   22  nagf_specfun_opt_jumpdiff_merton_greeks
Jump-diffusion, Merton's model, option pricing formula with Greeks
Related keywords: approximations of special functionsderivative, optionsfinancejump-diffusion model, option pricingMerton model, option pricingoption pricing
S30NBF   23  nagf_specfun_opt_heston_greeks
Heston's model option pricing formula with Greeks
Related keywords: approximations of special functionsderivative, optionsfinanceHeston model, optionsoption pricing
S30SBF   22  nagf_specfun_opt_asian_geom_greeks
Asian option, geometric continuous average rate pricing formula with Greeks
Related keywords: approximations of special functionsAsian optionderivative, optionsfinanceoption pricing
gridded data E02DFF   14  nagf_fit_2dspline_evalm
Evaluation of fitted bicubic spline at a mesh of points
Related keywords: bicubic splinesB-splinescurve and surface fittingfinance
E02JFF   24  nagf_fit_2dspline_ts_evalm
Evaluation at a mesh of points of a spline computed by E02JDF
Related keywords: curve and surface fittingscattered datasplinetwo-dimensional spline approximation
E02ZAF   nagf_fit_2dspline_sort
Sort two-dimensional data into panels for fitting bicubic splines
Related keywords: curve and surface fittingsorttwo-dimensional spline approximation
grid extraction D03RZF   18  nagf_pde_2d_gen_order2_rectilinear_extractgrid
Extract grid data from D03RBF
Related keywords: mesh refinementmethod of linesPDE, partial differential equationstwo-dimensional PDE
grouping data G07BBF   15  nagf_univar_estim_normal
Computes maximum likelihood estimates for parameters of the Normal distribution from grouped and/or censored data
Related keywords: censored dataGaussian distributionmaximum likelihoodNormal distributionunivariate estimation
GSVD, generalized singular value decomposition F08RAF   25  nagf_lapackeig_dorcsd
Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
Related keywords: complete CS decompositionDORCSDeigenproblemLAPACKLAPACKleast squaresreal, orthogonal matrix
F08RNF   25  nagf_lapackeig_zuncsd
Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices
Related keywords: complete CS decompositioncomplex, unitary matrixeigenproblemLAPACKLAPACKleast squaresZUNCSD
F08VAF   21  nagf_lapackeig_dggsvd
Computes the generalized singular value decomposition of a real matrix pair
Related keywords: DGGSVDeigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrixSVD, generalized
F08VCF   26  nagf_lapackeig_dggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair
Related keywords: DGGSVD3eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrixSVD, generalized
F08VEF   22  nagf_lapackeig_dggsvp
Produces orthogonal matrices that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
Related keywords: DGGSVPeigenproblemLAPACKLAPACKleast squaresorthogonal transformationsreal, m by n matrixSVD, generalized
F08VGF   26  nagf_lapackeig_dggsvp3
Produces orthogonal matrices, using BLAS-3, that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
Related keywords: DGGSVP3eigenproblemLAPACKLAPACKleast squaresorthogonal transformationsreal, m by n matrixSVD, generalized
F08VNF   21  nagf_lapackeig_zggsvd
Computes the generalized singular value decomposition of a complex matrix pair
Related keywords: complex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresSVD, generalizedZGGSVD
F08VQF   26  nagf_lapackeig_zggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair
Related keywords: complex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresSVD, generalizedZGGSVD3
F08VSF   22  nagf_lapackeig_zggsvp
Produces unitary matrices that simultaneously reduce the complex, m by n , matrix A and the complex, p by n , matrix B to upper triangular form
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresorthogonal transformationsSVD, generalizedZGGSVP
F08VUF   26  nagf_lapackeig_zggsvp3
Produces unitary matrices, using BLAS-3, that simultaneously reduce the complex, m by n , matrix A and the complex, p by n , matrix B to upper triangular form
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresorthogonal transformationsSVD, generalizedZGGSVP3
F08YEF   22  nagf_lapackeig_dtgsja
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
Related keywords: DTGSJAeigenproblemLAPACKLAPACKleast squaresreal, trapezoidal matrixreal, triangular matrixSVD, generalized
F08YSF   22  nagf_lapackeig_ztgsja
Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
Related keywords: complex, trapezoidal matrixcomplex, triangular matrixeigenproblemLAPACKLAPACKleast squaresZTGSJA
Gumbel–Hougard copula G05RKF   23  nagf_rand_copula_gumbel
Generates a matrix of pseudorandom numbers from a Gumbel–Hougaard copula
Related keywords: big datacopuladata analyticsrandom number generatorsrandom numbers
H 0 x , Struve function S17GAF   26  nagf_specfun_struve_h0
Struve function of order 0 , H 0 x
Related keywords: approximations of special functionsStruve function
H 1 x , Struve function S17GBF   26  nagf_specfun_struve_h1
Struve function of order 1 , H 1 x
Related keywords: approximations of special functionsStruve function
Haar wavelet C09AAF   22  nagf_wav_1d_init
One-dimensional wavelet filter initialization
Related keywords: biorthogonal waveletDaubechies waveletwaveletswavelets, one-dimensionalwavelet transforms
C09ABF   23  nagf_wav_2d_init
Two-dimensional wavelet filter initialization
Related keywords: biorthogonal waveletDaubechies waveletwaveletswavelets, two-dimensionalwavelet transforms
C09ACF   24  nagf_wav_3d_init
Three-dimensional wavelet filter initialization
Related keywords: biorthogonal waveletDaubechies waveletwaveletswavelets, three-dimensionalwavelet transforms
Hampel's piecewise linear function G02HAF   13  nagf_correg_robustm
Robust regression, standard M -estimates
Related keywords: Andrew's sine wavebig datacorrelation analysisdata analyticsfinanceHuber type regressionKrasker–Welsch weightsMallows type regressionMaronna's weights M -estimatesnonlinear regressionpolynomial regressionregressionregression analysisrobust regressionScheppe type regressionTukey's bi-weight
handle G22ZAF   26  nagf_blgm_handle_free
Destroy a and deallocate all the memory used
Related keywords: destroyfree
Hankel functions S17DLF   13  nagf_specfun_hankel_complex
Hankel functions H ν + a j z , j = 1 , 2 , real a 0 , complex z , ν = 0 , 1 , 2 ,
Related keywords: approximations of special functions
Harten–Lax-van Leer solver D03PWF   18  nagf_pde_1d_parab_euler_hll
Modified HLL Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
Related keywords: Euler equationsmodified HLL solverPDE, partial differential equationsRiemann solver, PDE
hazard rate G01MBF   15  nagf_stat_mills_ratio
Computes reciprocal of Mills' Ratio
Related keywords: financeMills' RatioSimple Calculations on Statistical Data
Helmholtz equation, PDE D03FAF   14  nagf_pde_3d_ellip_helmholtz
Elliptic PDE, Helmholtz equation, three-dimensional Cartesian coordinates
Related keywords: elliptic partial differential equationsPDE, partial differential equations
Hermite interpolation E01BEF   13  nagf_interp_1d_monotonic
Interpolating functions, monotonicity-preserving, piecewise cubic Hermite, one variable
Related keywords: cubic spline interpolationfinanceinterpolationmonotonicity-preserving spline
E01BFF   13  nagf_interp_1d_monotonic_eval
Interpolated values, interpolant computed by E01BEF, function only, one variable
Related keywords: financeinterpolationmonotonicity-preserving spline
E01BGF   13  nagf_interp_1d_monotonic_deriv
Interpolated values, interpolant computed by E01BEF, function and first derivative, one variable
Related keywords: financeinterpolationmonotonicity-preserving spline
E01BHF   13  nagf_interp_1d_monotonic_intg
Interpolated values, interpolant computed by E01BEF, definite integral, one variable
Related keywords: financeinterpolationmonotonicity-preserving spline
Hessian estimation E04XAF   12  nagf_opt_estimate_deriv_old
Estimate (using numerical differentiation) gradient and/or Hessian of a function
Related keywords: financeJacobian estimationmaximizing a functionminimizing a functionoptimization
E04YBF   nagf_opt_lsq_check_hessian
Check user's routine for calculating Hessian of a sum of squares
Related keywords: financemaximizing a functionminimizing a functionoptimizationservice routine
Heston S30NCF   25  nagf_specfun_opt_heston_term
Heston's model option pricing with term structure
Related keywords: approximations of special functionsEuropeanfinancestochastic volatilityterm structure
Heston model, options S30NAF   22  nagf_specfun_opt_heston_price
Heston's model option pricing formula
Related keywords: approximations of special functionsderivative, optionsfinancefinanceoption pricing
S30NBF   23  nagf_specfun_opt_heston_greeks
Heston's model option pricing formula with Greeks
Related keywords: approximations of special functionsderivative, optionsfinanceGreeks, optionsoption pricing
hierarchical classification G04AGF   nagf_anova_hier2
Two-way analysis of variance, hierarchical classification, subgroups of unequal size
Related keywords: analysis of varianceANOVAtwo-way analysis of variance
hierarchical cluster analysis G03ECF   16  nagf_mv_cluster_hier
Hierarchical cluster analysis
Related keywords: big datacluster analysisdata analyticsmultivariate methods
G03EHF   16  nagf_mv_cluster_hier_dendrogram
Constructs dendrogram (for use after G03ECF)
Related keywords: big datadata analyticsdendrogrammultivariate methods
G03EJF   16  nagf_mv_cluster_hier_indicator
Computes cluster indicator variable (for use after G03ECF)
Related keywords: allocatebig datacluster analysisdata analyticsmultivariate methods
hierarchical mixed effects regression G02JCF   23  nagf_correg_mixeff_hier_init
Hierarchical mixed effects regression, initialization routine for G02JDF G02JEF
Related keywords: big datacorrelation analysisdata analyticsmixed effects regressionnonlinear regressionpolynomial regressionregression analysis
G02JDF   23  nagf_correg_mixeff_hier_reml
Hierarchical mixed effects regression using Restricted Maximum Likelihood (REML)
Related keywords: big datacorrelation analysisdata analyticsmixed effects regressionnonlinear regressionpolynomial regressionregression analysisREML, Restricted Maximum Likelihood
G02JEF   23  nagf_correg_mixeff_hier_ml
Hierarchical mixed effects regression using Maximum Likelihood (ML)
Related keywords: big datacorrelation analysisdata analyticsmaximum likelihoodmixed effects regressionnonlinear regressionpolynomial regressionregression analysis
Hilbert transform D01AQF   nagf_quad_1d_fin_wcauchy
One-dimensional quadrature, adaptive, finite interval, weight function 1 / x - c , Cauchy principal value (Hilbert transform)
Related keywords: Cauchy principal valuefinanceGauss–Kronrod quadratureintegration, adaptiveQAWCQUADPACKquadraturequadrature, adaptive
hinges G01ALF   14  nagf_stat_5pt_summary
Computes a five-point summary (median, hinges and extremes)
Related keywords: financefive-point summarymaximum valuemedianminimum valueSimple Calculations on Statistical Data
Holt Winter G13AMF   22  nagf_tsa_uni_smooth_exp
Univariate time series, exponential smoothing
Related keywords: big dataBrowns Exponentialdata analyticsexponential smoothingfinanceLinear Holttime seriestime series analysisunivariate time series
Huber's weight function G02HKF   14  nagf_correg_robustm_corr_huber
Calculates a robust estimation of a covariance matrix, Huber's weight function
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
Huber type regression G02HAF   13  nagf_correg_robustm
Robust regression, standard M -estimates
Related keywords: Andrew's sine wavebig datacorrelation analysisdata analyticsfinanceHampel's piecewise linear functionKrasker–Welsch weightsMallows type regressionMaronna's weights M -estimatesnonlinear regressionpolynomial regressionregressionregression analysisrobust regressionScheppe type regressionTukey's bi-weight
hyperbolic cosine S10ACF   nagf_specfun_cosh
cosh x
Related keywords: approximations of special functionsfinance cosh x
hyperbolic equation D03PSF   17  nagf_pde_1d_parab_convdiff_remesh
General system of convection-diffusion PDEs, coupled DAEs, method of lines, upwind scheme, remeshing, one space variable
Related keywords: adaptive grid, PDEconvection-diffusion, PDEDAE, differential algebraic equationsmethod of linesone-dimensionalparabolic partial differential equationPDE, partial differential equations
hyperbolic sine S10ABF   nagf_specfun_sinh
sinh x
Related keywords: approximations of special functionsfinance
hyperbolic tangent S10AAF   nagf_specfun_tanh
tanh x
Related keywords: approximations of special functionsfinance tanh x
hypergeometric distribution G01BLF   13  nagf_stat_prob_hypergeom
Hypergeometric distribution function
Related keywords: CDF, cumulative distribution functionfinanceSimple Calculations on Statistical Data
G01SLF   24  nagf_stat_prob_hypergeom_vector
Computes a vector of probabilities for the hypergeometric distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticslower tail probabilitypoint probabilitySimple Calculations on Statistical Dataupper tail probability
G05TEF   22  nagf_rand_int_hypergeom
Generates a vector of pseudorandom integers from a hypergeometric distribution
Related keywords: big datadata analyticsfinancerandom integersrandom number generators
hypergeometric function S22BAF   24  nagf_specfun_1f1_real
Real confluent hypergeometric function F 1 1 a ; b ; x
Related keywords: 1 F 1 , hypergeometric functionapproximations of special functionsconfluent hypergeometric function
S22BBF   24  nagf_specfun_1f1_real_scaled
Real confluent hypergeometric function F 1 1 a ; b ; x in scaled form
Related keywords: 1 F 1 , hypergeometric functionapproximations of special functionsconfluent hypergeometric function
S22BEF   25  nagf_specfun_2f1_real
Real Gauss hypergeometric function F 1 2 a , b ; c ; x
Related keywords: 2 F 1 , hypergeometric functionapproximations of special functionsGauss hypergeometric function
S22BFF   25  nagf_specfun_2f1_real_scaled
Real Gauss hypergeometric function F 1 2 a , b ; c ; x in scaled form
Related keywords: 2 F 1 , hypergeometric functionapproximations of special functionsGauss hypergeometric function
I 0 , modified Bessel function S18AEF   nagf_specfun_bessel_i0_real
Modified Bessel function I 0 x
Related keywords: approximations of special functionsfinancemodified Bessel function
S18ASF   24  nagf_specfun_bessel_i0_real_vector
Modified Bessel function vectorized I 0 x
Related keywords: approximations of special functionsmodified Bessel function
S18CEF   10  nagf_specfun_bessel_i0_scaled
Scaled modified Bessel function e - x I 0 x
Related keywords: approximations of special functionsfinancemodified Bessel function
S18CSF   24  nagf_specfun_bessel_i0_scaled_vector
Scaled modified Bessel function vectorized e - x I 0 x
Related keywords: approximations of special functionsmodified Bessel function
I 0 x - L 0 x , Struve function S18GCF   26  nagf_specfun_struve_i0ml0
The function I 0 x - L 0 x , where I 0 x is a modified Bessel function and L 0 x is a Struve function
Related keywords: approximations of special functionsModified Struve function
I 1 , modified Bessel function S18AFF   nagf_specfun_bessel_i1_real
Modified Bessel function I 1 x
Related keywords: approximations of special functionsfinancemodified Bessel function
S18ATF   24  nagf_specfun_bessel_i1_real_vector
Modified Bessel function vectorized I 1 x
Related keywords: approximations of special functionsmodified Bessel function
S18CFF   10  nagf_specfun_bessel_i1_scaled
Scaled modified Bessel function e - x I 1 x
Related keywords: approximations of special functionsfinancemodified Bessel function
S18CTF   24  nagf_specfun_bessel_i1_scaled_vector
Scaled modified Bessel function vectorized e - x I 1 x
Related keywords: approximations of special functionsmodified Bessel function
I 1 x - L 1 x , Struve function S18GDF   26  nagf_specfun_struve_i1ml1
The function I 1 x - L 1 x , where I 1 x is a modified Bessel function and L 1 x is a Struve function
Related keywords: approximations of special functionsModified Struve function
ICC G04GAF   26  nagf_anova_icc
Intraclass correlation (ICC) for assessing rater reliability
Related keywords: analysis of varianceinterraterintraclassintraraterreliability
idamax F06JLF   12  nagf_blas_idamax
Index, real vector element with largest absolute value
Related keywords: BLASblas, real matriceselementary arithmeticlinear algebra support routines
identification A00AAF   18  nagf_info_impl_details
Library identification, details of implementation and mark
Related keywords: implementation detailslibrary detailslibrary identificationmark
A00ADF   22  nagf_info_impl_details_separate
Library identification, details of implementation, major and minor marks
Related keywords: implementation detailslibrary detailslibrary identificationmark
IEEE arithmetic X07 Chapter Introduction     IEEE Arithmetic
Imhof's method G01JDF   15  nagf_stat_prob_chisq_lincomb
Computes lower tail probability for a linear combination of (central) χ 2 variables
Related keywords: chi-squared distributionfinancelower tail probabilityPan's methodSimple Calculations on Statistical Data
implementation details A00AAF   18  nagf_info_impl_details
Library identification, details of implementation and mark
Related keywords: identificationlibrary detailslibrary identificationmark
A00ADF   22  nagf_info_impl_details_separate
Library identification, details of implementation, major and minor marks
Related keywords: identificationlibrary detailslibrary identificationmark
implicit algebraic ordinary differential equations D02MCF   22  nagf_ode_dae_dassl_cont
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method continuation for D02NEF
Related keywords: DAE, differential algebraic equationsDASSL, ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02MVF   14  nagf_ode_ivp_stiff_dassl
Ordinary differential equations, initial value problem, DASSL method, setup for d02m–n routines
Related keywords: DASSL, ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NEF   22  nagf_ode_dae_dassl_gen
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator
Related keywords: DAE, differential algebraic equationsDASSL, ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equations
D02NGF   12  nagf_ode_ivp_stiff_imp_fulljac
Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulainitial value problemIVP, initial value problemJacobianODE, ordinary differential equationsstiff differential equations
D02NHF   12  nagf_ode_ivp_stiff_imp_bandjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulainitial value problemIVP, initial value problemJacobianODE, ordinary differential equationsstiff differential equations
D02NJF   12  nagf_ode_ivp_stiff_imp_sparjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formuladiscretised systeminitial value problemIVP, initial value problemJacobianODEODE, ordinary differential equationsstiff differential equations
D02NNF   12  nagf_ode_ivp_stiff_imp_revcom
Implicit/algebraic ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
Related keywords: backward difference formulainitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NPF   22  nagf_ode_dae_dassl_linalg
Implicit ordinary differential equations/DAEs, initial value problem linear algebra setup routine for D02NEF
Related keywords: initial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
impulse response function G13CGF   10  nagf_tsa_multi_noise_bivar
Multivariate time series, noise spectrum, bounds, impulse response function and its standard error
Related keywords: big datadata analyticsfinancemultivariate time seriesnoise spectrumstandard errorstime seriestime series analysis
incomplete beta function S14CCF   24  nagf_specfun_beta_incomplete
Incomplete beta function I x a , b and its complement 1 - I x
Related keywords: approximations of special functionscomplement of incomplete beta function
incomplete Cholesky factorization F11JAF   17  nagf_sparse_real_symm_precon_ichol
Real sparse symmetric matrix, incomplete Cholesky factorization
Related keywords: big datadata analyticslarge scale linear systemslinear equations, pre-conditionersreal, sparse, symmetric matrix
F11JBF   17  nagf_sparse_real_symm_precon_ichol_solve
Solution of linear system involving incomplete Cholesky preconditioning matrix generated by F11JAF
Related keywords: big datadata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse, symmetric matrix
F11JCF   17  nagf_sparse_real_symm_solve_ichol
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JAF (Black Box)
Related keywords: big dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse, symmetric matrix
F11JNF   19  nagf_sparse_complex_herm_precon_ilu
Complex sparse Hermitian matrix, incomplete Cholesky factorization
Related keywords: big datacomplex, Hermitian, sparse matrixdata analyticslarge scale linear systems
F11JPF   19  nagf_sparse_complex_herm_precon_ilu_solve
Solution of complex linear system involving incomplete Cholesky preconditioning matrix generated by F11JNF
Related keywords: big datacomplex, Hermitian, sparse matrixdata analyticslarge scale linear systemslinear equations, pre-conditioners
incomplete gamma function S14BAF   14  nagf_specfun_gamma_incomplete
Incomplete gamma functions P a , x and Q a , x
Related keywords: approximations of special functionsfinance
incomplete L U factorization F11DAF   18  nagf_sparse_real_gen_precon_ilu
Real sparse nonsymmetric linear systems, incomplete L U factorization
Related keywords: big datadata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, pre-conditionersreal, sparse matrix
F11DBF   18  nagf_sparse_real_gen_precon_ilu_solve
Solution of linear system involving incomplete L U preconditioning matrix generated by F11DAF
Related keywords: big datadata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrix
F11DCF   18  nagf_sparse_real_gen_solve_ilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DAF
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DFF   24  nagf_sparse_real_gen_precon_bdilu
Real sparse nonsymmetric linear system, incomplete L U factorization of local or overlapping diagonal blocks
Related keywords: additive Schwarz preconditionerbig datadata analyticslarge scale linear systemslinear equations, pre-conditionersreal, sparse matrix
F11DGF   24  nagf_sparse_real_gen_solve_bdilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DFF
Related keywords: additive Schwarz preconditionerBi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DNF   19  nagf_sparse_complex_gen_precon_ilu
Complex sparse non-Hermitian linear systems, incomplete L U factorization
Related keywords: big datacomplex, sparse matrixdata analyticslarge scale linear systemslinear equations, pre-conditioners
F11DPF   19  nagf_sparse_complex_gen_precon_ilu_solve
Solution of complex linear system involving incomplete L U preconditioning matrix generated by F11DNF
Related keywords: big datacomplex, sparse matrixdata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative method
F11DQF   19  nagf_sparse_complex_gen_solve_ilu
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DNF (Black Box)
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DTF   24  nagf_sparse_complex_gen_precon_bdilu
Complex, sparse, non-Hermitian linear system, incomplete L U factorization of local or overlapping diagonal blocks
Related keywords: additive Schwarz preconditionerbig datacomplex, sparse matrixdata analyticslarge scale linear systemslinear equations, pre-conditioners
F11DUF   24  nagf_sparse_complex_gen_solve_bdilu
Solution of complex, sparse, non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DTF
Related keywords: additive Schwarz preconditionerBi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
infinity X07BAF   24  nagf_ieee_create_infinity
Creates a signed infinite value
Related keywords: IEEE arithmetic
infinity-norm F06RAF   15  nagf_blas_dlange
1 -norm, -norm, Frobenius norm, largest absolute element, real general matrix
Related keywords: 1-normBLASFrobenius normlinear algebra support routinesnorm, matrixreal, m by n matrix
F06RBF   15  nagf_blas_dlangb
1 -norm, -norm, Frobenius norm, largest absolute element, real band matrix
Related keywords: 1-normBLASFrobenius normlinear algebra support routinesmatrix, bandnorm, matrixreal, band, m by n matrix
F06RCF   15  nagf_blas_dlansy
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix
Related keywords: 1-normBLASFrobenius normlinear algebra support routinesnorm, matrixreal, indefinite, symmetric matrix
F06RDF   15  nagf_blas_dlansp
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage
Related keywords: 1-normBLASFrobenius normlinear algebra support routinesnorm, matrixreal, indefinite, symmetric matrix
F06REF   15  nagf_blas_dlansb
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric band matrix
Related keywords: 1-normBLASFrobenius normlinear algebra support routinesmatrix, bandnorm, matrixreal, band, symmetric matrix
F06RJF   15  nagf_blas_dlantr
1 -norm, -norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix
Related keywords: 1-normBLASFrobenius normlinear algebra support routinesnorm, matrixreal, trapezoidal matrixreal, triangular matrix
F06RKF   15  nagf_blas_dlantp
1 -norm, -norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage
Related keywords: 1-normBLASFrobenius normlinear algebra support routinesnorm, matrixreal, triangular matrix
F06RLF   15  nagf_blas_dlantb
1 -norm, -norm, Frobenius norm, largest absolute element, real triangular band matrix
Related keywords: 1-normBLASFrobenius normlinear algebra support routinesnorm, matrixreal, band, triangular matrix
F06RMF   15  nagf_blas_dlanhs
1 -norm, -norm, Frobenius norm, largest absolute element, real upper Hessenberg matrix
Related keywords: 1-normBLASFrobenius normlinear algebra support routinesnorm, matrixreal, Hessenberg matrix
F06RNF   21  nagf_blas_dlangt
1 -norm, -norm, Frobenius norm, largest absolute element, real tridiagonal matrix
Related keywords: 1-normBLASFrobenius normlinear algebra support routinesmatrix, bandnorm, matrixreal, tridiagonal matrix
F06RPF   21  nagf_blas_dlanst
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix
Related keywords: 1-normBLASFrobenius normlinear algebra support routinesmatrix, bandnorm, matrixreal, symmetric, tridiagonal matrix
F06UAF   15  nagf_blas_zlange
1 -norm, -norm, Frobenius norm, largest absolute element, complex general matrix
Related keywords: 1-normBLAScomplex, m by n matrixFrobenius normlinear algebra support routines
F06UBF   15  nagf_blas_zlangb
1 -norm, -norm, Frobenius norm, largest absolute element, complex band matrix
Related keywords: 1-normBLAScomplex, band matrixFrobenius normlinear algebra support routinesmatrix, band
F06UCF   15  nagf_blas_zlanhe
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix
Related keywords: 1-normBLAScomplex, band matrixFrobenius normlinear algebra support routines
F06UDF   15  nagf_blas_zlanhp
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage
Related keywords: 1-normBLAScomplex, Hermitian matrixFrobenius normlinear algebra support routines
F06UEF   15  nagf_blas_zlanhb
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian band matrix
Related keywords: 1-normBLAScomplex, band, Hermitian matrixFrobenius normlinear algebra support routinesmatrix, band
F06UFF   15  nagf_blas_zlansy
1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix
Related keywords: 1-normBLAScomplex, symmetric matrixFrobenius normlinear algebra support routines
F06UGF   15  nagf_blas_zlansp
1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage
Related keywords: 1-normBLAScomplex, symmetric matrixFrobenius normlinear algebra support routines
F06UHF   15  nagf_blas_zlansb
1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric band matrix
Related keywords: 1-normBLAScomplex, band, symmetric matrixFrobenius normlinear algebra support routinesmatrix, band
F06UJF   15  nagf_blas_zlantr
1 -norm, -norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix
Related keywords: 1-normBLAScomplex, trapezoidal matrixcomplex, triangular matrixFrobenius normlinear algebra support routines
F06UKF   15  nagf_blas_zlantp
1 -norm, -norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage
Related keywords: 1-normBLAScomplex, triangular matrixFrobenius normlinear algebra support routines
F06ULF   15  nagf_blas_zlantb
1 -norm, -norm, Frobenius norm, largest absolute element, complex triangular band matrix
Related keywords: 1-normBLAScomplex, band, triangular matrixFrobenius normlinear algebra support routinesmatrix, band
F06UMF   15  nagf_blas_zlanhs
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hessenberg matrix
Related keywords: 1-normBLAScomplex, Hessenberg matrixFrobenius normlinear algebra support routines
F06UNF   21  nagf_blas_zlangt
1 -norm, -norm, Frobenius norm, largest absolute element, complex tridiagonal matrix
Related keywords: 1-normBLAScomplex, triangular matrixFrobenius normlinear algebra support routinesmatrix, band
F06UPF   21  nagf_blas_zlanht
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian tridiagonal matrix
Related keywords: 1-normBLAScomplex, Hermitian, tridiagonal matrixFrobenius normlinear algebra support routinesmatrix, band
F06WAF   23  nagf_blas_dlansf
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format
Related keywords: 1-normBLASBLASblas, real matricesdlansfFrobenius normlinear algebra support routineslinear algebra support routines;real, symmetric matrix
F06WNF   23  nagf_blas_zlanhf
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format
Related keywords: 1-normBLASBLASblas, complex matricescomplex, Hermitian matrixFrobenius normlinear algebra support routineslinear algebra support routines;zlanhf
F11MLF   21  nagf_sparse_direct_real_gen_norm
1 -norm, -norm, largest absolute element, real, square, sparse matrix
Related keywords: 1-normabsolute valuebig datadata analyticslarge scale linear systemsnorm, matrixreal, sparse matrix
F16RBF   23  nagf_blast_dgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, real band matrix
Related keywords: 1-normabsolute valueabsolute valuebanded matrixFrobenius normfurther linear algebra support routinesmatrix, bandnorm, matrixreal, band, m by n matrix
F16UBF   23  nagf_blast_zgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, complex band matrix
Related keywords: 1-normabsolute valuebanded matrixcomplex, band matrixFrobenius normfurther linear algebra support routinesmatrix, bandnorm, matrix
influence statistics G02FAF   14  nagf_correg_linregm_stat_resinf
Calculates standardized residuals and influence statistics
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysisstandardized residuals
initialization E04RAF   26  nagf_opt_handle_init
Initialization of a handle for the NAG optimization modelling suite for problems, such as, linear programming (LP), quadratic programming (QP), nonlinear programming (NLP), least squares (LSQ) problems, linear semidefinite programming (SDP) or SDP with bilinear matrix inequalities (BMI-SDP)
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationSDPsemidefinite programming
initial value problem D02BGF   nagf_ode_ivp_rkm_val_simple
Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until a component attains given value (simple driver)
Related keywords: IVP, initial value problemODE, ordinary differential equationsRunge–Kutta–Merson, ODE
D02BHF   nagf_ode_ivp_rkm_zero_simple
Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until function of solution is zero (simple driver)
Related keywords: IVP, initial value problemODE, ordinary differential equationsRunge–Kutta–Merson, ODE
D02BJF   18  nagf_ode_ivp_rk_zero_simple
Ordinary differential equations, initial value problem, Runge–Kutta method, until function of solution is zero, integration over range with intermediate output (simple driver)
Related keywords: IVP, initial value problemODE, ordinary differential equationsRK45Runge–Kutta–Merson, ODE
D02CJF   13  nagf_ode_ivp_adams_zero_simple
Ordinary differential equations, initial value problem, Adams' method, until function of solution is zero, intermediate output (simple driver)
Related keywords: Adams' methodfirst-order systemIVP, initial value problemNonstiffODE, ordinary differential equationsstop at roots
D02EJF   12  nagf_ode_ivp_bdf_zero_simple
Ordinary differential equations, stiff initial value problem, backward differentiation formulae method, until function of solution is zero, intermediate output (simple driver)
Related keywords: backward difference formulaBDF, backward differentiation formulaIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02LAF   13  nagf_ode_ivp_2nd_rkn
Second-order ordinary differential equations, initial value problem, Runge–Kutta–Nystrom method
Related keywords: IVP, initial value problemODE, ordinary differential equationsRunge–Kutta–Nystrom, ODE
D02LXF   13  nagf_ode_ivp_2nd_rkn_setup
Second-order ordinary differential equations, initial value problem, setup for D02LAF
Related keywords: IVP, initial value problemODE, ordinary differential equationsRunge–Kutta–Nystrom, ODE
D02LYF   13  nagf_ode_ivp_2nd_rkn_diag
Second-order ordinary differential equations, initial value problem, diagnostics for D02LAF
Related keywords: IVP, initial value problemODE, ordinary differential equationsRunge–Kutta–Nystrom, ODE
D02LZF   13  nagf_ode_ivp_2nd_rkn_interp
Second-order ordinary differential equations, initial value problem, interpolation for D02LAF
Related keywords: IVP, initial value problemODE, ordinary differential equationsRunge–Kutta–Nystrom, ODE
D02MCF   22  nagf_ode_dae_dassl_cont
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method continuation for D02NEF
Related keywords: DAE, differential algebraic equationsDASSL, ordinary differential equationsimplicit algebraic ordinary differential equationsIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02MVF   14  nagf_ode_ivp_stiff_dassl
Ordinary differential equations, initial value problem, DASSL method, setup for d02m–n routines
Related keywords: DASSL, ordinary differential equationsimplicit algebraic ordinary differential equationsIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02MWF   22  nagf_ode_dae_dassl_setup
Implicit ordinary differential equations/DAEs, initial value problem, setup for D02NEF
Related keywords: DASSL, ordinary differential equationsIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02MZF   14  nagf_ode_ivp_stiff_interp
Ordinary differential equations, initial value problem, interpolation for d02m–n routines (all integration methods), natural interpolant
Related keywords: interpolationIVP, initial value problemODE, ordinary differential equations
D02NBF   12  nagf_ode_ivp_stiff_exp_fulljac
Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
Related keywords: backward difference formulaIVP, initial value problemJacobianODE, ordinary differential equationsstiff differential equations
D02NCF   12  nagf_ode_ivp_stiff_exp_bandjac
Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulaJacobianODE, ordinary differential equationsstiff differential equations
D02NDF   12  nagf_ode_ivp_stiff_exp_sparjac
Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulaIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NEF   22  nagf_ode_dae_dassl_gen
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator
Related keywords: DAE, differential algebraic equationsDASSL, ordinary differential equationsimplicit algebraic ordinary differential equationsIVP, initial value problemODE, ordinary differential equations
D02NGF   12  nagf_ode_ivp_stiff_imp_fulljac
Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulaimplicit algebraic ordinary differential equationsIVP, initial value problemJacobianODE, ordinary differential equationsstiff differential equations
D02NHF   12  nagf_ode_ivp_stiff_imp_bandjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulaimplicit algebraic ordinary differential equationsIVP, initial value problemJacobianODE, ordinary differential equationsstiff differential equations
D02NJF   12  nagf_ode_ivp_stiff_imp_sparjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formuladiscretised systemimplicit algebraic ordinary differential equationsIVP, initial value problemJacobianODEODE, ordinary differential equationsstiff differential equations
D02NMF   12  nagf_ode_ivp_stiff_exp_revcom
Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulaIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NNF   12  nagf_ode_ivp_stiff_imp_revcom
Implicit/algebraic ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
Related keywords: backward difference formulaimplicit algebraic ordinary differential equationsIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NPF   22  nagf_ode_dae_dassl_linalg
Implicit ordinary differential equations/DAEs, initial value problem linear algebra setup routine for D02NEF
Related keywords: implicit algebraic ordinary differential equationsIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NRF   12  nagf_ode_ivp_stiff_sparjac_enq
Ordinary differential equations, initial value problem, for use with d02m–n routines, sparse Jacobian, enquiry routine
Related keywords: ODE, ordinary differential equationsstiff differential equations
D02NSF   12  nagf_ode_ivp_stiff_fulljac_setup
Ordinary differential equations, initial value problem, for use with d02m–n routines, full Jacobian, linear algebra set up
Related keywords: ODE, ordinary differential equationsstiff differential equations
D02NTF   12  nagf_ode_ivp_stiff_bandjac_setup
Ordinary differential equations, initial value problem, for use with d02m–n routines, banded Jacobian, linear algebra set up
Related keywords: ODE, ordinary differential equationsstiff differential equations
D02NUF   12  nagf_ode_ivp_stiff_sparjac_setup
Ordinary differential equations, initial value problem, for use with d02m–n routines, sparse Jacobian, linear algebra set up
Related keywords: ODE, ordinary differential equationsstiff differential equations
D02NVF   12  nagf_ode_ivp_stiff_bdf
Ordinary differential equations, initial value problem, backward differentiation formulae method, setup for d02m–n routines
Related keywords: backward difference formulaODE, ordinary differential equationsstiff differential equations
D02NWF   12  nagf_ode_ivp_stiff_blend
Ordinary differential equations, initial value problem, Blend method, setup for d02m–n routines
Related keywords: Blend methodODE, ordinary differential equationsstiff differential equations
D02NXF   12  nagf_ode_ivp_stiff_sparjac_diag
Ordinary differential equations, initial value problem, sparse Jacobian, linear algebra diagnostics, for use with d02m–n routines
Related keywords: ODE, ordinary differential equationsstiff differential equations
D02NYF   12  nagf_ode_ivp_stiff_integ_diag
Ordinary differential equations, initial value problem, integrator diagnostics, for use with d02m–n routines
Related keywords: ODE, ordinary differential equationsstiff differential equations
D02NZF   12  nagf_ode_ivp_stiff_contin
Ordinary differential equations, initial value problem, setup for continuation calls to integrator, for use with d02m–n routines
Related keywords: ODE, ordinary differential equationsstiff differential equations
D02XJF   12  nagf_ode_ivp_stiff_nat_interp
Ordinary differential equations, initial value problem, interpolation for d02m–n routines (BLEND and BDF methods only), natural interpolant
Related keywords: backward difference formulaBlend methodinterpolationODE, ordinary differential equations
D02XKF   12  nagf_ode_ivp_stiff_c1_interp
Ordinary differential equations, initial value problem, interpolation for d02m–n routines, C 1 interpolant
Related keywords: interpolationODE, ordinary differential equations
D02ZAF   12  nagf_ode_ivp_stiff_errest
Ordinary differential equations, initial value problem, weighted norm of local error estimate for d02m–n routines
Related keywords: ODE, ordinary differential equations
inner product F06EAF   12  nagf_blas_ddot
Dot product of two real vectors
Related keywords: BLASblas, real matricesddotfinancelinear algebra support routines
F06ERF   14  nagf_blas_ddoti
Dot product of a real sparse and a full vector
Related keywords: BLASblas, real matricesddotilinear algebra support routines
F06GAF   12  nagf_blas_zdotu
Dot product of two complex vectors, unconjugated
Related keywords: BLASblas, complex matriceslinear algebra support routineszdotu
F06GBF   12  nagf_blas_zdotc
Dot product of two complex vectors, conjugated
Related keywords: BLASblas, complex matriceslinear algebra support routineszdotc
F06GRF   14  nagf_blas_zdotui
Dot product of a complex sparse and a full vector, unconjugated
Related keywords: BLASblas, complex matriceslinear algebra support routineszdotui
F06GSF   14  nagf_blas_zdotci
Dot product of a complex sparse and a full vector, conjugated
Related keywords: BLASblas, complex matriceslinear algebra support routineszdotci
F06GTF   14  nagf_blas_zaxpyi
Add scalar times complex sparse vector to a full vector
Related keywords: BLASblas, complex matriceslinear algebra support routineszaxpyi
F16EAF   25  nagf_blast_ddot
Dot product of two vectors, allows scaling and accumulation
Related keywords: dot productfurther linear algebra support routines
X03AAF   nagf_dot_real_prec
Real inner product added to initial value, basic/additional precision
Related keywords: additional precision accumulationdot productextended precision accumulationinner productsscalar product
X03ABF   nagf_dot_complex_prec
Complex inner product added to initial value, basic/additional precision
Related keywords: additional precision accumulationdot productextended precision accumulationinner productsscalar product
inner products X03 Chapter Introduction     Inner Products
input utilities X04 Chapter Introduction     Input/Output Utilities
Related keywords: output utilities
insert C09EZF   25  nagf_wav_2d_coeff_ins
Two-dimensional discrete wavelet transform coefficient insertion
Related keywords: coefficientstwo-dimensionalwaveletwavelet transforms
C09FZF   25  nagf_wav_3d_coeff_ins
Three-dimensional discrete wavelet transform coefficient insertion
Related keywords: coefficientsthree-dimensionalwaveletwavelet transforms
X10BBF   26 
Insert the location of the AD callback into the callback data object
Related keywords: AD callbackadjoint derivativesAD utility operationsautomatic differentiationcallback data objectlocation
integer programming H02BBF   14  nagf_mip_ilp_dense
Integer LP problem (dense)
Related keywords: branch and boundfinancemixed integer programmingoperations research
H02BFF   16  nagf_mip_ilp_mpsx
Interpret MPSX data file defining IP or LP problem, optimize and print solution
Related keywords: branch and boundmixed integer programmingMPSX formatoperations research
H02BVF   16  nagf_mip_ilp_print
Print IP or LP solutions with user-specified names for rows and columns
Related keywords: linear programmingoperations research
H02BZF   15  nagf_mip_ilp_info
Integer programming solution, supplies further information on solution obtained by H02BBF
Related keywords: operations research
H02CBF   19  nagf_mip_iqp_dense
Integer QP problem (dense)
Related keywords: branch and boundfinanceinteger quadratic programmixed integer programmingoperations researchQP, quadratic programming
H02CEF   19  nagf_mip_iqp_sparse
Integer LP or QP problem (sparse), using E04NKF
Related keywords: branch and boundfinanceinteger quadratic programmixed integer programmingoperations researchQP, quadratic programming
H02CFF   19  nagf_mip_iqp_sparse_optfile
Read values for H02CEF from external file
Related keywords: mixed integer programmingoperations researchoptions, computational
H02CGF   19  nagf_mip_iqp_sparse_optstr
Supply values to H02CEF
Related keywords: operations researchoptions, computational
H02DAF   25  nagf_mip_sqp
Mixed integer nonlinear programming
Related keywords: integer quadratic programmixed integer programmingnonlinear programmingoperations researchSQP, sequential quadratic programming
integer quadratic program H02CBF   19  nagf_mip_iqp_dense
Integer QP problem (dense)
Related keywords: branch and boundfinanceinteger programmingmixed integer programmingoperations researchQP, quadratic programming
H02CCF   19  nagf_mip_iqp_dense_optfile
Read values for H02CBF from external file
Related keywords: operations researchoptions, computational
H02CDF   19  nagf_mip_iqp_dense_optstr
Supply values to H02CBF
Related keywords: operations researchoptions, computational
H02CEF   19  nagf_mip_iqp_sparse
Integer LP or QP problem (sparse), using E04NKF
Related keywords: branch and boundfinanceinteger programmingmixed integer programmingoperations researchQP, quadratic programming
H02DAF   25  nagf_mip_sqp
Mixed integer nonlinear programming
Related keywords: integer programmingmixed integer programmingnonlinear programmingoperations researchSQP, sequential quadratic programming
integer scalar X10BEF   26 
Write an integer (working precision) scalar to the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationcallback data ojbectworking precisionwrite
X10CEF   26 
Read an integer scalar from the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationcallback data objectread
integral equations D05 Chapter Introduction     Integral Equations
integration D01TDF   26  nagf_quad_1d_gauss_wrec
Calculation of weights and abscissae for Gaussian quadrature rules, method of Golub and Welsch
Related keywords: abscissaecubatureGaussianGolubGolub and Welschnon-adaptivequadratureweights and abscissaeWelsch
D01TEF   26  nagf_quad_1d_gauss_recm
Generates recursion coefficients needed by D01TDF to calculate a Gaussian quadrature rule
Related keywords: abscissaecubatureGaussianGolubGolub and Welschnon-adaptivequadraturerecursion coefficientsWelsch
integration, adaptive D01AHF   nagf_quad_1d_fin_well
One-dimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands
Related keywords: financequadraturequadrature, adaptive
D01AJF   nagf_quad_1d_fin_bad
One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands
Related keywords: financeGauss–Kronrod quadratureQAGSQUADPACKquadraturequadrature, adaptive
D01AKF   nagf_quad_1d_fin_osc
One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions
Related keywords: financeGauss–Kronrod quadratureQAGQUADPACKquadraturequadrature, adaptive
D01ALF   nagf_quad_1d_fin_sing
One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points
Related keywords: financeGauss–Kronrod quadratureQAGPQUADPACKquadraturequadrature, adaptive
D01AMF   nagf_quad_1d_inf
One-dimensional quadrature, adaptive, infinite or semi-infinite interval
Related keywords: financeGauss–Kronrod quadratureintegration, infinite intervalQAGIQUADPACKquadraturequadrature, adaptive
D01ANF   nagf_quad_1d_fin_wtrig
One-dimensional quadrature, adaptive, finite interval, weight function cos ω x or sin ω x
Related keywords: financeGauss–Kronrod quadratureQFOURQUADPACKquadraturequadrature, adaptive
D01APF   nagf_quad_1d_fin_wsing
One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type
Related keywords: financeGauss–Kronrod quadratureQAWSEQUADPACKquadraturequadrature, adaptive
D01AQF   nagf_quad_1d_fin_wcauchy
One-dimensional quadrature, adaptive, finite interval, weight function 1 / x - c , Cauchy principal value (Hilbert transform)
Related keywords: Cauchy principal valuefinanceGauss–Kronrod quadratureHilbert transformQAWCQUADPACKquadraturequadrature, adaptive
D01ASF   13  nagf_quad_1d_inf_wtrig
One-dimensional quadrature, adaptive, semi-infinite interval, weight function cos ω x or sin ω x
Related keywords: financeGauss–Kronrod quadratureintegration, infinite intervalQAWFEQUADPACKquadraturequadrature, adaptivevectorized quadrature
D01ATF   13  nagf_quad_1d_fin_bad_vec
One-dimensional quadrature, adaptive, finite interval, variant of D01AJF efficient on vector machines
Related keywords: Gauss–Kronrod quadratureQAGQAGSQUADPACKquadraturequadrature, adaptivevectorized quadrature
D01AUF   13  nagf_quad_1d_fin_osc_vec
One-dimensional quadrature, adaptive, finite interval, variant of D01AKF efficient on vector machines
Related keywords: financequadraturequadrature, adaptive
D01EAF   12  nagf_quad_md_adapt_multi
Multidimensional adaptive quadrature over hyper-rectangle, multiple integrands
Related keywords: integration, multidimensionalquadraturequadrature, adaptivevectorized quadrature
D01FCF   nagf_quad_md_adapt
Multidimensional adaptive quadrature over hyper-rectangle
Related keywords: financeintegration, multidimensionalquadraturequadrature, adaptive
D01RAF   24  nagf_quad_1d_gen_vec_multi_rcomm
One-dimensional quadrature, adaptive, finite interval, multiple integrands, vectorized abscissae, reverse communication
Related keywords: quadraturequadrature, adaptive
D01RCF   24  nagf_quad_1d_gen_vec_multi_dimreq
Determine required array dimensions for D01RAF
Related keywords: quadraturequadrature, adaptive
D01RGF   24  nagf_quad_1d_fin_gonnet_vec
One-dimensional quadrature, adaptive, finite interval, strategy due to Gonnet, allowing for badly behaved integrands
Related keywords: financeGonnet method, quadraturequadraturequadrature, adaptive
integration, infinite interval D01AMF   nagf_quad_1d_inf
One-dimensional quadrature, adaptive, infinite or semi-infinite interval
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQAGIQUADPACKquadraturequadrature, adaptive
D01ASF   13  nagf_quad_1d_inf_wtrig
One-dimensional quadrature, adaptive, semi-infinite interval, weight function cos ω x or sin ω x
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQAWFEQUADPACKquadraturequadrature, adaptivevectorized quadrature
integration, multidimensional D01DAF   nagf_quad_2d_fin
Two-dimensional quadrature, finite region
Related keywords: financequadraturequadrature, adaptive
D01EAF   12  nagf_quad_md_adapt_multi
Multidimensional adaptive quadrature over hyper-rectangle, multiple integrands
Related keywords: integration, adaptivequadraturequadrature, adaptivevectorized quadrature
D01FBF   nagf_quad_md_gauss
Multidimensional Gaussian quadrature over hyper-rectangle
Related keywords: financeintegration, non-adaptivequadraturequadrature non-adaptive
D01FCF   nagf_quad_md_adapt
Multidimensional adaptive quadrature over hyper-rectangle
Related keywords: financeintegration, adaptivequadraturequadrature, adaptive
D01FDF   10  nagf_quad_md_sphere
Multidimensional quadrature, Sag–Szekeres method, general product region or n -sphere
Related keywords: quadratureSag–Szekeres method
D01GBF   10  nagf_quad_md_mcarlo
Multidimensional quadrature over hyper-rectangle, Monte–Carlo method
Related keywords: Monte–Carlo methodquadraturequadrature non-adaptive
D01GCF   10  nagf_quad_md_numth
Multidimensional quadrature, general product region, number-theoretic method
Related keywords: Korobov–Conroy method, numerical integrationnumerical integrationquadraturequadrature non-adaptive
D01GDF   14  nagf_quad_md_numth_vec
Multidimensional quadrature, general product region, number-theoretic method, variant of D01GCF efficient on vector machines
Related keywords: financequadraturequadrature non-adaptive
D01JAF   10  nagf_quad_md_sphere_bad
Multidimensional quadrature over an n -sphere, allowing for badly behaved integrands
Related keywords: financequadraturequadrature non-adaptive
D01PAF   10  nagf_quad_md_simplex
Multidimensional quadrature over an n -simplex
Related keywords: financequadraturequadrature non-adaptive
integration, non-adaptive D01BCF   nagf_quad_1d_gauss_wgen
Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule
Related keywords: abscissaecubaturefinancequadratureweights and abscissae
D01BDF   nagf_quad_1d_fin_smooth
One-dimensional quadrature, non-adaptive, finite interval
Related keywords: financequadraturequadrature non-adaptive
D01FBF   nagf_quad_md_gauss
Multidimensional Gaussian quadrature over hyper-rectangle
Related keywords: financeintegration, multidimensionalquadraturequadrature non-adaptive
D01GAF   nagf_quad_1d_data
One-dimensional quadrature, integration of function defined by data values, Gill–Miller method
Related keywords: financeGill–Miller quadraturequadraturequadrature non-adaptive
D01UAF   24  nagf_quad_1d_gauss_vec
One-dimensional Gaussian quadrature, choice of weight functions (vectorized)
Related keywords: quadraturequadrature non-adaptive
D01UBF   26  nagf_quad_1d_inf_exp_wt
Non-automatic routine to evaluate 0 exp - x 2 f x   d x
Related keywords: integration, semi-infinite intervalquadraturequadrature non-adaptive
integration, options D01ZKF   24  nagf_quad_opt_set
Option setting routine
Related keywords: options, computationalquadraturequadrature, options
D01ZLF   24  nagf_quad_opt_get
Option getting routine
Related keywords: options, computationalquadraturequadrature, options
integration, semi-infinite interval D01UBF   26  nagf_quad_1d_inf_exp_wt
Non-automatic routine to evaluate 0 exp - x 2 f x   d x
Related keywords: integration, non-adaptivequadraturequadrature non-adaptive
interior point method E04MTF   26  nagf_opt_handle_solve_lp_ipm
Linear programming (LP), sparse, interior point method (IPM)
Related keywords: ipmlinear programmingLPmaximizing a functionminimizing a functionoptimization
E04STF   26  nagf_opt_handle_solve_ipopt
Run an interior point solver on a sparse nonlinear programming problem (NLP) initialized by E04RAF and defined by other routines from the suite
Related keywords: IPMleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinear programmingoptimizationoptimization
interpolation D02MZF   14  nagf_ode_ivp_stiff_interp
Ordinary differential equations, initial value problem, interpolation for d02m–n routines (all integration methods), natural interpolant
Related keywords: initial value problemIVP, initial value problemODE, ordinary differential equations
D02PHF   26  nagf_ode_ivp_rk_interp_setup
Set up interpolant by reverse communication for solution and derivative evaluations at points within the range of the last integration step taken by D02PGF
Related keywords: first-order systemIVP, initial value problemNonstiffODE, ordinary differential equationsRunge–Kutta–Merson
D02PJF   26  nagf_ode_ivp_rk_interp_eval
Evaluate interpolant, set up using D02PQF, to approximate solution and/or solution derivatives at a point within the range of the last integration step taken by D02PGF
Related keywords: IVP, initial value problemODE, ordinary differential equationsRunge–Kutta–Merson
D02PSF   24  nagf_ode_ivp_rkts_interp
Ordinary differential equations, initial value problem, interpolation for D02PFF
Related keywords: IVP, initial value problemODE, ordinary differential equationsRunge–Kutta–Merson
D02QZF   13  nagf_ode_ivp_adams_interp
Ordinary differential equations, initial value problem, interpolation for D02QFF or D02QGF
Related keywords: Adams' methodIVP, initial value problemODE, ordinary differential equations
D02TYF   17  nagf_ode_bvp_coll_nlin_interp
Ordinary differential equations, general nonlinear boundary value problem, interpolation for D02TLF
Related keywords: BVP, boundary value problemcollocation methodODE, ordinary differential equations
D02TZF   17  nagf_ode_bvp_coll_nlin_diag
Ordinary differential equations, general nonlinear boundary value problem, diagnostics for D02TLF
Related keywords: BVP, boundary value problemcollocation methodODE, ordinary differential equations
D02UAF   23  nagf_ode_bvp_ps_lin_coeffs
Coefficients of Chebyshev interpolating polynomial from function values on Chebyshev grid
Related keywords: Chebyshev polynomial interpolationGauss–Lobatto gridODE, ordinary differential equations
D02UBF   23  nagf_ode_bvp_ps_lin_cgl_vals
Function or low-order-derivative values on Chebyshev grid from coefficients of Chebyshev interpolating polynomial
Related keywords: Chebyshev polynomial interpolationChebyshev series, solutionGauss–Lobatto gridODE, ordinary differential equations
D02UWF   23  nagf_ode_bvp_ps_lin_grid_vals
Interpolate a function from Chebyshev grid to uniform grid using barycentric Lagrange interpolation
Related keywords: barycentric Lagrange interpolationGauss–Lobatto gridODE, ordinary differential equations
D02XJF   12  nagf_ode_ivp_stiff_nat_interp
Ordinary differential equations, initial value problem, interpolation for d02m–n routines (BLEND and BDF methods only), natural interpolant
Related keywords: backward difference formulaBlend methodinitial value problemODE, ordinary differential equations
D02XKF   12  nagf_ode_ivp_stiff_c1_interp
Ordinary differential equations, initial value problem, interpolation for d02m–n routines, C 1 interpolant
Related keywords: initial value problemODE, ordinary differential equations
D03PYF   15  nagf_pde_1d_parab_coll_interp
PDEs, spatial interpolation with D03PDF or D03PJF
Related keywords: parabolic partial differential equationPDE, partial differential equations
D03PZF   15  nagf_pde_1d_parab_fd_interp
PDEs, spatial interpolation with D03PCF, D03PEF, D03PFF, D03PHF, D03PKF, D03PLF, D03PPF, D03PRF or D03PSF
Related keywords: parabolic partial differential equationPDE, partial differential equations
E01 Chapter Introduction     Interpolation
Interpolation E01EBF   25  nagf_interp_2d_triang_bary_eval
Barycentric interpolation on function values provided on a two-dimensional scattered grid
Related keywords: Barycentric interpolationBilinear interpolationfinanceinterpolationRenka and Cline methodScattered dataScattered data interpolationTriangulation
interrater G04GAF   26  nagf_anova_icc
Intraclass correlation (ICC) for assessing rater reliability
Related keywords: analysis of varianceICCintraclassintraraterreliability
intraclass G04GAF   26  nagf_anova_icc
Intraclass correlation (ICC) for assessing rater reliability
Related keywords: analysis of varianceICCinterraterintraraterreliability
intrarater G04GAF   26  nagf_anova_icc
Intraclass correlation (ICC) for assessing rater reliability
Related keywords: analysis of varianceICCinterraterintraclassreliability
inverse C09DBF   25  nagf_wav_1d_mxolap_inv
One-dimensional inverse maximal overlap discrete wavelet transform (IMODWT)
Related keywords: discretemaximal-overlapstationarywavelet transforms
C09DDF   25  nagf_wav_1d_mxolap_multi_inv
One-dimensional inverse multi-level maximal overlap discrete wavelet transform (IMODWT)
Related keywords: discretemaximal-overlapmulti-levelstationarywavelet transforms
inverse, matrix F01ABF   nagf_matop_real_symm_posdef_inv
Inverse of real symmetric positive definite matrix using iterative refinement
Related keywords: inversionmatrix inversematrix operationsreal, positive-definite, symmetric matrix
F01ADF   nagf_matop_real_symm_posdef_inv_noref
Inverse of real symmetric positive definite matrix
Related keywords: inversionmatrix inversematrix operationsreal, positive-definite, symmetric matrix
F07AJF   15  nagf_lapacklin_dgetri
Inverse of real matrix, matrix already factorized by F07ADF
Related keywords: DGETRIfinanceLAPACKlinear equations L U decompositionreal, nonsymmetric matrix
F07AWF   15  nagf_lapacklin_zgetri
Inverse of complex matrix, matrix already factorized by F07ARF
Related keywords: complex, nonsymmetric matrixLAPACKlinear equationsZGETRI
F07FJF   15  nagf_lapacklin_dpotri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07FDF
Related keywords: Cholesky decompositionDPOTRIfinanceLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FWF   15  nagf_lapacklin_zpotri
Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07FRF
Related keywords: complex, Hermitian, positive-definite matrixLAPACKlinear equationsZPOTRI
F07GJF   15  nagf_lapacklin_dpptri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07GDF, packed storage
Related keywords: Cholesky decompositionDPPTRILAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GWF   15  nagf_lapacklin_zpptri
Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07GRF, packed storage
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixLAPACKlinear equationsZPPTRI
F07MJF   15  nagf_lapacklin_dsytri
Inverse of real symmetric indefinite matrix, matrix already factorized by F07MDF
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodDSYTRILAPACKlinear equationsreal, indefinite, symmetric matrix
F07MWF   15  nagf_lapacklin_zhetri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07MRF
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACKlinear equationsZHETRI
F07NWF   15  nagf_lapacklin_zsytri
Inverse of complex symmetric matrix, matrix already factorized by F07NRF
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methodLAPACKlinear equationsZSYTRI
F07PJF   15  nagf_lapacklin_dsptri
Inverse of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodDSPTRILAPACKlinear equationsreal, indefinite, symmetric matrix
F07PNF   21  nagf_lapacklin_zhpsv
Computes the solution to a complex Hermitian system of linear equations, packed storage
Related keywords: complex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACK LDL H decompositionlinear equations UDU H decompositionZHPSV
F07PPF   21  nagf_lapacklin_zhpsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, Hermitian, system of linear equations, error bounds and condition estimates. Packed storage
Related keywords: backward errorcomplex, Hermitian, indefinite matrixdiagonal pivoting methodforward errorLAPACK LDL H decompositionlinear equations UDU H decompositionZHPSVX
F07PWF   15  nagf_lapacklin_zhptri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07PRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACKlinear equationsZHPTRI
F07QWF   15  nagf_lapacklin_zsptri
Inverse of complex symmetric matrix, matrix already factorized by F07QRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methodLAPACKlinear equationsZSPTRI
F07TJF   15  nagf_lapacklin_dtrtri
Inverse of real triangular matrix
Related keywords: DTRTRIfinanceLAPACKlinear equationsreal, triangular matrix
F07TWF   15  nagf_lapacklin_ztrtri
Inverse of complex triangular matrix
Related keywords: complex, triangular matrixLAPACKlinear equationsZTRTRI
F07UJF   15  nagf_lapacklin_dtptri
Inverse of real triangular matrix, packed storage
Related keywords: DTPTRILAPACKlinear equationsreal, triangular matrix
F07UWF   15  nagf_lapacklin_ztptri
Inverse of complex triangular matrix, packed storage
Related keywords: complex, triangular matrixLAPACKlinear equationsZTPTRI
F07WJF   23  nagf_lapacklin_dpftri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07WDF, Rectangular Full Packed format
Related keywords: Cholesky decompositionDPETRILAPACKlinear equationsreal, positive-definite, symmetric matrix
F07WKF   23  nagf_lapacklin_dtftri
Inverse of real triangular matrix, Rectangular Full Packed format
Related keywords: DTFTRILAPACKlinear equationsreal, triangular matrix
F07WXF   23  nagf_lapacklin_ztftri
Inverse of complex triangular matrix, Rectangular Full Packed format
Related keywords: complex, triangular matrixLAPACKlinear equationsZTFTRI
inverse CDF G01FAF   15  nagf_stat_inv_cdf_normal
Computes deviates for the standard Normal distribution
Related keywords: deviatesfinanceinverse cumulative distribution functionNormal distributionSimple Calculations on Statistical Data
G01FBF   14  nagf_stat_inv_cdf_students_t
Computes deviates for Student's t -distribution
Related keywords: deviatesfinanceinverse cumulative distribution functionSimple Calculations on Statistical DataStudent's t -distribution
G01FCF   14  nagf_stat_inv_cdf_chisq
Computes deviates for the χ 2 distribution
Related keywords: chi-squared distributiondeviatesfinanceinverse cumulative distribution functionSimple Calculations on Statistical Data
G01FDF   14  nagf_stat_inv_cdf_f
Computes deviates for the F -distribution
Related keywords: deviates F -distributionfinanceinverse cumulative distribution functionSimple Calculations on Statistical Data
G01FEF   14  nagf_stat_inv_cdf_beta
Computes deviates for the beta distribution
Related keywords: beta distributiondeviatesfinanceinverse cumulative distribution functionSimple Calculations on Statistical Data
G01FFF   14  nagf_stat_inv_cdf_gamma
Computes deviates for the gamma distribution
Related keywords: deviatesfinancegamma distributioninverse cumulative distribution functionSimple Calculations on Statistical Data
G01FMF   15  nagf_stat_inv_cdf_studentized_range
Computes deviates for the Studentized range statistic
Related keywords: deviatesfinanceinverse cumulative distribution functionSimple Calculations on Statistical DataStudentized range statistic
G01TAF   24  nagf_stat_inv_cdf_normal_vector
Computes a vector of deviates for the standard Normal distribution
Related keywords: big datadata analyticsdeviatesGaussian distributioninverse cumulative distribution functionNormal distributionSimple Calculations on Statistical Data
G01TBF   24  nagf_stat_inv_cdf_students_t_vector
Computes a vector of deviates for Student's t -distribution
Related keywords: big datadata analyticsdeviatesinverse cumulative distribution functionSimple Calculations on Statistical DataStudent's t -distribution
G01TCF   24  nagf_stat_inv_cdf_chisq_vector
Computes a vector of deviates for χ 2 distribution
Related keywords: big datachi-squared distributiondata analyticsdeviatesinverse cumulative distribution functionSimple Calculations on Statistical Data
G01TDF   24  nagf_stat_inv_cdf_f_vector
Computes a vector of deviates for F -distribution
Related keywords: big datadata analyticsdeviates F -distributioninverse cumulative distribution functionSimple Calculations on Statistical Datavariance-ratio distribution
G01TEF   24  nagf_stat_inv_cdf_beta_vector
Computes a vector of deviates for the beta distribution
Related keywords: beta distributionbig datadata analyticsdeviatesinverse cumulative distribution functionSimple Calculations on Statistical Data
G01TFF   24  nagf_stat_inv_cdf_gamma_vector
Computes a vector of deviates for the gamma distribution
Related keywords: big datadata analyticsdeviatesgamma distributioninverse cumulative distribution functionSimple Calculations on Statistical Data
inverse circular cosine S09ABF   nagf_specfun_arccos
arccos x
Related keywords: approximations of special functionsarccosfinance
inverse circular sine S09AAF   nagf_specfun_arcsin
arcsin x
Related keywords: approximations of special functionsarcsinefinance
inverse cumulative distribution function G01FAF   15  nagf_stat_inv_cdf_normal
Computes deviates for the standard Normal distribution
Related keywords: deviatesfinanceinverse CDFNormal distributionSimple Calculations on Statistical Data
G01FBF   14  nagf_stat_inv_cdf_students_t
Computes deviates for Student's t -distribution
Related keywords: deviatesfinanceinverse CDFSimple Calculations on Statistical DataStudent's t -distribution
G01FCF   14  nagf_stat_inv_cdf_chisq
Computes deviates for the χ 2 distribution
Related keywords: chi-squared distributiondeviatesfinanceinverse CDFSimple Calculations on Statistical Data
G01FDF   14  nagf_stat_inv_cdf_f
Computes deviates for the F -distribution
Related keywords: deviates F -distributionfinanceinverse CDFSimple Calculations on Statistical Data
G01FEF   14  nagf_stat_inv_cdf_beta
Computes deviates for the beta distribution
Related keywords: beta distributiondeviatesfinanceinverse CDFSimple Calculations on Statistical Data
G01FFF   14  nagf_stat_inv_cdf_gamma
Computes deviates for the gamma distribution
Related keywords: deviatesfinancegamma distributioninverse CDFSimple Calculations on Statistical Data
G01FMF   15  nagf_stat_inv_cdf_studentized_range
Computes deviates for the Studentized range statistic
Related keywords: deviatesfinanceinverse CDFSimple Calculations on Statistical DataStudentized range statistic
G01TAF   24  nagf_stat_inv_cdf_normal_vector
Computes a vector of deviates for the standard Normal distribution
Related keywords: big datadata analyticsdeviatesGaussian distributioninverse CDFNormal distributionSimple Calculations on Statistical Data
G01TBF   24  nagf_stat_inv_cdf_students_t_vector
Computes a vector of deviates for Student's t -distribution
Related keywords: big datadata analyticsdeviatesinverse CDFSimple Calculations on Statistical DataStudent's t -distribution
G01TCF   24  nagf_stat_inv_cdf_chisq_vector
Computes a vector of deviates for χ 2 distribution
Related keywords: big datachi-squared distributiondata analyticsdeviatesinverse CDFSimple Calculations on Statistical Data
G01TDF   24  nagf_stat_inv_cdf_f_vector
Computes a vector of deviates for F -distribution
Related keywords: big datadata analyticsdeviates F -distributioninverse CDFSimple Calculations on Statistical Datavariance-ratio distribution
G01TEF   24  nagf_stat_inv_cdf_beta_vector
Computes a vector of deviates for the beta distribution
Related keywords: beta distributionbig datadata analyticsdeviatesinverse CDFSimple Calculations on Statistical Data
G01TFF   24  nagf_stat_inv_cdf_gamma_vector
Computes a vector of deviates for the gamma distribution
Related keywords: big datadata analyticsdeviatesgamma distributioninverse CDFSimple Calculations on Statistical Data
inverse hyperbolic cosine S11ACF   nagf_specfun_arccosh
arccosh x
Related keywords: approximations of special functionsfinance
inverse hyperbolic sine S11ABF   nagf_specfun_arcsinh
arcsinh x
Related keywords: approximations of special functionsfinance
inverse hyperbolic tangent S11AAF   nagf_specfun_arctanh
arctanh x
Related keywords: approximations of special functionsfinance
inverse iteration F08JKF   16  nagf_lapackeig_dstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
Related keywords: DSTEINeigenproblemeigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
F08JXF   16  nagf_lapackeig_zstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
Related keywords: eigenproblemeigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrixZSTEIN
F08PKF   16  nagf_lapackeig_dhsein
Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
Related keywords: DHSEINeigenproblemeigenvectorsLAPACKLAPACKleast squaresreal, Hessenberg matrix
F08PXF   16  nagf_lapackeig_zhsein
Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
Related keywords: complex, Hessenberg matrixeigenproblemeigenvectorsLAPACKLAPACKleast squaresZHSEIN
inverse Landau function G01FTF   21  nagf_stat_inv_cdf_landau
Landau inverse function Ψ x
Related keywords: financeLandau distributionSimple Calculations on Statistical Data
inverse Laplace transform C06LAF   12  nagf_sum_invlaplace_crump
Inverse Laplace transform, Crump's method
Related keywords: Crump's methodLaplace transformsummation of series
C06LBF   14  nagf_sum_invlaplace_weeks
Inverse Laplace transform, modified Weeks' method
Related keywords: Laplace transformsummation of seriesWeeks method
C06LCF   14  nagf_sum_invlaplace_weeks_eval
Evaluate inverse Laplace transform as computed by C06LBF
Related keywords: summation of series
inversion F01 Chapter Introduction     Matrix Operations, Including Inversion
Related keywords: matrix operations
invert permutation M01ZAF   12  nagf_sort_permute_invert
Invert a permutation
Related keywords: big datadata analyticspermutationsearchingsorting
ipm E04MTF   26  nagf_opt_handle_solve_lp_ipm
Linear programming (LP), sparse, interior point method (IPM)
Related keywords: interior point methodlinear programmingLPmaximizing a functionminimizing a functionoptimization
IPM E04STF   26  nagf_opt_handle_solve_ipopt
Run an interior point solver on a sparse nonlinear programming problem (NLP) initialized by E04RAF and defined by other routines from the suite
Related keywords: interior point methodleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinear programmingoptimizationoptimization
iterative methods, linear equations F11BEF   19  nagf_sparse_real_gen_basic_solver
Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticslarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11BSF   19  nagf_sparse_complex_gen_basic_solver
Complex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DAF   18  nagf_sparse_real_gen_precon_ilu
Real sparse nonsymmetric linear systems, incomplete L U factorization
Related keywords: big datadata analyticsincomplete L U factorizationlarge scale linear systemslinear equations, pre-conditionersreal, sparse matrix
F11DBF   18  nagf_sparse_real_gen_precon_ilu_solve
Solution of linear system involving incomplete L U preconditioning matrix generated by F11DAF
Related keywords: big datadata analyticsincomplete L U factorizationlarge scale linear systemslinear equations, iterative methodreal, sparse matrix
F11DCF   18  nagf_sparse_real_gen_solve_ilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DAF
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsincomplete L U factorizationlarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DEF   18  nagf_sparse_real_gen_solve_jacssor
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsJacobi preconditioninglarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodSSOR method, symmetric successive over-relaxationTFQMR, transpose-free quasi-minimal residual method
F11DGF   24  nagf_sparse_real_gen_solve_bdilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DFF
Related keywords: additive Schwarz preconditionerBi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsincomplete L U factorizationlarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DPF   19  nagf_sparse_complex_gen_precon_ilu_solve
Solution of complex linear system involving incomplete L U preconditioning matrix generated by F11DNF
Related keywords: big datacomplex, sparse matrixdata analyticsincomplete L U factorizationlarge scale linear systemslinear equations, iterative method
F11DQF   19  nagf_sparse_complex_gen_solve_ilu
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DNF (Black Box)
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsincomplete L U factorizationlarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DSF   19  nagf_sparse_complex_gen_solve_jacssor
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsJacobi preconditioninglarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodSSOR method, symmetric successive over-relaxationTFQMR, transpose-free quasi-minimal residual method
F11DUF   24  nagf_sparse_complex_gen_solve_bdilu
Solution of complex, sparse, non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DTF
Related keywords: additive Schwarz preconditionerBi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsincomplete L U factorizationlarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11GEF   20  nagf_sparse_real_symm_basic_solver
Real sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos method or the MINRES algorithm
Related keywords: big dataCGS, conjugate gradient methoddata analyticsLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodMINRES, iterative linear equation solverreal, sparse, symmetric matrix
F11GSF   20  nagf_sparse_complex_herm_basic_solver
Complex sparse Hermitian linear systems, preconditioned conjugate gradient or Lanczos
Related keywords: big dataCGS, conjugate gradient methodcomplex, Hermitian, sparse matrixdata analyticsLanczos method, linear equationslarge scale linear systemslinear equations, iterative method
F11JBF   17  nagf_sparse_real_symm_precon_ichol_solve
Solution of linear system involving incomplete Cholesky preconditioning matrix generated by F11JAF
Related keywords: big datadata analyticsincomplete Cholesky factorizationlarge scale linear systemslinear equations, iterative methodreal, sparse, symmetric matrix
F11JCF   17  nagf_sparse_real_symm_solve_ichol
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JAF (Black Box)
Related keywords: big dataCGS, conjugate gradient methoddata analyticsincomplete Cholesky factorizationLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse, symmetric matrix
F11JEF   17  nagf_sparse_real_symm_solve_jacssor
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big dataCGS, conjugate gradient methoddata analyticsJacobi preconditioningLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse, symmetric matrixSSOR method, symmetric successive over-relaxation
F11JQF   19  nagf_sparse_complex_herm_solve_ilu
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JNF (Black Box)
Related keywords: big datacomplex, Hermitian, sparse matrixconjugate gradient methoddata analyticsLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodsparse linear equations
F11JRF   19  nagf_sparse_complex_herm_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse Hermitian matrix
Related keywords: big datacomplex, Hermitian, sparse matrixdata analyticslarge scale linear systemslinear equations, iterative methodsparse linear equationsSSOR method, symmetric successive over-relaxation
F11JSF   19  nagf_sparse_complex_herm_solve_jacssor
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big datacomplex, Hermitian, sparse matrixconjugate gradient methoddata analyticsJacobi methodLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodsparse linear equationsSSOR method, symmetric successive over-relaxation
iterative weighted least squares G02HDF   13  nagf_correg_robustm_user
Robust regression, compute regression with user-supplied functions and weights
Related keywords: big databounded influencecorrelation analysisdata analyticsfinance M -estimatesnonlinear regressionpolynomial regressionregression analysisrobust regression
IVP, initial value problem D02BGF   nagf_ode_ivp_rkm_val_simple
Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until a component attains given value (simple driver)
Related keywords: initial value problemODE, ordinary differential equationsRunge–Kutta–Merson, ODE
D02BHF   nagf_ode_ivp_rkm_zero_simple
Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until function of solution is zero (simple driver)
Related keywords: initial value problemODE, ordinary differential equationsRunge–Kutta–Merson, ODE
D02BJF   18  nagf_ode_ivp_rk_zero_simple
Ordinary differential equations, initial value problem, Runge–Kutta method, until function of solution is zero, integration over range with intermediate output (simple driver)
Related keywords: initial value problemODE, ordinary differential equationsRK45Runge–Kutta–Merson, ODE
D02CJF   13  nagf_ode_ivp_adams_zero_simple
Ordinary differential equations, initial value problem, Adams' method, until function of solution is zero, intermediate output (simple driver)
Related keywords: Adams' methodfirst-order systeminitial value problemNonstiffODE, ordinary differential equationsstop at roots
D02EJF   12  nagf_ode_ivp_bdf_zero_simple
Ordinary differential equations, stiff initial value problem, backward differentiation formulae method, until function of solution is zero, intermediate output (simple driver)
Related keywords: backward difference formulaBDF, backward differentiation formulainitial value problemODE, ordinary differential equationsstiff differential equations
D02LAF   13  nagf_ode_ivp_2nd_rkn
Second-order ordinary differential equations, initial value problem, Runge–Kutta–Nystrom method
Related keywords: initial value problemODE, ordinary differential equationsRunge–Kutta–Nystrom, ODE
D02LXF   13  nagf_ode_ivp_2nd_rkn_setup
Second-order ordinary differential equations, initial value problem, setup for D02LAF
Related keywords: initial value problemODE, ordinary differential equationsRunge–Kutta–Nystrom, ODE
D02LYF   13  nagf_ode_ivp_2nd_rkn_diag
Second-order ordinary differential equations, initial value problem, diagnostics for D02LAF
Related keywords: initial value problemODE, ordinary differential equationsRunge–Kutta–Nystrom, ODE
D02LZF   13  nagf_ode_ivp_2nd_rkn_interp
Second-order ordinary differential equations, initial value problem, interpolation for D02LAF
Related keywords: initial value problemODE, ordinary differential equationsRunge–Kutta–Nystrom, ODE
D02MCF   22  nagf_ode_dae_dassl_cont
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method continuation for D02NEF
Related keywords: DAE, differential algebraic equationsDASSL, ordinary differential equationsimplicit algebraic ordinary differential equationsinitial value problemODE, ordinary differential equationsstiff differential equations
D02MVF   14  nagf_ode_ivp_stiff_dassl
Ordinary differential equations, initial value problem, DASSL method, setup for d02m–n routines
Related keywords: DASSL, ordinary differential equationsimplicit algebraic ordinary differential equationsinitial value problemODE, ordinary differential equationsstiff differential equations
D02MWF   22  nagf_ode_dae_dassl_setup
Implicit ordinary differential equations/DAEs, initial value problem, setup for D02NEF
Related keywords: DASSL, ordinary differential equationsinitial value problemODE, ordinary differential equationsstiff differential equations
D02MZF   14  nagf_ode_ivp_stiff_interp
Ordinary differential equations, initial value problem, interpolation for d02m–n routines (all integration methods), natural interpolant
Related keywords: initial value probleminterpolationODE, ordinary differential equations
D02NBF   12  nagf_ode_ivp_stiff_exp_fulljac
Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
Related keywords: backward difference formulainitial value problemJacobianODE, ordinary differential equationsstiff differential equations
D02NDF   12  nagf_ode_ivp_stiff_exp_sparjac
Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulainitial value problemODE, ordinary differential equationsstiff differential equations
D02NEF   22  nagf_ode_dae_dassl_gen
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator
Related keywords: DAE, differential algebraic equationsDASSL, ordinary differential equationsimplicit algebraic ordinary differential equationsinitial value problemODE, ordinary differential equations
D02NGF   12  nagf_ode_ivp_stiff_imp_fulljac
Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulaimplicit algebraic ordinary differential equationsinitial value problemJacobianODE, ordinary differential equationsstiff differential equations
D02NHF   12  nagf_ode_ivp_stiff_imp_bandjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulaimplicit algebraic ordinary differential equationsinitial value problemJacobianODE, ordinary differential equationsstiff differential equations
D02NJF   12  nagf_ode_ivp_stiff_imp_sparjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formuladiscretised systemimplicit algebraic ordinary differential equationsinitial value problemJacobianODEODE, ordinary differential equationsstiff differential equations
D02NMF   12  nagf_ode_ivp_stiff_exp_revcom
Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulainitial value problemODE, ordinary differential equationsstiff differential equations
D02NNF   12  nagf_ode_ivp_stiff_imp_revcom
Implicit/algebraic ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
Related keywords: backward difference formulaimplicit algebraic ordinary differential equationsinitial value problemODE, ordinary differential equationsstiff differential equations
D02NPF   22  nagf_ode_dae_dassl_linalg
Implicit ordinary differential equations/DAEs, initial value problem linear algebra setup routine for D02NEF
Related keywords: implicit algebraic ordinary differential equationsinitial value problemODE, ordinary differential equationsstiff differential equations
D02PEF   24  nagf_ode_ivp_rkts_range
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output
Related keywords: first-order systemNonstiffODE, ordinary differential equationsRK23RK45RK78Runge–Kutta–Merson
D02PFF   24  nagf_ode_ivp_rkts_onestep
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step
Related keywords: first-order systemNonstiffODE, ordinary differential equationsRK23RK45RK78Runge–Kutta–Merson
D02PGF   26  nagf_ode_ivp_rk_step_revcomm
Ordinary differential equations, initial value problem, Runge–Kutta method, integration by reverse communication
Related keywords: ODE, ordinary differential equationsRK23RK45RK78Runge–Kutta–Merson
D02PHF   26  nagf_ode_ivp_rk_interp_setup
Set up interpolant by reverse communication for solution and derivative evaluations at points within the range of the last integration step taken by D02PGF
Related keywords: first-order systeminterpolationNonstiffODE, ordinary differential equationsRunge–Kutta–Merson
D02PJF   26  nagf_ode_ivp_rk_interp_eval
Evaluate interpolant, set up using D02PQF, to approximate solution and/or solution derivatives at a point within the range of the last integration step taken by D02PGF
Related keywords: interpolationODE, ordinary differential equationsRunge–Kutta–Merson
D02PQF   24  nagf_ode_ivp_rkts_setup
Ordinary differential equations, initial value problem, setup for D02PEF D02PFF
Related keywords: ODE, ordinary differential equationsRunge–Kutta–Merson
D02PRF   24  nagf_ode_ivp_rkts_reset_tend
Ordinary differential equations, initial value problem, resets end of range for D02PFF
Related keywords: ODE, ordinary differential equationsRunge–Kutta–Merson
D02PSF   24  nagf_ode_ivp_rkts_interp
Ordinary differential equations, initial value problem, interpolation for D02PFF
Related keywords: interpolationODE, ordinary differential equationsRunge–Kutta–Merson
D02PTF   24  nagf_ode_ivp_rkts_diag
Ordinary differential equations, initial value problem, integration diagnostics for D02PEF D02PFF
Related keywords: ODE, ordinary differential equationsRunge–Kutta–Merson
D02PUF   24  nagf_ode_ivp_rkts_errass
Ordinary differential equations, initial value problem, error assessment diagnostics for D02PEF D02PFF
Related keywords: ODE, ordinary differential equationsRunge–Kutta–Merson
D02QFF   13  nagf_ode_ivp_adams_roots
Ordinary differential equations, initial value problem, Adams' method with root-finding (direct communication, comprehensive)
Related keywords: Adams' methodODE, ordinary differential equations
D02QGF   13  nagf_ode_ivp_adams_roots_revcom
Ordinary differential equations, initial value problem, Adams' method with root-finding (reverse communication, comprehensive)
Related keywords: Adams' methodODE, ordinary differential equations
D02QWF   13  nagf_ode_ivp_adams_setup
Ordinary differential equations, initial value problem, setup for D02QFF and D02QGF
Related keywords: Adams' methodODE, ordinary differential equations
D02QXF   13  nagf_ode_ivp_adams_diag
Ordinary differential equations, initial value problem, diagnostics for D02QFF and D02QGF
Related keywords: Adams' methodODE, ordinary differential equations
D02QYF   13  nagf_ode_ivp_adams_rootdiag
Ordinary differential equations, initial value problem, root-finding diagnostics for D02QFF and D02QGF
Related keywords: Adams' methodODE, ordinary differential equations
D02QZF   13  nagf_ode_ivp_adams_interp
Ordinary differential equations, initial value problem, interpolation for D02QFF or D02QGF
Related keywords: Adams' methodinterpolationODE, ordinary differential equations
izamax F06JMF   12  nagf_blas_izamax
Index, complex vector element with largest absolute value
Related keywords: BLASblas, complex matriceselementary arithmeticlinear algebra support routines
J 0 , Bessel function S17AEF   nagf_specfun_bessel_j0_real
Bessel function J 0 x
Related keywords: approximations of special functionsBessel functionfinance
S17ASF   24  nagf_specfun_bessel_j0_real_vector
Bessel function vectorized J 0 x
Related keywords: approximations of special functionsBessel function
J 1 , Bessel function S17AFF   nagf_specfun_bessel_j1_real
Bessel function J 1 x
Related keywords: approximations of special functionsBessel functionfinance
S17ATF   24  nagf_specfun_bessel_j1_real_vector
Bessel function vectorized J 1 x
Related keywords: approximations of special functionsBessel function
jacknife G05PVF   25  nagf_rand_kfold_xyw
Permutes a matrix, vector, vector triplet into a form suitable for K -fold cross validation
Related keywords: big datacross-validationCVdata analyticsk-foldleave-one-outLOOpermuterandom number generators
Jacobian D02NBF   12  nagf_ode_ivp_stiff_exp_fulljac
Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
Related keywords: backward difference formulainitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NCF   12  nagf_ode_ivp_stiff_exp_bandjac
Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulainitial value problemODE, ordinary differential equationsstiff differential equations
D02NGF   12  nagf_ode_ivp_stiff_imp_fulljac
Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulaimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NHF   12  nagf_ode_ivp_stiff_imp_bandjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulaimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equationsstiff differential equations
D02NJF   12  nagf_ode_ivp_stiff_imp_sparjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formuladiscretised systemimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemODEODE, ordinary differential equationsstiff differential equations
Jacobian elliptic functions S21CAF   15  nagf_specfun_jacellip_real
Jacobian elliptic functions sn, cn and dn of real argument
Related keywords: approximations of special functionscn, Jacobian elliptic functiondn, Jacobian elliptic functionelliptic functionsfinancesn, Jacobian elliptic functions
S21CBF   20  nagf_specfun_jacellip_complex
Jacobian elliptic functions sn, cn and dn of complex argument
Related keywords: approximations of special functionscn, Jacobian elliptic functiondn, Jacobian elliptic functionelliptic functionsfinancesn, Jacobian elliptic functions
Jacobian estimation E04XAF   12  nagf_opt_estimate_deriv_old
Estimate (using numerical differentiation) gradient and/or Hessian of a function
Related keywords: financeHessian estimationmaximizing a functionminimizing a functionoptimization
E04YAF   nagf_opt_lsq_check_deriv
Check user's routine for calculating Jacobian of first derivatives
Related keywords: financemaximizing a functionminimizing a functionoptimizationservice routine
Jacobian theta functions S21CCF   20  nagf_specfun_jactheta_real
Jacobian theta functions θ k x , q of real argument
Related keywords: approximations of special functionsfinancetheta, Jacobian theta functions
Jacobi method F06BEF   12  nagf_blas_drotj
Generate real Jacobi plane rotation
Related keywords: BLASlinear algebra support routinesrotation, elementary
F08KHF   23  nagf_lapackeig_dgejsv
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
Related keywords: DGEJSVeigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrixsingular value decomposition
F08KJF   23  nagf_lapackeig_dgesvj
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
Related keywords: DGESVJeigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrixsingular value decomposition
F11JSF   19  nagf_sparse_complex_herm_solve_jacssor
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big datacomplex, Hermitian, sparse matrixconjugate gradient methoddata analyticsiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodsparse linear equationsSSOR method, symmetric successive over-relaxation
Jacobi preconditioning F11DEF   18  nagf_sparse_real_gen_solve_jacssor
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodSSOR method, symmetric successive over-relaxationTFQMR, transpose-free quasi-minimal residual method
F11DKF   20  nagf_sparse_real_gen_precon_jacobi
Real, sparse, symmetric or nonsymmetric, linear systems, line Jacobi preconditioner
Related keywords: big datadata analyticslarge scale linear systemslinear equations, pre-conditionersreal, sparse, symmetric matrixreal, sparse matrix
F11DSF   19  nagf_sparse_complex_gen_solve_jacssor
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodSSOR method, symmetric successive over-relaxationTFQMR, transpose-free quasi-minimal residual method
F11DXF   20  nagf_sparse_complex_gen_precon_jacobi
Complex, sparse, Hermitian or non-Hermitian, linear systems, line Jacobi preconditioner
Related keywords: big datacomplex, sparse matrixdata analyticslarge scale linear systemslinear equations, pre-conditioners
F11JEF   17  nagf_sparse_real_symm_solve_jacssor
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse, symmetric matrixSSOR method, symmetric successive over-relaxation
jump-diffusion model, option pricing S30JAF   22  nagf_specfun_opt_jumpdiff_merton_price
Jump-diffusion, Merton's model, option pricing formula
Related keywords: approximations of special functionsderivative, optionsfinanceMerton model, option pricingoption pricing
S30JBF   22  nagf_specfun_opt_jumpdiff_merton_greeks
Jump-diffusion, Merton's model, option pricing formula with Greeks
Related keywords: approximations of special functionsderivative, optionsfinanceGreeks, optionsMerton model, option pricingoption pricing
K 0 , modified Bessel function S18ACF   nagf_specfun_bessel_k0_real
Modified Bessel function K 0 x
Related keywords: approximations of special functionsfinancemodified Bessel function
S18AQF   24  nagf_specfun_bessel_k0_real_vector
Modified Bessel function vectorized K 0 x
Related keywords: approximations of special functionsmodified Bessel function
S18CCF   10  nagf_specfun_bessel_k0_scaled
Scaled modified Bessel function e x K 0 x
Related keywords: approximations of special functionsfinancemodified Bessel function
S18CQF   24  nagf_specfun_bessel_k0_scaled_vector
Scaled modified Bessel function vectorized e x K 0 x
Related keywords: approximations of special functionsmodified Bessel function
K 1 , modified Bessel function S18ADF   nagf_specfun_bessel_k1_real
Modified Bessel function K 1 x
Related keywords: approximations of special functionsfinancemodified Bessel function
S18ARF   24  nagf_specfun_bessel_k1_real_vector
Modified Bessel function vectorized K 1 x
Related keywords: approximations of special functionsmodified Bessel function
S18CDF   10  nagf_specfun_bessel_k1_scaled
Scaled modified Bessel function e x K 1 x
Related keywords: approximations of special functionsfinancemodified Bessel function
S18CRF   24  nagf_specfun_bessel_k1_scaled_vector
Scaled modified Bessel function vectorized e x K 1 x
Related keywords: approximations of special functionsmodified Bessel function
Kalman filter G13EAF   17  nagf_tsa_multi_kalman_sqrt_var
Combined measurement and time update, one iteration of Kalman filter, time-varying, square root covariance filter
Related keywords: big datadata analyticstime series analysis
G13EBF   17  nagf_tsa_multi_kalman_sqrt_invar
Combined measurement and time update, one iteration of Kalman filter, time-invariant, square root covariance filter
Related keywords: big datadata analyticstime series analysis
Kaplan–Meier estimate G12AAF   15  nagf_surviv_kaplanmeier
Computes Kaplan–Meier (product-limit) estimates of survival probabilities
Related keywords: product-limit, Kaplan–Meier estimatessurvival analysis
Keller box discretization D03PEF   16  nagf_pde_1d_parab_keller
General system of first-order PDEs, method of lines, Keller box discretization, one space variable
Related keywords: method of linesparabolic partial differential equationPDE, partial differential equations
D03PKF   16  nagf_pde_1d_parab_dae_keller
General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretization, one space variable
Related keywords: DAE, differential algebraic equationsmethod of linespartial differential equationsPDE, partial differential equations
D03PRF   16  nagf_pde_1d_parab_remesh_keller
General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretization, remeshing, one space variable
Related keywords: adaptive grid, PDEDAE, differential algebraic equationsmethod of linesPDE, partial differential equations
Kelvin functions S19AAF   11  nagf_specfun_kelvin_ber
Kelvin function ber x
Related keywords: approximations of special functionsfinance ber x , Kelvin function
S19ABF   11  nagf_specfun_kelvin_bei
Kelvin function bei x
Related keywords: approximations of special functionsfinance bei x , Kelvin function
S19ACF   11  nagf_specfun_kelvin_ker
Kelvin function ker x
Related keywords: approximations of special functionsfinance ker x , Kelvin function
S19ADF   11  nagf_specfun_kelvin_kei
Kelvin function kei x
Related keywords: approximations of special functionsfinance kei x , Kelvin function
S19ANF   24  nagf_specfun_kelvin_ber_vector
Kelvin function vectorized ber x
Related keywords: approximations of special functions ber x , Kelvin function
S19APF   24  nagf_specfun_kelvin_bei_vector
Kelvin function vectorized bei x
Related keywords: approximations of special functions bei x , Kelvin function
S19AQF   24  nagf_specfun_kelvin_ker_vector
Kelvin function vectorized ker x
Related keywords: approximations of special functions ker x , Kelvin function
S19ARF   24  nagf_specfun_kelvin_kei_vector
Kelvin function vectorized kei x
Related keywords: approximations of special functions kei x , Kelvin function
Kendall's coefficient of concordance G08DAF   nagf_nonpar_concordance_kendall
Kendall's coefficient of concordance
Related keywords: nonparametric statistics
Kendall's tau correlation coefficient G02BNF   nagf_correg_coeffs_kspearman_overwrite
Kendall/Spearman non-parametric rank correlation coefficients, no missing values, overwriting input data
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinancenonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02BPF   nagf_correg_coeffs_kspearman_miss_case_overwrite
Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinancemissing valuesnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02BQF   nagf_correg_coeffs_kspearman
Kendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinancenonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02BRF   nagf_correg_coeffs_kspearman_miss_case
Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinancemissing valuesnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02BSF   nagf_correg_coeffs_kspearman_miss_pair
Kendall/Spearman non-parametric rank correlation coefficients, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinancemissing valuesnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
kernel density G10BBF   25  nagf_smooth_kerndens_gauss
Kernel density estimate using Gaussian kernel (thread safe)
Related keywords: Smoothing in Statistics
k -factor structure G02AEF   23  nagf_correg_corrmat_nearest_kfactor
Computes the nearest correlation matrix with k -factor structure to a real square matrix
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsfinancenearest correlation matrixnonlinear regressionpolynomial regressionQi and Sun algorithmregression analysis
k-fold G05PVF   25  nagf_rand_kfold_xyw
Permutes a matrix, vector, vector triplet into a form suitable for K -fold cross validation
Related keywords: big datacross-validationCVdata analyticsjacknifeleave-one-outLOOpermuterandom number generators
K -means cluster analysis G03EFF   16  nagf_mv_cluster_kmeans
K -means cluster analysis
Related keywords: big datacluster analysisdata analyticsmultivariate methods
knots E02BAF   nagf_fit_1dspline_knots
Least squares curve cubic spline fit (including interpolation)
Related keywords: B-splinescubic splinescurve and surface fittingleast squares
E02DAF   nagf_fit_2dspline_panel
Least squares surface fit, bicubic splines
Related keywords: bicubic splinesB-splinescurve and surface fittingleast squarestwo-dimensional spline approximation
Kolmogorov–Smirnov distribution G01EYF   14  nagf_stat_prob_kolmogorov1
Computes probabilities for the one-sample Kolmogorov–Smirnov distribution
Related keywords: financeSimple Calculations on Statistical Dataupper tail probability
G01EZF   14  nagf_stat_prob_kolmogorov2
Computes probabilities for the two-sample Kolmogorov–Smirnov distribution
Related keywords: financeSimple Calculations on Statistical Dataupper tail probability
Kolmogorov–Smirnov test G08CBF   14  nagf_nonpar_test_ks_1sample
Performs the one-sample Kolmogorov–Smirnov test for standard distributions
Related keywords: nonparametric statistics
G08CCF   14  nagf_nonpar_test_ks_1sample_user
Performs the one-sample Kolmogorov–Smirnov test for a user-supplied distribution
Related keywords: nonparametric statistics
G08CDF   14  nagf_nonpar_test_ks_2sample
Performs the two-sample Kolmogorov–Smirnov test
Related keywords: nonparametric statistics
Korobov–Conroy method, numerical integration D01GCF   10  nagf_quad_md_numth
Multidimensional quadrature, general product region, number-theoretic method
Related keywords: integration, multidimensionalnumerical integrationquadraturequadrature non-adaptive
D01GYF   10  nagf_quad_md_numth_coeff_prime
Korobov optimal coefficients for use in D01GCF or D01GDF, when number of points is prime
Related keywords: financequadrature
D01GZF   10  nagf_quad_md_numth_coeff_2prime
Korobov optimal coefficients for use in D01GCF or D01GDF, when number of points is product of two primes
Related keywords: financequadrature
Krasker–Welsch weights G02HAF   13  nagf_correg_robustm
Robust regression, standard M -estimates
Related keywords: Andrew's sine wavebig datacorrelation analysisdata analyticsfinanceHampel's piecewise linear functionHuber type regressionMallows type regressionMaronna's weights M -estimatesnonlinear regressionpolynomial regressionregressionregression analysisrobust regressionScheppe type regressionTukey's bi-weight
Kruskal–Wallis analysis of variance G08AFF   nagf_nonpar_test_kruskal
Kruskal–Wallis one-way analysis of variance on k samples of unequal size
Related keywords: ANOVAnonparametric statistics
kurtosis G01ADF   nagf_stat_summary_freq
Mean, variance, skewness, kurtosis, etc., one variable, from frequency table
Related keywords: financemeanSimple Calculations on Statistical Dataskewnessstandard deviation
G01ATF   24  nagf_stat_summary_onevar
Computes univariate summary information: mean, variance, skewness, kurtosis
Related keywords: big datadata analyticsdata streammaximum valuemeanminimum valueSimple Calculations on Statistical Dataskewnessstandard deviationstreaming
L(infinity) approximation E02GCF   nagf_fit_glin_linf
L -approximation by general linear function
Related keywords: curve and surface fittingsupremum norm
L 0 x , Struve function S18GAF   26  nagf_specfun_struve_l0
Modified Struve function of order 0 , L 0 x
Related keywords: approximations of special functionsModified Struve function
L1 approximation E02GAF   nagf_fit_glin_l1sol
L 1 -approximation by general linear function
Related keywords: curve and surface fittingoutlier detection
E02GBF   nagf_fit_glinc_l1sol
L 1 -approximation by general linear function subject to linear inequality constraints
Related keywords: curve and surface fittingoutlier detection
L 1 x , Struve function S18GBF   26  nagf_specfun_struve_l1
Modified Struve function of order 1 , L 1 x
Related keywords: approximations of special functionsModified Struve function
Lagrangian E04SVF   26  nagf_opt_handle_solve_pennon
Run the Pennon solver on a compatible problem initialized by E04RAF and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI)
Related keywords: bilinear matrix inequalityBMIgeneralized augmented Lagrangian methodleast squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionmonitoring informationoptimizationoptimizationSDPsemidefinite programming
Laguerre's method C02AFF   14  nagf_zeros_poly_complex
All zeros of complex polynomial, modified Laguerre's method
Related keywords: root-findingzeros of polynomials
C02AGF   13  nagf_zeros_poly_real
All zeros of real polynomial, modified Laguerre's method
Related keywords: root-findingzeros of polynomials
Lambert function C05BAF   22  nagf_roots_lambertw_real
Real values of Lambert's W function, W x
Related keywords: roots of transcendental equations
C05BBF   23  nagf_roots_lambertw_complex
Values of Lambert's W function, W z
Related keywords: roots of transcendental equations
Lanczos method, linear equations F11GEF   20  nagf_sparse_real_symm_basic_solver
Real sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos method or the MINRES algorithm
Related keywords: big dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodMINRES, iterative linear equation solverreal, sparse, symmetric matrix
F11GSF   20  nagf_sparse_complex_herm_basic_solver
Complex sparse Hermitian linear systems, preconditioned conjugate gradient or Lanczos
Related keywords: big dataCGS, conjugate gradient methodcomplex, Hermitian, sparse matrixdata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative method
F11JCF   17  nagf_sparse_real_symm_solve_ichol
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JAF (Black Box)
Related keywords: big dataCGS, conjugate gradient methoddata analyticsincomplete Cholesky factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse, symmetric matrix
F11JEF   17  nagf_sparse_real_symm_solve_jacssor
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsJacobi preconditioninglarge scale linear systemslinear equations, iterative methodreal, sparse, symmetric matrixSSOR method, symmetric successive over-relaxation
F11JQF   19  nagf_sparse_complex_herm_solve_ilu
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JNF (Black Box)
Related keywords: big datacomplex, Hermitian, sparse matrixconjugate gradient methoddata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodsparse linear equations
F11JSF   19  nagf_sparse_complex_herm_solve_jacssor
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big datacomplex, Hermitian, sparse matrixconjugate gradient methoddata analyticsiterative methods, linear equationsJacobi methodlarge scale linear systemslinear equations, iterative methodsparse linear equationsSSOR method, symmetric successive over-relaxation
Landau density function G01MTF   21  nagf_stat_pdf_landau
Landau density function ϕ λ
Related keywords: financeSimple Calculations on Statistical Data
G01RTF   21  nagf_stat_pdf_landau_deriv
Landau derivative function ϕ λ
Related keywords: derivative, Landau density functionfinanceSimple Calculations on Statistical Data
Landau distribution G01ETF   21  nagf_stat_prob_landau
Landau distribution function
Related keywords: financeSimple Calculations on Statistical Data
G01FTF   21  nagf_stat_inv_cdf_landau
Landau inverse function Ψ x
Related keywords: financeinverse Landau functionSimple Calculations on Statistical Data
Landau moment function G01PTF   21  nagf_stat_pdf_landau_moment1
Landau first moment function Φ 1 x
Related keywords: financeSimple Calculations on Statistical Data
G01QTF   21  nagf_stat_pdf_landau_moment2
Landau second moment function Φ 2 x
Related keywords: financeSimple Calculations on Statistical Data
LAPACK F01VAF   23  nagf_matop_dtrttp
Copies a real triangular matrix from full format to packed format
Related keywords: DTRTTPfinanceinversionmatrix operationsreal, triangular matrix
F01VBF   23  nagf_matop_ztrttp
Copies a complex triangular matrix from full format to packed format
Related keywords: complex, triangular matrixfinanceinversionmatrix operationsZTRTTP
F01VCF   23  nagf_matop_dtpttr
Copies a real triangular matrix from packed format to full format
Related keywords: DTPTTRfinanceinversionmatrix operationsreal, triangular matrix
F01VDF   23  nagf_matop_ztpttr
Copies a complex triangular matrix from packed format to full format
Related keywords: complex, triangular matrixfinanceinversionmatrix operationsZTPTTR
F01VEF   23  nagf_matop_dtrttf
Copies a real triangular matrix from full format to Rectangular Full Packed format
Related keywords: DTRTTPfinanceinversionmatrix operationsreal, triangular matrix
F01VFF   23  nagf_matop_ztrttf
Copies a complex triangular matrix from full format to Rectangular Full Packed format
Related keywords: complex, triangular matrixfinanceinversionmatrix operationsZTRTTF
F01VGF   23  nagf_matop_dtfttr
Copies a real triangular matrix from Rectangular Full Packed format to full format
Related keywords: DTFTTRfinanceinversionmatrix operationsreal, triangular matrix
F01VHF   23  nagf_matop_ztfttr
Copies a complex triangular matrix from Rectangular Full Packed format to full format
Related keywords: complex, triangular matrixfinanceinversionmatrix operationsZTFTTR
F01VJF   23  nagf_matop_dtpttf
Copies a real triangular matrix from packed format to Rectangular Full Packed format
Related keywords: DTPTTFfinanceinversionmatrix operationsreal, triangular matrix
F01VKF   23  nagf_matop_ztpttf
Copies a complex triangular matrix from packed format to Rectangular Full Packed format
Related keywords: complex, triangular matrixfinanceinversionmatrix operationsZTPTTF
F01VLF   23  nagf_matop_dtfttp
Copies a real triangular matrix from Rectangular Full Packed format to packed format
Related keywords: DTFTTPfinanceinversionmatrix operationsreal, triangular matrix
F01VMF   23  nagf_matop_ztfttp
Copies a complex triangular matrix from Rectangular Full Packed format to packed format
Related keywords: complex, triangular matrixfinanceinversionmatrix operationsZTFTTP
F07 Chapter Introduction     Linear Equations (LAPACK)
Related keywords: linear equations
F08 Chapter Introduction     Least Squares and Eigenvalue Problems (LAPACK)
Related keywords: eigenproblemleast squares
F08AAF   21  nagf_lapackeig_dgels
Solves a real linear least squares problem of full rank
Related keywords: DGELSeigenproblemfinanceleast squareslinear least squares LQ decompositionoverdetermined linear equations QR factorizationreal, m by n matrixunderdetermined linear system
F08AEF   16  nagf_lapackeig_dgeqrf
Performs a Q R factorization of real general rectangular matrix
Related keywords: DGEQRFeigenproblemfinanceleast squares QR factorizationreal, m by n matrix
F08AFF   16  nagf_lapackeig_dorgqr
Forms all or part of orthogonal Q from Q R factorization determined by F08AEF F08BEF F08BFF
Related keywords: DORGQReigenproblemleast squaresorthogonal matrix, generationorthogonal transformations QR factorization
F08AGF   16  nagf_lapackeig_dormqr
Applies an orthogonal transformation determined by F08AEF F08BEF F08BFF
Related keywords: DORMQReigenproblemfinanceleast squaresorthogonal transformations QR factorization
F08AHF   16  nagf_lapackeig_dgelqf
Performs a L Q factorization of real general rectangular matrix
Related keywords: DGELQFeigenproblemleast squares LQ factorizationreal, m by n matrix
F08AJF   16  nagf_lapackeig_dorglq
Forms all or part of orthogonal Q from L Q factorization determined by F08AHF
Related keywords: DORGLQeigenproblemleast squares LQ factorizationorthogonal matrix, generationorthogonal transformations
F08AKF   16  nagf_lapackeig_dormlq
Applies the orthogonal transformation determined by F08AHF
Related keywords: DORMLQeigenproblemleast squares LQ factorizationorthogonal transformations
F08ANF   21  nagf_lapackeig_zgels
Solves a complex linear least problem of full rank
Related keywords: complex, m by n matrixeigenproblemfinanceleast squareslinear least squares LQ decompositionoverdetermined linear equations QR factorizationunderdetermined linear systemZGELS
F08ASF   16  nagf_lapackeig_zgeqrf
Performs a Q R factorization of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemleast squares QR factorizationZGEQRF
F08ATF   16  nagf_lapackeig_zungqr
Forms all or part of unitary Q from Q R factorization determined by F08ASF F08BSF F08BTF
Related keywords: eigenproblemleast squares QR factorizationunitary matrix, generationunitary transformationsZUNGQR
F08AUF   16  nagf_lapackeig_zunmqr
Applies a unitary transformation determined by F08ASF F08BSF F08BTF
Related keywords: eigenproblemleast squares QR factorizationunitary transformationsZUNMQR
F08AVF   16  nagf_lapackeig_zgelqf
Performs a L Q factorization of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemleast squares LQ factorizationZGELQF
F08AWF   16  nagf_lapackeig_zunglq
Forms all or part of unitary Q from L Q factorization determined by F08AVF
Related keywords: eigenproblemleast squares LQ factorizationunitary matrix, generationunitary transformationsZUNGLQ
F08AXF   16  nagf_lapackeig_zunmlq
Applies the unitary transformation determined by F08AVF
Related keywords: eigenproblemleast squares LQ factorizationunitary transformationsZUNMLQ
F08BAF   21  nagf_lapackeig_dgelsy
Computes the minimum-norm solution to a real linear least squares problem
Related keywords: DGELSYeigenproblemfinanceleast squareslinear least squaresminimal least squaresreal, m by n matrix
F08BEF   16  nagf_lapackeig_dgeqpf
Q R factorization, with column pivoting, of real general rectangular matrix
Related keywords: DGEQPFeigenproblemfinanceleast squaresorthogonal transformations QR factorizationreal, m by n matrix
F08BFF   22  nagf_lapackeig_dgeqp3
Q R factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
Related keywords: DGEQP3eigenproblemfinanceleast squaresorthogonal transformations QR factorizationreal, m by n matrix
F08BHF   22  nagf_lapackeig_dtzrzf
Reduces a real upper trapezoidal matrix to upper triangular form
Related keywords: DTZRZFeigenproblemleast squaresmatrix, upper trapezoidalmatrix, upper triangularorthogonal transformationsreal, trapezoidal matrix
F08BKF   22  nagf_lapackeig_dormrz
Applies the orthogonal transformation determined by F08BHF
Related keywords: DORMRZeigenproblemleast squaresorthogonal transformations
F08BNF   21  nagf_lapackeig_zgelsy
Computes the minimum-norm solution to a complex linear least squares problem
Related keywords: complex, m by n matrixeigenproblemleast squareslinear least squaresminimal least squaresZGELSY
F08BSF   16  nagf_lapackeig_zgeqpf
Q R factorization, with column pivoting, of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemleast squares QR factorizationZGEQPF
F08BTF   22  nagf_lapackeig_zgeqp3
Q R factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemleast squares QR factorizationZGEQP3
F08BVF   22  nagf_lapackeig_ztzrzf
Reduces a complex upper trapezoidal matrix to upper triangular form
Related keywords: complex, trapezoidal matrixeigenproblemleast squaresmatrix, upper trapezoidalmatrix, upper triangularZTZRZF
F08BXF   22  nagf_lapackeig_zunmrz
Applies the unitary transformation determined by F08BVF
Related keywords: eigenproblemleast squaresunitary transformationsZUNMRZ
F08CEF   22  nagf_lapackeig_dgeqlf
Q L factorization of real general rectangular matrix
Related keywords: DGEQLFeigenproblemleast squares QL factorizationreal, m by n matrix
F08CFF   22  nagf_lapackeig_dorgql
Form all or part of orthogonal Q from Q L factorization determined by F08CEF
Related keywords: DORGQLeigenproblemleast squaresorthogonal matrix, generationorthogonal transformations QL factorization
F08CGF   22  nagf_lapackeig_dormql
Applies the orthogonal transformation determined by F08CEF
Related keywords: DORMQLeigenproblemleast squaresorthogonal transformations QL factorization
F08CHF   22  nagf_lapackeig_dgerqf
R Q factorization of real general rectangular matrix
Related keywords: DGERQFeigenproblemleast squaresreal, m by n matrixRQ factorizations
F08CJF   22  nagf_lapackeig_dorgrq
Form all or part of orthogonal Q from R Q factorization determined by F08CHF
Related keywords: DORGRQeigenproblemleast squaresorthogonal matrix, generationorthogonal transformationsRQ factorizations
F08CKF   22  nagf_lapackeig_dormrq
Applies the orthogonal transformation determined by F08CHF
Related keywords: DORGRQeigenproblemleast squaresorthogonal transformationsRQ factorizations
F08CSF   22  nagf_lapackeig_zgeqlf
Q L factorization of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemleast squares QL factorizationZGEQLF
F08CTF   22  nagf_lapackeig_zungql
Form all or part of unitary Q from Q L factorization determined by F08CSF
Related keywords: eigenproblemleast squares QL factorizationunitary matrix, generationunitary transformationsZUNGQL
F08CUF   22  nagf_lapackeig_zunmql
Applies the unitary transformation determined by F08CSF
Related keywords: eigenproblemleast squares QL factorizationunitary transformationsZUNMQL
F08CVF   22  nagf_lapackeig_zgerqf
R Q factorization of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemleast squaresRQ factorizationsZGERQF
F08CWF   22  nagf_lapackeig_zungrq
Form all or part of unitary Q from R Q factorization determined by F08CVF
Related keywords: eigenproblemleast squaresRQ factorizationsunitary matrix, generationunitary transformationsZUNGRQ
F08CXF   22  nagf_lapackeig_zunmrq
Applies the unitary transformation determined by F08CVF
Related keywords: eigenproblemleast squaresRQ factorizationsunitary transformationsZUNMRQ
F08FAF   21  nagf_lapackeig_dsyev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Related keywords: DSYEVeigenproblemeigenvalueseigenvectorsfinanceleast squaresreal, indefinite, symmetric matrix
F08FBF   21  nagf_lapackeig_dsyevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Related keywords: DSYEVXeigenproblemeigenvalueseigenvectorsfinanceleast squaresreal, indefinite, symmetric matrix
F08FCF   19  nagf_lapackeig_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
Related keywords: divide-and-conquer methodDSYEVDeigenproblemeigenvalueseigenvectorsfinanceleast squaresreal, indefinite, symmetric matrix
F08FDF   21  nagf_lapackeig_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
Related keywords: dqds algorithmDSYEVReigenproblemeigenvalueseigenvectorsleast squaresreal, indefinite, symmetric matrixrelatively robust representations
F08FEF   16  nagf_lapackeig_dsytrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
Related keywords: DSYTRDeigenproblemleast squaresorthogonal transformationsreal, indefinite, symmetric matrix
F08FFF   16  nagf_lapackeig_dorgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF
Related keywords: DORGTReigenproblemleast squaresorthogonal matrix, generationorthogonal transformations
F08FGF   16  nagf_lapackeig_dormtr
Applies the orthogonal transformation determined by F08FEF
Related keywords: DORMTReigenproblemleast squaresorthogonal transformations
F08FLF   22  nagf_lapackeig_ddisna
Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix
Related keywords: complex, Hermitian, indefinite matrixcondition number, matrixDDISNAeigenproblemeigenvectorsfinanceleast squaresreal, indefinite, symmetric matrix
F08FNF   21  nagf_lapackeig_zheev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvalueseigenvectorsleast squaresZHEEV
F08FPF   21  nagf_lapackeig_zheevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvalueseigenvectorsfinanceleast squaresZHEEVX
F08FQF   19  nagf_lapackeig_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
Related keywords: complex, Hermitian, indefinite matrixdivide-and-conquer methodeigenproblemeigenvalueseigenvectorsfinanceleast squaresZHEEVD
F08FRF   21  nagf_lapackeig_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvalueseigenvectorsleast squaresrelatively robust representationsunitary transformationsZHEEVR
F08FSF   16  nagf_lapackeig_zhetrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
Related keywords: complex, Hermitian, indefinite matrixeigenproblemleast squaresunitary transformationsZHETRD
F08FTF   16  nagf_lapackeig_zungtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF
Related keywords: eigenproblemleast squaresunitary matrix, generationunitary transformationsZUNGTR
F08FUF   16  nagf_lapackeig_zunmtr
Applies the unitary transformation matrix determined by F08FSF
Related keywords: eigenproblemleast squaresunitary transformationsZUNMTR
F08GAF   21  nagf_lapackeig_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Related keywords: DSPEVeigenproblemeigenvalueseigenvectorsleast squaresorthogonal transformations QR algorithmreal, indefinite, symmetric matrix
F08GBF   21  nagf_lapackeig_dspevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Related keywords: DSPEVXeigenproblemeigenvalueseigenvectorsleast squaresorthogonal transformationsreal, indefinite, symmetric matrix
F08GCF   19  nagf_lapackeig_dspevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: divide-and-conquer methodDSPEVDeigenproblemeigenvalueseigenvectorsleast squaresPal–Walker–Kahan ( QL or QR ) algorithmreal, indefinite, symmetric matrix
F08GEF   16  nagf_lapackeig_dsptrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
Related keywords: DSPTRDeigenproblemleast squaresorthogonal transformationsreal, indefinite, symmetric matrix
F08GFF   16  nagf_lapackeig_dopgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF
Related keywords: DOPGTReigenproblemleast squaresorthogonal matrix, generationorthogonal transformations
F08GGF   16  nagf_lapackeig_dopmtr
Applies the orthogonal transformation determined by F08GEF
Related keywords: DOPMTReigenproblemleast squaresorthogonal transformations
F08GNF   21  nagf_lapackeig_zhpev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvalueseigenvectorsleast squaresZHPEV
F08GPF   21  nagf_lapackeig_zhpevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvalueseigenvectorsleast squaresZHPEVX
F08GQF   19  nagf_lapackeig_zhpevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: complex, Hermitian, indefinite matrixdivide-and-conquer methodeigenproblemeigenvalueseigenvectorsleast squaresPal–Walker–Kahan ( QL or QR ) algorithmZHPEVD
F08GSF   16  nagf_lapackeig_zhptrd
Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
Related keywords: complex, Hermitian, indefinite matrixeigenproblemleast squaresunitary transformationsZHPTRD
F08GTF   16  nagf_lapackeig_zupgtr
Generates a unitary transformation matrix from reduction to tridiagonal form determined by F08GSF
Related keywords: eigenproblemleast squaresunitary matrix, generationunitary transformationsZUPGTR
F08GUF   16  nagf_lapackeig_zupmtr
Applies the unitary transformation matrix determined by F08GSF
Related keywords: eigenproblemleast squaresunitary transformationsZUPGTR
F08HAF   21  nagf_lapackeig_dsbev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
Related keywords: DSBEVeigenproblemleast squaresmatrix, band QR algorithmreal, band, symmetric matrix
F08HBF   21  nagf_lapackeig_dsbevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
Related keywords: DSBEVXeigenproblemeigenvalueseigenvectorsleast squaresmatrix, bandreal, band, symmetric matrix
F08HCF   19  nagf_lapackeig_dsbevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: divide-and-conquer methodDSBEVXeigenproblemeigenvalueseigenvectorsleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithmreal, band, symmetric matrix
F08HEF   16  nagf_lapackeig_dsbtrd
Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
Related keywords: DSBTRDeigenproblemleast squaresmatrix, bandorthogonal transformationsreal, band, symmetric matrix
F08HNF   21  nagf_lapackeig_zhbev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
Related keywords: complex, band, Hermitian matrixeigenproblemleast squaresmatrix, band QR algorithmunitary transformationsZHBEV
F08HPF   21  nagf_lapackeig_zhbevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
Related keywords: complex, band, Hermitian matrixeigenproblemleast squaresmatrix, bandunitary transformationsZHBEVX
F08HQF   19  nagf_lapackeig_zhbevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
Related keywords: complex, band, Hermitian matrixdivide-and-conquer methodeigenproblemeigenvalueseigenvectorsleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithmZHBEVD
F08HSF   16  nagf_lapackeig_zhbtrd
Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
Related keywords: complex, band, Hermitian matrixeigenproblemleast squaresmatrix, bandunitary transformationsZHBTRD
F08JAF   21  nagf_lapackeig_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: DSTEVeigenproblemeigenvalueseigenvectorsleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JBF   21  nagf_lapackeig_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: bisection methodDSTEVXeigenproblemeigenvalueseigenvectorsleast squaresmatrix, band QR algorithmreal, symmetric, tridiagonal matrix
F08JCF   19  nagf_lapackeig_dstevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
Related keywords: divide-and-conquer methodDSTEVXeigenproblemeigenvalueseigenvectorsleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithmreal, symmetric, tridiagonal matrix
F08JDF   21  nagf_lapackeig_dstevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
Related keywords: dqds algorithmDSTEVReigenproblemeigenvalueseigenvectorsleast squaresmatrix, bandreal, symmetric, tridiagonal matrixrelatively robust representations
F08JEF   16  nagf_lapackeig_dsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit Q L or Q R algorithm
Related keywords: DSTEQReigenproblemeigenvalueseigenvectorsleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JFF   16  nagf_lapackeig_dsterf
Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the Q L or Q R algorithm
Related keywords: DSTERFeigenproblemeigenvalueseigenvectorsleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JGF   16  nagf_lapackeig_dpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
Related keywords: DPTEQReigenproblemeigenvalueseigenvectorsleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
F08JHF   22  nagf_lapackeig_dstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
Related keywords: divide-and-conquer methodDSTEDCeigenproblemeigenvalueseigenvectorsleast squaresmatrix, band QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JJF   16  nagf_lapackeig_dstebz
Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection
Related keywords: bisection methodDSTEBZeigenproblemeigenvaluesleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
F08JKF   16  nagf_lapackeig_dstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
Related keywords: DSTEINeigenproblemeigenvectorsinverse iterationleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
F08JLF   22  nagf_lapackeig_dstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
Related keywords: dqds algorithmDSTEGReigenproblemeigenvalueseigenvectorsleast squaresmatrix, bandreal, symmetric, tridiagonal matrixrelatively robust representations
F08JSF   16  nagf_lapackeig_zsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit Q L or Q R algorithm
Related keywords: eigenproblemeigenvalueseigenvectorsleast squares QR algorithmreal, symmetric, tridiagonal matrixZSTEQR
F08JUF   16  nagf_lapackeig_zpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
Related keywords: eigenproblemeigenvalueseigenvectors LDL H decompositionleast squaresreal, symmetric, tridiagonal matrixZPTEQR
F08JVF   22  nagf_lapackeig_zstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenvalueseigenvectorsleast squares QL algorithm QR algorithmreal, symmetric, tridiagonal matrixZSTEDC
F08JXF   16  nagf_lapackeig_zstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
Related keywords: eigenproblemeigenvectorsinverse iterationleast squaresmatrix, bandreal, symmetric, tridiagonal matrixZSTEIN
F08JYF   22  nagf_lapackeig_zstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
Related keywords: dqds algorithmeigenproblemeigenvalueseigenvectorsleast squaresmatrix, bandreal, symmetric, tridiagonal matrixrelatively robust representationsZSTEGR
F08KAF   21  nagf_lapackeig_dgelss
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
Related keywords: DGELSSeigenproblemleast squareslinear least squaresminimal least squaresreal, m by n matrixSVD, singular value decomposition
F08KBF   21  nagf_lapackeig_dgesvd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
Related keywords: DGESVDeigenproblemfinanceleast squaresreal, nonsymmetric matrixSVD, singular value decomposition
F08KCF   21  nagf_lapackeig_dgelsd
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
Related keywords: DGELSDdivide-and-conquer methodeigenproblemfinanceleast squareslinear least squaresminimal least squaresreal, m by n matrixSVD, singular value decomposition
F08KDF   21  nagf_lapackeig_dgesdd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
Related keywords: DGESDDdivide-and-conquer methodeigenproblemfinanceleast squaresreal, nonsymmetric matrixSVD, singular value decomposition
F08KEF   16  nagf_lapackeig_dgebrd
Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
Related keywords: DGEBRDeigenproblemleast squaresorthogonal transformationsreal, m by n matrix
F08KFF   16  nagf_lapackeig_dorgbr
Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF
Related keywords: DORGBReigenproblemleast squaresorthogonal matrix, generationorthogonal matrix, generationorthogonal transformations
F08KGF   16  nagf_lapackeig_dormbr
Applies the orthogonal transformations from reduction to bidiagonal form determined by F08KEF
Related keywords: DORMBReigenproblemleast squaresorthogonal transformations
F08KHF   23  nagf_lapackeig_dgejsv
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
Related keywords: DGEJSVeigenproblemJacobi methodleast squaresreal, nonsymmetric matrixsingular value decomposition
F08KJF   23  nagf_lapackeig_dgesvj
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
Related keywords: DGESVJeigenproblemJacobi methodleast squaresreal, nonsymmetric matrixsingular value decomposition
F08KNF   21  nagf_lapackeig_zgelss
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
Related keywords: complex, m by n matrixeigenproblemleast squareslinear least squaresminimal least squaresSVD, singular value decompositionZGELSS
F08KPF   21  nagf_lapackeig_zgesvd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
Related keywords: complex, nonsymmetric matrixeigenproblemfinanceleast squaresSVD, singular value decompositionZGESVD
F08KQF   21  nagf_lapackeig_zgelsd
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
Related keywords: complex, m by n matrixdivide-and-conquer methodeigenproblemleast squareslinear least squaresminimal least squaresSVD, singular value decompositionZGELSD
F08KRF   21  nagf_lapackeig_zgesdd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
Related keywords: complex, nonsymmetric matrixdivide-and-conquer methodeigenproblemleast squaresSVD, singular value decompositionZGESDD
F08KSF   16  nagf_lapackeig_zgebrd
Performs a unitary reduction of complex general rectangular matrix to bidiagonal form
Related keywords: complex, m by n matrixeigenproblemleast squaresunitary transformationsZGEBRD
F08KTF   16  nagf_lapackeig_zungbr
Generates unitary transformation matrices from the reduction to bidiagonal form determined by F08KSF
Related keywords: eigenproblemleast squaresunitary matrix, generationunitary transformationsZUNGBR
F08KUF   16  nagf_lapackeig_zunmbr
Applies the unitary transformations from reduction to bidiagonal form determined by F08KSF
Related keywords: eigenproblemleast squaresunitary transformationsZUNMBR
F08LEF   19  nagf_lapackeig_dgbbrd
Performs a reduction of real rectangular band matrix to upper bidiagonal form
Related keywords: DGBBRDeigenproblemGivens rotationsleast squaresmatrix, bandreal, band, m by n matrix
F08LSF   19  nagf_lapackeig_zgbbrd
Reduction of complex rectangular band matrix to upper bidiagonal form
Related keywords: eigenproblemGivens rotationsleast squaresmatrix, bandreal, band, m by n matrixZGBBRD
F08MDF   22  nagf_lapackeig_dbdsdc
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
Related keywords: DBDSDCdivide-and-conquer methodeigenproblemleast squaresmatrix, band QR algorithmreal, bidiagonal matrixSVD, singular value decomposition
F08MEF   16  nagf_lapackeig_dbdsqr
Performs an SVD of real bidiagonal matrix reduced from real general matrix
Related keywords: DBDSQRdifferential qd algorithmeigenproblemleast squaresmatrix, band QL algorithm QR algorithmreal, bidiagonal matrixSVD, singular value decomposition
F08MSF   16  nagf_lapackeig_zbdsqr
Performs an SVD of real bidiagonal matrix reduced from complex general matrix
Related keywords: differential qd algorithmeigenproblemleast squaresmatrix, band QL algorithm QR algorithmreal, bidiagonal matrixSVD, singular value decompositionZBDSQR
F08NAF   21  nagf_lapackeig_dgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
Related keywords: DGEEVeigenproblemeigenvalueseigenvectorsleast squaresorthogonal transformations QR algorithmreal, nonsymmetric matrix
F08NBF   21  nagf_lapackeig_dgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGEEVXeigenproblemeigenvalueseigenvectorsfinanceforward errorleast squaresorthogonal transformations QR algorithmreal, nonsymmetric matrix
F08NEF   16  nagf_lapackeig_dgehrd
Performs an orthogonal reduction of real general matrix to upper Hessenberg form
Related keywords: DGEHRDeigenproblemleast squaresorthogonal transformationsreal, nonsymmetric matrix
F08NFF   16  nagf_lapackeig_dorghr
Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF
Related keywords: DORGHReigenproblemleast squaresorthogonal matrix, generationorthogonal matrix, generation
F08NGF   16  nagf_lapackeig_dormhr
Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF
Related keywords: DORMHReigenproblemleast squaresorthogonal transformations
F08NHF   16  nagf_lapackeig_dgebal
Balances a real general matrix
Related keywords: balancingDGEBALeigenproblemleast squaresreal, nonsymmetric matrix
F08NJF   16  nagf_lapackeig_dgebak
Transforms eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF
Related keywords: balancingDGEBAKeigenproblemeigenvectorsleast squaresreal, nonsymmetric matrix
F08NNF   21  nagf_lapackeig_zgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
Related keywords: complex, nonsymmetric matrixDGEEVeigenproblemeigenvalueseigenvectorsleast squares
F08NPF   21  nagf_lapackeig_zgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixcondition number, matrixDGEEVeigenproblemeigenvalueseigenvectorsfinanceforward errorleast squares
F08NSF   16  nagf_lapackeig_zgehrd
Performs a unitary reduction of complex general matrix to upper Hessenberg form
Related keywords: complex, nonsymmetric matrixeigenproblemleast squaresunitary transformationsZGEHRD
F08NTF   16  nagf_lapackeig_zunghr
Generates a unitary transformation matrix from reduction to Hessenberg form determined by F08NSF
Related keywords: eigenproblemleast squaresunitary matrix, generationunitary matrix, generationZUNGHR
F08NUF   16  nagf_lapackeig_zunmhr
Applies the unitary transformation matrix from reduction to Hessenberg form determined by F08NSF
Related keywords: eigenproblemleast squaresunitary transformationsZUNMHR
F08NVF   16  nagf_lapackeig_zgebal
Balances a complex general matrix
Related keywords: balancingcomplex, nonsymmetric matrixeigenproblemleast squaresZGEBAL
F08NWF   16  nagf_lapackeig_zgebak
Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF
Related keywords: balancingcomplex, nonsymmetric matrixeigenproblemleast squaresZGEBAK
F08PAF   21  nagf_lapackeig_dgees
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
Related keywords: DGEESeigenproblemeigenvaluesleast squaresreal, nonsymmetric matrixSchur formSchur vectors
F08PBF   21  nagf_lapackeig_dgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: condition number, matrixDGEESeigenproblemeigenvaluesleast squaresreal, nonsymmetric matrixSchur formSchur vectors
F08PEF   16  nagf_lapackeig_dhseqr
Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
Related keywords: DHSEQReigenproblemeigenvaluesleast squaresreal, nonsymmetric matrixSchur form
F08PKF   16  nagf_lapackeig_dhsein
Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
Related keywords: DHSEINeigenproblemeigenvectorsinverse iterationleast squaresreal, Hessenberg matrix
F08PNF   21  nagf_lapackeig_zgees
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenvaluesleast squaresSchur formSchur vectorsZGEES
F08PPF   21  nagf_lapackeig_zgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also computes a reciprocal condition number for the average of the selected eigenvalues and for the right invariant subspace corresponding to these eigenvalues
Related keywords: condition number, matrixeigenproblemeigenvaluesleast squaresreal, nonsymmetric matrixSchur formSchur vectorsZGEESX
F08PSF   16  nagf_lapackeig_zhseqr
Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
Related keywords: complex, Hessenberg matrixeigenproblemeigenvaluesleast squaresSchur formZHSEQR
F08PXF   16  nagf_lapackeig_zhsein
Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
Related keywords: complex, Hessenberg matrixeigenproblemeigenvectorsinverse iterationleast squaresZHSEIN
F08QFF   16  nagf_lapackeig_dtrexc
Reorders a Schur factorization of real matrix using orthogonal similarity transformation
Related keywords: DTREXCeigenproblemleast squaresorthogonal transformationsreal, nonsymmetric matrixSchur form
F08QGF   16  nagf_lapackeig_dtrsen
Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
Related keywords: condition number, matrixDTREXCeigenproblemleast squaresorthogonal transformationsSchur form
F08QHF   16  nagf_lapackeig_dtrsyl
Solves the real Sylvester matrix equation A X + X B = C , A and B are upper quasi-triangular or transposes
Related keywords: DTRSYLeigenproblemleast squaresreal, quasi-triangular matrixSylvester equation
F08QKF   16  nagf_lapackeig_dtrevc
Computes left and right eigenvectors of real upper quasi-triangular matrix
Related keywords: DTREVCeigenproblemeigenvectorsleast squaresreal, quasi-triangular matrix
F08QLF   16  nagf_lapackeig_dtrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
Related keywords: condition number, matrixDTRSNAeigenproblemeigenvalueseigenvectorsleast squaresreal, quasi-triangular matrix
F08QTF   16  nagf_lapackeig_ztrexc
Reorders a Schur factorization of complex matrix using unitary similarity transformation
Related keywords: eigenproblemleast squaresSchur formunitary transformationsZTREXC
F08QUF   16  nagf_lapackeig_ztrsen
Reorders a Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
Related keywords: condition number, matrixeigenproblemleast squaresSchur formZTRSEN
F08QVF   16  nagf_lapackeig_ztrsyl
Solves the complex Sylvester matrix equation A X + X B = C , A and B are upper triangular or conjugate-transposes
Related keywords: complex, triangular matrixeigenproblemleast squaresSylvester equationZTRSYL
F08QXF   16  nagf_lapackeig_ztrevc
Computes left and right eigenvectors of complex upper triangular matrix
Related keywords: complex, triangular matrixeigenproblemeigenvectorsleast squaresZTREVC
F08QYF   16  nagf_lapackeig_ztrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
Related keywords: complex, triangular matrixcondition number, matrixDTRSNAeigenproblemeigenvalueseigenvectorsleast squares
F08RAF   25  nagf_lapackeig_dorcsd
Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
Related keywords: complete CS decompositionDORCSDeigenproblemGSVD, generalized singular value decompositionleast squaresreal, orthogonal matrix
F08RNF   25  nagf_lapackeig_zuncsd
Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices
Related keywords: complete CS decompositioncomplex, unitary matrixeigenproblemGSVD, generalized singular value decompositionleast squaresZUNCSD
F08SAF   21  nagf_lapackeig_dsygv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Related keywords: DSYGVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresreal, positive-definite, symmetric matrix
F08SBF   21  nagf_lapackeig_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Related keywords: DSYGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresreal, positive-definite, symmetric matrix
F08SCF   21  nagf_lapackeig_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodDSYGVDeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresreal, positive-definite, symmetric matrix
F08SEF   16  nagf_lapackeig_dsygst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , B factorized by F07FDF
Related keywords: DSYGSTeigenproblemeigenproblem, generalizedgeneralized eigenproblemleast squaresreal, positive-definite, symmetric matrix
F08SNF   21  nagf_lapackeig_zhegv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresZHEGV
F08SPF   21  nagf_lapackeig_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresZHEGVX
F08SQF   21  nagf_lapackeig_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: complex, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresZHEGVD
F08SSF   16  nagf_lapackeig_zhegst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , B factorized by F07FRF
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedgeneralized eigenproblemleast squaresZHEGST
F08TAF   21  nagf_lapackeig_dspgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Related keywords: DSPGVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresreal, positive-definite, symmetric matrix
F08TBF   21  nagf_lapackeig_dspgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Related keywords: DSPGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresreal, positive-definite, symmetric matrix
F08TCF   21  nagf_lapackeig_dspgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: divide-and-conquer methodDSPGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresreal, positive-definite, symmetric matrix
F08TEF   16  nagf_lapackeig_dspgst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , packed storage, B factorized by F07GDF
Related keywords: DSPGVXeigenproblemeigenproblem, generalizedgeneralized eigenproblemleast squaresreal, positive-definite, symmetric matrix
F08TNF   21  nagf_lapackeig_zhpgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresZHPGV
F08TPF   21  nagf_lapackeig_zhpgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresZHPGVX
F08TQF   21  nagf_lapackeig_zhpgvd
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: complex, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresZHPGVD
F08TSF   16  nagf_lapackeig_zhpgst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , packed storage, B factorized by F07GRF
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedgeneralized eigenproblemleast squaresZHPGVD
F08UAF   21  nagf_lapackeig_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: DSBGVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UBF   21  nagf_lapackeig_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: DSBGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UCF   21  nagf_lapackeig_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodDSBGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UEF   19  nagf_lapackeig_dsbgst
Performs a reduction of real symmetric-definite banded generalized eigenproblem A x = λ B x to standard form C y = λ y , such that C has the same bandwidth as A
Related keywords: DSBGSTeigenproblemeigenproblem, generalizedgeneralized eigenproblemleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UFF   19  nagf_lapackeig_dpbstf
Computes a split Cholesky factorization of real symmetric positive definite band matrix A
Related keywords: Cholesky decompositionDPBSTFDSBGSTeigenproblemeigenproblem, generalizedgeneralized eigenproblemleast squaresmatrix, bandreal, band, positive-definite, symmetric matrix
F08UNF   21  nagf_lapackeig_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresmatrix, bandZHBGV
F08UPF   21  nagf_lapackeig_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresmatrix, bandZHBGVX
F08UQF   21  nagf_lapackeig_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: complex, band, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresmatrix, bandZHBGVD
F08USF   19  nagf_lapackeig_zhbgst
Performs a reduction of complex Hermitian-definite banded generalized eigenproblem A x = λ B x to standard form C y = λ y , such that C has the same bandwidth as A
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedgeneralized eigenproblemleast squaresmatrix, bandZHBGST
F08UTF   19  nagf_lapackeig_zpbstf
Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedgeneralized eigenproblemleast squaresmatrix, bandSplit Cholesky factorizationZPBSTF
F08VAF   21  nagf_lapackeig_dggsvd
Computes the generalized singular value decomposition of a real matrix pair
Related keywords: DGGSVDeigenproblemGSVD, generalized singular value decompositionleast squaresreal, nonsymmetric matrixSVD, generalized
F08VCF   26  nagf_lapackeig_dggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair
Related keywords: DGGSVD3eigenproblemGSVD, generalized singular value decompositionleast squaresreal, nonsymmetric matrixSVD, generalized
F08VEF   22  nagf_lapackeig_dggsvp
Produces orthogonal matrices that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
Related keywords: DGGSVPeigenproblemGSVD, generalized singular value decompositionleast squaresorthogonal transformationsreal, m by n matrixSVD, generalized
F08VGF   26  nagf_lapackeig_dggsvp3
Produces orthogonal matrices, using BLAS-3, that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
Related keywords: DGGSVP3eigenproblemGSVD, generalized singular value decompositionleast squaresorthogonal transformationsreal, m by n matrixSVD, generalized
F08VNF   21  nagf_lapackeig_zggsvd
Computes the generalized singular value decomposition of a complex matrix pair
Related keywords: complex, nonsymmetric matrixeigenproblemGSVD, generalized singular value decompositionleast squaresSVD, generalizedZGGSVD
F08VQF   26  nagf_lapackeig_zggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair
Related keywords: complex, nonsymmetric matrixeigenproblemGSVD, generalized singular value decompositionleast squaresSVD, generalizedZGGSVD3
F08VSF   22  nagf_lapackeig_zggsvp
Produces unitary matrices that simultaneously reduce the complex, m by n , matrix A and the complex, p by n , matrix B to upper triangular form
Related keywords: complex, m by n matrixeigenproblemGSVD, generalized singular value decompositionleast squaresorthogonal transformationsSVD, generalizedZGGSVP
F08VUF   26  nagf_lapackeig_zggsvp3
Produces unitary matrices, using BLAS-3, that simultaneously reduce the complex, m by n , matrix A and the complex, p by n , matrix B to upper triangular form
Related keywords: complex, m by n matrixeigenproblemGSVD, generalized singular value decompositionleast squaresorthogonal transformationsSVD, generalizedZGGSVP3
F08WAF   21  nagf_lapackeig_dggev
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: DGGEVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresreal, nonsymmetric matrix
F08WBF   21  nagf_lapackeig_dggevx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGGEVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsfinanceforward errorgeneralized eigenproblemleast squaresreal, nonsymmetric matrix
F08WCF   26  nagf_lapackeig_dggev3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: DGGEVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresreal, nonsymmetric matrix
F08WEF   20  nagf_lapackeig_dgghrd
Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Related keywords: DGGHRDeigenproblemeigenproblem, generalizedgeneralized eigenproblemleast squaresorthogonal transformationsreal, nonsymmetric matrix
F08WFF   26  nagf_lapackeig_dgghd3
Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Related keywords: DGGHD3eigenproblemeigenproblem, generalizedgeneralized eigenproblemleast squaresorthogonal transformationsreal, nonsymmetric matrix
F08WHF   20  nagf_lapackeig_dggbal
Balances a pair of real, square, matrices
Related keywords: balancingDGGHRDeigenproblemeigenproblem, generalizedgeneralized eigenproblemleast squares
F08WJF   20  nagf_lapackeig_dggbak
Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF
Related keywords: balancingDGGBAKeigenproblemeigenproblem, generalizedeigenvectorsgeneralized eigenproblemleast squares
F08WNF   21  nagf_lapackeig_zggev
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresZGGEV
F08WPF   21  nagf_lapackeig_zggevx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixcondition number, matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsfinanceforward errorgeneralized eigenproblemleast squaresZGGEVX
F08WQF   26  nagf_lapackeig_zggev3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemleast squaresZGGEV3
F08WSF   20  nagf_lapackeig_zgghrd
Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
Related keywords: complex, nonsymmetric matrixeigenproblemleast squaresunitary transformationsZGGHRD
F08WTF   26  nagf_lapackeig_zgghd3
Performs, using BLAS-3, a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
Related keywords: complex, nonsymmetric matrixeigenproblemleast squaresunitary transformationsZGGHD3
F08WVF   20  nagf_lapackeig_zggbal
Balances a pair of complex, square, matrices
Related keywords: balancingcomplex, nonsymmetric matrixeigenproblemleast squaresZGGBAL
F08WWF   20  nagf_lapackeig_zggbak
Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF
Related keywords: balancingcomplex, nonsymmetric matrixeigenproblemeigenvectorsleast squaresZGGBAL
F08XAF   21  nagf_lapackeig_dgges
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: DGGESeigenproblemeigenvaluesgeneralized Schur formleast squaresreal, nonsymmetric matrixSchur form, generalizedSchur vectors
F08XBF   21  nagf_lapackeig_dggesx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: condition number, matrixDGGESXeigenproblemeigenvaluesgeneralized Schur formleast squaresreal, nonsymmetric matrixSchur form, generalizedSchur vectors
F08XCF   26  nagf_lapackeig_dgges3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: DGGES3eigenproblemeigenvaluesgeneralized Schur formleast squaresreal, nonsymmetric matrixSchur form, generalizedSchur vectors
F08XEF   20  nagf_lapackeig_dhgeqz
Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
Related keywords: DHGEQZeigenproblemeigenvaluesgeneralized Schur formleast squaresreal, Hessenberg matrix
F08XNF   21  nagf_lapackeig_zgges
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formleast squaresSchur vectorsZGGES
F08XPF   21  nagf_lapackeig_zggesx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formleast squaresSchur vectorsZGGES
F08XQF   26  nagf_lapackeig_zgges3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formleast squaresSchur vectorsZGGES3
F08XSF   20  nagf_lapackeig_zhgeqz
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formleast squaresQZ algorithmZHGEQZ
F08YEF   22  nagf_lapackeig_dtgsja
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
Related keywords: DTGSJAeigenproblemGSVD, generalized singular value decompositionleast squaresreal, trapezoidal matrixreal, triangular matrixSVD, generalized
F08YFF   22  nagf_lapackeig_dtgexc
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
Related keywords: DTGEXCeigenproblemgeneralized Schur formleast squaresorthogonal transformations
F08YGF   22  nagf_lapackeig_dtgsen
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Related keywords: condition number, matrixDTGSENeigenproblemeigenvaluesgeneralized Schur formleast squaresorthogonal transformationsreal, nonsymmetric matrix
F08YHF   22  nagf_lapackeig_dtgsyl
Solves the real-valued, generalized, quasi-trangular, Sylvester equation
Related keywords: DTGSYLeigenproblemleast squaresreal, quasi-triangular matrixSylvester equation
F08YKF   20  nagf_lapackeig_dtgevc
Computes right and left generalized eigenvectors of the matrix pair A , B which is assumed to be in generalized upper Schur form
Related keywords: DTGEVCeigenproblemeigenvectorsgeneralized Schur formleast squares
F08YLF   22  nagf_lapackeig_dtgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
Related keywords: condition number, matrixDTGSNAeigenproblemgeneralized Schur formleast squaresreal, nonsymmetric matrix
F08YSF   22  nagf_lapackeig_ztgsja
Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
Related keywords: complex, trapezoidal matrixcomplex, triangular matrixeigenproblemGSVD, generalized singular value decompositionleast squaresZTGSJA
F08YTF   22  nagf_lapackeig_ztgexc
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
Related keywords: complex, nonsymmetric matrixeigenproblemgeneralized Schur formleast squaresunitary transformationsZTGEXC
F08YUF   22  nagf_lapackeig_ztgsen
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemeigenvaluesgeneralized Schur formleast squaresunitary transformationsZTGEXC
F08YVF   22  nagf_lapackeig_ztgsyl
Solves the complex generalized Sylvester equation
Related keywords: complex, triangular matrixeigenproblemleast squaresSylvester equationZTGSYL
F08YXF   20  nagf_lapackeig_ztgevc
Computes left and right eigenvectors of a pair of complex upper triangular matrices
Related keywords: complex, triangular matrixeigenproblemeigenvectorsgeneralized Schur formleast squaresZTGEVC
F08YYF   22  nagf_lapackeig_ztgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemgeneralized Schur formleast squaresZTGSNA
F08ZAF   21  nagf_lapackeig_dgglse
Solves the real linear equality-constrained least squares (LSE) problem
Related keywords: DGGLSEeigenproblemleast squareslinear least squaresreal, m by n matrixRQ factorizations
F08ZBF   21  nagf_lapackeig_dggglm
Solves a real general Gauss–Markov linear model (GLM) problem
Related keywords: DGGGLMeigenproblemGauss–Markov linear modelleast squares QR factorizationreal, m by n matrix
F08ZEF   22  nagf_lapackeig_dggqrf
Computes a generalized Q R factorization of a real matrix pair
Related keywords: DGGQRFeigenproblemleast squares QR factorizationreal, m by n matrix
F08ZFF   22  nagf_lapackeig_dggrqf
Computes a generalized R Q factorization of a real matrix pair
Related keywords: DGGRQFeigenproblemleast squaresreal, m by n matrixRQ factorizations
F08ZNF   21  nagf_lapackeig_zgglse
Solves the complex linear equality-constrained least squares (LSE) problem
Related keywords: complex, m by n matrixeigenproblemleast squareslinear least squaresRQ factorizationsZGGLSE
F08ZPF   21  nagf_lapackeig_zggglm
Solves a complex general Gauss–Markov linear model (GLM) problem
Related keywords: complex, m by n matrixeigenproblemGauss–Markov linear modelleast squaresZGGGLM
F08ZSF   22  nagf_lapackeig_zggqrf
Computes a generalized Q R factorization of a complex matrix pair
Related keywords: complex, m by n matrixeigenproblemleast squares QR factorizationZGGQRF
F08ZTF   22  nagf_lapackeig_zggrqf
Computes a generalized R Q factorization of a complex matrix pair
Related keywords: complex, m by n matrixeigenproblemleast squaresRQ factorizationsZGGRQF
Laplace's equation D03EAF   nagf_pde_2d_laplace
Elliptic PDE, Laplace's equation, two-dimensional arbitrary domain
Related keywords: elliptic partial differential equationsPDE, partial differential equations
D03EBF   nagf_pde_2d_ellip_fd
Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, iterate to convergence
Related keywords: elliptic partial differential equationsPDE, partial differential equationsStone's strongly implicit procedure
D03ECF   nagf_pde_3d_ellip_fd
Elliptic PDE, solution of finite difference equations by SIP for seven-point three-dimensional molecule, iterate to convergence
Related keywords: cuboidelliptic partial differential equationsPDE, partial differential equationsStone's strongly implicit procedure
Laplace transform C06LAF   12  nagf_sum_invlaplace_crump
Inverse Laplace transform, Crump's method
Related keywords: Crump's methodinverse Laplace transformsummation of series
C06LBF   14  nagf_sum_invlaplace_weeks
Inverse Laplace transform, modified Weeks' method
Related keywords: inverse Laplace transformsummation of seriesWeeks method
large scale eigenproblems F02EKF   24  nagf_eigen_real_gen_sparse_arnoldi
Selected eigenvalues and eigenvectors of a real sparse general matrix
Related keywords: big datadata analyticseigenvalueseigenvectorsmatrix, sparsereal, sparse matrix
F02FKF   25  nagf_eigen_real_symm_sparse_arnoldi
Selected eigenvalues and eigenvectors of a real symmetric sparse matrix
Related keywords: big datadata analyticseigenproblemeigenvalueseigenvalueseigenvectorseigenvectorsmatrix, sparsereal, sparse, symmetric matrixsparse eigenproblem
F12 Chapter Introduction     Large Scale Eigenproblems
Related keywords: big datadata analytics
large scale linear systems F11 Chapter Introduction     Large Scale Linear Systems
Related keywords: big datadata analytics
largest floating-point number X02ALF   12  nagf_machine_real_largest
The largest positive model number
Related keywords: machine constants
largest integer X02BBF   nagf_machine_integer_max
The largest representable integer
Related keywords: machine constants
largest trigonometric function argument X02AHF   nagf_machine_sinarg_max
The largest permissible argument for sin and cos
Related keywords: machine constants
LARS G02MAF   25  nagf_correg_lars
Least angle regression (LARS), least absolute shrinkage and selection operator (LASSO) and forward stagewise regression
Related keywords: big datacorrelation analysisdata analyticsforward stagewiseLASSOleast angle regressionmodel selectionnonlinear regressionpolynomial regressionregression analysis
G02MBF   25  nagf_correg_lars_xtx
Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) and forward stagewise regression using the cross-products matrix
Related keywords: big datacorrelation analysiscross-productdata analyticsforward stagewiseLASSOleast angle regressionmodel selectionnonlinear regressionpolynomial regressionregression analysis
G02MCF   25  nagf_correg_lars_param
Calculates additional parameter estimates following Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) or forward stagewise regression
Related keywords: big datacorrelation analysisdata analyticsforward stagewiseLASSOleast angle regressionnonlinear regressionpolynomial regressionregression analysis
LASSO G02MAF   25  nagf_correg_lars
Least angle regression (LARS), least absolute shrinkage and selection operator (LASSO) and forward stagewise regression
Related keywords: big datacorrelation analysisdata analyticsforward stagewiseLARSleast angle regressionmodel selectionnonlinear regressionpolynomial regressionregression analysis
G02MBF   25  nagf_correg_lars_xtx
Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) and forward stagewise regression using the cross-products matrix
Related keywords: big datacorrelation analysiscross-productdata analyticsforward stagewiseLARSleast angle regressionmodel selectionnonlinear regressionpolynomial regressionregression analysis
G02MCF   25  nagf_correg_lars_param
Calculates additional parameter estimates following Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) or forward stagewise regression
Related keywords: big datacorrelation analysisdata analyticsforward stagewiseLARSleast angle regressionnonlinear regressionpolynomial regressionregression analysis
latent variable model G11SAF   12  nagf_contab_binary
Contingency table, latent variable model for binary data
Related keywords: contingency table analysisfactor scoresscore patternstheta scores
LDL T decomposition F01MCF   nagf_matop_real_vband_posdef_fac
L D L T factorization of real symmetric positive definite variable-bandwidth matrix
Related keywords: inversionmatrix, bandmatrix operationsreal, band, positive-definite, symmetric matrix
F07MNF   21  nagf_lapacklin_zhesv
Computes the solution to a complex Hermitian system of linear equations
Related keywords: complex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACKlinear equations UDU H decompositionZHESV
F07MPF   21  nagf_lapacklin_zhesvx
Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations
Related keywords: backward errorcomplex, Hermitian, indefinite matrixdiagonal pivoting methodforward errorLAPACKlinear equations UDU H decompositionZHESVX
F07NNF   21  nagf_lapacklin_zsysv
Computes the solution to a complex symmetric system of linear equations
Related keywords: complex, symmetric matrixdiagonal pivoting methodLAPACKlinear equations UDU H decompositionZSYSV
F07NPF   21  nagf_lapacklin_zsysvx
Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations
Related keywords: backward errorcomplex, symmetric matrixdiagonal pivoting methodforward errorLAPACKlinear equations UDU H decompositionZSYSVX
F07PAF   21  nagf_lapacklin_dspsv
Computes the solution to a real symmetric system of linear equations, packed storage
Related keywords: diagonal pivoting methodDSPSVLAPACKlinear equationsreal, indefinite, symmetric matrix UDU T decomposition
F07PBF   21  nagf_lapacklin_dspsvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage. Error bounds and a condition estimate are also computed
Related keywords: backward errorcondition number, matrixdiagonal pivoting methodDSPSVXerror bound, matrixforward errorLAPACKlinear equationsreal, indefinite, symmetric matrix UDU H decomposition
F07PNF   21  nagf_lapacklin_zhpsv
Computes the solution to a complex Hermitian system of linear equations, packed storage
Related keywords: complex, Hermitian, indefinite matrixdiagonal pivoting methodinverse, matrixLAPACKlinear equations UDU H decompositionZHPSV
F07PPF   21  nagf_lapacklin_zhpsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, Hermitian, system of linear equations, error bounds and condition estimates. Packed storage
Related keywords: backward errorcomplex, Hermitian, indefinite matrixdiagonal pivoting methodforward errorinverse, matrixLAPACKlinear equations UDU H decompositionZHPSVX
F07QNF   21  nagf_lapacklin_zspsv
Computes the solution to a complex symmetric system of linear equations, packed storage
Related keywords: complex, symmetric matrixdiagonal pivoting methodLAPACKlinear equations UDU T decompositionZSPSV
F07QPF   21  nagf_lapacklin_zspsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, symmetric, system of linear equations, error bounds and condition estimates. Packed storage
Related keywords: backward errorcomplex, symmetric matrixdiagonal pivoting methodforward errorLAPACKlinear equations UDU T decompositionZSPSVX
F08JUF   16  nagf_lapackeig_zpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, symmetric, tridiagonal matrixZPTEQR
LDLT decomposition F07MAF   21  nagf_lapacklin_dsysv
Computes the solution to a real symmetric system of linear equations
Related keywords: diagonal pivoting methodDSYSVLAPACKlinear equationsreal, indefinite, symmetric matrix UDU T decompositiuon
F07MBF   21  nagf_lapacklin_dsysvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations
Related keywords: backward errordiagonal pivoting methodDSYSVXforward errorLAPACKlinear equationsreal, indefinite, symmetric matrix UDU T decompositiuon
least angle regression G02MAF   25  nagf_correg_lars
Least angle regression (LARS), least absolute shrinkage and selection operator (LASSO) and forward stagewise regression
Related keywords: big datacorrelation analysisdata analyticsforward stagewiseLARSLASSOmodel selectionnonlinear regressionpolynomial regressionregression analysis
G02MBF   25  nagf_correg_lars_xtx
Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) and forward stagewise regression using the cross-products matrix
Related keywords: big datacorrelation analysiscross-productdata analyticsforward stagewiseLARSLASSOmodel selectionnonlinear regressionpolynomial regressionregression analysis
G02MCF   25  nagf_correg_lars_param
Calculates additional parameter estimates following Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) or forward stagewise regression
Related keywords: big datacorrelation analysisdata analyticsforward stagewiseLARSLASSOnonlinear regressionpolynomial regressionregression analysis
least squares E02ADF   nagf_fit_1dcheb_arb
Least squares curve fit, by polynomials, arbitrary data points
Related keywords: curve and surface fittingpolynomial approximation
E02AFF   nagf_fit_1dcheb_glp
Least squares polynomial fit, special data points (including interpolation)
Related keywords: curve and surface fittingpolynomial approximation
E02AGF   nagf_fit_1dcheb_con
Least squares polynomial fit, values and derivatives may be constrained, arbitrary data points
Related keywords: curve and surface fittingpolynomial approximation
E02BAF   nagf_fit_1dspline_knots
Least squares curve cubic spline fit (including interpolation)
Related keywords: B-splinescubic splinescurve and surface fittingknots
E02BEF   13  nagf_fit_1dspline_auto
Least squares cubic spline curve fit, automatic knot placement
Related keywords: B-splinescubic splinescurve and surface fittingsmoothing
E02CAF   nagf_fit_2dcheb_lines
Least squares surface fit by polynomials, data on lines parallel to one independent coordinate axis
Related keywords: bivariate polynomial approximationChebyshev polynomial approximationcurve and surface fittingdata-on-lines polynomial approximationpolynomial approximationtwo-dimensional polynomial approximation
E02DAF   nagf_fit_2dspline_panel
Least squares surface fit, bicubic splines
Related keywords: bicubic splinesB-splinescurve and surface fittingknotstwo-dimensional spline approximation
E02DCF   13  nagf_fit_2dspline_grid
Least squares surface fit by bicubic splines with automatic knot placement, data on rectangular grid
Related keywords: bicubic splinesB-splinescurve and surface fittingsmoothingtwo-dimensional spline approximation
E02DDF   13  nagf_fit_2dspline_sctr
Least squares surface fit by bicubic splines with automatic knot placement, scattered data
Related keywords: bicubic splinesB-splinescurve and surface fittingscattered datasmoothing
E04NCF   12  nagf_opt_lsq_lincon_solve_old
Linear programming (LP) convex quadratic programming (QP) or linearly-constrained linear least squares problem, dense
Related keywords: active-setconvex optimizationdata fittingfinancemaximizing a functionminimizing a functionnonlinear least squaresoptimizationQP, quadratic programming
E04NDF   12  nagf_opt_lsq_lincon_option_file_old
Supply values for E04NCF from external file
Related keywords: convex optimizationmaximizing a functionminimizing a functionoptimizationoptions, computationalQP, quadratic programming
E04NEF   12  nagf_opt_lsq_lincon_option_string_old
Supply values to E04NCF from a character string
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalQP, quadratic programming
F04QAF   11  nagf_linsys_real_gen_sparse_lsqsol
Sparse linear least squares problem, m real equations in n unknowns
Related keywords: big datadata analyticsmatrix, sparsereal, m by n matrixregressionridgesimultaneous linear equations
F04YAF   11  nagf_linsys_real_gen_lsq_covmat
Covariance matrix for linear least squares problems, m real equations in n unknowns
Related keywords: big datacovariance matrixdata analyticsreal, m by n matrixsimultaneous linear equations
F08 Chapter Introduction     Least Squares and Eigenvalue Problems (LAPACK)
Related keywords: eigenproblemLAPACK
least squares fitting E04RAF   26  nagf_opt_handle_init
Initialization of a handle for the NAG optimization modelling suite for problems, such as, linear programming (LP), quadratic programming (QP), nonlinear programming (NLP), least squares (LSQ) problems, linear semidefinite programming (SDP) or SDP with bilinear matrix inequalities (BMI-SDP)
Related keywords: initializationmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationSDPsemidefinite programming
E04RDF   26  nagf_opt_sdp_read_sdpa
A reader of sparse SDPA data files for linear SDP problems
Related keywords: linear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationSDPsemidefinite programmingservice routine
E04REF   26  nagf_opt_handle_set_linobj
Define a linear objective function to a problem initialized by E04RAF
Related keywords: maximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04RFF   26  nagf_opt_handle_set_quadobj
Define a linear or a quadratic objective function to a problem initialized by E04RAF
Related keywords: maximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationQP
E04RGF   26  nagf_opt_handle_set_nlnobj
Define a nonlinear objective function to a problem initialized by E04RAF
Related keywords: maximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPoptimizationoptimization
E04RHF   26  nagf_opt_handle_set_simplebounds
Define bounds of variables of a problem initialized by E04RAF
Related keywords: bound boxmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04RJF   26  nagf_opt_handle_set_linconstr
Define a block of linear constraints to a problem initialized by E04RAF
Related keywords: linearly-constrainedmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04RKF   26  nagf_opt_handle_set_nlnconstr
Define a block of nonlinear constraints to a problem initialized by E04RAF
Related keywords: maximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinearly-constrainedoptimizationoptimization
E04RLF   26  nagf_opt_handle_set_nlnhess
Define a structure of Hessian of the objective, constraints or the Lagrangian to a problem initialized by E04RAF
Related keywords: maximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPoptimizationoptimization
E04RMF   26  nagf_opt_handle_set_nlnls
Define a nonlinear least squares objective function to a problem initialized by E04RAF
Related keywords: calibrationdata fittingderivative-free optimizationDFOmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinear least squaresoptimizationoptimizationoptimizationsum of squares
E04RNF   26  nagf_opt_handle_set_linmatineq
Add one or more linear matrix inequality constraints to a problem initialized by E04RAF
Related keywords: linear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04RPF   26  nagf_opt_handle_set_quadmatineq
Define bilinear matrix terms to a problem initialized by E04RAF
Related keywords: bilinear matrix inequalityBMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04RZF   26  nagf_opt_handle_free
Destroy the problem handle initialized by E04RAF and deallocate all the memory used
Related keywords: freemaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04STF   26  nagf_opt_handle_solve_ipopt
Run an interior point solver on a sparse nonlinear programming problem (NLP) initialized by E04RAF and defined by other routines from the suite
Related keywords: interior point methodIPMmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinear programmingoptimizationoptimization
E04SVF   26  nagf_opt_handle_solve_pennon
Run the Pennon solver on a compatible problem initialized by E04RAF and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI)
Related keywords: bilinear matrix inequalityBMIgeneralized augmented Lagrangian methodLagrangianlinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionmonitoring informationoptimizationoptimizationSDPsemidefinite programming
E04ZMF   26  nagf_opt_handle_opt_set
Option setting routine for the solvers from the NAG optimization modelling suite
Related keywords: maximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04ZNF   26  nagf_opt_handle_opt_get
Option getting routine for the solvers from the NAG optimization modelling suite
Related keywords: maximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
leave-one-out G05PVF   25  nagf_rand_kfold_xyw
Permutes a matrix, vector, vector triplet into a form suitable for K -fold cross validation
Related keywords: big datacross-validationCVdata analyticsjacknifek-foldLOOpermuterandom number generators
Legendre functions S22AAF   20  nagf_specfun_legendre_p
Legendre functions of 1st kind P n m x or P n m ¯ x
Related keywords: approximations of special functionsfinance
library details A00AAF   18  nagf_info_impl_details
Library identification, details of implementation and mark
Related keywords: identificationimplementation detailslibrary identificationmark
A00ADF   22  nagf_info_impl_details_separate
Library identification, details of implementation, major and minor marks
Related keywords: identificationimplementation detailslibrary identificationmark
library identification A00 Chapter Introduction     Library Identification
licence, availability check A00ACF   21  nagf_info_licence
Check availability of a valid licence key
Related keywords: library identification
linear algebra support routines F06 Chapter Introduction     Linear Algebra Support Routines
Related keywords: BLAS
linear algebra support routines; F06WAF   23  nagf_blas_dlansf
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format
Related keywords: 1-normBLASBLASblas, real matricesdlansfFrobenius norminfinity-normlinear algebra support routinesreal, symmetric matrix
F06WBF   23  nagf_blas_dtfsm
Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix, Rectangular Full Packed format
Related keywords: BLASBLASblas, real matricesdtfsmlinear algebra support routineslinear equationsreal, triangular matrix
F06WNF   23  nagf_blas_zlanhf
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format
Related keywords: 1-normBLASBLASblas, complex matricescomplex, Hermitian matrixFrobenius norminfinity-normlinear algebra support routineszlanhf
F06WPF   23  nagf_blas_ztfsm
Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix, Rectangular Full Packed format
Related keywords: BLASBLASblas, complex matricescomplex, triangular matrixlinear algebra support routineslinear equationsztfsm
linear equations F04AXF   nagf_linsys_real_sparse_fac_solve
Solution of real sparse simultaneous linear equations (coefficient matrix already factorized)
Related keywords: big datadata analyticsmatrix, sparsereal, sparse matrixsimultaneous linear equations
F04BAF   21  nagf_linsys_real_square_solve
Computes the solution, estimated condition number and error-bound to a real system of linear equations
Related keywords: big datadata analyticsforward errorreal, nonsymmetric matrixsimultaneous linear equations
F04BBF   21  nagf_linsys_real_band_solve
Computes the solution, estimated condition number and error-bound to a real banded system of linear equations
Related keywords: big datadata analyticsforward errormatrix, bandreal, band matrixsimultaneous linear equations
F04BCF   21  nagf_linsys_real_tridiag_solve
Computes the solution, estimated condition number and error-bound to a real tridiagonal system of linear equations
Related keywords: big datadata analyticsforward errormatrix, bandreal, tridiagonal matrixsimultaneous linear equations
F04BDF   21  nagf_linsys_real_posdef_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite system of linear equations
Related keywords: big datadata analyticsforward errorreal, positive-definite, symmetric matrixsimultaneous linear equations
F04BEF   21  nagf_linsys_real_posdef_packed_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite system of linear equations, packed storage
Related keywords: big datadata analyticsforward errorreal, positive-definite, symmetric matrixsimultaneous linear equations
F04BFF   21  nagf_linsys_real_posdef_band_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite banded system of linear equations
Related keywords: big datadata analyticsforward errorreal, band, positive-definite, symmetric matrixsimultaneous linear equations
F04BGF   21  nagf_linsys_real_posdef_tridiag_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite tridiagonal system of linear equations
Related keywords: big datadata analyticsforward errorreal, positive-definite, symmetric, tridiagonal matrixsimultaneous linear equations
F04BHF   21  nagf_linsys_real_symm_solve
Computes the solution, estimated condition number and error-bound to a real symmetric system of linear equations
Related keywords: big datadata analyticsforward errorreal, indefinite, symmetric matrixsimultaneous linear equations
F04BJF   21  nagf_linsys_real_symm_packed_solve
Computes the solution, estimated condition number and error-bound to a real symmetric system of linear equations, packed storage
Related keywords: big datadata analyticsforward errorreal, indefinite, symmetric matrixsimultaneous linear equations
F04CAF   21  nagf_linsys_complex_square_solve
Computes the solution, estimated condition number and error-bound to a complex system of linear equations
Related keywords: big datacomplex, nonsymmetric matrixdata analyticsforward errorsimultaneous linear equations
F04CBF   21  nagf_linsys_complex_band_solve
Computes the solution, estimated condition number and error-bound to a complex banded system of linear equations
Related keywords: big datacomplex, band matrixdata analyticsforward errormatrix, bandsimultaneous linear equations
F04CCF   21  nagf_linsys_complex_tridiag_solve
Computes the solution, estimated condition number and error-bound to a complex tridiagonal system of linear equations
Related keywords: big datacomplex, tridiagonal matrixdata analyticsforward errormatrix, bandsimultaneous linear equations
F04CDF   21  nagf_linsys_complex_posdef_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite system of linear equations
Related keywords: big datacomplex, Hermitian, positive-definite matrixdata analyticsforward errorsimultaneous linear equations
F04CEF   21  nagf_linsys_complex_posdef_packed_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite system of linear equations, packed storage
Related keywords: big datacomplex, Hermitian, positive-definite matrixdata analyticsforward errorsimultaneous linear equations
F04CFF   21  nagf_linsys_complex_posdef_band_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite banded system of linear equations
Related keywords: big datacomplex, band, Hermitian, positive-definite matrixdata analyticsforward errormatrix, bandsimultaneous linear equations
F04CGF   21  nagf_linsys_complex_posdef_tridiag_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: big datacomplex, Hermitian, positive-definite, tridiagonal matrixdata analyticsforward errormatrix, bandsimultaneous linear equations
F04CHF   21  nagf_linsys_complex_herm_solve
Computes the solution and error-bound to a complex Hermitian system of linear equations
Related keywords: big datacomplex, Hermitian, indefinite matrixdata analyticsforward errorsimultaneous linear equations
F04CJF   21  nagf_linsys_complex_herm_packed_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian system of linear equations, packed storage
Related keywords: big datacomplex, Hermitian, indefinite matrixdata analyticsforward errorsimultaneous linear equations
F04DHF   21  nagf_linsys_complex_symm_solve
Computes the solution, estimated condition number and error-bound to a complex symmetric system of linear equations
Related keywords: big datacomplex, symmetric matrixdata analyticsforward errorsimultaneous linear equations
F04DJF   21  nagf_linsys_complex_symm_packed_solve
Computes the solution, estimated condition number and error-bound to a complex symmetric system of linear equations, packed storage
Related keywords: big datacomplex, symmetric matrixdata analyticsforward errorsimultaneous linear equations
F04LEF   11  nagf_linsys_real_tridiag_fac_solve
Solution of real tridiagonal simultaneous linear equations (coefficient matrix already factorized by F01LEF)
Related keywords: big datadata analyticsmatrix, bandreal, tridiagonal matrixsimultaneous linear equations
F04LHF   13  nagf_linsys_real_blkdiag_fac_solve
Solution of real almost block diagonal simultaneous linear equations (coefficient matrix already factorized by F01LHF)
Related keywords: big datadata analyticsreal, almost block-diagonal matrixsimultaneous linear equations
F04MCF   nagf_linsys_real_posdef_vband_solve
Solution of real symmetric positive definite variable-bandwidth simultaneous linear equations (coefficient matrix already factorized by F01MCF)
Related keywords: big datadata analyticsmatrix, bandreal, band, positive-definite, symmetric matrixsimultaneous linear equations
F06PJF   12  nagf_blas_dtrsv
System of equations, real triangular matrix
Related keywords: BLASblas, real matricesdtrsvfinancelinear algebra support routinesreal, triangular matrix
F06PKF   12  nagf_blas_dtbsv
System of equations, real triangular band matrix
Related keywords: BLASblas, real matricesdtbsvlinear algebra support routinesmatrix, bandreal, band, triangular matrix
F06PLF   12  nagf_blas_dtpsv
System of equations, real triangular packed matrix
Related keywords: BLASblas, real matricesdtpsvlinear algebra support routinesreal, triangular matrix
F06SJF   12  nagf_blas_ztrsv
System of equations, complex triangular matrix
Related keywords: BLASblas, complex matricescomplex, triangular matrixlinear algebra support routinesztrsv
F06SKF   12  nagf_blas_ztbsv
System of equations, complex triangular band matrix
Related keywords: BLASblas, complex matricescomplex, band, triangular matrixlinear algebra support routinesmatrix, bandztbsv
F06SLF   12  nagf_blas_ztpsv
System of equations, complex triangular packed matrix
Related keywords: BLASblas, complex matricescomplex, triangular matrixlinear algebra support routinesztbsv
F06WBF   23  nagf_blas_dtfsm
Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix, Rectangular Full Packed format
Related keywords: BLASBLASblas, real matricesdtfsmlinear algebra support routineslinear algebra support routines;real, triangular matrix
F06WPF   23  nagf_blas_ztfsm
Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix, Rectangular Full Packed format
Related keywords: BLASBLASblas, complex matricescomplex, triangular matrixlinear algebra support routineslinear algebra support routines;ztfsm
F06YJF   14  nagf_blas_dtrsm
Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix
Related keywords: BLASblas, real matricesfinancelinear algebra support routinesreal, triangular matrix
F07 Chapter Introduction     Linear Equations (LAPACK)
Related keywords: LAPACK
F11MFF   21  nagf_sparse_direct_real_gen_solve
Solution of real sparse simultaneous linear equations (coefficient matrix already factorized)
Related keywords: big datadata analyticsdiscretised systemlarge scale linear systemsreal, sparse matrixsparse linear system
F11MHF   21  nagf_sparse_direct_real_gen_refine
Refined solution with error bounds of real system of linear equations, multiple right-hand sides
Related keywords: backward errorbig datadata analyticsforward errorlarge scale linear systemsreal, sparse matrix
F11MMF   21  nagf_sparse_direct_real_gen_diag
Real sparse nonsymmetric linear systems, diagnostic for F11MEF
Related keywords: big datadata analyticslarge scale linear systemsreal, sparse matrix
linear equations, direct method, setup F11MDF   21  nagf_sparse_direct_real_gen_setup
Real sparse nonsymmetric linear systems, setup for F11MEF
Related keywords: big datadata analyticslarge scale linear systemsreal, sparse matrix
linear equations, iterative method F11BEF   19  nagf_sparse_real_gen_basic_solver
Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationslarge scale linear systemsreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11BSF   19  nagf_sparse_complex_gen_basic_solver
Complex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsiterative methods, linear equationslarge scale linear systemsRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DBF   18  nagf_sparse_real_gen_precon_ilu_solve
Solution of linear system involving incomplete L U preconditioning matrix generated by F11DAF
Related keywords: big datadata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemsreal, sparse matrix
F11DCF   18  nagf_sparse_real_gen_solve_ilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DAF
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemsreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DEF   18  nagf_sparse_real_gen_solve_jacssor
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsJacobi preconditioninglarge scale linear systemsreal, sparse matrixRGMRES, restarted generalized minimum residual methodSSOR method, symmetric successive over-relaxationTFQMR, transpose-free quasi-minimal residual method
F11DGF   24  nagf_sparse_real_gen_solve_bdilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DFF
Related keywords: additive Schwarz preconditionerBi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemsreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DPF   19  nagf_sparse_complex_gen_precon_ilu_solve
Solution of complex linear system involving incomplete L U preconditioning matrix generated by F11DNF
Related keywords: big datacomplex, sparse matrixdata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systems
F11DQF   19  nagf_sparse_complex_gen_solve_ilu
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DNF (Black Box)
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemsRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DSF   19  nagf_sparse_complex_gen_solve_jacssor
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsiterative methods, linear equationsJacobi preconditioninglarge scale linear systemsRGMRES, restarted generalized minimum residual methodSSOR method, symmetric successive over-relaxationTFQMR, transpose-free quasi-minimal residual method
F11DUF   24  nagf_sparse_complex_gen_solve_bdilu
Solution of complex, sparse, non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DTF
Related keywords: additive Schwarz preconditionerBi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemsRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11GEF   20  nagf_sparse_real_symm_basic_solver
Real sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos method or the MINRES algorithm
Related keywords: big dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemsMINRES, iterative linear equation solverreal, sparse, symmetric matrix
F11GSF   20  nagf_sparse_complex_herm_basic_solver
Complex sparse Hermitian linear systems, preconditioned conjugate gradient or Lanczos
Related keywords: big dataCGS, conjugate gradient methodcomplex, Hermitian, sparse matrixdata analyticsiterative methods, linear equationsLanczos method, linear equationslarge scale linear systems
F11JBF   17  nagf_sparse_real_symm_precon_ichol_solve
Solution of linear system involving incomplete Cholesky preconditioning matrix generated by F11JAF
Related keywords: big datadata analyticsincomplete Cholesky factorizationiterative methods, linear equationslarge scale linear systemsreal, sparse, symmetric matrix
F11JCF   17  nagf_sparse_real_symm_solve_ichol
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JAF (Black Box)
Related keywords: big dataCGS, conjugate gradient methoddata analyticsincomplete Cholesky factorizationiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemsreal, sparse, symmetric matrix
F11JEF   17  nagf_sparse_real_symm_solve_jacssor
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsJacobi preconditioningLanczos method, linear equationslarge scale linear systemsreal, sparse, symmetric matrixSSOR method, symmetric successive over-relaxation
F11JQF   19  nagf_sparse_complex_herm_solve_ilu
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JNF (Black Box)
Related keywords: big datacomplex, Hermitian, sparse matrixconjugate gradient methoddata analyticsiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemssparse linear equations
F11JRF   19  nagf_sparse_complex_herm_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse Hermitian matrix
Related keywords: big datacomplex, Hermitian, sparse matrixdata analyticsiterative methods, linear equationslarge scale linear systemssparse linear equationsSSOR method, symmetric successive over-relaxation
F11JSF   19  nagf_sparse_complex_herm_solve_jacssor
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big datacomplex, Hermitian, sparse matrixconjugate gradient methoddata analyticsiterative methods, linear equationsJacobi methodLanczos method, linear equationslarge scale linear systemssparse linear equationsSSOR method, symmetric successive over-relaxation
linear equations, iterative method, diagnostic F11BFF   19  nagf_sparse_real_gen_basic_diag
Real sparse nonsymmetric linear systems, diagnostic for F11BEF
Related keywords: big datadata analyticslarge scale linear systemsreal, sparse matrix
F11BTF   19  nagf_sparse_complex_gen_basic_diag
Complex sparse non-Hermitian linear systems, diagnostic for F11BSF
Related keywords: big datacomplex, sparse matrixdata analyticslarge scale linear systems
F11GFF   20  nagf_sparse_real_symm_basic_diag
Real sparse symmetric linear systems, diagnostic for F11GEF
Related keywords: big datadata analyticslarge scale linear systemsreal, sparse, symmetric matrix
F11GTF   20  nagf_sparse_complex_herm_basic_diag
Complex sparse Hermitian linear systems, diagnostic for F11GSF
Related keywords: big datacomplex, Hermitian, sparse matrixdata analyticslarge scale linear systems
linear equations, iterative method, setup F11BDF   19  nagf_sparse_real_gen_basic_setup
Real sparse nonsymmetric linear systems, setup for F11BEF
Related keywords: big datadata analyticslarge scale linear systemsreal, sparse matrix
F11BRF   19  nagf_sparse_complex_gen_basic_setup
Complex sparse non-Hermitian linear systems, setup for F11BSF
Related keywords: big datacomplex, sparse matrixdata analyticslarge scale linear systems
F11GDF   20  nagf_sparse_real_symm_basic_setup
Real sparse symmetric linear systems, setup for F11GEF
Related keywords: big datadata analyticslarge scale linear systemsreal, sparse, symmetric matrix
F11GRF   20  nagf_sparse_complex_herm_basic_setup
Complex sparse Hermitian linear systems, setup for F11GSF
Related keywords: big datacomplex, Hermitian, sparse matrixdata analyticslarge scale linear systems
linear equations, overdetermined F04AMF   nagf_linsys_real_gen_lsqsol
Least squares solution of m real equations in n unknowns, rank = n , m n using iterative refinement (Black Box)
Related keywords: big datadata analyticslinear least squaresreal, m by n matrixsimultaneous linear equations
F04JGF   nagf_linsys_real_gen_solve
Least squares (if rank = n ) or minimal least squares (if rank < n ) solution of m real equations in n unknowns, m n
Related keywords: big datadata analyticslinear least squaresreal, m by n matrixsimultaneous linear equations
linear equations, pre-conditioners F11DAF   18  nagf_sparse_real_gen_precon_ilu
Real sparse nonsymmetric linear systems, incomplete L U factorization
Related keywords: big datadata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemsreal, sparse matrix
F11DDF   18  nagf_sparse_real_gen_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse nonsymmetric matrix
Related keywords: big datadata analyticslarge scale linear systemsreal, sparse matrixSSOR method, successive over-relaxation
F11DFF   24  nagf_sparse_real_gen_precon_bdilu
Real sparse nonsymmetric linear system, incomplete L U factorization of local or overlapping diagonal blocks
Related keywords: additive Schwarz preconditionerbig datadata analyticsincomplete L U factorizationlarge scale linear systemsreal, sparse matrix
F11DKF   20  nagf_sparse_real_gen_precon_jacobi
Real, sparse, symmetric or nonsymmetric, linear systems, line Jacobi preconditioner
Related keywords: big datadata analyticsJacobi preconditioninglarge scale linear systemsreal, sparse, symmetric matrixreal, sparse matrix
F11DNF   19  nagf_sparse_complex_gen_precon_ilu
Complex sparse non-Hermitian linear systems, incomplete L U factorization
Related keywords: big datacomplex, sparse matrixdata analyticsincomplete L U factorizationlarge scale linear systems
F11DRF   19  nagf_sparse_complex_gen_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse non-Hermitian matrix
Related keywords: big datacomplex, sparse matrixdata analyticslarge scale linear systemsSSOR method, symmetric successive over-relaxation
F11DTF   24  nagf_sparse_complex_gen_precon_bdilu
Complex, sparse, non-Hermitian linear system, incomplete L U factorization of local or overlapping diagonal blocks
Related keywords: additive Schwarz preconditionerbig datacomplex, sparse matrixdata analyticsincomplete L U factorizationlarge scale linear systems
F11DXF   20  nagf_sparse_complex_gen_precon_jacobi
Complex, sparse, Hermitian or non-Hermitian, linear systems, line Jacobi preconditioner
Related keywords: big datacomplex, sparse matrixdata analyticsJacobi preconditioninglarge scale linear systems
F11JAF   17  nagf_sparse_real_symm_precon_ichol
Real sparse symmetric matrix, incomplete Cholesky factorization
Related keywords: big datadata analyticsincomplete Cholesky factorizationlarge scale linear systemsreal, sparse, symmetric matrix
F11JDF   17  nagf_sparse_real_symm_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse symmetric matrix
Related keywords: big datadata analyticslarge scale linear systemsreal, sparse, symmetric matrixSSOR method, symmetric successive over-relaxation
F11JPF   19  nagf_sparse_complex_herm_precon_ilu_solve
Solution of complex linear system involving incomplete Cholesky preconditioning matrix generated by F11JNF
Related keywords: big datacomplex, Hermitian, sparse matrixdata analyticsincomplete Cholesky factorizationlarge scale linear systems
Linear Holt G13AMF   22  nagf_tsa_uni_smooth_exp
Univariate time series, exponential smoothing
Related keywords: big dataBrowns Exponentialdata analyticsexponential smoothingfinanceHolt Wintertime seriestime series analysisunivariate time series
linear least squares F04AMF   nagf_linsys_real_gen_lsqsol
Least squares solution of m real equations in n unknowns, rank = n , m n using iterative refinement (Black Box)
Related keywords: big datadata analyticslinear equations, overdeterminedreal, m by n matrixsimultaneous linear equations
F04JGF   nagf_linsys_real_gen_solve
Least squares (if rank = n ) or minimal least squares (if rank < n ) solution of m real equations in n unknowns, m n
Related keywords: big datadata analyticslinear equations, overdeterminedreal, m by n matrixsimultaneous linear equations
F06ZJF   14  nagf_blas_ztrsm
Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix
Related keywords: BLASblas, complex matricescomplex, triangular matrixlinear algebra support routinesztrsm
F08AAF   21  nagf_lapackeig_dgels
Solves a real linear least squares problem of full rank
Related keywords: DGELSeigenproblemfinanceLAPACKLAPACKleast squares LQ decompositionoverdetermined linear equations QR factorizationreal, m by n matrixunderdetermined linear system
F08ANF   21  nagf_lapackeig_zgels
Solves a complex linear least problem of full rank
Related keywords: complex, m by n matrixeigenproblemfinanceLAPACKLAPACKleast squares LQ decompositionoverdetermined linear equations QR factorizationunderdetermined linear systemZGELS
F08BAF   21  nagf_lapackeig_dgelsy
Computes the minimum-norm solution to a real linear least squares problem
Related keywords: DGELSYeigenproblemfinanceLAPACKLAPACKleast squaresminimal least squaresreal, m by n matrix
F08BNF   21  nagf_lapackeig_zgelsy
Computes the minimum-norm solution to a complex linear least squares problem
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresminimal least squaresZGELSY
F08KAF   21  nagf_lapackeig_dgelss
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
Related keywords: DGELSSeigenproblemLAPACKLAPACKleast squaresminimal least squaresreal, m by n matrixSVD, singular value decomposition
F08KCF   21  nagf_lapackeig_dgelsd
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
Related keywords: DGELSDdivide-and-conquer methodeigenproblemfinanceLAPACKLAPACKleast squaresminimal least squaresreal, m by n matrixSVD, singular value decomposition
F08KNF   21  nagf_lapackeig_zgelss
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresminimal least squaresSVD, singular value decompositionZGELSS
F08KQF   21  nagf_lapackeig_zgelsd
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
Related keywords: complex, m by n matrixdivide-and-conquer methodeigenproblemLAPACKLAPACKleast squaresminimal least squaresSVD, singular value decompositionZGELSD
F08ZAF   21  nagf_lapackeig_dgglse
Solves the real linear equality-constrained least squares (LSE) problem
Related keywords: DGGLSEeigenproblemLAPACKLAPACKleast squaresreal, m by n matrixRQ factorizations
F08ZNF   21  nagf_lapackeig_zgglse
Solves the complex linear equality-constrained least squares (LSE) problem
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresRQ factorizationsZGGLSE
linearly-constrained E04RJF   26  nagf_opt_handle_set_linconstr
Define a block of linear constraints to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
linear matrix inequality E04RDF   26  nagf_opt_sdp_read_sdpa
A reader of sparse SDPA data files for linear SDP problems
Related keywords: least squares fittingLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationSDPsemidefinite programmingservice routine
E04RNF   26  nagf_opt_handle_set_linmatineq
Add one or more linear matrix inequality constraints to a problem initialized by E04RAF
Related keywords: least squares fittingLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04SVF   26  nagf_opt_handle_solve_pennon
Run the Pennon solver on a compatible problem initialized by E04RAF and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI)
Related keywords: bilinear matrix inequalityBMIgeneralized augmented Lagrangian methodLagrangianleast squares fittingLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionmonitoring informationoptimizationoptimizationSDPsemidefinite programming
linear programming E04MTF   26  nagf_opt_handle_solve_lp_ipm
Linear programming (LP), sparse, interior point method (IPM)
Related keywords: interior point methodipmLPmaximizing a functionminimizing a functionoptimization
H02BVF   16  nagf_mip_ilp_print
Print IP or LP solutions with user-specified names for rows and columns
Related keywords: integer programmingoperations research
linear programming,integer E04MWF   26  nagf_opt_miqp_mps_write
Write MPS data file defining LP, QP, MILP or MIQP problem
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionMPS formatMPSX formatoptimizationQP, quadratic programmingservice routine
E04MXF   24  nagf_opt_miqp_mps_read
Read MPS data file defining LP, QP, MILP or MIQP problem
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionMPSX formatoptimizationQP, quadratic programmingservice routine
linear quantile regression G02QFF   23  nagf_correg_quantile_linreg_easy
Linear quantile regression, simple interface, independent, identically distributed (IID) errors
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionquantile regressionregression analysis
G02QGF   23  nagf_correg_quantile_linreg
Linear quantile regression, comprehensive interface
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionquantile regressionregression analysis
linear regression G02CAF   nagf_correg_linregs_const
Simple linear regression with constant term, no missing values
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregressionregression analysis
G02CBF   nagf_correg_linregs_noconst
Simple linear regression without constant term, no missing values
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregressionregression analysis
G02CCF   nagf_correg_linregs_const_miss
Simple linear regression with constant term, missing values
Related keywords: big datacorrelation analysisdata analyticsfinancemissing valuesnonlinear regressionpolynomial regressionregressionregression analysis
G02CDF   nagf_correg_linregs_noconst_miss
Simple linear regression without constant term, missing values
Related keywords: big datacorrelation analysisdata analyticsfinancemissing valuesnonlinear regressionpolynomial regressionregressionregression analysis
G02CEF   nagf_correg_linregm_service_select
Service routine for multiple linear regression, select elements from vectors and matrices
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02CFF   nagf_correg_linregm_service_reorder
Service routine for multiple linear regression, reorder elements of vectors and matrices
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02DCF   14  nagf_correg_linregm_obs_edit
Add/delete an observation to/from a general linear regression model
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregressionregression analysisstandard errorsvariance-covariance matrix
G02DDF   14  nagf_correg_linregm_update
Estimates of linear parameters and general linear regression model from updated model
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregressionregression analysis
G02DEF   14  nagf_correg_linregm_var_add
Add a new independent variable to a general linear regression model
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02DFF   14  nagf_correg_linregm_var_del
Delete an independent variable from a general linear regression model
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02DGF   14  nagf_correg_linregm_fit_newvar
Fits a general linear regression model to new dependent variable
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02DKF   14  nagf_correg_linregm_constrain
Estimates and standard errors of parameters of a general linear regression model for given constraints
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysisstandard errors
G02DNF   14  nagf_correg_linregm_estfunc
Computes estimable function of a general linear regression model and its standard error
Related keywords: big datacorrelation analysisdata analyticsestimable functionfinancenonlinear regressionpolynomial regressionregression analysis
G02EEF   14  nagf_correg_linregm_fit_onestep
Fits a linear regression model by forward selection
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionpolynomial regressionregression analysis
LMI E04RDF   26  nagf_opt_sdp_read_sdpa
A reader of sparse SDPA data files for linear SDP problems
Related keywords: least squares fittinglinear matrix inequalitymatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationSDPsemidefinite programmingservice routine
E04RNF   26  nagf_opt_handle_set_linmatineq
Add one or more linear matrix inequality constraints to a problem initialized by E04RAF
Related keywords: least squares fittinglinear matrix inequalitymatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04SVF   26  nagf_opt_handle_solve_pennon
Run the Pennon solver on a compatible problem initialized by E04RAF and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI)
Related keywords: bilinear matrix inequalityBMIgeneralized augmented Lagrangian methodLagrangianleast squares fittinglinear matrix inequalitymatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionmonitoring informationoptimizationoptimizationSDPsemidefinite programming
location X10BBF   26 
Insert the location of the AD callback into the callback data object
Related keywords: AD callbackadjoint derivativesAD utility operationsautomatic differentiationcallback data objectinsert
location, robust estimation G07DBF   13  nagf_univar_robust_1var_mestim
Robust estimation, M -estimates for location and scale parameters, standard weight functions
Related keywords: M -estimatesrobust estimationscale parametersunivariate estimation
G07DCF   13  nagf_univar_robust_1var_mestim_wgt
Robust estimation, M -estimates for location and scale parameters, user-defined weight functions
Related keywords: M -estimatesrobust estimationscale parametersunivariate estimation
logarithm, matrix F01EJF   24  nagf_matop_real_gen_matrix_log
Real matrix logarithm
Related keywords: inversionmatrix logarithmmatrix operationsreal, nonsymmetric matrix
F01FJF   24  nagf_matop_complex_gen_matrix_log
Complex matrix logarithm
Related keywords: complex, nonsymmetric matrixinversionmatrix logarithmmatrix operations
F01JAF   24  nagf_matop_real_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix
Related keywords: condition number, matrixcosh, matrixcosine, matrixexponential, matrixinversionmatrix operationsreal, nonsymmetric matrixsine, matrixsinh, matrix
F01KAF   24  nagf_matop_complex_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix
Related keywords: complex, nonsymmetric matrixcondition number, matrixcosh, matrixcosine, matrixexponential, matrixinversionmatrix operationssine, matrixsinh, matrix
logarithm, pdf G01KQF   24  nagf_stat_pdf_normal_vector
Computes a vector of values for the probability density function of the Normal distribution
Related keywords: Gaussian distributionNormal distributionpdfprobability density functionSimple Calculations on Statistical Data
G01LBF   24  nagf_stat_pdf_multi_normal_vector
Computes a vector of values for the probability density function of the multivariate Normal distribution
Related keywords: Gaussian distributionmultivariate Normal distributionNormal distributionpdfprobability density functionSimple Calculations on Statistical Data
logarithmic distribution G05TFF   22  nagf_rand_int_log
Generates a vector of pseudorandom integers from a logarithmic distribution
Related keywords: big datadata analyticsfinancerandom integersrandom number generators
logarithmic function S01BAF   14  nagf_specfun_log_shifted
ln 1 + x
Related keywords: approximations of special functionsfinanceshifted logarithmic function
log beta function S14CBF   24  nagf_specfun_beta_log_real
Logarithm of the beta function ln B a , b
Related keywords: approximations of special functionsbeta function
log gamma function S14ABF   nagf_specfun_gamma_log_real
Log gamma function, real argument
Related keywords: approximations of special functionsfinance
S14AGF   21  nagf_specfun_gamma_log_complex
Logarithm of the gamma function ln Γ z , complex argument
Related keywords: approximations of special functions
S14AHF   23  nagf_specfun_gamma_log_scaled_real
Scaled log gamma function
Related keywords: approximations of special functions
logistic analysis G11CAF   19  nagf_contab_condl_logistic
Returns parameter estimates for the conditional analysis of stratified data
Related keywords: conditional logistic analysiscontingency table analysisparameter estimatesstratified data
logistic distribution G05SLF   22  nagf_rand_dist_logistic
Generates a vector of pseudorandom numbers from a logistic distribution
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
logistic regression G02GBF   14  nagf_correg_glm_binomial
Fits a generalized linear model with binomial errors
Related keywords: big datacorrelation analysisdata analyticsfinancegeneralized linear modellogitnonlinear regressionpolynomial regressionprobitregression analysis
logit G02GBF   14  nagf_correg_glm_binomial
Fits a generalized linear model with binomial errors
Related keywords: big datacorrelation analysisdata analyticsfinancegeneralized linear modellogistic regressionnonlinear regressionpolynomial regressionprobitregression analysis
log-normal distribution G05SMF   22  nagf_rand_dist_lognormal
Generates a vector of pseudorandom numbers from a log-normal distribution
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
G05YKF   21  nagf_rand_quasi_lognormal
Generates a log-normal quasi-random number sequence
Related keywords: big datadata analyticsFaure, quasi-random numberslow-discrepancy sequencesNiederreiter method, quasi-random numbersquasi-random numbersrandom number generatorsrandom numbersSobol, quasi-random numbers
log rank test G12ABF   23  nagf_surviv_logrank
Computes rank statistics for comparing survival curves
Related keywords: rank statisticssurvival analysis
LOO G05PVF   25  nagf_rand_kfold_xyw
Permutes a matrix, vector, vector triplet into a form suitable for K -fold cross validation
Related keywords: big datacross-validationCVdata analyticsjacknifek-foldleave-one-outpermuterandom number generators
low-discrepancy sequences G05YJF   21  nagf_rand_quasi_normal
Generates a Normal quasi-random number sequence
Related keywords: big datadata analyticsFaure, quasi-random numbersGaussian distributionNiederreiter method, quasi-random numbersNormal distributionquasi-random numbersrandom number generatorsrandom numbersSobol, quasi-random numbers
G05YKF   21  nagf_rand_quasi_lognormal
Generates a log-normal quasi-random number sequence
Related keywords: big datadata analyticsFaure, quasi-random numberslog-normal distributionNiederreiter method, quasi-random numbersquasi-random numbersrandom number generatorsrandom numbersSobol, quasi-random numbers
G05YLF   22  nagf_rand_quasi_init
Initializes a quasi-random number generator
Related keywords: big datadata analyticsFaure, quasi-random numbersfinanceNiederreiter method, quasi-random numbersquasi-random numbersrandom number generatorsrandom numbersrectangular distributionSobol, quasi-random numbersuniform distribution
G05YMF   22  nagf_rand_quasi_uniform
Generates a uniform quasi-random number sequence
Related keywords: big datadata analyticsfinanceoptions, computationalquasi-random numbersrandom number generatorsrandom numbers
lower tail probability G01EAF   15  nagf_stat_prob_normal
Computes probabilities for the standard Normal distribution
Related keywords: CDF, cumulative distribution functionfinanceNormal distributionprobabilitySimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01EBF   14  nagf_stat_prob_students_t
Computes probabilities for Student's t -distribution
Related keywords: CDF, cumulative distribution functionfinanceprobabilitySimple Calculations on Statistical DataStudent's t -distributiontwo-tail probabilityupper tail probability
G01ECF   14  nagf_stat_prob_chisq
Computes probabilities for χ 2 distribution
Related keywords: CDF, cumulative distribution functionchi-squared distributionfinanceprobabilitySimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01EDF   14  nagf_stat_prob_f
Computes probabilities for F -distribution
Related keywords: CDF, cumulative distribution function F -distributionfinanceprobabilitySimple Calculations on Statistical Dataupper tail probabilityvariance-ratio distribution
G01EEF   14  nagf_stat_prob_beta
Computes upper and lower tail probabilities and probability density function for the beta distribution
Related keywords: beta distributionCDF, cumulative distribution functionfinanceprobabilitySimple Calculations on Statistical Dataupper tail probability
G01EFF   14  nagf_stat_prob_gamma
Computes probabilities for the gamma distribution
Related keywords: CDF, cumulative distribution functionfinancegamma distributionprobabilitySimple Calculations on Statistical Dataupper tail probability
G01ERF   16  nagf_stat_prob_vonmises
Computes probability for von Mises distribution
Related keywords: CDF, cumulative distribution functionfinanceSimple Calculations on Statistical Datavon Mises distribution
G01GBF   14  nagf_stat_prob_students_t_noncentral
Computes probabilities for the non-central Student's t -distribution
Related keywords: financeSimple Calculations on Statistical DataStudent's t -distribution
G01GCF   14  nagf_stat_prob_chisq_noncentral
Computes probabilities for the non-central χ 2 distribution
Related keywords: chi-squared distributionfinanceSimple Calculations on Statistical Data
G01GDF   14  nagf_stat_prob_f_noncentral
Computes probabilities for the non-central F -distribution
Related keywords: F -distributionfinanceSimple Calculations on Statistical Datavariance-ratio distribution
G01GEF   14  nagf_stat_prob_beta_noncentral
Computes probabilities for the non-central beta distribution
Related keywords: beta distributionfinanceSimple Calculations on Statistical Data
G01HAF   14  nagf_stat_prob_bivariate_normal
Computes probability for the bivariate Normal distribution
Related keywords: bivariate Normal distributionfinanceNormal distributionSimple Calculations on Statistical Data
G01HBF   15  nagf_stat_prob_multi_normal
Computes probabilities for the multivariate Normal distribution
Related keywords: central probabilityfinancemultivariate Normal distributionNormal distributionSimple Calculations on Statistical Dataupper tail probability
G01JCF   14  nagf_stat_prob_chisq_noncentral_lincomb
Computes probability for a positive linear combination of χ 2 variables
Related keywords: chi-squared distributionfinanceSimple Calculations on Statistical Data
G01JDF   15  nagf_stat_prob_chisq_lincomb
Computes lower tail probability for a linear combination of (central) χ 2 variables
Related keywords: chi-squared distributionfinanceImhof's methodPan's methodSimple Calculations on Statistical Data
G01SAF   24  nagf_stat_prob_normal_vector
Computes a vector of probabilities for the standard Normal distribution
Related keywords: big dataCDF, cumulative distribution functionconfidence intervaldata analyticsGaussian distributionNormal distributionsignificanceSimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01SBF   24  nagf_stat_prob_students_t_vector
Computes a vector of probabilities for the Student's t -distribution
Related keywords: big dataCDF, cumulative distribution functionconfidence intervaldata analyticssignificanceSimple Calculations on Statistical DataStudent's t -distributiontwo-tail probabilityupper tail probability
G01SCF   24  nagf_stat_prob_chisq_vector
Computes a vector of probabilities for χ 2 distribution
Related keywords: big dataCDF, cumulative distribution functionchi-squared distributiondata analyticsSimple Calculations on Statistical Dataupper tail probability
G01SDF   24  nagf_stat_prob_f_vector
Computes a vector of probabilities for F -distribution
Related keywords: big dataCDF, cumulative distribution functiondata analytics F -distributionSimple Calculations on Statistical Dataupper tail probabilityvariance-ratio distribution
G01SEF   24  nagf_stat_prob_beta_vector
Computes a vector of probabilities for the beta distribution
Related keywords: beta distributionbig dataCDF, cumulative distribution functiondata analyticsSimple Calculations on Statistical Dataupper tail probability
G01SFF   24  nagf_stat_prob_gamma_vector
Computes a vector of probabilities for the gamma distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticsgamma distributionSimple Calculations on Statistical Dataupper tail probability
G01SJF   24  nagf_stat_prob_binomial_vector
Computes a vector of probabilities for the binomial distribution
Related keywords: big databinomial distributionCDF, cumulative distribution functiondata analyticspoint probabilitySimple Calculations on Statistical Dataupper tail probability
G01SKF   24  nagf_stat_prob_poisson_vector
Computes a vector of probabilities for the Poisson distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticspoint probabilityPoisson distributionSimple Calculations on Statistical Dataupper tail probability
G01SLF   24  nagf_stat_prob_hypergeom_vector
Computes a vector of probabilities for the hypergeometric distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticshypergeometric distributionpoint probabilitySimple Calculations on Statistical Dataupper tail probability
LP E04MTF   26  nagf_opt_handle_solve_lp_ipm
Linear programming (LP), sparse, interior point method (IPM)
Related keywords: interior point methodipmlinear programmingmaximizing a functionminimizing a functionoptimization
LP, linear programming E04MFF   16  nagf_opt_lp_solve_old
Linear programming (LP), dense, active-set method
Related keywords: active-set methodfinancemaximizing a functionminimizing a functionoptimization
E04MGF   16  nagf_opt_lp_option_file_old
Supply values for E04MFF from external file
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computational
E04MHF   16  nagf_opt_lp_option_string_old
Supply values to E04MFF from a character string
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computational
E04MWF   26  nagf_opt_miqp_mps_write
Write MPS data file defining LP, QP, MILP or MIQP problem
Related keywords: linear programming,integermaximizing a functionminimizing a functionMPS formatMPSX formatoptimizationQP, quadratic programmingservice routine
E04MXF   24  nagf_opt_miqp_mps_read
Read MPS data file defining LP, QP, MILP or MIQP problem
Related keywords: linear programming,integermaximizing a functionminimizing a functionMPSX formatoptimizationQP, quadratic programmingservice routine
E04MZF   18  nagf_opt_qpconvex1_sparse_mps
Read MPS data file defining LP or QP problem, deprecated
Related keywords: maximizing a functionminimizing a functionMPSX formatoptimizationQP, quadratic programmingservice routine
E04NKF   18  nagf_opt_qpconvex1_sparse_solve_old
Linear programming (LP) or convex quadratic programming (QP), sparse, active-set method
Related keywords: financemaximizing a functionminimizing a functionoptimizationQP, quadratic programmingservice routine
E04NLF   18  nagf_opt_qpconvex1_sparse_option_file_old
Supply values for E04NKF from external file
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalQP, quadratic programming
E04NMF   18  nagf_opt_qpconvex1_sparse_option_string_old
Supply values to E04NKF from a character string
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalQP, quadratic programming
E04NPF   21  nagf_opt_qpconvex2_sparse_init
Initialization routine for E04NQF
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalQP, quadratic programming
E04NQF   21  nagf_opt_qpconvex2_sparse_solve
Linear programming (LP) or convex quadratic programming (QP), sparse, active-set method, recommended
Related keywords: active-set methodfinancemaximizing a functionminimizing a functionoptimizationQP, quadratic programmingservice routinesparse convex QP prolem
E04NRF   21  nagf_opt_qpconvex2_sparse_option_file
Supply values for E04NQF from external file
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalQP, quadratic programming
E04NSF   21  nagf_opt_qpconvex2_sparse_option_string
Set a single option for E04NQF from a character string
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalQP, quadratic programming
E04NTF   21  nagf_opt_qpconvex2_sparse_option_integer_set
Set a single option for E04NQF from an integer argument
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalQP, quadratic programming
E04NUF   21  nagf_opt_qpconvex2_sparse_option_double_set
Set a single option for E04NQF from a real argument
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalQP, quadratic programming
E04NXF   21  nagf_opt_qpconvex2_sparse_option_integer_get
Get the setting of an integer valued option of E04NQF
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalQP, quadratic programming
E04NYF   21  nagf_opt_qpconvex2_sparse_option_double_get
Get the setting of a real valued option of E04NQF
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalQP, quadratic programming
E04VHF   21  nagf_opt_nlp2_sparse_solve
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: financemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton algorithmsequential QP methodsimplex algorithmSQP
LQ decomposition F08AAF   21  nagf_lapackeig_dgels
Solves a real linear least squares problem of full rank
Related keywords: DGELSeigenproblemfinanceLAPACKLAPACKleast squareslinear least squaresoverdetermined linear equations QR factorizationreal, m by n matrixunderdetermined linear system
F08ANF   21  nagf_lapackeig_zgels
Solves a complex linear least problem of full rank
Related keywords: complex, m by n matrixeigenproblemfinanceLAPACKLAPACKleast squareslinear least squaresoverdetermined linear equations QR factorizationunderdetermined linear systemZGELS
LQ factorization F08AHF   16  nagf_lapackeig_dgelqf
Performs a L Q factorization of real general rectangular matrix
Related keywords: DGELQFeigenproblemLAPACKLAPACKleast squaresreal, m by n matrix
F08AJF   16  nagf_lapackeig_dorglq
Forms all or part of orthogonal Q from L Q factorization determined by F08AHF
Related keywords: DORGLQeigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generationorthogonal transformations
F08AKF   16  nagf_lapackeig_dormlq
Applies the orthogonal transformation determined by F08AHF
Related keywords: DORMLQeigenproblemLAPACKLAPACKleast squaresorthogonal transformations
F08AVF   16  nagf_lapackeig_zgelqf
Performs a L Q factorization of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresZGELQF
F08AWF   16  nagf_lapackeig_zunglq
Forms all or part of unitary Q from L Q factorization determined by F08AVF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary matrix, generationunitary transformationsZUNGLQ
F08AXF   16  nagf_lapackeig_zunmlq
Applies the unitary transformation determined by F08AVF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformationsZUNMLQ
LU decomposition F01BRF   nagf_matop_real_gen_sparse_lu
L U factorization of real sparse matrix
Related keywords: inversionmatrix operationsreal, sparse matrixsparse linear equations
F01BSF   nagf_matop_real_gen_sparse_lu_reuse
L U factorization of real sparse matrix with known sparsity pattern
Related keywords: inversionmatrix operationsreal, sparse matrixsparse linear equations
F01LEF   11  nagf_matop_real_gen_tridiag_lu
L U factorization of real tridiagonal matrix
Related keywords: complex, nonsymmetric matrixinversionmatrix, bandmatrix operations
F01LHF   13  nagf_matop_real_gen_blkdiag_lu
L U factorization of real almost block diagonal matrix
Related keywords: inversionmatrix operationsreal, almost block-diagonal matrix
F07AAF   21  nagf_lapacklin_dgesv
Computes the solution to a real system of linear equations
Related keywords: DGESVfinanceLAPACKlinear equationsreal, nonsymmetric matrix
F07ABF   21  nagf_lapacklin_dgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
Related keywords: backward errorcondition number, matrixDGESVXerror bound, matrixfinanceforward errorLAPACKlinear equationsreal, nonsymmetric matrix
F07ADF   15  nagf_lapacklin_dgetrf
L U factorization of real m by n matrix
Related keywords: DGETRFfinanceLAPACKlinear equationsreal, m by n matrix
F07AEF   15  nagf_lapacklin_dgetrs
Solution of real system of linear equations, multiple right-hand sides, matrix already factorized by F07ADF
Related keywords: DGETRSLAPACKlinear equationsreal, nonsymmetric matrix
F07AGF   15  nagf_lapacklin_dgecon
Estimate condition number of real matrix, matrix already factorized by F07ADF
Related keywords: condition number, matrixDGECONLAPACKlinear equationsreal, nonsymmetric matrix
F07AHF   15  nagf_lapacklin_dgerfs
Refined solution with error bounds of real system of linear equations, multiple right-hand sides
Related keywords: backward errorDGERFSerror bound, matrixforward errorLAPACKlinear equationsreal, nonsymmetric matrix
F07AJF   15  nagf_lapacklin_dgetri
Inverse of real matrix, matrix already factorized by F07ADF
Related keywords: DGETRIfinanceinverse, matrixLAPACKlinear equationsreal, nonsymmetric matrix
F07ANF   21  nagf_lapacklin_zgesv
Computes the solution to a complex system of linear equations
Related keywords: complex, nonsymmetric matrixLAPACKlinear equationsZGESV
F07APF   21  nagf_lapacklin_zgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
Related keywords: backward errorcomplex, nonsymmetric matrixcondition number, matrixerror bound, matrixfinanceforward errorLAPACKlinear equationsZGESVX
F07ARF   15  nagf_lapacklin_zgetrf
L U factorization of complex m by n matrix
Related keywords: complex, m by n matrixfinanceLAPACKlinear equationsZGETRF
F07ASF   15  nagf_lapacklin_zgetrs
Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by F07ARF
Related keywords: complex, nonsymmetric matrixfinanceLAPACKlinear equationsZGETRS
F07BAF   21  nagf_lapacklin_dgbsv
Computes the solution to a real banded system of linear equations
Related keywords: DGBSVLAPACKlinear equationsmatrix, bandreal, band matrix
F07BBF   21  nagf_lapacklin_dgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
Related keywords: backward errorcondition number, matrixDGBSVXerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandreal, band matrix
F07BDF   15  nagf_lapacklin_dgbtrf
L U factorization of real m by n band matrix
Related keywords: DGBTRFLAPACKlinear equationsmatrix, bandreal, band matrix
F07BEF   15  nagf_lapacklin_dgbtrs
Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by F07BDF
Related keywords: DGBTRSLAPACKlinear equationsmatrix, bandreal, band matrix
F07BHF   15  nagf_lapacklin_dgbrfs
Refined solution with error bounds of real band system of linear equations, multiple right-hand sides
Related keywords: backward errorDGBRFSforward errorLAPACKlinear equationsmatrix, bandreal, band matrix
F07BNF   21  nagf_lapacklin_zgbsv
Computes the solution to a complex banded system of linear equations
Related keywords: complex, band matrixLAPACKlinear equationsmatrix, bandZGBSV
F07BPF   21  nagf_lapacklin_zgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
Related keywords: backward errorcomplex, band matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandZGBSVX
F07BRF   15  nagf_lapacklin_zgbtrf
L U factorization of complex m by n band matrix
Related keywords: complex, m by n matrixLAPACKlinear equationsmatrix, bandZGBSVX
F07BSF   15  nagf_lapacklin_zgbtrs
Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by F07BRF
Related keywords: complex, band matrixLAPACKlinear equationsmatrix, bandZGBTRS
F07CAF   21  nagf_lapacklin_dgtsv
Computes the solution to a real tridiagonal system of linear equations
Related keywords: DGTSVfinanceLAPACKlinear equationsmatrix, bandreal, tridiagonal matrix
F07CBF   21  nagf_lapacklin_dgtsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
Related keywords: backward errorcondition number, matrixDGTSVXerror bound, matrixforward errorLAPACKlinear equationsmatrix, bandreal, tridiagonal matrix
F07CDF   22  nagf_lapacklin_dgttrf
L U factorization of real tridiagonal matrix
Related keywords: DGTTRFfinanceLAPACKlinear equationsmatrix, bandreal, tridiagonal matrix
F07CEF   22  nagf_lapacklin_dgttrs
Solves a real tridiagonal system of linear equations using the L U factorization computed by F07CDF
Related keywords: DGTTRSfinanceLAPACKlinear equationsmatrix, bandreal, tridiagonal matrix
F07CGF   22  nagf_lapacklin_dgtcon
Estimates the reciprocal of the condition number of a real tridiagonal matrix using the L U factorization computed by F07CDF
Related keywords: condition number, matrixDGTCONLAPACKlinear equationsmatrix, bandreal, tridiagonal matrix
F07CHF   22  nagf_lapacklin_dgtrfs
Refined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorDGTCONforward errorLAPACKlinear equationsmatrix, bandreal, tridiagonal matrix
F07CNF   21  nagf_lapacklin_zgtsv
Computes the solution to a complex tridiagonal system of linear equations
Related keywords: complex, tridiagonal matrixLAPACKlinear equationsmatrix, bandZGTSV
F07CPF   21  nagf_lapacklin_zgtsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations
Related keywords: backward errorcomplex, tridiagonal matrixforward errorLAPACKlinear equationsmatrix, bandZGTSVX
F07CRF   22  nagf_lapacklin_zgttrf
L U factorization of complex tridiagonal matrix
Related keywords: complex, tridiagonal matrixLAPACKlinear equationsmatrix, bandZGTTRF
F07CSF   22  nagf_lapacklin_zgttrs
Solves a complex tridiagonal system of linear equations using the L U factorization computed by F07CDF
Related keywords: complex, tridiagonal matrixLAPACKlinear equationsmatrix, bandZGTTRS
F07CUF   22  nagf_lapacklin_zgtcon
Estimates the reciprocal of the condition number of a complex tridiagonal matrix using the L U factorization computed by F07CDF
Related keywords: complex, tridiagonal matrixcondition number, matrixLAPACKlinear equationsmatrix, bandZGTCON
F07CVF   22  nagf_lapacklin_zgtrfs
Refined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, tridiagonal matrixforward errorLAPACKlinear equationsmatrix, bandZGTRFS
F11MEF   21  nagf_sparse_direct_real_gen_lu
L U factorization of real sparse matrix
Related keywords: big datadata analyticsdiscretised systemlarge scale linear systemsreal, sparse matrixsparse linear system
machine constants X02 Chapter Introduction     Machine Constants
machine precision X02AJF   12  nagf_machine_precision
The machine precision
Related keywords: machine constants
Mahalanobis distances G03DBF   15  nagf_mv_discrim_mahal
Computes Mahalanobis squared distances for group or pooled variance-covariance matrices (for use after G03DAF)
Related keywords: discriminant analysismultivariate methods
Mallows type regression G02HAF   13  nagf_correg_robustm
Robust regression, standard M -estimates
Related keywords: Andrew's sine wavebig datacorrelation analysisdata analyticsfinanceHampel's piecewise linear functionHuber type regressionKrasker–Welsch weightsMaronna's weights M -estimatesnonlinear regressionpolynomial regressionregressionregression analysisrobust regressionScheppe type regressionTukey's bi-weight
Mann–Whitney U statistic G08AHF   14  nagf_nonpar_test_mwu
Performs the Mann–Whitney U test on two independent samples
Related keywords: nonparametric statisticstail probabilities
G08AJF   14  nagf_nonpar_prob_mwu_noties
Computes the exact probabilities for the Mann–Whitney U statistic, no ties in pooled sample
Related keywords: nonparametric statisticspooled sampletail probabilities
G08AKF   14  nagf_nonpar_prob_mwu_ties
Computes the exact probabilities for the Mann–Whitney U statistic, ties in pooled sample
Related keywords: Neumann algorithmnonparametric statisticspooled sampletail probabilities
marginal likelihood G13BEF   11  nagf_tsa_multi_inputmod_estim
Multivariate time series, estimation of multi-input model
Related keywords: ARIMAbig datadata analyticsexact likelihoodfinancemultivariate time seriesnonlinear least squarestime seriestime series analysisunivariate time series
marginal tables G11BCF   17  nagf_contab_tabulate_margin
Computes marginal tables for multiway table computed by G11BAF or G11BBF
Related keywords: contingency table analysis
mark A00AAF   18  nagf_info_impl_details
Library identification, details of implementation and mark
Related keywords: identificationimplementation detailslibrary detailslibrary identification
A00ADF   22  nagf_info_impl_details_separate
Library identification, details of implementation, major and minor marks
Related keywords: identificationimplementation detailslibrary detailslibrary identification
Maronna's weights G02HAF   13  nagf_correg_robustm
Robust regression, standard M -estimates
Related keywords: Andrew's sine wavebig datacorrelation analysisdata analyticsfinanceHampel's piecewise linear functionHuber type regressionKrasker–Welsch weightsMallows type regression M -estimatesnonlinear regressionpolynomial regressionregressionregression analysisrobust regressionScheppe type regressionTukey's bi-weight
mathematical constants X01 Chapter Introduction     Mathematical Constants
matrix, band F01BUF   nagf_matop_real_symm_posdef_fac
U L D L T U T factorization of real symmetric positive definite band matrix
Related keywords: decomposition, matrixinversionmatrix operationsreal, band, positive-definite, symmetric matrix U L D L T U T decomposition
F01BVF   nagf_matop_real_symm_posdef_geneig
Reduction to standard form, generalized real symmetric-definite banded eigenproblem
Related keywords: eigenproblem, generalizedgeneralized eigenprobleminversionmatrix operationsreal, band, positive-definite, symmetric matrix
F01LEF   11  nagf_matop_real_gen_tridiag_lu
L U factorization of real tridiagonal matrix
Related keywords: complex, nonsymmetric matrixinversionLU decompositionmatrix operations
F01MCF   nagf_matop_real_vband_posdef_fac
L D L T factorization of real symmetric positive definite variable-bandwidth matrix
Related keywords: inversion LDL T decompositionmatrix operationsreal, band, positive-definite, symmetric matrix
F04BBF   21  nagf_linsys_real_band_solve
Computes the solution, estimated condition number and error-bound to a real banded system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationsreal, band matrixsimultaneous linear equations
F04BCF   21  nagf_linsys_real_tridiag_solve
Computes the solution, estimated condition number and error-bound to a real tridiagonal system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationsreal, tridiagonal matrixsimultaneous linear equations
F04CBF   21  nagf_linsys_complex_band_solve
Computes the solution, estimated condition number and error-bound to a complex banded system of linear equations
Related keywords: big datacomplex, band matrixdata analyticsforward errorlinear equationssimultaneous linear equations
F04CCF   21  nagf_linsys_complex_tridiag_solve
Computes the solution, estimated condition number and error-bound to a complex tridiagonal system of linear equations
Related keywords: big datacomplex, tridiagonal matrixdata analyticsforward errorlinear equationssimultaneous linear equations
F04CFF   21  nagf_linsys_complex_posdef_band_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite banded system of linear equations
Related keywords: big datacomplex, band, Hermitian, positive-definite matrixdata analyticsforward errorlinear equationssimultaneous linear equations
F04CGF   21  nagf_linsys_complex_posdef_tridiag_solve
Computes the solution, estimated condition number and error-bound to a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: big datacomplex, Hermitian, positive-definite, tridiagonal matrixdata analyticsforward errorlinear equationssimultaneous linear equations
F04LEF   11  nagf_linsys_real_tridiag_fac_solve
Solution of real tridiagonal simultaneous linear equations (coefficient matrix already factorized by F01LEF)
Related keywords: big datadata analyticslinear equationsreal, tridiagonal matrixsimultaneous linear equations
F04MCF   nagf_linsys_real_posdef_vband_solve
Solution of real symmetric positive definite variable-bandwidth simultaneous linear equations (coefficient matrix already factorized by F01MCF)
Related keywords: big datadata analyticslinear equationsreal, band, positive-definite, symmetric matrixsimultaneous linear equations
F06PBF   12  nagf_blas_dgbmv
Matrix-vector product, real rectangular band matrix
Related keywords: BLASblas, real matricesdgbmvlinear algebra support routinesmultiply, matrixreal, band, m by n matrix
F06PDF   12  nagf_blas_dsbmv
Matrix-vector product, real symmetric band matrix
Related keywords: BLASblas, real matricesdsbmvlinear algebra support routinesmultiply, matrixreal, band, symmetric matrix
F06PGF   12  nagf_blas_dtbmv
Matrix-vector product, real triangular band matrix
Related keywords: BLASblas, real matricesdtbmvlinear algebra support routinesmultiply, matrixreal, band, triangular matrix
F06PKF   12  nagf_blas_dtbsv
System of equations, real triangular band matrix
Related keywords: BLASblas, real matricesdtbsvlinear algebra support routineslinear equationsreal, band, triangular matrix
F06RBF   15  nagf_blas_dlangb
1 -norm, -norm, Frobenius norm, largest absolute element, real band matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrixreal, band, m by n matrix
F06REF   15  nagf_blas_dlansb
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric band matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrixreal, band, symmetric matrix
F06RNF   21  nagf_blas_dlangt
1 -norm, -norm, Frobenius norm, largest absolute element, real tridiagonal matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrixreal, tridiagonal matrix
F06RPF   21  nagf_blas_dlanst
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrixreal, symmetric, tridiagonal matrix
F06SBF   12  nagf_blas_zgbmv
Matrix-vector product, complex rectangular band matrix
Related keywords: BLASblas, complex matricescomplex, band, m by n matrixlinear algebra support routinesmultiply, matrixzgbmv
F06SDF   12  nagf_blas_zhbmv
Matrix-vector product, complex Hermitian band matrix
Related keywords: BLASblas, complex matricescomplex, band, Hermitian matrixlinear algebra support routinesmultiply, matrixzhbmv
F06SGF   12  nagf_blas_ztbmv
Matrix-vector product, complex triangular band matrix
Related keywords: BLASblas, complex matricescomplex, band, triangular matrixlinear algebra support routinesmultiply, matrixztbmv
F06SKF   12  nagf_blas_ztbsv
System of equations, complex triangular band matrix
Related keywords: BLASblas, complex matricescomplex, band, triangular matrixlinear algebra support routineslinear equationsztbsv
F06UBF   15  nagf_blas_zlangb
1 -norm, -norm, Frobenius norm, largest absolute element, complex band matrix
Related keywords: 1-normBLAScomplex, band matrixFrobenius norminfinity-normlinear algebra support routines
F06UEF   15  nagf_blas_zlanhb
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian band matrix
Related keywords: 1-normBLAScomplex, band, Hermitian matrixFrobenius norminfinity-normlinear algebra support routines
F06UHF   15  nagf_blas_zlansb
1 -norm, -norm, Frobenius norm, largest absolute element, complex symmetric band matrix
Related keywords: 1-normBLAScomplex, band, symmetric matrixFrobenius norminfinity-normlinear algebra support routines
F06ULF   15  nagf_blas_zlantb
1 -norm, -norm, Frobenius norm, largest absolute element, complex triangular band matrix
Related keywords: 1-normBLAScomplex, band, triangular matrixFrobenius norminfinity-normlinear algebra support routines
F06UNF   21  nagf_blas_zlangt
1 -norm, -norm, Frobenius norm, largest absolute element, complex tridiagonal matrix
Related keywords: 1-normBLAScomplex, triangular matrixFrobenius norminfinity-normlinear algebra support routines
F06UPF   21  nagf_blas_zlanht
1 -norm, -norm, Frobenius norm, largest absolute element, complex Hermitian tridiagonal matrix
Related keywords: 1-normBLAScomplex, Hermitian, tridiagonal matrixFrobenius norminfinity-normlinear algebra support routines
F07BAF   21  nagf_lapacklin_dgbsv
Computes the solution to a real banded system of linear equations
Related keywords: DGBSVLAPACKlinear equations L U decompositionreal, band matrix
F07BBF   21  nagf_lapacklin_dgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
Related keywords: backward errorcondition number, matrixDGBSVXerror bound, matrixforward errorLAPACKlinear equations L U decompositionreal, band matrix
F07BDF   15  nagf_lapacklin_dgbtrf
L U factorization of real m by n band matrix
Related keywords: DGBTRFLAPACKlinear equations L U decompositionreal, band matrix
F07BEF   15  nagf_lapacklin_dgbtrs
Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by F07BDF
Related keywords: DGBTRSLAPACKlinear equations L U decompositionreal, band matrix
F07BFF   22  nagf_lapacklin_dgbequ
Computes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number
Related keywords: DGBEQUequilibrationLAPACKlinear equationsreal, band matrixscaling
F07BGF   15  nagf_lapacklin_dgbcon
Estimate condition number of real band matrix, matrix already factorized by F07BDF
Related keywords: condition number, matrixDGBCONLAPACKlinear equationsreal, band matrix
F07BHF   15  nagf_lapacklin_dgbrfs
Refined solution with error bounds of real band system of linear equations, multiple right-hand sides
Related keywords: backward errorDGBRFSforward errorLAPACKlinear equations L U decompositionreal, band matrix
F07BNF   21  nagf_lapacklin_zgbsv
Computes the solution to a complex banded system of linear equations
Related keywords: complex, band matrixLAPACKlinear equations L U decompositionZGBSV
F07BPF   21  nagf_lapacklin_zgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
Related keywords: backward errorcomplex, band matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equations L U decompositionZGBSVX
F07BRF   15  nagf_lapacklin_zgbtrf
L U factorization of complex m by n band matrix
Related keywords: complex, m by n matrixLAPACKlinear equations L U decompositionZGBSVX
F07BSF   15  nagf_lapacklin_zgbtrs
Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by F07BRF
Related keywords: complex, band matrixLAPACKlinear equations L U decompositionZGBTRS
F07BTF   22  nagf_lapacklin_zgbequ
Computes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number
Related keywords: complex, band matrixequilibrationLAPACKlinear equationsscalingZGBEQU
F07BUF   15  nagf_lapacklin_zgbcon
Estimate condition number of complex band matrix, matrix already factorized by F07BRF
Related keywords: complex, band matrixcondition number, matrixLAPACKlinear equationsZGBEQU
F07BVF   15  nagf_lapacklin_zgbrfs
Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, band matrixerror bound, matrixforward errorLAPACKlinear equationsZGBRFS
F07CAF   21  nagf_lapacklin_dgtsv
Computes the solution to a real tridiagonal system of linear equations
Related keywords: DGTSVfinanceLAPACKlinear equations L U decompositionreal, tridiagonal matrix
F07CBF   21  nagf_lapacklin_dgtsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
Related keywords: backward errorcondition number, matrixDGTSVXerror bound, matrixforward errorLAPACKlinear equations L U decompositionreal, tridiagonal matrix
F07CDF   22  nagf_lapacklin_dgttrf
L U factorization of real tridiagonal matrix
Related keywords: DGTTRFfinanceLAPACKlinear equations L U decompositionreal, tridiagonal matrix
F07CEF   22  nagf_lapacklin_dgttrs
Solves a real tridiagonal system of linear equations using the L U factorization computed by F07CDF
Related keywords: DGTTRSfinanceLAPACKlinear equations L U decompositionreal, tridiagonal matrix
F07CGF   22  nagf_lapacklin_dgtcon
Estimates the reciprocal of the condition number of a real tridiagonal matrix using the L U factorization computed by F07CDF
Related keywords: condition number, matrixDGTCONLAPACKlinear equations L U decompositionreal, tridiagonal matrix
F07CHF   22  nagf_lapacklin_dgtrfs
Refined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorDGTCONforward errorLAPACKlinear equations L U decompositionreal, tridiagonal matrix
F07CNF   21  nagf_lapacklin_zgtsv
Computes the solution to a complex tridiagonal system of linear equations
Related keywords: complex, tridiagonal matrixLAPACKlinear equations L U decompositionZGTSV
F07CPF   21  nagf_lapacklin_zgtsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations
Related keywords: backward errorcomplex, tridiagonal matrixforward errorLAPACKlinear equations L U decompositionZGTSVX
F07CRF   22  nagf_lapacklin_zgttrf
L U factorization of complex tridiagonal matrix
Related keywords: complex, tridiagonal matrixLAPACKlinear equations L U decompositionZGTTRF
F07CSF   22  nagf_lapacklin_zgttrs
Solves a complex tridiagonal system of linear equations using the L U factorization computed by F07CDF
Related keywords: complex, tridiagonal matrixLAPACKlinear equations L U decompositionZGTTRS
F07CUF   22  nagf_lapacklin_zgtcon
Estimates the reciprocal of the condition number of a complex tridiagonal matrix using the L U factorization computed by F07CDF
Related keywords: complex, tridiagonal matrixcondition number, matrixLAPACKlinear equations L U decompositionZGTCON
F07CVF   22  nagf_lapacklin_zgtrfs
Refined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, tridiagonal matrixforward errorLAPACKlinear equations L U decompositionZGTRFS
F07HAF   21  nagf_lapacklin_dpbsv
Computes the solution to a real symmetric positive definite banded system of linear equations
Related keywords: Cholesky decompositionDPBSVLAPACKlinear equationsreal, band, positive-definite, symmetric matrix
F07HBF   21  nagf_lapacklin_dpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite banded system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixDPBSVXerror bound, matrixforward errorLAPACKlinear equationsreal, band, positive-definite, symmetric matrix
F07HDF   15  nagf_lapacklin_dpbtrf
Cholesky factorization of real symmetric positive definite band matrix
Related keywords: Cholesky decompositionDPBTRFfinanceLAPACKlinear equationsreal, band, positive-definite, symmetric matrix
F07HEF   15  nagf_lapacklin_dpbtrs
Solution of real symmetric positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HDF
Related keywords: Cholesky decompositionDPBTRSfinanceLAPACKlinear equationsreal, band, positive-definite, symmetric matrix
F07HFF   22  nagf_lapacklin_dpbequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite banded matrix and reduce its condition number
Related keywords: DPBEQUequilibrationLAPACKlinear equationsreal, band, positive-definite, symmetric matrixscaling
F07HGF   15  nagf_lapacklin_dpbcon
Estimate condition number of real symmetric positive definite band matrix, matrix already factorized by F07HDF
Related keywords: condition number, matrixDPBCONLAPACKlinear equationsreal, band, positive-definite, symmetric matrix
F07HHF   15  nagf_lapacklin_dpbrfs
Refined solution with error bounds of real symmetric positive definite band system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositionDPBRFSforward errorLAPACKlinear equationsreal, band, positive-definite, symmetric matrix
F07HNF   21  nagf_lapacklin_zpbsv
Computes the solution to a complex Hermitian positive definite banded system of linear equations
Related keywords: Cholesky decompositioncomplex, band, Hermitian, positive-definite matrixLAPACKlinear equationsZPBSV
F07HPF   21  nagf_lapacklin_zpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite banded system of linear equations
Related keywords: backward errorCholesky decompositioncomplex, band, Hermitian, positive-definite matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsZPBSVX
F07HRF   15  nagf_lapacklin_zpbtrf
Cholesky factorization of complex Hermitian positive definite band matrix
Related keywords: Cholesky decompositioncomplex, band, Hermitian, positive-definite matrixLAPACKlinear equationsZPBTRF
F07HSF   15  nagf_lapacklin_zpbtrs
Solution of complex Hermitian positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HRF
Related keywords: Cholesky decompositioncomplex, band, Hermitian, positive-definite matrixLAPACKlinear equationsZPBTRS
F07HTF   22  nagf_lapacklin_zpbequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite banded matrix and reduce its condition number
Related keywords: complex, band, Hermitian, positive-definite matrixequilibrationLAPACKlinear equationsscalingZPBEQU
F07HUF   15  nagf_lapacklin_zpbcon
Estimate condition number of complex Hermitian positive definite band matrix, matrix already factorized by F07HRF
Related keywords: complex, band, Hermitian, positive-definite matrixcondition number, matrixLAPACKlinear equationsZPBCON
F07HVF   15  nagf_lapacklin_zpbrfs
Refined solution with error bounds of complex Hermitian positive definite band system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositioncomplex, band, Hermitian, positive-definite matrixerror bound, matrixforward errorLAPACKlinear equationsZPBRFS
F07JAF   21  nagf_lapacklin_dptsv
Computes the solution to a real symmetric positive definite tridiagonal system of linear equations
Related keywords: Cholesky decompositionDPTSVLAPACKlinear equationsreal, positive-definite, symmetric, tridiagonal matrix
F07JBF   21  nagf_lapacklin_dptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixDPTSVXerror bound, matrixforward errorLAPACKlinear equationsreal, positive-definite, symmetric, tridiagonal matrix
F07JDF   22  nagf_lapacklin_dpttrf
Computes the LDL T factorization of a real symmetric positive definite tridiagonal matrix
Related keywords: Cholesky decompositionDPTTRFLAPACKlinear equationsreal, positive-definite, symmetric, tridiagonal matrix
F07JEF   22  nagf_lapacklin_dpttrs
Solves a real symmetric positive definite tridiagonal system using the LDL T factorization computed by F07JDF
Related keywords: Cholesky decompositionDPTTRSLAPACKlinear equationsreal, positive-definite, symmetric, tridiagonal matrix
F07JGF   22  nagf_lapacklin_dptcon
Computes the reciprocal of the condition number of a real symmetric positive definite tridiagonal system using the LDL T factorization computed by F07JDF
Related keywords: condition number, matrixDPTCONLAPACKlinear equationsreal, positive-definite, symmetric, tridiagonal matrix
F07JHF   22  nagf_lapacklin_dptrfs
Refined solution with error bounds of real symmetric positive definite tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositionDPTRFSforward errorLAPACKlinear equationsreal, positive-definite, symmetric, tridiagonal matrix
F07JNF   21  nagf_lapacklin_zptsv
Computes the solution to a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixLAPACKlinear equationsZPTSV
F07JPF   21  nagf_lapacklin_zptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsZPTSVX
F07JRF   22  nagf_lapacklin_zpttrf
Computes the LDL H factorization of a complex Hermitian positive definite tridiagonal matrix
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixLAPACKlinear equationsZPPTRF
F07JSF   22  nagf_lapacklin_zpttrs
Solves a complex Hermitian positive definite tridiagonal system using the LDL H factorization computed by F07JRF
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixLAPACKlinear equationsZPPTRS
F07JUF   22  nagf_lapacklin_zptcon
Computes the reciprocal of the condition number of a complex Hermitian positive definite tridiagonal system using the LDL H factorization computed by F07JRF
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixcondition number, matrixLAPACKlinear equationsZPTCON
F07JVF   22  nagf_lapacklin_zptrfs
Refined solution with error bounds of complex Hermitian positive definite tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixforward errorLAPACKlinear equationsZPTRFS
F07VEF   15  nagf_lapacklin_dtbtrs
Solution of real band triangular system of linear equations, multiple right-hand sides
Related keywords: DTBTRSLAPACKlinear equationsreal, band, triangular matrix
F07VGF   15  nagf_lapacklin_dtbcon
Estimate condition number of real band triangular matrix
Related keywords: condition number, matrixDTBCONLAPACKlinear equationsreal, band, triangular matrix
F07VHF   15  nagf_lapacklin_dtbrfs
Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorDTBRFSerror bound, matrixforward errorLAPACKlinear equationsreal, band, triangular matrix
F07VSF   15  nagf_lapacklin_ztbtrs
Solution of complex band triangular system of linear equations, multiple right-hand sides
Related keywords: complex, band, triangular matrixLAPACKlinear equationsZTBTRS
F07VUF   15  nagf_lapacklin_ztbcon
Estimate condition number of complex band triangular matrix
Related keywords: complex, band, triangular matrixcondition number, matrixLAPACKlinear equationsZTBCON
F07VVF   15  nagf_lapacklin_ztbrfs
Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, band, triangular matrixerror bound, matrixforward errorLAPACKlinear equationsZTBRFS
F08HAF   21  nagf_lapackeig_dsbev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
Related keywords: DSBEVeigenproblemLAPACKLAPACKleast squares QR algorithmreal, band, symmetric matrix
F08HBF   21  nagf_lapackeig_dsbevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
Related keywords: DSBEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, band, symmetric matrix
F08HCF   19  nagf_lapackeig_dsbevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: divide-and-conquer methodDSBEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresPal–Walker–Kahan ( QL or QR ) algorithmreal, band, symmetric matrix
F08HEF   16  nagf_lapackeig_dsbtrd
Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
Related keywords: DSBTRDeigenproblemLAPACKLAPACKleast squaresorthogonal transformationsreal, band, symmetric matrix
F08HNF   21  nagf_lapackeig_zhbev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
Related keywords: complex, band, Hermitian matrixeigenproblemLAPACKLAPACKleast squares QR algorithmunitary transformationsZHBEV
F08HPF   21  nagf_lapackeig_zhbevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
Related keywords: complex, band, Hermitian matrixeigenproblemLAPACKLAPACKleast squaresunitary transformationsZHBEVX
F08HQF   19  nagf_lapackeig_zhbevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
Related keywords: complex, band, Hermitian matrixdivide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresPal–Walker–Kahan ( QL or QR ) algorithmZHBEVD
F08HSF   16  nagf_lapackeig_zhbtrd
Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
Related keywords: complex, band, Hermitian matrixeigenproblemLAPACKLAPACKleast squaresunitary transformationsZHBTRD
F08JAF   21  nagf_lapackeig_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: DSTEVeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JBF   21  nagf_lapackeig_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: bisection methodDSTEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares QR algorithmreal, symmetric, tridiagonal matrix
F08JCF   19  nagf_lapackeig_dstevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
Related keywords: divide-and-conquer methodDSTEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresPal–Walker–Kahan ( QL or QR ) algorithmreal, symmetric, tridiagonal matrix
F08JDF   21  nagf_lapackeig_dstevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
Related keywords: dqds algorithmDSTEVReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, symmetric, tridiagonal matrixrelatively robust representations
F08JEF   16  nagf_lapackeig_dsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit Q L or Q R algorithm
Related keywords: DSTEQReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JFF   16  nagf_lapackeig_dsterf
Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the Q L or Q R algorithm
Related keywords: DSTERFeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JGF   16  nagf_lapackeig_dpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
Related keywords: DPTEQReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, symmetric, tridiagonal matrix
F08JHF   22  nagf_lapackeig_dstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
Related keywords: divide-and-conquer methodDSTEDCeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
F08JJF   16  nagf_lapackeig_dstebz
Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection
Related keywords: bisection methodDSTEBZeigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, symmetric, tridiagonal matrix
F08JKF   16  nagf_lapackeig_dstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
Related keywords: DSTEINeigenproblemeigenvectorsinverse iterationLAPACKLAPACKleast squaresreal, symmetric, tridiagonal matrix
F08JLF   22  nagf_lapackeig_dstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
Related keywords: dqds algorithmDSTEGReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, symmetric, tridiagonal matrixrelatively robust representations
F08JXF   16  nagf_lapackeig_zstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
Related keywords: eigenproblemeigenvectorsinverse iterationLAPACKLAPACKleast squaresreal, symmetric, tridiagonal matrixZSTEIN
F08JYF   22  nagf_lapackeig_zstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
Related keywords: dqds algorithmeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, symmetric, tridiagonal matrixrelatively robust representationsZSTEGR
F08LEF   19  nagf_lapackeig_dgbbrd
Performs a reduction of real rectangular band matrix to upper bidiagonal form
Related keywords: DGBBRDeigenproblemGivens rotationsLAPACKLAPACKleast squaresreal, band, m by n matrix
F08LSF   19  nagf_lapackeig_zgbbrd
Reduction of complex rectangular band matrix to upper bidiagonal form
Related keywords: eigenproblemGivens rotationsLAPACKLAPACKleast squaresreal, band, m by n matrixZGBBRD
F08MDF   22  nagf_lapackeig_dbdsdc
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
Related keywords: DBDSDCdivide-and-conquer methodeigenproblemLAPACKLAPACKleast squares QR algorithmreal, bidiagonal matrixSVD, singular value decomposition
F08MEF   16  nagf_lapackeig_dbdsqr
Performs an SVD of real bidiagonal matrix reduced from real general matrix
Related keywords: DBDSQRdifferential qd algorithmeigenproblemLAPACKLAPACKleast squares QL algorithm QR algorithmreal, bidiagonal matrixSVD, singular value decomposition
F08MSF   16  nagf_lapackeig_zbdsqr
Performs an SVD of real bidiagonal matrix reduced from complex general matrix
Related keywords: differential qd algorithmeigenproblemLAPACKLAPACKleast squares QL algorithm QR algorithmreal, bidiagonal matrixSVD, singular value decompositionZBDSQR
F08UAF   21  nagf_lapackeig_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: DSBGVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, band, positive-definite, symmetric matrix
F08UBF   21  nagf_lapackeig_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: DSBGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, band, positive-definite, symmetric matrix
F08UCF   21  nagf_lapackeig_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodDSBGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresreal, band, positive-definite, symmetric matrix
F08UEF   19  nagf_lapackeig_dsbgst
Performs a reduction of real symmetric-definite banded generalized eigenproblem A x = λ B x to standard form C y = λ y , such that C has the same bandwidth as A
Related keywords: DSBGSTeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresreal, band, positive-definite, symmetric matrix
F08UFF   19  nagf_lapackeig_dpbstf
Computes a split Cholesky factorization of real symmetric positive definite band matrix A
Related keywords: Cholesky decompositionDPBSTFDSBGSTeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresreal, band, positive-definite, symmetric matrix
F08UNF   21  nagf_lapackeig_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHBGV
F08UPF   21  nagf_lapackeig_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHBGVX
F08UQF   21  nagf_lapackeig_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: complex, band, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresZHBGVD
F08USF   19  nagf_lapackeig_zhbgst
Performs a reduction of complex Hermitian-definite banded generalized eigenproblem A x = λ B x to standard form C y = λ y , such that C has the same bandwidth as A
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresZHBGST
F08UTF   19  nagf_lapackeig_zpbstf
Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresSplit Cholesky factorizationZPBSTF
F16RBF   23  nagf_blast_dgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, real band matrix
Related keywords: 1-normabsolute valueabsolute valuebanded matrixFrobenius normfurther linear algebra support routinesinfinity-normnorm, matrixreal, band, m by n matrix
F16UBF   23  nagf_blast_zgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, complex band matrix
Related keywords: 1-normabsolute valuebanded matrixcomplex, band matrixFrobenius normfurther linear algebra support routinesinfinity-normnorm, matrix
matrix, rank F01BLF   nagf_matop_real_gen_pseudinv
Pseudo-inverse and rank of real m by n matrix m n
Related keywords: inversionmatrix operationspseudo-inversereal, m by n matrix
matrix, reorder F11ZAF   18  nagf_sparse_real_gen_sort
Real sparse nonsymmetric matrix reorder routine
Related keywords: big datadata analyticslarge scale linear systemsreal, sparse matrix
F11ZBF   17  nagf_sparse_real_symm_sort
Real sparse symmetric matrix reorder routine
Related keywords: big datadata analyticslarge scale linear systemsreal, sparse, symmetric matrix
F11ZNF   19  nagf_sparse_complex_gen_sort
Complex sparse non-Hermitian matrix reorder routine
Related keywords: big datacomplex, sparse matrixdata analyticslarge scale linear systems
F11ZPF   19  nagf_sparse_complex_herm_sort
Complex sparse Hermitian matrix reorder routine
Related keywords: big datacomplex, Hermitian, sparse matrixdata analyticslarge scale linear systems
matrix, sparse F02EKF   24  nagf_eigen_real_gen_sparse_arnoldi
Selected eigenvalues and eigenvectors of a real sparse general matrix
Related keywords: big datadata analyticseigenvalueseigenvectorslarge scale eigenproblemsreal, sparse matrix
F02FJF   11  nagf_eigen_real_symm_sparse_eigsys
Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box)
Related keywords: big datadata analyticseigenvalueseigenvectorsreal, sparse, symmetric matrix
F02FKF   25  nagf_eigen_real_symm_sparse_arnoldi
Selected eigenvalues and eigenvectors of a real symmetric sparse matrix
Related keywords: big datadata analyticseigenproblemeigenvalueseigenvalueseigenvectorseigenvectorslarge scale eigenproblemsreal, sparse, symmetric matrixsparse eigenproblem
F04AXF   nagf_linsys_real_sparse_fac_solve
Solution of real sparse simultaneous linear equations (coefficient matrix already factorized)
Related keywords: big datadata analyticslinear equationsreal, sparse matrixsimultaneous linear equations
F04QAF   11  nagf_linsys_real_gen_sparse_lsqsol
Sparse linear least squares problem, m real equations in n unknowns
Related keywords: big datadata analyticsleast squaresreal, m by n matrixregressionridgesimultaneous linear equations
matrix, upper trapezoidal F08BHF   22  nagf_lapackeig_dtzrzf
Reduces a real upper trapezoidal matrix to upper triangular form
Related keywords: DTZRZFeigenproblemLAPACKLAPACKleast squaresmatrix, upper triangularorthogonal transformationsreal, trapezoidal matrix
F08BVF   22  nagf_lapackeig_ztzrzf
Reduces a complex upper trapezoidal matrix to upper triangular form
Related keywords: complex, trapezoidal matrixeigenproblemLAPACKLAPACKleast squaresmatrix, upper triangularZTZRZF
matrix, upper triangular F08BHF   22  nagf_lapackeig_dtzrzf
Reduces a real upper trapezoidal matrix to upper triangular form
Related keywords: DTZRZFeigenproblemLAPACKLAPACKleast squaresmatrix, upper trapezoidalorthogonal transformationsreal, trapezoidal matrix
F08BVF   22  nagf_lapackeig_ztzrzf
Reduces a complex upper trapezoidal matrix to upper triangular form
Related keywords: complex, trapezoidal matrixeigenproblemLAPACKLAPACKleast squaresmatrix, upper trapezoidalZTZRZF
matrix constraints E04RDF   26  nagf_opt_sdp_read_sdpa
A reader of sparse SDPA data files for linear SDP problems
Related keywords: least squares fittinglinear matrix inequalityLMImaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationSDPsemidefinite programmingservice routine
E04RNF   26  nagf_opt_handle_set_linmatineq
Add one or more linear matrix inequality constraints to a problem initialized by E04RAF
Related keywords: least squares fittinglinear matrix inequalityLMImaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04RPF   26  nagf_opt_handle_set_quadmatineq
Define bilinear matrix terms to a problem initialized by E04RAF
Related keywords: bilinear matrix inequalityBMIleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04SVF   26  nagf_opt_handle_solve_pennon
Run the Pennon solver on a compatible problem initialized by E04RAF and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI)
Related keywords: bilinear matrix inequalityBMIgeneralized augmented Lagrangian methodLagrangianleast squares fittinglinear matrix inequalityLMImaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionmonitoring informationoptimizationoptimizationSDPsemidefinite programming
matrix exponential F01ECF   22  nagf_matop_real_gen_matrix_exp
Real matrix exponential
Related keywords: exponential, matrixinversionmatrix operationsreal, nonsymmetric matrix
F01EDF   23  nagf_matop_real_symm_matrix_exp
Real symmetric matrix exponential
Related keywords: exponential, matrixfinanceinversionmatrix operationsreal, indefinite, symmetric matrix
F01FCF   23  nagf_matop_complex_gen_matrix_exp
Complex matrix exponential
Related keywords: complex, nonsymmetric matrixexponential, matrixfinanceinversionmatrix operations
F01FDF   23  nagf_matop_complex_herm_matrix_exp
Complex Hermitian matrix exponential
Related keywords: complex, Hermitian, indefinite matrixexponential, matrixfinanceinversionmatrix operations
F01GAF   24  nagf_matop_real_gen_matrix_actexp
Action of a real matrix exponential on a real matrix
Related keywords: exponential, matrixinversionmatrix operationsproduct, matricesreal, nonsymmetric matrix
F01GBF   24  nagf_matop_real_gen_matrix_actexp_rcomm
Action of a real matrix exponential on a real matrix (reverse communication)
Related keywords: exponential, matrixinversionmatrix operationsproduct, matricesreal, nonsymmetric matrix
F01HAF   24  nagf_matop_complex_gen_matrix_actexp
Action of a complex matrix exponential on a complex matrix
Related keywords: complex, nonsymmetric matrixexponential, matrixinversionmatrix operationsproduct, matrices
F01HBF   24  nagf_matop_complex_gen_matrix_actexp_rcomm
Action of a complex matrix exponential on a complex matrix (reverse communication)
Related keywords: complex, nonsymmetric matrixexponential, matrixinversionmatrix operationsproduct, matrices
matrix functions F01EFF   23  nagf_matop_real_symm_matrix_fun
Function of a real symmetric matrix
Related keywords: financefunctions, matrixinversionmatrix operationsreal, indefinite, symmetric matrix
F01ELF   24  nagf_matop_real_gen_matrix_fun_num
Function of a real matrix (using numerical differentiation)
Related keywords: functions, matrixinversionmatrix operationsreal, nonsymmetric matrix
F01EMF   24  nagf_matop_real_gen_matrix_fun_usd
Function of a real matrix (using user-supplied derivatives)
Related keywords: functions, matrixinversionmatrix operationsreal, nonsymmetric matrix
F01FFF   23  nagf_matop_complex_herm_matrix_fun
Function of a complex Hermitian matrix
Related keywords: complex, Hermitian, indefinite matrixfinancefunctions, matrixinversionmatrix operations
F01FLF   24  nagf_matop_complex_gen_matrix_fun_num
Function of a complex matrix (using numerical differentiation)
Related keywords: complex, nonsymmetric matrixfunctions, matrixinversionmatrix operations
F01FMF   24  nagf_matop_complex_gen_matrix_fun_usd
Function of a complex matrix (using user-supplied derivatives)
Related keywords: complex, nonsymmetric matrixfunctions, matrixinversionmatrix operations
F01JBF   24  nagf_matop_real_gen_matrix_cond_num
Condition number for a function of a real matrix (using numerical differentiation)
Related keywords: condition number, matrixinversionmatrix operationsreal, nonsymmetric matrix
F01JCF   24  nagf_matop_real_gen_matrix_cond_usd
Condition number for a function of a real matrix (using user-supplied derivatives)
Related keywords: condition number, matrixinversionmatrix operationsreal, nonsymmetric matrix
F01KBF   24  nagf_matop_complex_gen_matrix_cond_num
Condition number for a function of a complex matrix (using numerical differentiation)
Related keywords: complex, nonsymmetric matrixcondition number, matrixinversionmatrix operations
F01KCF   24  nagf_matop_complex_gen_matrix_cond_usd
Condition number for a function of a complex matrix (using user-supplied derivatives)
Related keywords: complex, nonsymmetric matrixcondition number, matrixinversionmatrix operations
matrix inverse F01ABF   nagf_matop_real_symm_posdef_inv
Inverse of real symmetric positive definite matrix using iterative refinement
Related keywords: inverse, matrixinversionmatrix operationsreal, positive-definite, symmetric matrix
F01ADF   nagf_matop_real_symm_posdef_inv_noref
Inverse of real symmetric positive definite matrix
Related keywords: inverse, matrixinversionmatrix operationsreal, positive-definite, symmetric matrix
matrix logarithm F01EJF   24  nagf_matop_real_gen_matrix_log
Real matrix logarithm
Related keywords: inversionlogarithm, matrixmatrix operationsreal, nonsymmetric matrix
F01FJF   24  nagf_matop_complex_gen_matrix_log
Complex matrix logarithm
Related keywords: complex, nonsymmetric matrixinversionlogarithm, matrixmatrix operations
matrix operations F01 Chapter Introduction     Matrix Operations, Including Inversion
Related keywords: inversion
matrix operations including inversion F01EQF   25  nagf_matop_real_gen_matrix_pow
General power of a real matrix
Related keywords: general powerinversionmatrix operations
F01FQF   25  nagf_matop_complex_gen_matrix_pow
General power of a complex matrix
Related keywords: eigenvalues and eigenvectorsgeneral powerinversionmatrix operations
F01JEF   25  nagf_matop_real_gen_matrix_cond_pow
Condition number for real matrix power
Related keywords: condition numberinversionmatrix operations
F01JFF   25  nagf_matop_real_gen_matrix_frcht_pow
Fréchet derivative of real matrix power
Related keywords: Fréchet derivativeinversionmatrix operations
F01KEF   25  nagf_matop_complex_gen_matrix_cond_pow
Condition number for complex matrix power
Related keywords: condition numbereigenvalues and eigenvectorsinversionmatrix operations
F01KFF   25  nagf_matop_complex_gen_matrix_frcht_pow
Fréchet derivative of complex matrix power
Related keywords: eigenvalues and eigenvectorsFréchet derivativeinversionmatrix operations
maximal-overlap C09DAF   25  nagf_wav_1d_mxolap_fwd
One-dimensional maximal overlap discrete wavelet transform (MODWT)
Related keywords: discretestationarywavelet transforms
C09DBF   25  nagf_wav_1d_mxolap_inv
One-dimensional inverse maximal overlap discrete wavelet transform (IMODWT)
Related keywords: discreteinversestationarywavelet transforms
C09DCF   25  nagf_wav_1d_mxolap_multi_fwd
One-dimensional multi-level maximal overlap discrete wavelet transform (MODWT)
Related keywords: discretemulti-levelstationarywavelet transforms
C09DDF   25  nagf_wav_1d_mxolap_multi_inv
One-dimensional inverse multi-level maximal overlap discrete wavelet transform (IMODWT)
Related keywords: discreteinversemulti-levelstationarywavelet transforms
maximization E04RAF   26  nagf_opt_handle_init
Initialization of a handle for the NAG optimization modelling suite for problems, such as, linear programming (LP), quadratic programming (QP), nonlinear programming (NLP), least squares (LSQ) problems, linear semidefinite programming (SDP) or SDP with bilinear matrix inequalities (BMI-SDP)
Related keywords: initializationleast squares fittingmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationSDPsemidefinite programming
E04RDF   26  nagf_opt_sdp_read_sdpa
A reader of sparse SDPA data files for linear SDP problems
Related keywords: least squares fittinglinear matrix inequalityLMImatrix constraintsmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationSDPsemidefinite programmingservice routine
E04REF   26  nagf_opt_handle_set_linobj
Define a linear objective function to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04RFF   26  nagf_opt_handle_set_quadobj
Define a linear or a quadratic objective function to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationQP
E04RGF   26  nagf_opt_handle_set_nlnobj
Define a nonlinear objective function to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPoptimizationoptimization
E04RHF   26  nagf_opt_handle_set_simplebounds
Define bounds of variables of a problem initialized by E04RAF
Related keywords: bound boxleast squares fittingmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04RJF   26  nagf_opt_handle_set_linconstr
Define a block of linear constraints to a problem initialized by E04RAF
Related keywords: least squares fittinglinearly-constrainedmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04RKF   26  nagf_opt_handle_set_nlnconstr
Define a block of nonlinear constraints to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinearly-constrainedoptimizationoptimization
E04RLF   26  nagf_opt_handle_set_nlnhess
Define a structure of Hessian of the objective, constraints or the Lagrangian to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPoptimizationoptimization
E04RMF   26  nagf_opt_handle_set_nlnls
Define a nonlinear least squares objective function to a problem initialized by E04RAF
Related keywords: calibrationdata fittingderivative-free optimizationDFOleast squares fittingmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinear least squaresoptimizationoptimizationoptimizationsum of squares
E04RNF   26  nagf_opt_handle_set_linmatineq
Add one or more linear matrix inequality constraints to a problem initialized by E04RAF
Related keywords: least squares fittinglinear matrix inequalityLMImatrix constraintsmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04RPF   26  nagf_opt_handle_set_quadmatineq
Define bilinear matrix terms to a problem initialized by E04RAF
Related keywords: bilinear matrix inequalityBMIleast squares fittingmatrix constraintsmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04RZF   26  nagf_opt_handle_free
Destroy the problem handle initialized by E04RAF and deallocate all the memory used
Related keywords: freeleast squares fittingmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04STF   26  nagf_opt_handle_solve_ipopt
Run an interior point solver on a sparse nonlinear programming problem (NLP) initialized by E04RAF and defined by other routines from the suite
Related keywords: interior point methodIPMleast squares fittingmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinear programmingoptimizationoptimization
E04SVF   26  nagf_opt_handle_solve_pennon
Run the Pennon solver on a compatible problem initialized by E04RAF and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI)
Related keywords: bilinear matrix inequalityBMIgeneralized augmented Lagrangian methodLagrangianleast squares fittinglinear matrix inequalityLMImatrix constraintsmaximizing a functionminimizing a functionminimizing or maximizing a functionmonitoring informationoptimizationoptimizationSDPsemidefinite programming
E04ZMF   26  nagf_opt_handle_opt_set
Option setting routine for the solvers from the NAG optimization modelling suite
Related keywords: least squares fittingmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04ZNF   26  nagf_opt_handle_opt_get
Option getting routine for the solvers from the NAG optimization modelling suite
Related keywords: least squares fittingmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04ZPF   26  nagf_opt_handle_opt_set_file
Option setting routine for the solvers from the NAG optimization modelling suite from external file
Related keywords: maximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationoptions, computational
maximizing a function E04 Chapter Introduction     Minimizing or Maximizing a Function
Related keywords: minimizing a functionoptimization
maximum exponent X02BLF   12  nagf_machine_model_maxexp
The floating-point model parameter e max
Related keywords: floating-point modelmachine constants
maximum likelihood G02JAF   21  nagf_correg_mixeff_reml
Linear mixed effects regression using Restricted Maximum Likelihood (REML)
Related keywords: big datacorrelation analysisdata analyticsfinancemixed effects regressionnonlinear regressionpolynomial regressionregression analysisREML, Restricted Maximum Likelihood
G02JBF   21  nagf_correg_mixeff_ml
Linear mixed effects regression using Maximum Likelihood (ML)
Related keywords: big datacorrelation analysisdata analyticsfinancemixed effects regressionnonlinear regressionpolynomial regressionregression analysis
G02JEF   23  nagf_correg_mixeff_hier_ml
Hierarchical mixed effects regression using Maximum Likelihood (ML)
Related keywords: big datacorrelation analysisdata analyticshierarchical mixed effects regressionmixed effects regressionnonlinear regressionpolynomial regressionregression analysis
G03CAF   15  nagf_mv_factor
Computes maximum likelihood estimates of the parameters of a factor analysis model, factor loadings, communalities and residual correlations
Related keywords: communalities, maximum likelihoodfactor analysisfactor loadingsmultivariate methodsresidual correlations
G03CCF   15  nagf_mv_factor_score
Computes factor score coefficients (for use after G03CAF)
Related keywords: factor analysisfactor score coefficientsmultivariate methods
G07BBF   15  nagf_univar_estim_normal
Computes maximum likelihood estimates for parameters of the Normal distribution from grouped and/or censored data
Related keywords: censored dataGaussian distributiongrouping dataNormal distributionunivariate estimation
G07BEF   15  nagf_univar_estim_weibull
Computes maximum likelihood estimates for parameters of the Weibull distribution
Related keywords: univariate estimationWeibull distribution
G07BFF   23  nagf_univar_estim_genpareto
Estimates parameter values of the generalized Pareto distribution
Related keywords: momentsPareto distributionunivariate estimation
G13DDF   22  nagf_tsa_multi_varma_estimate
Multivariate time series, estimation of VARMA model
Related keywords: big datacorrelation matrixdata analyticsfinancemultivariate time seriesstandard errorstime seriestime series analysisVARMA, vector autoregressive moving average model
maximum value F16DNF   22  nagf_blast_imax_val
Maximum value and location, integer vector
Related keywords: further linear algebra support routines
F16DQF   22  nagf_blast_iamax_val
Maximum absolute value and location, integer vector
Related keywords: absolute valuefurther linear algebra support routines
F16JNF   22  nagf_blast_dmax_val
Maximum value and location, real vector
Related keywords: blasblas_dmax_valfurther linear algebra support routines
F16JQF   22  nagf_blast_damax_val
Maximum absolute value and location, real vector
Related keywords: absolute valueblasblas_damax_valfurther linear algebra support routines
F16JSF   22  nagf_blast_zamax_val
Maximum absolute value and location, complex vector
Related keywords: absolute valueblasblas_zamax_valfurther linear algebra support routines
G01ABF   nagf_stat_summary_2var
Means, corrected sums of squares and cross-products, etc., two variables, from raw data
Related keywords: cross-productsmeanminimum valueproduct-moment correlation coefficientsSimple Calculations on Statistical Datasum of squares
G01ALF   14  nagf_stat_5pt_summary
Computes a five-point summary (median, hinges and extremes)
Related keywords: financefive-point summaryhingesmedianminimum valueSimple Calculations on Statistical Data
G01ATF   24  nagf_stat_summary_onevar
Computes univariate summary information: mean, variance, skewness, kurtosis
Related keywords: big datadata analyticsdata streamkurtosismeanminimum valueSimple Calculations on Statistical Dataskewnessstandard deviationstreaming
mean G01ABF   nagf_stat_summary_2var
Means, corrected sums of squares and cross-products, etc., two variables, from raw data
Related keywords: cross-productsmaximum valueminimum valueproduct-moment correlation coefficientsSimple Calculations on Statistical Datasum of squares
G01ADF   nagf_stat_summary_freq
Mean, variance, skewness, kurtosis, etc., one variable, from frequency table
Related keywords: financekurtosisSimple Calculations on Statistical Dataskewnessstandard deviation
G01ATF   24  nagf_stat_summary_onevar
Computes univariate summary information: mean, variance, skewness, kurtosis
Related keywords: big datadata analyticsdata streamkurtosismaximum valueminimum valueSimple Calculations on Statistical Dataskewnessstandard deviationstreaming
G01WAF   24  nagf_stat_moving_average
Computes the mean and standard deviation using a rolling window
Related keywords: big datadata analyticsdata streammoving averageSimple Calculations on Statistical Datastandard deviationstreaming
G02BDF   nagf_correg_coeffs_zero
Correlation-like coefficients (about zero), all variables, no missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancenonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BEF   nagf_correg_coeffs_zero_miss_case
Correlation-like coefficients (about zero), all variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BFF   nagf_correg_coeffs_zero_miss_pair
Correlation-like coefficients (about zero), all variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BGF   nagf_correg_coeffs_pearson_subset
Pearson product-moment correlation coefficients, subset of variables, no missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancenonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviationsum of squares
G02BHF   nagf_correg_coeffs_pearson_subset_miss_case
Pearson product-moment correlation coefficients, subset of variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemissing valuesnonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviationsum of squares
G02BJF   nagf_correg_coeffs_pearson_subset_miss_pair
Pearson product-moment correlation coefficients, subset of variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemissing valuesnonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviationsum of squares
G02BKF   nagf_correg_coeffs_zero_subset
Correlation-like coefficients (about zero), subset of variables, no missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancenonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BLF   nagf_correg_coeffs_zero_subset_miss_case
Correlation-like coefficients (about zero), subset of variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BMF   nagf_correg_coeffs_zero_subset_miss_pair
Correlation-like coefficients (about zero), subset of variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BTF   14  nagf_correg_ssqmat_update
Update a weighted sum of squares matrix with a new observation
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancenonlinear regressionpolynomial regressionregression analysissum of squares
G02BUF   14  nagf_correg_ssqmat
Computes a weighted sum of squares matrix
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancenonlinear regressionpolynomial regressionregression analysissum of squaresWest's WV2 algorithm
G02BXF   14  nagf_correg_corrmat
Computes (optionally weighted) correlation and covariance matrices
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviationvariance-covariance matrix
G02BZF   24  nagf_correg_ssqmat_combine
Combines two sums of squares matrices, for use after G02BUF
Related keywords: big datacorrelation analysiscross-productsdata analyticsdata streamnonlinear regressionpolynomial regressionregression analysisstreamingsum of squares
G07DAF   13  nagf_univar_robust_1var_median
Robust estimation, median, median absolute deviation, robust standard deviation
Related keywords: medianrobust estimationstandard deviationunivariate estimation
G13ABF   nagf_tsa_uni_autocorr
Univariate time series, sample autocorrelation function
Related keywords: autocorrelation coefficientsbig datadata analyticsfinancetest statistictime seriestime series analysisunivariate time seriesvariance
G13AUF   14  nagf_tsa_uni_means
Computes quantities needed for range-mean or standard deviation-mean plot
Related keywords: big datadata analyticsfinancerangerange-mean plotstandard deviationtime seriestime series analysis
median G01ALF   14  nagf_stat_5pt_summary
Computes a five-point summary (median, hinges and extremes)
Related keywords: financefive-point summaryhingesmaximum valueminimum valueSimple Calculations on Statistical Data
G07DAF   13  nagf_univar_robust_1var_median
Robust estimation, median, median absolute deviation, robust standard deviation
Related keywords: meanrobust estimationstandard deviationunivariate estimation
median test G08ACF   nagf_nonpar_test_median
Median test on two samples of unequal size
Related keywords: nonparametric statistics
mersenne twister G05KFF   22  nagf_rand_init_repeat
Initializes a pseudorandom number generator to give a repeatable sequence
Related keywords: ACORNbig datadata analyticsMRG32k3aoptions, computationalrandom number generatorsrandom numbersWichmann Hill
G05KGF   22  nagf_rand_init_nonrepeat
Initializes a pseudorandom number generator to give a non-repeatable sequence
Related keywords: ACORNbig datadata analyticsMRG32k3aoptions, computationalrandom number generatorsrandom numbersWichmann Hill
Merton model, option pricing S30JAF   22  nagf_specfun_opt_jumpdiff_merton_price
Jump-diffusion, Merton's model, option pricing formula
Related keywords: approximations of special functionsderivative, optionsfinancejump-diffusion model, option pricingoption pricing
S30JBF   22  nagf_specfun_opt_jumpdiff_merton_greeks
Jump-diffusion, Merton's model, option pricing formula with Greeks
Related keywords: approximations of special functionsderivative, optionsfinanceGreeks, optionsjump-diffusion model, option pricingoption pricing
mesh generation D03MAF   nagf_pde_2d_triangulate
Triangulation of plane region
Related keywords: PDE, partial differential equationstriangularization, mesh generation
D06 Chapter Introduction     Mesh Generation
mesh joining D06DBF   20  nagf_mesh_2d_join
Joins together two given adjacent (possibly overlapping) meshes
Related keywords: mesh generation
mesh refinement D03RAF   18  nagf_pde_2d_gen_order2_rectangle
General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region
Related keywords: method of linesPDE, partial differential equationstwo-dimensional PDE
D03RBF   18  nagf_pde_2d_gen_order2_rectilinear
General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectilinear region
Related keywords: method of linesPDE, partial differential equationstwo-dimensional PDE
D03RZF   18  nagf_pde_2d_gen_order2_rectilinear_extractgrid
Extract grid data from D03RBF
Related keywords: grid extractionmethod of linesPDE, partial differential equationstwo-dimensional PDE
mesh renumbering D06CCF   20  nagf_mesh_2d_renumber
Renumbers a given mesh using Gibbs method
Related keywords: Gibbs methodmesh generation
M -estimates G02HAF   13  nagf_correg_robustm
Robust regression, standard M -estimates
Related keywords: Andrew's sine wavebig datacorrelation analysisdata analyticsfinanceHampel's piecewise linear functionHuber type regressionKrasker–Welsch weightsMallows type regressionMaronna's weightsnonlinear regressionpolynomial regressionregressionregression analysisrobust regressionScheppe type regressionTukey's bi-weight
G02HDF   13  nagf_correg_robustm_user
Robust regression, compute regression with user-supplied functions and weights
Related keywords: big databounded influencecorrelation analysisdata analyticsfinanceiterative weighted least squaresnonlinear regressionpolynomial regressionregression analysisrobust regression
G07DBF   13  nagf_univar_robust_1var_mestim
Robust estimation, M -estimates for location and scale parameters, standard weight functions
Related keywords: location, robust estimationrobust estimationscale parametersunivariate estimation
G07DCF   13  nagf_univar_robust_1var_mestim_wgt
Robust estimation, M -estimates for location and scale parameters, user-defined weight functions
Related keywords: location, robust estimationrobust estimationscale parametersunivariate estimation
method of lines D03PCF   15  nagf_pde_1d_parab_fd_old
General system of parabolic PDEs, method of lines, finite differences, one space variable
Related keywords: parabolic partial differential equationPDE, partial differential equations
D03PDF   15  nagf_pde_1d_parab_coll_old
General system of parabolic PDEs, method of lines, Chebyshev C 0 collocation, one space variable
Related keywords: collocation methodparabolic partial differential equationPDE, partial differential equations
D03PEF   16  nagf_pde_1d_parab_keller
General system of first-order PDEs, method of lines, Keller box discretization, one space variable
Related keywords: Keller box discretizationparabolic partial differential equationPDE, partial differential equations
D03PFF   17  nagf_pde_1d_parab_convdiff
General system of convection-diffusion PDEs with source terms in conservative form, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable
Related keywords: convection-diffusion, PDEpartial differential equationsPDE, partial differential equations
D03PHF   15  nagf_pde_1d_parab_dae_fd_old
General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable
Related keywords: DAE, differential algebraic equationsfinite difference discretizationparabolic partial differential equationpartial differential equationsPDE, partial differential equations
D03PJF   15  nagf_pde_1d_parab_dae_coll_old
General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C 0 collocation, one space variable
Related keywords: DAE, differential algebraic equationsparabolic partial differential equationpartial differential equationsPDE, partial differential equations
D03PKF   16  nagf_pde_1d_parab_dae_keller
General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretization, one space variable
Related keywords: DAE, differential algebraic equationsKeller box discretizationpartial differential equationsPDE, partial differential equations
D03PPF   16  nagf_pde_1d_parab_remesh_fd_old
General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable
Related keywords: DAE, differential algebraic equationsone-dimensionalparabolic partial differential equationPDE, partial differential equations
D03PRF   16  nagf_pde_1d_parab_remesh_keller
General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretization, remeshing, one space variable
Related keywords: adaptive grid, PDEDAE, differential algebraic equationsKeller box discretizationPDE, partial differential equations
D03PSF   17  nagf_pde_1d_parab_convdiff_remesh
General system of convection-diffusion PDEs, coupled DAEs, method of lines, upwind scheme, remeshing, one space variable
Related keywords: adaptive grid, PDEconvection-diffusion, PDEDAE, differential algebraic equationshyperbolic equationone-dimensionalparabolic partial differential equationPDE, partial differential equations
D03RAF   18  nagf_pde_2d_gen_order2_rectangle
General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region
Related keywords: mesh refinementPDE, partial differential equationstwo-dimensional PDE
D03RBF   18  nagf_pde_2d_gen_order2_rectilinear
General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectilinear region
Related keywords: mesh refinementPDE, partial differential equationstwo-dimensional PDE
D03RZF   18  nagf_pde_2d_gen_order2_rectilinear_extractgrid
Extract grid data from D03RBF
Related keywords: grid extractionmesh refinementPDE, partial differential equationstwo-dimensional PDE
Mexican hat wavelet C09BAF   23  nagf_wav_1d_cont
One-dimensional real continuous wavelet transform
Related keywords: derivative of a Gaussian waveletMorlet waveletwavelet continuouswaveletswavelets, one-dimensionalwavelet transforms
Mills' Ratio G01MBF   15  nagf_stat_mills_ratio
Computes reciprocal of Mills' Ratio
Related keywords: financehazard rateSimple Calculations on Statistical Data
minimal least squares F08BAF   21  nagf_lapackeig_dgelsy
Computes the minimum-norm solution to a real linear least squares problem
Related keywords: DGELSYeigenproblemfinanceLAPACKLAPACKleast squareslinear least squaresreal, m by n matrix
F08BNF   21  nagf_lapackeig_zgelsy
Computes the minimum-norm solution to a complex linear least squares problem
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squareslinear least squaresZGELSY
F08KAF   21  nagf_lapackeig_dgelss
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
Related keywords: DGELSSeigenproblemLAPACKLAPACKleast squareslinear least squaresreal, m by n matrixSVD, singular value decomposition
F08KCF   21  nagf_lapackeig_dgelsd
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
Related keywords: DGELSDdivide-and-conquer methodeigenproblemfinanceLAPACKLAPACKleast squareslinear least squaresreal, m by n matrixSVD, singular value decomposition
F08KNF   21  nagf_lapackeig_zgelss
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squareslinear least squaresSVD, singular value decompositionZGELSS
F08KQF   21  nagf_lapackeig_zgelsd
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
Related keywords: complex, m by n matrixdivide-and-conquer methodeigenproblemLAPACKLAPACKleast squareslinear least squaresSVD, singular value decompositionZGELSD
minimax E02ALF   25  nagf_fit_1d_minimax_polynomial
Minimax curve fit by polynomials
Related keywords: curve and surface fittingsurface fitting
minimization, nonlinear constraints E04UCF   12  nagf_opt_nlp1_solve_old
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: densefinancemaximizing a functionminimizing a functionNLPnonlinear programmingoptimizationsequential QP methodSQP
E04UDF   12  nagf_opt_nlp1_option_file_old
Supply values for E04UCF or E04UFF from external file
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalSQP
E04UEF   12  nagf_opt_nlp1_option_string_old
Supply values to E04UCF or E04UFF from a character string
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalSQP
E04UFF   18  nagf_opt_nlp1_rcomm_old
Nonlinear programming (NLP), dense, active-set, SQP method, using function values and optionally first derivatives (reverse communication, comprehensive)
Related keywords: densefinancemaximizing a functionminimizing a functionNLPnonlinear programmingoptimizationsequential QP methodSQP
E04UGF   19  nagf_opt_nlp1_sparse_solve_old
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives
Related keywords: financemaximizing a functionminimizing a functionNLPnonlinear programmingoptimizationsequential QP methodSQP
E04UQF   14  nagf_opt_lsq_gencon_deriv_option_file_old
Supply values for E04USF from external file
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationoptions, computationalSQPsum of squares
E04URF   14  nagf_opt_lsq_gencon_deriv_option_string_old
Supply values to E04USF from a character string
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationoptions, computationalSQPsum of squares
E04USF   14  nagf_opt_lsq_gencon_deriv_old
Minimum of a sum of squares, nonlinear constraints, dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: data fittingfinancemaximizing a functionminimizing a functionNLPnonlinear least squaresnonlinear programmingoptimizationquasi-Newton approximationsequential QP methodsum of squares
E04VGF   21  nagf_opt_nlp2_sparse_init
Initialization routine for E04VHF
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationoptions, computationalSQP
E04VHF   21  nagf_opt_nlp2_sparse_solve
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: financeLP, linear programmingmaximizing a functionminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton algorithmsequential QP methodsimplex algorithmSQP
E04VJF   21  nagf_opt_nlp2_sparse_jacobian
Determine the pattern of nonzeros in the Jacobian matrix for E04VHF
Related keywords: financemaximizing a functionminimizing a functionoptimizationsparsity structureSQP
E04VKF   21  nagf_opt_nlp2_sparse_option_file
Supply values for E04VHF from external file
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalSQP
E04VLF   21  nagf_opt_nlp2_sparse_option_string
Set a single option for E04VHF from a character string
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalSQP
E04VMF   21  nagf_opt_nlp2_sparse_option_integer_set
Set a single option for E04VHF from an integer argument
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalSQP
E04VNF   21  nagf_opt_nlp2_sparse_option_double_set
Set a single option for E04VHF from a real argument
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalSQP
E04VRF   21  nagf_opt_nlp2_sparse_option_integer_get
Get the setting of an integer valued option of E04VHF
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalSQP
E04VSF   21  nagf_opt_nlp2_sparse_option_double_get
Get the setting of a real valued option of E04VHF
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computationalSQP
E04WDF   21  nagf_opt_nlp2_solve
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: densefinancemaximizing a functionminimizing a functionNLPnonlinear programmingoptimizationsequential QP methodSQP
E04WEF   21  nagf_opt_nlp2_option_file
Supply values for E04WDF from external file
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationoptions, computationalSQP
E04WFF   21  nagf_opt_nlp2_option_string
Set a single option for E04WDF from a character string
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationoptions, computationalSQP
E04WGF   21  nagf_opt_nlp2_option_integer_set
Set a single option for E04WDF from an integer argument
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationoptions, computationalSQP
E05SBF   23  nagf_glopt_nlp_pso
Global optimization using particle swarm algorithm (PSO), comprehensive
Related keywords: global optimizationparticle swarm algorithmPSO, particle swarm algorithm
E05UCF   24  nagf_glopt_nlp_multistart_sqp
Global optimization using multi-start, nonlinear constraints
Related keywords: financeglobal optimizationmulti-start algorithmsequential QP method
minimization, simple bound constraints E04JCF   23  nagf_opt_bounds_bobyqa_func
Bound constrained minimum, model-based algorithm, using function values only
Related keywords: BOBYQA methodfinancemaximizing a functionminimizing a functionNLPnonlinear programmingoptimization
E04JYF   18  nagf_opt_bounds_quasi_func_easy
Bound constrained minimum, quasi-Newton algorithm, using function values only (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmfinancemaximizing a functionminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton algorithm
E04KDF   nagf_opt_bounds_mod_deriv_comp
Bound constrained minimum, modified Newton algorithm, using first derivatives (comprehensive)
Related keywords: financemaximizing a functionminimizing a functionNewton algorithmNLPnonlinear programmingoptimization
E04KYF   18  nagf_opt_bounds_quasi_deriv_easy
Bound constrained minimum, quasi-Newton algorithm, using first derivatives (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmfinancemaximizing a functionminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton algorithm
E04KZF   18  nagf_opt_bounds_mod_deriv_easy
Bound constrained minimum, modified Newton algorithm, using first derivatives (easy-to-use)
Related keywords: financemaximizing a functionminimizing a functionNewton algorithmNLPnonlinear programmingoptimization
E04LBF   nagf_opt_bounds_mod_deriv2_comp
Bound constrained minimum, modified Newton algorithm, using first and second derivatives (comprehensive)
Related keywords: financemaximizing a functionminimizing a functionNewton algorithmNLPnonlinear programmingoptimization
E04LYF   18  nagf_opt_bounds_mod_deriv2_easy
Bound constrained minimum, modified Newton algorithm, using first and second derivatives (easy-to-use)
Related keywords: financemaximizing a functionminimizing a functionNewton algorithmNLPnonlinear programmingoptimization
E05JAF   22  nagf_glopt_bnd_mcs_init
Initialization routine for E05JBF
Related keywords: global optimizationoptions, computational
E05JBF   22  nagf_glopt_bnd_mcs_solve
Global optimization by multi-level coordinate search, simple bounds, using function values only
Related keywords: financeglobal optimizationmulti-level coordinate searchoptions, computational
E05JCF   22  nagf_glopt_bnd_mcs_optset_file
Supply values for E05JBF from external file
Related keywords: global optimizationoptions, computational
E05JDF   22  nagf_glopt_bnd_mcs_optset_string
Set a single for E05JBF from a character string
Related keywords: global optimizationoptions, computational
E05JEF   22  nagf_glopt_bnd_mcs_optset_char
Set a single for E05JBF from an ON/OFF-valued character argument
Related keywords: global optimizationoptions, computational
E05JFF   22  nagf_glopt_bnd_mcs_optset_int
Set a single for E05JBF from an integer argument
Related keywords: global optimizationoptions, computational
E05JGF   22  nagf_glopt_bnd_mcs_optset_real
Set a single for E05JBF from a real argument
Related keywords: global optimizationoptions, computational
E05JHF   22  nagf_glopt_bnd_mcs_option_check
Determine whether an for E05JBF has been set by you or not
Related keywords: global optimizationoptions, computational
E05JKF   22  nagf_glopt_bnd_mcs_optget_int
Get the setting of an integer valued of E05JBF
Related keywords: global optimizationoptions, computational
E05JLF   22  nagf_glopt_bnd_mcs_optget_real
Get the setting of a real valued of E05JBF
Related keywords: global optimizationoptions, computational
E05SAF   23  nagf_glopt_bnd_pso
Global optimization using particle swarm algorithm (PSO), bound constraints only
Related keywords: global optimizationparticle swarm algorithmPSO, particle swarm algorithm
minimization, unconstrained E04ABF   nagf_opt_one_var_func_old
Minimum, function of one variable, using function values only
Related keywords: derivative-free minimizationfinancemaximizing a functionminimizing a functionNLPnonlinear programmingone-dimensional quadratic interpolationoptimizationunivariate minimization
E04CBF   22  nagf_opt_uncon_simplex
Unconstrained minimum, Nelder–Mead simplex algorithm, using function values only
Related keywords: derivative-free minimizationfinancemaximizing a functionminimizing a functionNelder–Mead algorithmNLPnonlinear programmingoptimizationsimplex algorithm
E04DGF   12  nagf_opt_uncon_conjgrd_comp_old
Unconstrained minimum, preconditioned conjugate gradient algorithm, using first derivatives (comprehensive)
Related keywords: conjugate gradient methodfinancemaximizing a functionminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton
E04DJF   12  nagf_opt_uncon_conjgrd_option_file_old
Supply values for E04DGF from external file
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computational
E04DKF   12  nagf_opt_uncon_conjgrd_option_string_old
Supply values to E04DGF from a character string
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computational
E04FCF   nagf_opt_lsq_uncon_mod_func_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (comprehensive)
Related keywords: data fittingderivative-free minimizationfinanceGauss–Newton optimizationmaximizing a functionminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04FYF   18  nagf_opt_lsq_uncon_mod_func_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (easy-to-use)
Related keywords: data fittingderivative-free minimizationfinanceGauss–Newton optimizationmaximizing a functionminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04GBF   nagf_opt_lsq_uncon_quasi_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (comprehensive)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmdata fittingfinanceGauss–Newton optimizationmaximizing a functionminimizing a functionnonlinear least squaresoptimizationquasi-Newton algorithmsum-of-squares minimization
E04GDF   nagf_opt_lsq_uncon_mod_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (comprehensive)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04GYF   18  nagf_opt_lsq_uncon_quasi_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmdata fittingfinanceGauss–Newton optimizationmaximizing a functionminimizing a functionnonlinear least squaresoptimizationquasi-Newton algorithmsum-of-squares minimization
E04GZF   18  nagf_opt_lsq_uncon_mod_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (easy-to-use)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04HCF   nagf_opt_check_deriv
Check user's routine for calculating first derivatives of function
Related keywords: check derivativefinancemaximizing a functionminimizing a functionoptimizationservice routine
E04HDF   nagf_opt_check_deriv2
Check user's routine for calculating second derivatives of function
Related keywords: check derivativefinancemaximizing a functionminimizing a functionoptimizationservice routine
E04HEF   nagf_opt_lsq_uncon_mod_deriv2_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
E04HYF   18  nagf_opt_lsq_uncon_mod_deriv2_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimizing a functionNewton algorithmnonlinear least squaresoptimizationsum-of-squares minimization
minimizing a function E04 Chapter Introduction     Minimizing or Maximizing a Function
Related keywords: maximizing a functionoptimization
minimizing or maximizing a function E04RAF   26  nagf_opt_handle_init
Initialization of a handle for the NAG optimization modelling suite for problems, such as, linear programming (LP), quadratic programming (QP), nonlinear programming (NLP), least squares (LSQ) problems, linear semidefinite programming (SDP) or SDP with bilinear matrix inequalities (BMI-SDP)
Related keywords: initializationleast squares fittingmaximizationmaximizing a functionminimizing a functionoptimizationoptimizationSDPsemidefinite programming
E04RDF   26  nagf_opt_sdp_read_sdpa
A reader of sparse SDPA data files for linear SDP problems
Related keywords: least squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionoptimizationoptimizationSDPsemidefinite programmingservice routine
E04REF   26  nagf_opt_handle_set_linobj
Define a linear objective function to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionoptimizationoptimization
E04RFF   26  nagf_opt_handle_set_quadobj
Define a linear or a quadratic objective function to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionoptimizationoptimizationQP
E04RGF   26  nagf_opt_handle_set_nlnobj
Define a nonlinear objective function to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionNLPoptimizationoptimization
E04RHF   26  nagf_opt_handle_set_simplebounds
Define bounds of variables of a problem initialized by E04RAF
Related keywords: bound boxleast squares fittingmaximizationmaximizing a functionminimizing a functionoptimizationoptimization
E04RJF   26  nagf_opt_handle_set_linconstr
Define a block of linear constraints to a problem initialized by E04RAF
Related keywords: least squares fittinglinearly-constrainedmaximizationmaximizing a functionminimizing a functionoptimizationoptimization
E04RKF   26  nagf_opt_handle_set_nlnconstr
Define a block of nonlinear constraints to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionNLPnonlinearly-constrainedoptimizationoptimization
E04RLF   26  nagf_opt_handle_set_nlnhess
Define a structure of Hessian of the objective, constraints or the Lagrangian to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionNLPoptimizationoptimization
E04RMF   26  nagf_opt_handle_set_nlnls
Define a nonlinear least squares objective function to a problem initialized by E04RAF
Related keywords: calibrationdata fittingderivative-free optimizationDFOleast squares fittingmaximizationmaximizing a functionminimizing a functionNLPnonlinear least squaresoptimizationoptimizationoptimizationsum of squares
E04RNF   26  nagf_opt_handle_set_linmatineq
Add one or more linear matrix inequality constraints to a problem initialized by E04RAF
Related keywords: least squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionoptimizationoptimization
E04RPF   26  nagf_opt_handle_set_quadmatineq
Define bilinear matrix terms to a problem initialized by E04RAF
Related keywords: bilinear matrix inequalityBMIleast squares fittingmatrix constraintsmaximizationmaximizing a functionminimizing a functionoptimizationoptimization
E04RZF   26  nagf_opt_handle_free
Destroy the problem handle initialized by E04RAF and deallocate all the memory used
Related keywords: freeleast squares fittingmaximizationmaximizing a functionminimizing a functionoptimizationoptimization
E04STF   26  nagf_opt_handle_solve_ipopt
Run an interior point solver on a sparse nonlinear programming problem (NLP) initialized by E04RAF and defined by other routines from the suite
Related keywords: interior point methodIPMleast squares fittingmaximizationmaximizing a functionminimizing a functionNLPnonlinear programmingoptimizationoptimization
E04SVF   26  nagf_opt_handle_solve_pennon
Run the Pennon solver on a compatible problem initialized by E04RAF and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI)
Related keywords: bilinear matrix inequalityBMIgeneralized augmented Lagrangian methodLagrangianleast squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionmonitoring informationoptimizationoptimizationSDPsemidefinite programming
E04ZMF   26  nagf_opt_handle_opt_set
Option setting routine for the solvers from the NAG optimization modelling suite
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionoptimizationoptimization
E04ZNF   26  nagf_opt_handle_opt_get
Option getting routine for the solvers from the NAG optimization modelling suite
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionoptimizationoptimization
E04ZPF   26  nagf_opt_handle_opt_set_file
Option setting routine for the solvers from the NAG optimization modelling suite from external file
Related keywords: maximizationmaximizing a functionminimizing a functionoptimizationoptimizationoptions, computational
minimum exponent X02BKF   12  nagf_machine_model_minexp
The floating-point model parameter e min
Related keywords: floating-point modelmachine constants
minimum value F16DPF   22  nagf_blast_imin_val
Minimum value and location, integer vector
Related keywords: further linear algebra support routines
F16DRF   22  nagf_blast_iamin_val
Minimum absolute value and location, integer vector
Related keywords: absolute valuefurther linear algebra support routines
F16JPF   22  nagf_blast_dmin_val
Minimum value and location, real vector
Related keywords: blasblas_dmax_valfurther linear algebra support routines
F16JRF   22  nagf_blast_damin_val
Minimum absolute value and location, real vector
Related keywords: absolute valueblasblas_damin_valfurther linear algebra support routines
F16JTF   22  nagf_blast_zamin_val
Minimum absolute value and location, complex vector
Related keywords: absolute valueblasblas_zamin_valfurther linear algebra support routines
G01ABF   nagf_stat_summary_2var
Means, corrected sums of squares and cross-products, etc., two variables, from raw data
Related keywords: cross-productsmaximum valuemeanproduct-moment correlation coefficientsSimple Calculations on Statistical Datasum of squares
G01ALF   14  nagf_stat_5pt_summary
Computes a five-point summary (median, hinges and extremes)
Related keywords: financefive-point summaryhingesmaximum valuemedianSimple Calculations on Statistical Data
G01ATF   24  nagf_stat_summary_onevar
Computes univariate summary information: mean, variance, skewness, kurtosis
Related keywords: big datadata analyticsdata streamkurtosismaximum valuemeanSimple Calculations on Statistical Dataskewnessstandard deviationstreaming
MINRES, iterative linear equation solver F11GEF   20  nagf_sparse_real_symm_basic_solver
Real sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos method or the MINRES algorithm
Related keywords: big dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse, symmetric matrix
missing values G02BBF   nagf_correg_coeffs_pearson_miss_case
Pearson product-moment correlation coefficients, all variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinancenonlinear regressionPearson product moment correlationpolynomial regressionregression analysis
G02BCF   nagf_correg_coeffs_pearson_miss_pair
Pearson product-moment correlation coefficients, all variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinancenonlinear regressionPearson product moment correlationpolynomial regressionregression analysis
G02BEF   nagf_correg_coeffs_zero_miss_case
Correlation-like coefficients (about zero), all variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BFF   nagf_correg_coeffs_zero_miss_pair
Correlation-like coefficients (about zero), all variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BHF   nagf_correg_coeffs_pearson_subset_miss_case
Pearson product-moment correlation coefficients, subset of variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeannonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviationsum of squares
G02BJF   nagf_correg_coeffs_pearson_subset_miss_pair
Pearson product-moment correlation coefficients, subset of variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeannonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviationsum of squares
G02BLF   nagf_correg_coeffs_zero_subset_miss_case
Correlation-like coefficients (about zero), subset of variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BMF   nagf_correg_coeffs_zero_subset_miss_pair
Correlation-like coefficients (about zero), subset of variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BPF   nagf_correg_coeffs_kspearman_miss_case_overwrite
Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinanceKendall's tau correlation coefficientnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02BRF   nagf_correg_coeffs_kspearman_miss_case
Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinanceKendall's tau correlation coefficientnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02BSF   nagf_correg_coeffs_kspearman_miss_pair
Kendall/Spearman non-parametric rank correlation coefficients, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinanceKendall's tau correlation coefficientnonlinear regressionpolynomial regressionregression analysisSpearman's rank correlation coefficients
G02CCF   nagf_correg_linregs_const_miss
Simple linear regression with constant term, missing values
Related keywords: big datacorrelation analysisdata analyticsfinancelinear regressionnonlinear regressionpolynomial regressionregressionregression analysis
G02CDF   nagf_correg_linregs_noconst_miss
Simple linear regression without constant term, missing values
Related keywords: big datacorrelation analysisdata analyticsfinancelinear regressionnonlinear regressionpolynomial regressionregressionregression analysis
mixed effects regression G02JAF   21  nagf_correg_mixeff_reml
Linear mixed effects regression using Restricted Maximum Likelihood (REML)
Related keywords: big datacorrelation analysisdata analyticsfinancemaximum likelihoodnonlinear regressionpolynomial regressionregression analysisREML, Restricted Maximum Likelihood
G02JBF   21  nagf_correg_mixeff_ml
Linear mixed effects regression using Maximum Likelihood (ML)
Related keywords: big datacorrelation analysisdata analyticsfinancemaximum likelihoodnonlinear regressionpolynomial regressionregression analysis
G02JCF   23  nagf_correg_mixeff_hier_init
Hierarchical mixed effects regression, initialization routine for G02JDF G02JEF
Related keywords: big datacorrelation analysisdata analyticshierarchical mixed effects regressionnonlinear regressionpolynomial regressionregression analysis
G02JDF   23  nagf_correg_mixeff_hier_reml
Hierarchical mixed effects regression using Restricted Maximum Likelihood (REML)
Related keywords: big datacorrelation analysisdata analyticshierarchical mixed effects regressionnonlinear regressionpolynomial regressionregression analysisREML, Restricted Maximum Likelihood
G02JEF   23  nagf_correg_mixeff_hier_ml
Hierarchical mixed effects regression using Maximum Likelihood (ML)
Related keywords: big datacorrelation analysisdata analyticshierarchical mixed effects regressionmaximum likelihoodnonlinear regressionpolynomial regressionregression analysis
mixed integer programming H02BBF   14  nagf_mip_ilp_dense
Integer LP problem (dense)
Related keywords: branch and boundfinanceinteger programmingoperations research
H02BFF   16  nagf_mip_ilp_mpsx
Interpret MPSX data file defining IP or LP problem, optimize and print solution
Related keywords: branch and boundinteger programmingMPSX formatoperations research
H02CBF   19  nagf_mip_iqp_dense
Integer QP problem (dense)
Related keywords: branch and boundfinanceinteger programminginteger quadratic programoperations researchQP, quadratic programming
H02CEF   19  nagf_mip_iqp_sparse
Integer LP or QP problem (sparse), using E04NKF
Related keywords: branch and boundfinanceinteger programminginteger quadratic programoperations researchQP, quadratic programming
H02CFF   19  nagf_mip_iqp_sparse_optfile
Read values for H02CEF from external file
Related keywords: integer programmingoperations researchoptions, computational
H02DAF   25  nagf_mip_sqp
Mixed integer nonlinear programming
Related keywords: integer programminginteger quadratic programnonlinear programmingoperations researchSQP, sequential quadratic programming
mixed-precision F07ACF   22  nagf_lapacklin_dsgesv
Computes the solution to a real system of linear equations using mixed precision arithmetic
Related keywords: DSGESVLAPACKlinear equationsreal, nonsymmetric matrix
F07AQF   22  nagf_lapacklin_zcgesv
Computes the solution to a complex system of linear equations using mixed precision arithmetic
Related keywords: complex, nonsymmetric matrixLAPACKlinear equationsZCGESV
F07FCF   23  nagf_lapacklin_dsposv
Computes the solution to a real symmetric positive definite system of linear equations using mixed precision arithmetic
Related keywords: Cholesky decompositionDSPOSVLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FQF   23  nagf_lapacklin_zcposv
Computes the solution to a complex Hermitian positive definite system of linear equations using mixed precision arithmetic
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixLAPACKlinear equationsZCPOSV
model selection G02MAF   25  nagf_correg_lars
Least angle regression (LARS), least absolute shrinkage and selection operator (LASSO) and forward stagewise regression
Related keywords: big datacorrelation analysisdata analyticsforward stagewiseLARSLASSOleast angle regressionnonlinear regressionpolynomial regressionregression analysis
G02MBF   25  nagf_correg_lars_xtx
Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) and forward stagewise regression using the cross-products matrix
Related keywords: big datacorrelation analysiscross-productdata analyticsforward stagewiseLARSLASSOleast angle regressionnonlinear regressionpolynomial regressionregression analysis
modified Bessel function S18ACF   nagf_specfun_bessel_k0_real
Modified Bessel function K 0 x
Related keywords: approximations of special functionsfinance K 0 , modified Bessel function
S18ADF   nagf_specfun_bessel_k1_real
Modified Bessel function K 1 x
Related keywords: approximations of special functionsfinance K 1 , modified Bessel function
S18AEF   nagf_specfun_bessel_i0_real
Modified Bessel function I 0 x
Related keywords: approximations of special functionsfinance I 0 , modified Bessel function
S18AFF   nagf_specfun_bessel_i1_real
Modified Bessel function I 1 x
Related keywords: approximations of special functionsfinance I 1 , modified Bessel function
S18AQF   24  nagf_specfun_bessel_k0_real_vector
Modified Bessel function vectorized K 0 x
Related keywords: approximations of special functions K 0 , modified Bessel function
S18ARF   24  nagf_specfun_bessel_k1_real_vector
Modified Bessel function vectorized K 1 x
Related keywords: approximations of special functions K 1 , modified Bessel function
S18ASF   24  nagf_specfun_bessel_i0_real_vector
Modified Bessel function vectorized I 0 x
Related keywords: approximations of special functions I 0 , modified Bessel function
S18ATF   24  nagf_specfun_bessel_i1_real_vector
Modified Bessel function vectorized I 1 x
Related keywords: approximations of special functions I 1 , modified Bessel function
S18CCF   10  nagf_specfun_bessel_k0_scaled
Scaled modified Bessel function e x K 0 x
Related keywords: approximations of special functionsfinance K 0 , modified Bessel function
S18CDF   10  nagf_specfun_bessel_k1_scaled
Scaled modified Bessel function e x K 1 x
Related keywords: approximations of special functionsfinance K 1 , modified Bessel function
S18CEF   10  nagf_specfun_bessel_i0_scaled
Scaled modified Bessel function e - x I 0 x
Related keywords: approximations of special functionsfinance I 0 , modified Bessel function
S18CFF   10  nagf_specfun_bessel_i1_scaled
Scaled modified Bessel function e - x I 1 x
Related keywords: approximations of special functionsfinance I 1 , modified Bessel function
S18CQF   24  nagf_specfun_bessel_k0_scaled_vector
Scaled modified Bessel function vectorized e x K 0 x
Related keywords: approximations of special functions K 0 , modified Bessel function
S18CRF   24  nagf_specfun_bessel_k1_scaled_vector
Scaled modified Bessel function vectorized e x K 1 x
Related keywords: approximations of special functions K 1 , modified Bessel function
S18CSF   24  nagf_specfun_bessel_i0_scaled_vector
Scaled modified Bessel function vectorized e - x I 0 x
Related keywords: approximations of special functions I 0 , modified Bessel function
S18CTF   24  nagf_specfun_bessel_i1_scaled_vector
Scaled modified Bessel function vectorized e - x I 1 x
Related keywords: approximations of special functions I 1 , modified Bessel function
S18DCF   13  nagf_specfun_bessel_k_complex
Modified Bessel functions K ν + a z , real a 0 , complex z , ν = 0 , 1 , 2 ,
Related keywords: approximations of special functions
S18DEF   13  nagf_specfun_bessel_i_complex
Modified Bessel functions I ν + a z , real a 0 , complex z , ν = 0 , 1 , 2 ,
Related keywords: approximations of special functions
S18GKF   21  nagf_specfun_bessel_j_seq_complex
Bessel function of the 1st kind J α ± n z
Related keywords: approximations of special functions
modified HLL solver D03PWF   18  nagf_pde_1d_parab_euler_hll
Modified HLL Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
Related keywords: Euler equationsHarten–Lax-van Leer solverPDE, partial differential equationsRiemann solver, PDE
Modified Struve function S18GAF   26  nagf_specfun_struve_l0
Modified Struve function of order 0 , L 0 x
Related keywords: approximations of special functions L 0 x , Struve function
S18GBF   26  nagf_specfun_struve_l1
Modified Struve function of order 1 , L 1 x
Related keywords: approximations of special functions L 1 x , Struve function
S18GCF   26  nagf_specfun_struve_i0ml0
The function I 0 x - L 0 x , where I 0 x is a modified Bessel function and L 0 x is a Struve function
Related keywords: approximations of special functions I 0 x - L 0 x , Struve function
S18GDF   26  nagf_specfun_struve_i1ml1
The function I 1 x - L 1 x , where I 1 x is a modified Bessel function and L 1 x is a Struve function
Related keywords: approximations of special functions I 1 x - L 1 x , Struve function
modulus complex number A02ABF   nagf_complex_abs
Modulus of complex number
Related keywords: complex arithmetic
moments G07BFF   23  nagf_univar_estim_genpareto
Estimates parameter values of the generalized Pareto distribution
Related keywords: maximum likelihoodPareto distributionunivariate estimation
moments quadratic form G01NAF   16  nagf_stat_moments_quad_form
Cumulants and moments of quadratic forms in Normal variables
Related keywords: cumulantfinanceGaussian distributionmultivariate Normal distributionNormal distributionSimple Calculations on Statistical Data
G01NBF   16  nagf_stat_moments_ratio_quad_forms
Moments of ratios of quadratic forms in Normal variables, and related statistics
Related keywords: financeGaussian distributionmultivariate Normal distributionNormal distributionSimple Calculations on Statistical Data
monitoring information E04SVF   26  nagf_opt_handle_solve_pennon
Run the Pennon solver on a compatible problem initialized by E04RAF and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI)
Related keywords: bilinear matrix inequalityBMIgeneralized augmented Lagrangian methodLagrangianleast squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationSDPsemidefinite programming
F12AEF   21  nagf_sparseig_real_monit
Provides monitoring information for F12ABF
Related keywords: big datadata analyticseigenproblemlarge scale eigenproblemsreal, sparse matrixsparse eigenproblems, monitoring
F12ASF   21  nagf_sparseig_complex_monit
Provides monitoring information for F12APF
Related keywords: big datacomplex, sparse matrixdata analyticseigenproblemlarge scale eigenproblemssparse eigenproblems, monitoring
monotonicity-preserving spline E01BEF   13  nagf_interp_1d_monotonic
Interpolating functions, monotonicity-preserving, piecewise cubic Hermite, one variable
Related keywords: cubic spline interpolationfinanceHermite interpolationinterpolation
E01BFF   13  nagf_interp_1d_monotonic_eval
Interpolated values, interpolant computed by E01BEF, function only, one variable
Related keywords: financeHermite interpolationinterpolation
E01BGF   13  nagf_interp_1d_monotonic_deriv
Interpolated values, interpolant computed by E01BEF, function and first derivative, one variable
Related keywords: financeHermite interpolationinterpolation
E01BHF   13  nagf_interp_1d_monotonic_intg
Interpolated values, interpolant computed by E01BEF, definite integral, one variable
Related keywords: financeHermite interpolationinterpolation
Monte–Carlo method D01GBF   10  nagf_quad_md_mcarlo
Multidimensional quadrature over hyper-rectangle, Monte–Carlo method
Related keywords: integration, multidimensionalquadraturequadrature non-adaptive
Mood's test for dispersion differences G08BAF   nagf_nonpar_test_mooddavid
Mood's and David's tests on two samples of unequal size
Related keywords: David's testdispersionnonparametric statistics
Morlet wavelet C09BAF   23  nagf_wav_1d_cont
One-dimensional real continuous wavelet transform
Related keywords: derivative of a Gaussian waveletMexican hat waveletwavelet continuouswaveletswavelets, one-dimensionalwavelet transforms
moving average G01WAF   24  nagf_stat_moving_average
Computes the mean and standard deviation using a rolling window
Related keywords: big datadata analyticsdata streammeanSimple Calculations on Statistical Datastandard deviationstreaming
G13MEF   24  nagf_tsa_inhom_iema
Computes the iterated exponential moving average for a univariate inhomogeneous time series
Related keywords: big datadata analyticsdata streamexponential moving averagestreamingtime seriestime series analysisunivariate time series
G13MFF   24  nagf_tsa_inhom_iema_all
Computes the iterated exponential moving average for a univariate inhomogeneous time series, intermediate results are also returned
Related keywords: big datadata analyticsdata streamexponential moving averagestreamingtime seriestime series analysisunivariate time series
G13MGF   24  nagf_tsa_inhom_ma
Computes the exponential moving average for a univariate inhomogeneous time series
Related keywords: big datadata analyticsdata streamexponential moving averagestreamingtime seriestime series analysisunivariate time series
MPS format E04MWF   26  nagf_opt_miqp_mps_write
Write MPS data file defining LP, QP, MILP or MIQP problem
Related keywords: linear programming,integerLP, linear programmingmaximizing a functionminimizing a functionMPSX formatoptimizationQP, quadratic programmingservice routine
MPSX format E04MWF   26  nagf_opt_miqp_mps_write
Write MPS data file defining LP, QP, MILP or MIQP problem
Related keywords: linear programming,integerLP, linear programmingmaximizing a functionminimizing a functionMPS formatoptimizationQP, quadratic programmingservice routine
E04MXF   24  nagf_opt_miqp_mps_read
Read MPS data file defining LP, QP, MILP or MIQP problem
Related keywords: linear programming,integerLP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programmingservice routine
E04MZF   18  nagf_opt_qpconvex1_sparse_mps
Read MPS data file defining LP or QP problem, deprecated
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programmingservice routine
H02BFF   16  nagf_mip_ilp_mpsx
Interpret MPSX data file defining IP or LP problem, optimize and print solution
Related keywords: branch and boundinteger programmingmixed integer programmingoperations research
H02BUF   16  nagf_mip_ilp_mpsx_convert
Convert MPSX data file defining IP or LP problem to format required by H02BBF or E04MFF
Related keywords: operations research
MRG32k3a G05KFF   22  nagf_rand_init_repeat
Initializes a pseudorandom number generator to give a repeatable sequence
Related keywords: ACORNbig datadata analyticsmersenne twisteroptions, computationalrandom number generatorsrandom numbersWichmann Hill
G05KGF   22  nagf_rand_init_nonrepeat
Initializes a pseudorandom number generator to give a non-repeatable sequence
Related keywords: ACORNbig datadata analyticsmersenne twisteroptions, computationalrandom number generatorsrandom numbersWichmann Hill
multidimensional D01ESF   25  nagf_quad_md_sgq_multi_vec
Multi-dimensional quadrature using sparse grids
Related keywords: automaticmultiple integrandsquadraturesparsevectorized
multigrid method D03EDF   12  nagf_pde_2d_ellip_mgrid
Elliptic PDE, solution of finite difference equations by a multigrid technique
Related keywords: elliptic partial differential equationsPDE, partial differential equationsrectangulartwo-dimensional
multi-level C09DCF   25  nagf_wav_1d_mxolap_multi_fwd
One-dimensional multi-level maximal overlap discrete wavelet transform (MODWT)
Related keywords: discretemaximal-overlapstationarywavelet transforms
C09DDF   25  nagf_wav_1d_mxolap_multi_inv
One-dimensional inverse multi-level maximal overlap discrete wavelet transform (IMODWT)
Related keywords: discreteinversemaximal-overlapstationarywavelet transforms
multi-level coordinate search E05JBF   22  nagf_glopt_bnd_mcs_solve
Global optimization by multi-level coordinate search, simple bounds, using function values only
Related keywords: financeglobal optimizationminimization, simple bound constraintsoptions, computational
multi-level discrete transform C09CCF   22  nagf_wav_1d_multi_fwd
One-dimensional multi-level discrete wavelet transform
Related keywords: financewaveletswavelets, one-dimensionalwavelet transforms
C09CDF   22  nagf_wav_1d_multi_inv
One-dimensional inverse multi-level discrete wavelet transform
Related keywords: financewaveletswavelets, one-dimensionalwavelet transforms
C09ECF   23  nagf_wav_2d_multi_fwd
Two-dimensional multi-level discrete wavelet transform
Related keywords: discrete transformwaveletswavelets, two-dimensionalwavelet transforms
C09EDF   23  nagf_wav_2d_multi_inv
Two-dimensional inverse multi-level discrete wavelet transform
Related keywords: discrete transformwaveletswavelets, two-dimensionalwavelet transforms
C09FCF   24  nagf_wav_3d_multi_fwd
Three-dimensional multi-level discrete wavelet transform
Related keywords: discrete transformwaveletswavelets, three-dimensionalwavelet transforms
C09FDF   24  nagf_wav_3d_mxolap_multi_inv
Three-dimensional inverse multi-level discrete wavelet transform
Related keywords: discrete transformwaveletswavelets, three-dimensionalwavelet transforms
multinomial distribution G05TGF   22  nagf_rand_int_multinomial
Generates a vector of pseudorandom integers from a multinomial distribution
Related keywords: big datadata analyticsfinancerandom integersrandom number generators
multiple integrands D01ESF   25  nagf_quad_md_sgq_multi_vec
Multi-dimensional quadrature using sparse grids
Related keywords: automaticmultidimensionalquadraturesparsevectorized
multiple linear regression G02CGF   nagf_correg_linregm_coeffs_const
Multiple linear regression, from correlation coefficients, with constant term
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02CHF   nagf_correg_linregm_coeffs_noconst
Multiple linear regression, from correlation-like coefficients, without constant term
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02DAF   14  nagf_correg_linregm_fit
Fits a general (multiple) linear regression model
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
multiply, matrix F01CKF   nagf_matop_real_gen_matmul
Multiplication of real matrices
Related keywords: inversionmatrix operationsreal, nonsymmetric matrix
F06PAF   12  nagf_blas_dgemv
Matrix-vector product, real rectangular matrix
Related keywords: BLASblas, real matricesdgemvfinancelinear algebra support routinesreal, m by n matrix
F06PBF   12  nagf_blas_dgbmv
Matrix-vector product, real rectangular band matrix
Related keywords: BLASblas, real matricesdgbmvlinear algebra support routinesmatrix, bandreal, band, m by n matrix
F06PCF   12  nagf_blas_dsymv
Matrix-vector product, real symmetric matrix
Related keywords: BLASblas, real matricesdsymvlinear algebra support routinesreal, indefinite, symmetric matrix
F06PDF   12  nagf_blas_dsbmv
Matrix-vector product, real symmetric band matrix
Related keywords: BLASblas, real matricesdsbmvlinear algebra support routinesmatrix, bandreal, band, symmetric matrix
F06PEF   12  nagf_blas_dspmv
Matrix-vector product, real symmetric packed matrix
Related keywords: BLASblas, real matricesdspmvlinear algebra support routinesreal, indefinite, symmetric matrix
F06PFF   12  nagf_blas_dtrmv
Matrix-vector product, real triangular matrix
Related keywords: BLASblas, real matricesdtrmvlinear algebra support routinesreal, triangular matrix
F06PGF   12  nagf_blas_dtbmv
Matrix-vector product, real triangular band matrix
Related keywords: BLASblas, real matricesdtbmvlinear algebra support routinesmatrix, bandreal, band, triangular matrix
F06PHF   12  nagf_blas_dtpmv
Matrix-vector product, real triangular packed matrix
Related keywords: BLASblas, real matricesdtpmvlinear algebra support routinesreal, triangular matrix
F06SAF   12  nagf_blas_zgemv
Matrix-vector product, complex rectangular matrix
Related keywords: BLASblas, complex matricescomplex, m by n matrixlinear algebra support routineszgemv
F06SBF   12  nagf_blas_zgbmv
Matrix-vector product, complex rectangular band matrix
Related keywords: BLASblas, complex matricescomplex, band, m by n matrixlinear algebra support routinesmatrix, bandzgbmv
F06SCF   12  nagf_blas_zhemv
Matrix-vector product, complex Hermitian matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian matrixlinear algebra support routineszhemv
F06SDF   12  nagf_blas_zhbmv
Matrix-vector product, complex Hermitian band matrix
Related keywords: BLASblas, complex matricescomplex, band, Hermitian matrixlinear algebra support routinesmatrix, bandzhbmv
F06SEF   12  nagf_blas_zhpmv
Matrix-vector product, complex Hermitian packed matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian matrixlinear algebra support routineszhpmv
F06SFF   12  nagf_blas_ztrmv
Matrix-vector product, complex triangular matrix
Related keywords: BLASblas, complex matricescomplex, triangular matrixlinear algebra support routinesztrmv
F06SGF   12  nagf_blas_ztbmv
Matrix-vector product, complex triangular band matrix
Related keywords: BLASblas, complex matricescomplex, band, triangular matrixlinear algebra support routinesmatrix, bandztbmv
F06SHF   12  nagf_blas_ztpmv
Matrix-vector product, complex triangular packed matrix
Related keywords: BLASblas, complex matricescomplex, triangular matrixlinear algebra support routinesztpmv
F06TAF   21  nagf_blas_zsymv
Matrix-vector product, complex symmetric matrix
Related keywords: BLAScomplex, symmetric matrixlinear algebra support routines
F06TCF   21  nagf_blas_zspmv
Matrix-vector product, complex symmetric packed matrix
Related keywords: BLAScomplex, symmetric matrixlinear algebra support routines
F06YAF   14  nagf_blas_dgemm
Matrix-matrix product, two real rectangular matrices
Related keywords: BLASblas, real matricesdgemmfinancelinear algebra support routinesreal, m by n matrix
F06YCF   14  nagf_blas_dsymm
Matrix-matrix product, one real symmetric matrix, one real rectangular matrix
Related keywords: BLASblas, real matricesdsymmlinear algebra support routinesreal, indefinite, symmetric matrixreal, m by n matrix
F06YFF   14  nagf_blas_dtrmm
Matrix-matrix product, one real triangular matrix, one real rectangular matrix
Related keywords: BLASblas, real matricesdsymmlinear algebra support routinesreal, m by n matrixreal, triangular matrix
F06ZAF   14  nagf_blas_zgemm
Matrix-matrix product, two complex rectangular matrices
Related keywords: BLASblas, complex matricescomplex, m by n matrixlinear algebra support routineszgemm
F06ZCF   14  nagf_blas_zhemm
Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian, indefinite matrixcomplex, m by n matrixlinear algebra support routineszgemm
F06ZFF   14  nagf_blas_ztrmm
Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix
Related keywords: BLASblas, complex matricescomplex, m by n matrixcomplex, triangular matrixlinear algebra support routinesztrmm
F06ZTF   14  nagf_blas_zsymm
Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix
Related keywords: BLASblas, complex matricescomplex, m by n matrixcomplex, symmetric matrixlinear algebra support routineszsymm
F11MKF   21  nagf_sparse_direct_real_gen_matmul
Real sparse nonsymmetric matrix-matrix multiply, compressed column storage
Related keywords: big datadata analyticslarge scale linear systemsreal, sparse matrix
F11XAF   18  nagf_sparse_real_gen_matvec
Real, sparse, nonsymmetric matrix-vector multiply
Related keywords: big datadata analyticslarge scale linear systemsreal, sparse matrix
F11XEF   17  nagf_sparse_real_symm_matvec
Real sparse symmetric matrix-vector multiply
Related keywords: big datadata analyticslarge scale linear systemsreal, sparse, symmetric matrix
F11XNF   19  nagf_sparse_complex_gen_matvec
Complex sparse non-Hermitian matrix-vector multiply
Related keywords: big datacomplex, sparse matrixdata analyticslarge scale linear systems
F11XSF   19  nagf_sparse_complex_herm_matvec
Complex sparse Hermitian matrix-vector multiply
Related keywords: big datacomplex, Hermitian, sparse matrixdata analyticslarge scale linear systems
multi-start algorithm E05UCF   24  nagf_glopt_nlp_multistart_sqp
Global optimization using multi-start, nonlinear constraints
Related keywords: financeglobal optimizationminimization, nonlinear constraintssequential QP method
E05USF   24  nagf_glopt_nlp_multistart_sqp_lsq
Global optimization of a sum of squares problem using multi-start, nonlinear constraints
Related keywords: financeglobal optimizationsequential QP methodsum of squares
multivariate methods G03 Chapter Introduction     Multivariate Methods
multivariate Normal distribution G01HBF   15  nagf_stat_prob_multi_normal
Computes probabilities for the multivariate Normal distribution
Related keywords: central probabilityfinancelower tail probabilityNormal distributionSimple Calculations on Statistical Dataupper tail probability
G01LBF   24  nagf_stat_pdf_multi_normal_vector
Computes a vector of values for the probability density function of the multivariate Normal distribution
Related keywords: Gaussian distributionlogarithm, pdfNormal distributionpdfprobability density functionSimple Calculations on Statistical Data
G01NAF   16  nagf_stat_moments_quad_form
Cumulants and moments of quadratic forms in Normal variables
Related keywords: cumulantfinanceGaussian distributionmoments quadratic formNormal distributionSimple Calculations on Statistical Data
G01NBF   16  nagf_stat_moments_ratio_quad_forms
Moments of ratios of quadratic forms in Normal variables, and related statistics
Related keywords: financeGaussian distributionmoments quadratic formNormal distributionSimple Calculations on Statistical Data
G05RZF   22  nagf_rand_multivar_normal
Generates a matrix of pseudorandom numbers from a multivariate Normal distribution
Related keywords: big datadata analyticsfinanceGaussian distributionNormal distributionrandom number generatorsrandom numbers
multivariate Student's t -distribution G01HDF   24  nagf_stat_prob_multi_students_t
Computes the probability for the multivariate Student's t -distribution
Related keywords: probabilitySimple Calculations on Statistical DataStudent's t -distribution
G05RYF   22  nagf_rand_multivar_students_t
Generates a matrix of pseudorandom numbers from a multivariate Student's t -distribution
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbersStudent's t -distribution
multivariate time series G13BAF   10  nagf_tsa_multi_filter_arima
Multivariate time series, filtering (pre-whitening) by an ARIMA model
Related keywords: ARIMAbig datadata analyticsfilteringfinancepre-whitening, filteringtime seriestime series analysis
G13BBF   11  nagf_tsa_multi_filter_transf
Multivariate time series, filtering by a transfer function model
Related keywords: big datadata analyticsfilteringfinancetime seriestime series analysis
G13BCF   10  nagf_tsa_multi_xcorr
Multivariate time series, cross-correlations
Related keywords: big datacross-correlationdata analyticsfinancetime seriestime series analysis
G13BDF   11  nagf_tsa_multi_transf_prelim
Multivariate time series, preliminary estimation of transfer function model
Related keywords: big datadata analyticsfinancetime seriestime series analysis
G13BEF   11  nagf_tsa_multi_inputmod_estim
Multivariate time series, estimation of multi-input model
Related keywords: ARIMAbig datadata analyticsexact likelihoodfinancemarginal likelihoodnonlinear least squarestime seriestime series analysisunivariate time series
G13BGF   11  nagf_tsa_multi_inputmod_update
Multivariate time series, update state set for forecasting from multi-input model
Related keywords: big datadata analyticsfinanceforecastingtime seriestime series analysis
G13BHF   11  nagf_tsa_multi_inputmod_forecast_state
Multivariate time series, forecasting from state set of multi-input model
Related keywords: big datadata analyticsforecastingtime seriestime series analysis
G13BJF   11  nagf_tsa_multi_inputmod_forecast
Multivariate time series, state set and forecasts from fully specified multi-input model
Related keywords: big datadata analyticsfinanceforecastingtime seriestime series analysis
G13CCF   10  nagf_tsa_multi_spectrum_lag
Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: Bartlett lag windowbig datacross-spectrumdata analyticsfinanceParzen lag windowrectangular lag windowsmoothingtime seriestime series analysisTukey lag window
G13CDF   10  nagf_tsa_multi_spectrum_daniell
Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window
Related keywords: big datacross-spectrumDaniell windowdata analyticsfinancesmoothingspectral smoothingtime seriestime series analysistrapezium frequency window
G13CEF   10  nagf_tsa_multi_spectrum_bivar
Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra
Related keywords: big databivariate spectracoherency, squared, time seriescross amplitude spectrumdata analyticsfinancesquared coherencytime seriestime series analysis
G13CFF   10  nagf_tsa_multi_gain_bivar
Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra
Related keywords: big databivariate time seriescross-spectrumdata analyticsfinancegain, time seriesphase, time seriestime seriestime series analysis
G13CGF   10  nagf_tsa_multi_noise_bivar
Multivariate time series, noise spectrum, bounds, impulse response function and its standard error
Related keywords: big datadata analyticsfinanceimpulse response functionnoise spectrumstandard errorstime seriestime series analysis
G13DBF   11  nagf_tsa_multi_autocorr_part
Multivariate time series, multiple squared partial autocorrelations
Related keywords: big datadata analyticspartial autocorrelation coefficientstime seriestime series analysis
G13DDF   22  nagf_tsa_multi_varma_estimate
Multivariate time series, estimation of VARMA model
Related keywords: big datacorrelation matrixdata analyticsfinancemaximum likelihoodstandard errorstime seriestime series analysisVARMA, vector autoregressive moving average model
G13DJF   15  nagf_tsa_multi_varma_forecast
Multivariate time series, forecasts and their standard errors
Related keywords: big datadata analyticsfinanceforecastingstandard errorstime seriestime series analysis
G13DKF   15  nagf_tsa_multi_varma_update
Multivariate time series, updates forecasts and their standard errors
Related keywords: big datadata analyticsfinanceforecastingstandard errorstime seriestime series analysis
G13DLF   15  nagf_tsa_multi_diff
Multivariate time series, differences and/or transforms
Related keywords: big datadata analyticsfinancetime seriestime series analysisVARMA, vector autoregressive moving average model
G13DMF   15  nagf_tsa_multi_corrmat_cross
Multivariate time series, sample cross-correlation or cross-covariance matrices
Related keywords: big datacross-correlationcross-covariancedata analyticstime seriestime series analysis
G13DNF   15  nagf_tsa_multi_corrmat_partlag
Multivariate time series, sample partial lag correlation matrices, χ 2 statistics and significance levels
Related keywords: big datachi squared statisticsdata analyticspartial lagsignificancetime seriestime series analysis
G13DPF   16  nagf_tsa_multi_regmat_partial
Multivariate time series, partial autoregression matrices
Related keywords: big datadata analyticspartial autoregression matricestime seriestime series analysis
G13DSF   13  nagf_tsa_multi_varma_diag
Multivariate time series, diagnostic checking of residuals, following G13DDF
Related keywords: big datadata analyticstime seriestime series analysis
nagad_a1w_w_rtype X10BJF   26 
Write a scalar of type nagad_a1w_w_rtype to the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationcallback data objectwrite
X10CJF   26 
Read a scalar of type nagad_a1w_w_rtype from the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationcallback dataobjectread
NaN X07ABF   24  nagf_ieee_is_nan
Determines whether its argument is a NaN (Not A Number)
Related keywords: IEEE arithmetic
X07BBF   24  nagf_ieee_create_nan
Creates a NaN (Not A Number)
Related keywords: IEEE arithmetic
nearest correlation matrix G02AAF   22  nagf_correg_corrmat_nearest
Computes the nearest correlation matrix to a real square matrix, using the method of Qi and Sun
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsfinancenonlinear regressionpolynomial regressionQi and Sun algorithmregression analysis
G02ABF   23  nagf_correg_corrmat_nearest_bounded
Computes the nearest correlation matrix to a real square matrix, augmenting G02AAF to incorporate weights and bounds
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsfinancenonlinear regressionpolynomial regressionQi and Sun algorithmregression analysis
G02AEF   23  nagf_correg_corrmat_nearest_kfactor
Computes the nearest correlation matrix with k -factor structure to a real square matrix
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsfinance k -factor structurenonlinear regressionpolynomial regressionQi and Sun algorithmregression analysis
G02AJF   24  nagf_correg_corrmat_h_weight
Computes the nearest correlation matrix to a real square matrix, using element-wise weighting
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsnonlinear regressionpolynomial regressionQi and Sun algorithmregression analysis
G02ANF   25  nagf_correg_corrmat_shrinking
Computes a correlation matrix from an approximate matrix with fixed submatrix
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsnonlinear regressionpolynomial regressionregression analysisshrinking method
G02APF   26  nagf_correg_corrmat_target
Computes a correlation matrix from an approximate one using a specified target matrix
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticselementwise weightsnonlinear regressionpolynomial regressionregression analysisshrinkageshrinking method
negative binomial distribution G05THF   22  nagf_rand_int_negbin
Generates a vector of pseudorandom integers from a negative binomial distribution
Related keywords: big datadata analyticsfinancePascal distributionPolya distributionrandom integersrandom number generators
Nelder–Mead algorithm E04CBF   22  nagf_opt_uncon_simplex
Unconstrained minimum, Nelder–Mead simplex algorithm, using function values only
Related keywords: derivative-free minimizationfinancemaximizing a functionminimization, unconstrainedminimizing a functionNLPnonlinear programmingoptimizationsimplex algorithm
Neumann algorithm G08AKF   14  nagf_nonpar_prob_mwu_ties
Computes the exact probabilities for the Mann–Whitney U statistic, ties in pooled sample
Related keywords: Mann–Whitney U statisticnonparametric statisticspooled sampletail probabilities
Newton algorithm E04FCF   nagf_opt_lsq_uncon_mod_func_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (comprehensive)
Related keywords: data fittingderivative-free minimizationfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationsum-of-squares minimization
E04FYF   18  nagf_opt_lsq_uncon_mod_func_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (easy-to-use)
Related keywords: data fittingderivative-free minimizationfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationsum-of-squares minimization
E04GDF   nagf_opt_lsq_uncon_mod_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (comprehensive)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationsum-of-squares minimization
E04GZF   18  nagf_opt_lsq_uncon_mod_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (easy-to-use)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationsum-of-squares minimization
E04HEF   nagf_opt_lsq_uncon_mod_deriv2_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationsum-of-squares minimization
E04HYF   18  nagf_opt_lsq_uncon_mod_deriv2_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationsum-of-squares minimization
E04KDF   nagf_opt_bounds_mod_deriv_comp
Bound constrained minimum, modified Newton algorithm, using first derivatives (comprehensive)
Related keywords: financemaximizing a functionminimization, simple bound constraintsminimizing a functionNLPnonlinear programmingoptimization
E04KZF   18  nagf_opt_bounds_mod_deriv_easy
Bound constrained minimum, modified Newton algorithm, using first derivatives (easy-to-use)
Related keywords: financemaximizing a functionminimization, simple bound constraintsminimizing a functionNLPnonlinear programmingoptimization
E04LBF   nagf_opt_bounds_mod_deriv2_comp
Bound constrained minimum, modified Newton algorithm, using first and second derivatives (comprehensive)
Related keywords: financemaximizing a functionminimization, simple bound constraintsminimizing a functionNLPnonlinear programmingoptimization
E04LYF   18  nagf_opt_bounds_mod_deriv2_easy
Bound constrained minimum, modified Newton algorithm, using first and second derivatives (easy-to-use)
Related keywords: financemaximizing a functionminimization, simple bound constraintsminimizing a functionNLPnonlinear programmingoptimization
Niederreiter G05YNF   22  nagf_rand_quasi_init_scrambled
Initializes a scrambled quasi-random number generator
Related keywords: big datadata analyticsFaure–TezukafinanceOwenrandom number generatorsrandom numbersscrambleSobol
Niederreiter method, quasi-random numbers G05YJF   21  nagf_rand_quasi_normal
Generates a Normal quasi-random number sequence
Related keywords: big datadata analyticsFaure, quasi-random numbersGaussian distributionlow-discrepancy sequencesNormal distributionquasi-random numbersrandom number generatorsrandom numbersSobol, quasi-random numbers
G05YKF   21  nagf_rand_quasi_lognormal
Generates a log-normal quasi-random number sequence
Related keywords: big datadata analyticsFaure, quasi-random numberslog-normal distributionlow-discrepancy sequencesquasi-random numbersrandom number generatorsrandom numbersSobol, quasi-random numbers
G05YLF   22  nagf_rand_quasi_init
Initializes a quasi-random number generator
Related keywords: big datadata analyticsFaure, quasi-random numbersfinancelow-discrepancy sequencesquasi-random numbersrandom number generatorsrandom numbersrectangular distributionSobol, quasi-random numbersuniform distribution
NLP E04ABF   nagf_opt_one_var_func_old
Minimum, function of one variable, using function values only
Related keywords: derivative-free minimizationfinancemaximizing a functionminimization, unconstrainedminimizing a functionnonlinear programmingone-dimensional quadratic interpolationoptimizationunivariate minimization
E04BBF   nagf_opt_one_var_deriv_old
Minimum, function of one variable, using first derivative
Related keywords: financemaximizing a functionminimizing a functionnonlinear programmingone-dimensional cubic interpolationoptimization
E04CBF   22  nagf_opt_uncon_simplex
Unconstrained minimum, Nelder–Mead simplex algorithm, using function values only
Related keywords: derivative-free minimizationfinancemaximizing a functionminimization, unconstrainedminimizing a functionNelder–Mead algorithmnonlinear programmingoptimizationsimplex algorithm
E04DGF   12  nagf_opt_uncon_conjgrd_comp_old
Unconstrained minimum, preconditioned conjugate gradient algorithm, using first derivatives (comprehensive)
Related keywords: conjugate gradient methodfinancemaximizing a functionminimization, unconstrainedminimizing a functionnonlinear programmingoptimizationquasi-Newton
E04JCF   23  nagf_opt_bounds_bobyqa_func
Bound constrained minimum, model-based algorithm, using function values only
Related keywords: BOBYQA methodfinancemaximizing a functionminimization, simple bound constraintsminimizing a functionnonlinear programmingoptimization
E04JYF   18  nagf_opt_bounds_quasi_func_easy
Bound constrained minimum, quasi-Newton algorithm, using function values only (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmfinancemaximizing a functionminimization, simple bound constraintsminimizing a functionnonlinear programmingoptimizationquasi-Newton algorithm
E04KDF   nagf_opt_bounds_mod_deriv_comp
Bound constrained minimum, modified Newton algorithm, using first derivatives (comprehensive)
Related keywords: financemaximizing a functionminimization, simple bound constraintsminimizing a functionNewton algorithmnonlinear programmingoptimization
E04KYF   18  nagf_opt_bounds_quasi_deriv_easy
Bound constrained minimum, quasi-Newton algorithm, using first derivatives (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmfinancemaximizing a functionminimization, simple bound constraintsminimizing a functionnonlinear programmingoptimizationquasi-Newton algorithm
E04KZF   18  nagf_opt_bounds_mod_deriv_easy
Bound constrained minimum, modified Newton algorithm, using first derivatives (easy-to-use)
Related keywords: financemaximizing a functionminimization, simple bound constraintsminimizing a functionNewton algorithmnonlinear programmingoptimization
E04LBF   nagf_opt_bounds_mod_deriv2_comp
Bound constrained minimum, modified Newton algorithm, using first and second derivatives (comprehensive)
Related keywords: financemaximizing a functionminimization, simple bound constraintsminimizing a functionNewton algorithmnonlinear programmingoptimization
E04LYF   18  nagf_opt_bounds_mod_deriv2_easy
Bound constrained minimum, modified Newton algorithm, using first and second derivatives (easy-to-use)
Related keywords: financemaximizing a functionminimization, simple bound constraintsminimizing a functionNewton algorithmnonlinear programmingoptimization
E04RGF   26  nagf_opt_handle_set_nlnobj
Define a nonlinear objective function to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04RKF   26  nagf_opt_handle_set_nlnconstr
Define a block of nonlinear constraints to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionnonlinearly-constrainedoptimizationoptimization
E04RLF   26  nagf_opt_handle_set_nlnhess
Define a structure of Hessian of the objective, constraints or the Lagrangian to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E04RMF   26  nagf_opt_handle_set_nlnls
Define a nonlinear least squares objective function to a problem initialized by E04RAF
Related keywords: calibrationdata fittingderivative-free optimizationDFOleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionnonlinear least squaresoptimizationoptimizationoptimizationsum of squares
E04STF   26  nagf_opt_handle_solve_ipopt
Run an interior point solver on a sparse nonlinear programming problem (NLP) initialized by E04RAF and defined by other routines from the suite
Related keywords: interior point methodIPMleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionnonlinear programmingoptimizationoptimization
E04UCF   12  nagf_opt_nlp1_solve_old
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: densefinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionnonlinear programmingoptimizationsequential QP methodSQP
E04UFF   18  nagf_opt_nlp1_rcomm_old
Nonlinear programming (NLP), dense, active-set, SQP method, using function values and optionally first derivatives (reverse communication, comprehensive)
Related keywords: densefinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionnonlinear programmingoptimizationsequential QP methodSQP
E04UGF   19  nagf_opt_nlp1_sparse_solve_old
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives
Related keywords: financemaximizing a functionminimization, nonlinear constraintsminimizing a functionnonlinear programmingoptimizationsequential QP methodSQP
E04UHF   19  nagf_opt_nlp1_sparse_option_file_old
Supply values for E04UGF from external file
Related keywords: maximizing a functionminimizing a functionnonlinear programmingoptimizationoptions, computationalSQP
E04UJF   19  nagf_opt_nlp1_sparse_option_string_old
Supply values to E04UGF from a character string
Related keywords: maximizing a functionminimizing a functionnonlinear programmingoptimizationoptions, computationalSQP
E04UQF   14  nagf_opt_lsq_gencon_deriv_option_file_old
Supply values for E04USF from external file
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionnonlinear programmingoptimizationoptions, computationalSQPsum of squares
E04URF   14  nagf_opt_lsq_gencon_deriv_option_string_old
Supply values to E04USF from a character string
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionnonlinear programmingoptimizationoptions, computationalSQPsum of squares
E04USF   14  nagf_opt_lsq_gencon_deriv_old
Minimum of a sum of squares, nonlinear constraints, dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: data fittingfinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionnonlinear least squaresnonlinear programmingoptimizationquasi-Newton approximationsequential QP methodsum of squares
E04VGF   21  nagf_opt_nlp2_sparse_init
Initialization routine for E04VHF
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionnonlinear programmingoptimizationoptions, computationalSQP
E04VHF   21  nagf_opt_nlp2_sparse_solve
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: financeLP, linear programmingmaximizing a functionminimization, nonlinear constraintsminimizing a functionnonlinear programmingoptimizationquasi-Newton algorithmsequential QP methodsimplex algorithmSQP
E04WCF   21  nagf_opt_nlp2_init
Initialization routine for E04WDF
Related keywords: maximizing a functionminimizing a functionnonlinear programmingoptimizationoptions, computational
E04WDF   21  nagf_opt_nlp2_solve
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: densefinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionnonlinear programmingoptimizationsequential QP methodSQP
E04WEF   21  nagf_opt_nlp2_option_file
Supply values for E04WDF from external file
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionnonlinear programmingoptimizationoptions, computationalSQP
E04WFF   21  nagf_opt_nlp2_option_string
Set a single option for E04WDF from a character string
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionnonlinear programmingoptimizationoptions, computationalSQP
E04WGF   21  nagf_opt_nlp2_option_integer_set
Set a single option for E04WDF from an integer argument
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionnonlinear programmingoptimizationoptions, computationalSQP
E04WHF   21  nagf_opt_nlp2_option_double_set
Set a single option for E04WDF from a real argument
Related keywords: maximizing a functionminimizing a functionnonlinear programmingoptimizationoptions, computationalSQP
E04WKF   21  nagf_opt_nlp2_option_integer_get
Get the setting of an integer valued option of E04WDF
Related keywords: maximizing a functionminimizing a functionnonlinear programmingoptimizationoptions, computationalSQP
E04WLF   21  nagf_opt_nlp2_option_double_get
Get the setting of a real valued option of E04WDF
Related keywords: maximizing a functionminimizing a functionnonlinear programmingoptimizationoptions, computationalSQP
NNLS, non-negative least squares E04PCF   24  nagf_opt_bnd_lin_lsq
Computes the least squares solution to a set of linear equations subject to fixed upper and lower bounds on the variables. An option is provided to return a minimal length solution if a solution is not unique
Related keywords: BVLS, bounded variable least squaresdata fittingfinancemaximizing a functionminimizing a functionnonlinear least squaresnon-negative least squaresoptimization
noise spectrum G13CGF   10  nagf_tsa_multi_noise_bivar
Multivariate time series, noise spectrum, bounds, impulse response function and its standard error
Related keywords: big datadata analyticsfinanceimpulse response functionmultivariate time seriesstandard errorstime seriestime series analysis
non-adaptive D01TDF   26  nagf_quad_1d_gauss_wrec
Calculation of weights and abscissae for Gaussian quadrature rules, method of Golub and Welsch
Related keywords: abscissaecubatureGaussianGolubGolub and Welschintegrationquadratureweights and abscissaeWelsch
D01TEF   26  nagf_quad_1d_gauss_recm
Generates recursion coefficients needed by D01TDF to calculate a Gaussian quadrature rule
Related keywords: abscissaecubatureGaussianGolubGolub and Welschintegrationquadraturerecursion coefficientsWelsch
nonlinear least squares E04FCF   nagf_opt_lsq_uncon_mod_func_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (comprehensive)
Related keywords: data fittingderivative-free minimizationfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmoptimizationsum-of-squares minimization
E04FFF   26  nagf_opt_handle_solve_dfls
Derivative-free (DFO) solver for a nonlinear least squares objective function with bounded variables
Related keywords: calibrationdata fittingderivative-free optimizationDFODFOmaximizing a functionminimizing a functionoptimizationoptimizationsum of squares
E04FYF   18  nagf_opt_lsq_uncon_mod_func_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (easy-to-use)
Related keywords: data fittingderivative-free minimizationfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmoptimizationsum-of-squares minimization
E04GBF   nagf_opt_lsq_uncon_quasi_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (comprehensive)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmdata fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionoptimizationquasi-Newton algorithmsum-of-squares minimization
E04GDF   nagf_opt_lsq_uncon_mod_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (comprehensive)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmoptimizationsum-of-squares minimization
E04GYF   18  nagf_opt_lsq_uncon_quasi_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmdata fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionoptimizationquasi-Newton algorithmsum-of-squares minimization
E04GZF   18  nagf_opt_lsq_uncon_mod_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (easy-to-use)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmoptimizationsum-of-squares minimization
E04HEF   nagf_opt_lsq_uncon_mod_deriv2_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmoptimizationsum-of-squares minimization
E04HYF   18  nagf_opt_lsq_uncon_mod_deriv2_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmoptimizationsum-of-squares minimization
E04NCF   12  nagf_opt_lsq_lincon_solve_old
Linear programming (LP) convex quadratic programming (QP) or linearly-constrained linear least squares problem, dense
Related keywords: active-setconvex optimizationdata fittingfinanceleast squaresmaximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04PCF   24  nagf_opt_bnd_lin_lsq
Computes the least squares solution to a set of linear equations subject to fixed upper and lower bounds on the variables. An option is provided to return a minimal length solution if a solution is not unique
Related keywords: BVLS, bounded variable least squaresdata fittingfinancemaximizing a functionminimizing a functionNNLS, non-negative least squaresnon-negative least squaresoptimization
E04RMF   26  nagf_opt_handle_set_nlnls
Define a nonlinear least squares objective function to a problem initialized by E04RAF
Related keywords: calibrationdata fittingderivative-free optimizationDFOleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPoptimizationoptimizationoptimizationsum of squares
E04USF   14  nagf_opt_lsq_gencon_deriv_old
Minimum of a sum of squares, nonlinear constraints, dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: data fittingfinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton approximationsequential QP methodsum of squares
E04YCF   11  nagf_opt_lsq_uncon_covariance
Covariance matrix for nonlinear least squares problem (unconstrained)
Related keywords: covariance matrixmaximizing a functionminimizing a functionoptimizationservice routine
G13BEF   11  nagf_tsa_multi_inputmod_estim
Multivariate time series, estimation of multi-input model
Related keywords: ARIMAbig datadata analyticsexact likelihoodfinancemarginal likelihoodmultivariate time seriestime seriestime series analysisunivariate time series
nonlinearly-constrained E04RKF   26  nagf_opt_handle_set_nlnconstr
Define a block of nonlinear constraints to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPoptimizationoptimization
nonlinear mixed order D02TLF   25  nagf_ode_bvp_coll_nlin_solve
Ordinary differential equations, general nonlinear boundary value problem, collocation technique (thread safe)
Related keywords: boundary value problemBVPdifferential equationsODE, ordinary differential equationsordinary differential equationstwo-point boundary value problem
nonlinear programming E04ABF   nagf_opt_one_var_func_old
Minimum, function of one variable, using function values only
Related keywords: derivative-free minimizationfinancemaximizing a functionminimization, unconstrainedminimizing a functionNLPone-dimensional quadratic interpolationoptimizationunivariate minimization
E04BBF   nagf_opt_one_var_deriv_old
Minimum, function of one variable, using first derivative
Related keywords: financemaximizing a functionminimizing a functionNLPone-dimensional cubic interpolationoptimization
E04CBF   22  nagf_opt_uncon_simplex
Unconstrained minimum, Nelder–Mead simplex algorithm, using function values only
Related keywords: derivative-free minimizationfinancemaximizing a functionminimization, unconstrainedminimizing a functionNelder–Mead algorithmNLPoptimizationsimplex algorithm
E04DGF   12  nagf_opt_uncon_conjgrd_comp_old
Unconstrained minimum, preconditioned conjugate gradient algorithm, using first derivatives (comprehensive)
Related keywords: conjugate gradient methodfinancemaximizing a functionminimization, unconstrainedminimizing a functionNLPoptimizationquasi-Newton
E04JCF   23  nagf_opt_bounds_bobyqa_func
Bound constrained minimum, model-based algorithm, using function values only
Related keywords: BOBYQA methodfinancemaximizing a functionminimization, simple bound constraintsminimizing a functionNLPoptimization
E04JYF   18  nagf_opt_bounds_quasi_func_easy
Bound constrained minimum, quasi-Newton algorithm, using function values only (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmfinancemaximizing a functionminimization, simple bound constraintsminimizing a functionNLPoptimizationquasi-Newton algorithm
E04KDF   nagf_opt_bounds_mod_deriv_comp
Bound constrained minimum, modified Newton algorithm, using first derivatives (comprehensive)
Related keywords: financemaximizing a functionminimization, simple bound constraintsminimizing a functionNewton algorithmNLPoptimization
E04KYF   18  nagf_opt_bounds_quasi_deriv_easy
Bound constrained minimum, quasi-Newton algorithm, using first derivatives (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmfinancemaximizing a functionminimization, simple bound constraintsminimizing a functionNLPoptimizationquasi-Newton algorithm
E04KZF   18  nagf_opt_bounds_mod_deriv_easy
Bound constrained minimum, modified Newton algorithm, using first derivatives (easy-to-use)
Related keywords: financemaximizing a functionminimization, simple bound constraintsminimizing a functionNewton algorithmNLPoptimization
E04LBF   nagf_opt_bounds_mod_deriv2_comp
Bound constrained minimum, modified Newton algorithm, using first and second derivatives (comprehensive)
Related keywords: financemaximizing a functionminimization, simple bound constraintsminimizing a functionNewton algorithmNLPoptimization
E04LYF   18  nagf_opt_bounds_mod_deriv2_easy
Bound constrained minimum, modified Newton algorithm, using first and second derivatives (easy-to-use)
Related keywords: financemaximizing a functionminimization, simple bound constraintsminimizing a functionNewton algorithmNLPoptimization
E04STF   26  nagf_opt_handle_solve_ipopt
Run an interior point solver on a sparse nonlinear programming problem (NLP) initialized by E04RAF and defined by other routines from the suite
Related keywords: interior point methodIPMleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPoptimizationoptimization
E04UCF   12  nagf_opt_nlp1_solve_old
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: densefinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPoptimizationsequential QP methodSQP
E04UFF   18  nagf_opt_nlp1_rcomm_old
Nonlinear programming (NLP), dense, active-set, SQP method, using function values and optionally first derivatives (reverse communication, comprehensive)
Related keywords: densefinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPoptimizationsequential QP methodSQP
E04UGF   19  nagf_opt_nlp1_sparse_solve_old
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives
Related keywords: financemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPoptimizationsequential QP methodSQP
E04UHF   19  nagf_opt_nlp1_sparse_option_file_old
Supply values for E04UGF from external file
Related keywords: maximizing a functionminimizing a functionNLPoptimizationoptions, computationalSQP
E04UJF   19  nagf_opt_nlp1_sparse_option_string_old
Supply values to E04UGF from a character string
Related keywords: maximizing a functionminimizing a functionNLPoptimizationoptions, computationalSQP
E04UQF   14  nagf_opt_lsq_gencon_deriv_option_file_old
Supply values for E04USF from external file
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPoptimizationoptions, computationalSQPsum of squares
E04URF   14  nagf_opt_lsq_gencon_deriv_option_string_old
Supply values to E04USF from a character string
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPoptimizationoptions, computationalSQPsum of squares
E04USF   14  nagf_opt_lsq_gencon_deriv_old
Minimum of a sum of squares, nonlinear constraints, dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: data fittingfinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear least squaresoptimizationquasi-Newton approximationsequential QP methodsum of squares
E04VGF   21  nagf_opt_nlp2_sparse_init
Initialization routine for E04VHF
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPoptimizationoptions, computationalSQP
E04VHF   21  nagf_opt_nlp2_sparse_solve
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: financeLP, linear programmingmaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPoptimizationquasi-Newton algorithmsequential QP methodsimplex algorithmSQP
E04WCF   21  nagf_opt_nlp2_init
Initialization routine for E04WDF
Related keywords: maximizing a functionminimizing a functionNLPoptimizationoptions, computational
E04WDF   21  nagf_opt_nlp2_solve
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: densefinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPoptimizationsequential QP methodSQP
E04WEF   21  nagf_opt_nlp2_option_file
Supply values for E04WDF from external file
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPoptimizationoptions, computationalSQP
E04WFF   21  nagf_opt_nlp2_option_string
Set a single option for E04WDF from a character string
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPoptimizationoptions, computationalSQP
E04WGF   21  nagf_opt_nlp2_option_integer_set
Set a single option for E04WDF from an integer argument
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPoptimizationoptions, computationalSQP
E04WHF   21  nagf_opt_nlp2_option_double_set
Set a single option for E04WDF from a real argument
Related keywords: maximizing a functionminimizing a functionNLPoptimizationoptions, computationalSQP
E04WKF   21  nagf_opt_nlp2_option_integer_get
Get the setting of an integer valued option of E04WDF
Related keywords: maximizing a functionminimizing a functionNLPoptimizationoptions, computationalSQP
E04WLF   21  nagf_opt_nlp2_option_double_get
Get the setting of a real valued option of E04WDF
Related keywords: maximizing a functionminimizing a functionNLPoptimizationoptions, computationalSQP
H02DAF   25  nagf_mip_sqp
Mixed integer nonlinear programming
Related keywords: integer programminginteger quadratic programmixed integer programmingoperations researchSQP, sequential quadratic programming
nonlinear regression G02 Chapter Introduction     Correlation and Regression Analysis
Related keywords: big datacorrelation analysisdata analyticspolynomial regressionregression analysis
non-metric (ordinal) scaling G03FCF   17  nagf_mv_multidimscal_ordinal
Performs non-metric (ordinal) multidimensional scaling
Related keywords: multivariate methodsordinal scaling
non-negative least squares E04PCF   24  nagf_opt_bnd_lin_lsq
Computes the least squares solution to a set of linear equations subject to fixed upper and lower bounds on the variables. An option is provided to return a minimal length solution if a solution is not unique
Related keywords: BVLS, bounded variable least squaresdata fittingfinancemaximizing a functionminimizing a functionNNLS, non-negative least squaresnonlinear least squaresoptimization
nonparametric statistics G08 Chapter Introduction     Nonparametric Statistics
non-seasonal differencing G13AAF   nagf_tsa_uni_diff
Univariate time series, seasonal and non-seasonal differencing
Related keywords: big datadata analyticsdifferencing, time seriesfinanceseasonal differencingtime seriestime series analysisunivariate time series
Nonstiff D02CJF   13  nagf_ode_ivp_adams_zero_simple
Ordinary differential equations, initial value problem, Adams' method, until function of solution is zero, intermediate output (simple driver)
Related keywords: Adams' methodfirst-order systeminitial value problemIVP, initial value problemODE, ordinary differential equationsstop at roots
D02PEF   24  nagf_ode_ivp_rkts_range
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output
Related keywords: first-order systemIVP, initial value problemODE, ordinary differential equationsRK23RK45RK78Runge–Kutta–Merson
D02PFF   24  nagf_ode_ivp_rkts_onestep
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step
Related keywords: first-order systemIVP, initial value problemODE, ordinary differential equationsRK23RK45RK78Runge–Kutta–Merson
D02PHF   26  nagf_ode_ivp_rk_interp_setup
Set up interpolant by reverse communication for solution and derivative evaluations at points within the range of the last integration step taken by D02PGF
Related keywords: first-order systeminterpolationIVP, initial value problemODE, ordinary differential equationsRunge–Kutta–Merson
norm, matrix F04YDF   24  nagf_linsys_real_gen_norm_rcomm
Norm estimation (for use in condition estimation), real rectangular matrix
Related keywords: 1 -normbig datadata analyticsreal, m by n matrixsimultaneous linear equations
F04ZDF   24  nagf_linsys_complex_gen_norm_rcomm
Norm estimation (for use in condition estimation), complex rectangular matrix
Related keywords: 1 -normbig datacomplex, m by n matrixdata analyticssimultaneous linear equations
F06RAF   15  nagf_blas_dlange
1 -norm, -norm, Frobenius norm, largest absolute element, real general matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesreal, m by n matrix
F06RBF   15  nagf_blas_dlangb
1 -norm, -norm, Frobenius norm, largest absolute element, real band matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesmatrix, bandreal, band, m by n matrix
F06RCF   15  nagf_blas_dlansy
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesreal, indefinite, symmetric matrix
F06RDF   15  nagf_blas_dlansp
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesreal, indefinite, symmetric matrix
F06REF   15  nagf_blas_dlansb
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric band matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesmatrix, bandreal, band, symmetric matrix
F06RJF   15  nagf_blas_dlantr
1 -norm, -norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesreal, trapezoidal matrixreal, triangular matrix
F06RKF   15  nagf_blas_dlantp
1 -norm, -norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesreal, triangular matrix
F06RLF   15  nagf_blas_dlantb
1 -norm, -norm, Frobenius norm, largest absolute element, real triangular band matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesreal, band, triangular matrix
F06RMF   15  nagf_blas_dlanhs
1 -norm, -norm, Frobenius norm, largest absolute element, real upper Hessenberg matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesreal, Hessenberg matrix
F06RNF   21  nagf_blas_dlangt
1 -norm, -norm, Frobenius norm, largest absolute element, real tridiagonal matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesmatrix, bandreal, tridiagonal matrix
F06RPF   21  nagf_blas_dlanst
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesmatrix, bandreal, symmetric, tridiagonal matrix
F11MLF   21  nagf_sparse_direct_real_gen_norm
1 -norm, -norm, largest absolute element, real, square, sparse matrix
Related keywords: 1-normabsolute valuebig datadata analyticsinfinity-normlarge scale linear systemsreal, sparse matrix
F16RBF   23  nagf_blast_dgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, real band matrix
Related keywords: 1-normabsolute valueabsolute valuebanded matrixFrobenius normfurther linear algebra support routinesinfinity-normmatrix, bandreal, band, m by n matrix
F16UBF   23  nagf_blast_zgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, complex band matrix
Related keywords: 1-normabsolute valuebanded matrixcomplex, band matrixFrobenius normfurther linear algebra support routinesinfinity-normmatrix, band
norm, vector F06BMF   12  nagf_blas_dnorm
Compute Euclidean norm from scaled form
Related keywords: BLASEuclidean normlinear algebra support routines
Normal distribution G01EAF   15  nagf_stat_prob_normal
Computes probabilities for the standard Normal distribution
Related keywords: CDF, cumulative distribution functionfinancelower tail probabilityprobabilitySimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01FAF   15  nagf_stat_inv_cdf_normal
Computes deviates for the standard Normal distribution
Related keywords: deviatesfinanceinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01HAF   14  nagf_stat_prob_bivariate_normal
Computes probability for the bivariate Normal distribution
Related keywords: bivariate Normal distributionfinancelower tail probabilitySimple Calculations on Statistical Data
G01HBF   15  nagf_stat_prob_multi_normal
Computes probabilities for the multivariate Normal distribution
Related keywords: central probabilityfinancelower tail probabilitymultivariate Normal distributionSimple Calculations on Statistical Dataupper tail probability
G01KAF   23  nagf_stat_pdf_normal
Calculates the value for the probability density function of the Normal distribution at a chosen point
Related keywords: Gaussian distributionpdfprobability density functionSimple Calculations on Statistical Data
G01KQF   24  nagf_stat_pdf_normal_vector
Computes a vector of values for the probability density function of the Normal distribution
Related keywords: Gaussian distributionlogarithm, pdfpdfprobability density functionSimple Calculations on Statistical Data
G01LBF   24  nagf_stat_pdf_multi_normal_vector
Computes a vector of values for the probability density function of the multivariate Normal distribution
Related keywords: Gaussian distributionlogarithm, pdfmultivariate Normal distributionpdfprobability density functionSimple Calculations on Statistical Data
G01NAF   16  nagf_stat_moments_quad_form
Cumulants and moments of quadratic forms in Normal variables
Related keywords: cumulantfinanceGaussian distributionmoments quadratic formmultivariate Normal distributionSimple Calculations on Statistical Data
G01NBF   16  nagf_stat_moments_ratio_quad_forms
Moments of ratios of quadratic forms in Normal variables, and related statistics
Related keywords: financeGaussian distributionmoments quadratic formmultivariate Normal distributionSimple Calculations on Statistical Data
G01SAF   24  nagf_stat_prob_normal_vector
Computes a vector of probabilities for the standard Normal distribution
Related keywords: big dataCDF, cumulative distribution functionconfidence intervaldata analyticsGaussian distributionlower tail probabilitysignificanceSimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01TAF   24  nagf_stat_inv_cdf_normal_vector
Computes a vector of deviates for the standard Normal distribution
Related keywords: big datadata analyticsdeviatesGaussian distributioninverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G05RZF   22  nagf_rand_multivar_normal
Generates a matrix of pseudorandom numbers from a multivariate Normal distribution
Related keywords: big datadata analyticsfinanceGaussian distributionmultivariate Normal distributionrandom number generatorsrandom numbers
G05SKF   22  nagf_rand_dist_normal
Generates a vector of pseudorandom numbers from a Normal distribution
Related keywords: big datadata analyticsfinanceGaussian distributionrandom number generatorsrandom numbers
G05YJF   21  nagf_rand_quasi_normal
Generates a Normal quasi-random number sequence
Related keywords: big datadata analyticsFaure, quasi-random numbersGaussian distributionlow-discrepancy sequencesNiederreiter method, quasi-random numbersquasi-random numbersrandom number generatorsrandom numbersSobol, quasi-random numbers
G07BBF   15  nagf_univar_estim_normal
Computes maximum likelihood estimates for parameters of the Normal distribution from grouped and/or censored data
Related keywords: censored dataGaussian distributiongrouping datamaximum likelihoodunivariate estimation
G07CAF   15  nagf_univar_ttest_2normal
Computes t -test statistic for a difference in means between two Normal populations, confidence interval
Related keywords: confidence intervalGaussian distributiont-test statisticunivariate estimation
G08CKF   23  nagf_nonpar_gofstat_anddar_normal
Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of a fully-unspecified Normal distribution
Related keywords: Anderson–Darling test statisticGaussian distributionnonparametric statisticsprobability
S15ABF   nagf_specfun_cdf_normal
Cumulative Normal distribution function P x
Related keywords: approximations of special functionscumulative Normal distributionfinanceGaussian distribution
Normal scores G01DAF   nagf_stat_normal_scores_exact
Normal scores, accurate values
Related keywords: financeSimple Calculations on Statistical Data
G01DBF   12  nagf_stat_normal_scores_approx
Normal scores, approximate values
Related keywords: financeSimple Calculations on Statistical Data
G01DCF   12  nagf_stat_normal_scores_var
Normal scores, approximate variance-covariance matrix
Related keywords: covariance matrixfinanceSimple Calculations on Statistical Datavariance-covariance matrix
numerical differentiation D04 Chapter Introduction     Numerical Differentiation
numerical integration D01GCF   10  nagf_quad_md_numth
Multidimensional quadrature, general product region, number-theoretic method
Related keywords: integration, multidimensionalKorobov–Conroy method, numerical integrationquadraturequadrature non-adaptive
ODE D02NJF   12  nagf_ode_ivp_stiff_imp_sparjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formuladiscretised systemimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemJacobianODE, ordinary differential equationsstiff differential equations
ODE, ordinary differential equations D02 Chapter Introduction     Ordinary Differential Equations
one-dimensional C06PQF   19  nagf_sum_fft_realherm_1d_multi_col
Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using column ordered complex storage format for Hermitian sequences
Related keywords: discreteFast Fourier TransformFFTsummation of series
D03NCF   20  nagf_pde_1d_blackscholes_fd
Finite difference solution of the Black–Scholes equations
Related keywords: Black–Scholes option pricingparabolic partial differential equationPDE, partial differential equations
D03PPF   16  nagf_pde_1d_parab_remesh_fd_old
General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable
Related keywords: DAE, differential algebraic equationsmethod of linesparabolic partial differential equationPDE, partial differential equations
D03PSF   17  nagf_pde_1d_parab_convdiff_remesh
General system of convection-diffusion PDEs, coupled DAEs, method of lines, upwind scheme, remeshing, one space variable
Related keywords: adaptive grid, PDEconvection-diffusion, PDEDAE, differential algebraic equationshyperbolic equationmethod of linesparabolic partial differential equationPDE, partial differential equations
E01BAF   nagf_interp_1d_spline
Interpolating functions, cubic spline interpolant, one variable
Related keywords: cubic splinefinanceinterpolation
E01RAF   nagf_interp_1d_ratnl
Interpolating functions, rational interpolant, one variable
Related keywords: interpolationrational interpolant
E01RBF   nagf_interp_1d_ratnl_eval
Interpolated values, evaluate rational interpolant computed by E01RAF, one variable
Related keywords: interpolationrational interpolant
one-dimensional cubic interpolation E04BBF   nagf_opt_one_var_deriv_old
Minimum, function of one variable, using first derivative
Related keywords: financemaximizing a functionminimizing a functionNLPnonlinear programmingoptimization
one-dimensional quadratic interpolation E04ABF   nagf_opt_one_var_func_old
Minimum, function of one variable, using function values only
Related keywords: derivative-free minimizationfinancemaximizing a functionminimization, unconstrainedminimizing a functionNLPnonlinear programmingoptimizationunivariate minimization
open file X04ACF   19  nagf_file_open
Open unit number for reading, writing or appending, and associate unit with named file
Related keywords: file openinginput utilitiesoutput utilities
openMP X06 Chapter Introduction     OpenMP Utilities
Related keywords: constants and utilitiesthread
X06AAF   25  nagf_omp_set_num_threads
Sets the number of threads for OpenMP parallel regions
Related keywords: constants and utilitiesconstants and utilitiesthreadthread
X06ABF   25  nagf_omp_get_num_threads
The number of OpenMP threads in the current team
Related keywords: constants and utilitiesconstants and utilitiesthreadthread
X06ACF   25  nagf_omp_get_max_threads
An upper bound on the number of threads in the next parallel region
Related keywords: constants and utilitiesconstants and utilitiesthreadthread
X06ADF   25  nagf_omp_get_thread_num
The OpenMP thread number of the calling thread
Related keywords: constants and utilitiesconstants and utilitiesthreadthread
X06AFF   25  nagf_omp_in_parallel
Tests for an active OpenMP parallel region
Related keywords: constants and utilitiesconstants and utilitiesthreadthread
X06AGF   25  nagf_omp_set_nested
Enables or disables nested OpenMP parallelism
Related keywords: constants and utilitiesconstants and utilitiesthreadthread
X06AHF   25  nagf_omp_get_nested
Tests the status of nested OpenMP parallelism
Related keywords: constants and utilitiesconstants and utilitiesthreadthread
X06XAF   26  nagf_omp_using_threaded_impl
Tests whether a threaded NAG Library is being used
Related keywords: constants and utilitiesconstants and utilitiesthreadthread
operations research H Chapter Introduction     Operations Research
optimization E04 Chapter Introduction     Minimizing or Maximizing a Function
Related keywords: maximizing a functionminimizing a function
E04FFF   26  nagf_opt_handle_solve_dfls
Derivative-free (DFO) solver for a nonlinear least squares objective function with bounded variables
Related keywords: calibrationdata fittingderivative-free optimizationDFODFOmaximizing a functionminimizing a functionnonlinear least squaresnonlinear least squaressum of squares
E04RAF   26  nagf_opt_handle_init
Initialization of a handle for the NAG optimization modelling suite for problems, such as, linear programming (LP), quadratic programming (QP), nonlinear programming (NLP), least squares (LSQ) problems, linear semidefinite programming (SDP) or SDP with bilinear matrix inequalities (BMI-SDP)
Related keywords: initializationleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionSDPsemidefinite programming
E04RDF   26  nagf_opt_sdp_read_sdpa
A reader of sparse SDPA data files for linear SDP problems
Related keywords: least squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionSDPsemidefinite programmingservice routine
E04REF   26  nagf_opt_handle_set_linobj
Define a linear objective function to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a function
E04RFF   26  nagf_opt_handle_set_quadobj
Define a linear or a quadratic objective function to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionQP
E04RGF   26  nagf_opt_handle_set_nlnobj
Define a nonlinear objective function to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLP
E04RHF   26  nagf_opt_handle_set_simplebounds
Define bounds of variables of a problem initialized by E04RAF
Related keywords: bound boxleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a function
E04RJF   26  nagf_opt_handle_set_linconstr
Define a block of linear constraints to a problem initialized by E04RAF
Related keywords: least squares fittinglinearly-constrainedmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a function
E04RKF   26  nagf_opt_handle_set_nlnconstr
Define a block of nonlinear constraints to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinearly-constrained
E04RLF   26  nagf_opt_handle_set_nlnhess
Define a structure of Hessian of the objective, constraints or the Lagrangian to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLP
E04RMF   26  nagf_opt_handle_set_nlnls
Define a nonlinear least squares objective function to a problem initialized by E04RAF
Related keywords: calibrationdata fittingderivative-free optimizationDFOleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinear least squaressum of squares
E04RNF   26  nagf_opt_handle_set_linmatineq
Add one or more linear matrix inequality constraints to a problem initialized by E04RAF
Related keywords: least squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a function
E04RPF   26  nagf_opt_handle_set_quadmatineq
Define bilinear matrix terms to a problem initialized by E04RAF
Related keywords: bilinear matrix inequalityBMIleast squares fittingmatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a function
E04RZF   26  nagf_opt_handle_free
Destroy the problem handle initialized by E04RAF and deallocate all the memory used
Related keywords: freeleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a function
E04STF   26  nagf_opt_handle_solve_ipopt
Run an interior point solver on a sparse nonlinear programming problem (NLP) initialized by E04RAF and defined by other routines from the suite
Related keywords: interior point methodIPMleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinear programming
E04SVF   26  nagf_opt_handle_solve_pennon
Run the Pennon solver on a compatible problem initialized by E04RAF and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI)
Related keywords: bilinear matrix inequalityBMIgeneralized augmented Lagrangian methodLagrangianleast squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionmonitoring informationSDPsemidefinite programming
E04ZMF   26  nagf_opt_handle_opt_set
Option setting routine for the solvers from the NAG optimization modelling suite
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a function
E04ZNF   26  nagf_opt_handle_opt_get
Option getting routine for the solvers from the NAG optimization modelling suite
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a function
E04ZPF   26  nagf_opt_handle_opt_set_file
Option setting routine for the solvers from the NAG optimization modelling suite from external file
Related keywords: maximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptions, computational
option pricing S30AAF   22  nagf_specfun_opt_bsm_price
Black–Scholes–Merton option pricing formula
Related keywords: approximations of special functionsBlack–Scholes option pricingderivative, optionsfinance
S30ABF   22  nagf_specfun_opt_bsm_greeks
Black–Scholes–Merton option pricing formula with Greeks
Related keywords: approximations of special functionsBlack–Scholes option pricingderivative, optionsfinanceGreeks, options
S30BAF   22  nagf_specfun_opt_lookback_fls_price
Floating-strike lookback option pricing formula in the Black-Scholes-Merton model
Related keywords: approximations of special functionsderivative, optionsfinancefloating-strike lookback option
S30BBF   22  nagf_specfun_opt_lookback_fls_greeks
Floating-strike lookback option pricing formula with Greeks in the Black-Scholes-Merton model
Related keywords: approximations of special functionsderivative, optionsfinancefloating-strike lookback optionGreeks, options
S30CAF   22  nagf_specfun_opt_binary_con_price
Binary option, cash-or-nothing pricing formula
Related keywords: approximations of special functionsbinary optioncash-or-nothing optionderivative, optionsfinance
S30CBF   22  nagf_specfun_opt_binary_con_greeks
Binary option, cash-or-nothing pricing formula with Greeks
Related keywords: approximations of special functionsbinary optioncash-or-nothing optionderivative, optionsfinanceGreeks, options
S30CCF   22  nagf_specfun_opt_binary_aon_price
Binary option, asset-or-nothing pricing formula
Related keywords: approximations of special functionsbinary optioncash-or-nothing optionderivative, optionsfinance
S30CDF   22  nagf_specfun_opt_binary_aon_greeks
Binary option, asset-or-nothing pricing formula with Greeks
Related keywords: approximations of special functionsbinary optioncash-or-nothing optionderivative, optionsfinanceGreeks, options
S30FAF   22  nagf_specfun_opt_barrier_std_price
Standard barrier option pricing formula
Related keywords: approximations of special functionsbarrier optionderivative, optionsfinance
S30JAF   22  nagf_specfun_opt_jumpdiff_merton_price
Jump-diffusion, Merton's model, option pricing formula
Related keywords: approximations of special functionsderivative, optionsfinancejump-diffusion model, option pricingMerton model, option pricing
S30JBF   22  nagf_specfun_opt_jumpdiff_merton_greeks
Jump-diffusion, Merton's model, option pricing formula with Greeks
Related keywords: approximations of special functionsderivative, optionsfinanceGreeks, optionsjump-diffusion model, option pricingMerton model, option pricing
S30NAF   22  nagf_specfun_opt_heston_price
Heston's model option pricing formula
Related keywords: approximations of special functionsderivative, optionsfinancefinanceHeston model, options
S30NBF   23  nagf_specfun_opt_heston_greeks
Heston's model option pricing formula with Greeks
Related keywords: approximations of special functionsderivative, optionsfinanceGreeks, optionsHeston model, options
S30SAF   22  nagf_specfun_opt_asian_geom_price
Asian option, geometric continuous average rate pricing formula
Related keywords: approximations of special functionsAsian optionderivative, optionsfinance
S30SBF   22  nagf_specfun_opt_asian_geom_greeks
Asian option, geometric continuous average rate pricing formula with Greeks
Related keywords: approximations of special functionsAsian optionderivative, optionsfinanceGreeks, options
options G22ZMF   26  nagf_blgm_optset
Option setting routine for
G22ZNF   26  nagf_blgm_optget
Option getting routine for
options, computational D01ZKF   24  nagf_quad_opt_set
Option setting routine
Related keywords: integration, optionsquadraturequadrature, options
D01ZLF   24  nagf_quad_opt_get
Option getting routine
Related keywords: integration, optionsquadraturequadrature, options
E02ZKF   24  nagf_fit_opt_set
Option setting routine
Related keywords: curve and surface fitting
E02ZLF   24  nagf_fit_opt_get
Option getting routine
Related keywords: curve and surface fitting
E04DJF   12  nagf_opt_uncon_conjgrd_option_file_old
Supply values for E04DGF from external file
Related keywords: maximizing a functionminimization, unconstrainedminimizing a functionoptimization
E04DKF   12  nagf_opt_uncon_conjgrd_option_string_old
Supply values to E04DGF from a character string
Related keywords: maximizing a functionminimization, unconstrainedminimizing a functionoptimization
E04MGF   16  nagf_opt_lp_option_file_old
Supply values for E04MFF from external file
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimization
E04MHF   16  nagf_opt_lp_option_string_old
Supply values to E04MFF from a character string
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimization
E04NDF   12  nagf_opt_lsq_lincon_option_file_old
Supply values for E04NCF from external file
Related keywords: convex optimizationleast squaresmaximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04NEF   12  nagf_opt_lsq_lincon_option_string_old
Supply values to E04NCF from a character string
Related keywords: least squaresmaximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04NGF   16  nagf_opt_qp_dense_option_file_old
Supply values for E04NFF from external file
Related keywords: maximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04NHF   16  nagf_opt_qp_dense_option_string_old
Supply values to E04NFF from a character string
Related keywords: maximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04NLF   18  nagf_opt_qpconvex1_sparse_option_file_old
Supply values for E04NKF from external file
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04NMF   18  nagf_opt_qpconvex1_sparse_option_string_old
Supply values to E04NKF from a character string
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04NPF   21  nagf_opt_qpconvex2_sparse_init
Initialization routine for E04NQF
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04NRF   21  nagf_opt_qpconvex2_sparse_option_file
Supply values for E04NQF from external file
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04NSF   21  nagf_opt_qpconvex2_sparse_option_string
Set a single option for E04NQF from a character string
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04NTF   21  nagf_opt_qpconvex2_sparse_option_integer_set
Set a single option for E04NQF from an integer argument
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04NUF   21  nagf_opt_qpconvex2_sparse_option_double_set
Set a single option for E04NQF from a real argument
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04NXF   21  nagf_opt_qpconvex2_sparse_option_integer_get
Get the setting of an integer valued option of E04NQF
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04NYF   21  nagf_opt_qpconvex2_sparse_option_double_get
Get the setting of a real valued option of E04NQF
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04UDF   12  nagf_opt_nlp1_option_file_old
Supply values for E04UCF or E04UFF from external file
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationSQP
E04UEF   12  nagf_opt_nlp1_option_string_old
Supply values to E04UCF or E04UFF from a character string
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationSQP
E04UHF   19  nagf_opt_nlp1_sparse_option_file_old
Supply values for E04UGF from external file
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationSQP
E04UJF   19  nagf_opt_nlp1_sparse_option_string_old
Supply values to E04UGF from a character string
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationSQP
E04UQF   14  nagf_opt_lsq_gencon_deriv_option_file_old
Supply values for E04USF from external file
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationSQPsum of squares
E04URF   14  nagf_opt_lsq_gencon_deriv_option_string_old
Supply values to E04USF from a character string
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationSQPsum of squares
E04VGF   21  nagf_opt_nlp2_sparse_init
Initialization routine for E04VHF
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationSQP
E04VKF   21  nagf_opt_nlp2_sparse_option_file
Supply values for E04VHF from external file
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationSQP
E04VLF   21  nagf_opt_nlp2_sparse_option_string
Set a single option for E04VHF from a character string
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationSQP
E04VMF   21  nagf_opt_nlp2_sparse_option_integer_set
Set a single option for E04VHF from an integer argument
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationSQP
E04VNF   21  nagf_opt_nlp2_sparse_option_double_set
Set a single option for E04VHF from a real argument
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationSQP
E04VRF   21  nagf_opt_nlp2_sparse_option_integer_get
Get the setting of an integer valued option of E04VHF
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationSQP
E04VSF   21  nagf_opt_nlp2_sparse_option_double_get
Get the setting of a real valued option of E04VHF
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationSQP
E04WBF   20  nagf_opt_init
Initialization routine for E04DGA E04MFA E04NCA E04NFA E04NKA E04UCA E04UFA E04UGA E04USA
Related keywords: maximizing a functionminimizing a functionoptimization
E04WCF   21  nagf_opt_nlp2_init
Initialization routine for E04WDF
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimization
E04WEF   21  nagf_opt_nlp2_option_file
Supply values for E04WDF from external file
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationSQP
E04WFF   21  nagf_opt_nlp2_option_string
Set a single option for E04WDF from a character string
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationSQP
E04WGF   21  nagf_opt_nlp2_option_integer_set
Set a single option for E04WDF from an integer argument
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationSQP
E04WHF   21  nagf_opt_nlp2_option_double_set
Set a single option for E04WDF from a real argument
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationSQP
E04WKF   21  nagf_opt_nlp2_option_integer_get
Get the setting of an integer valued option of E04WDF
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationSQP
E04WLF   21  nagf_opt_nlp2_option_double_get
Get the setting of a real valued option of E04WDF
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationSQP
E04ZPF   26  nagf_opt_handle_opt_set_file
Option setting routine for the solvers from the NAG optimization modelling suite from external file
Related keywords: maximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
E05JAF   22  nagf_glopt_bnd_mcs_init
Initialization routine for E05JBF
Related keywords: global optimizationminimization, simple bound constraints
E05JBF   22  nagf_glopt_bnd_mcs_solve
Global optimization by multi-level coordinate search, simple bounds, using function values only
Related keywords: financeglobal optimizationminimization, simple bound constraintsmulti-level coordinate search
E05JCF   22  nagf_glopt_bnd_mcs_optset_file
Supply values for E05JBF from external file
Related keywords: global optimizationminimization, simple bound constraints
E05JDF   22  nagf_glopt_bnd_mcs_optset_string
Set a single for E05JBF from a character string
Related keywords: global optimizationminimization, simple bound constraints
E05JEF   22  nagf_glopt_bnd_mcs_optset_char
Set a single for E05JBF from an ON/OFF-valued character argument
Related keywords: global optimizationminimization, simple bound constraints
E05JFF   22  nagf_glopt_bnd_mcs_optset_int
Set a single for E05JBF from an integer argument
Related keywords: global optimizationminimization, simple bound constraints
E05JGF   22  nagf_glopt_bnd_mcs_optset_real
Set a single for E05JBF from a real argument
Related keywords: global optimizationminimization, simple bound constraints
E05JHF   22  nagf_glopt_bnd_mcs_option_check
Determine whether an for E05JBF has been set by you or not
Related keywords: global optimizationminimization, simple bound constraints
E05JJF   22  nagf_glopt_bnd_mcs_optget_char
Get the setting of an ON/OFF-valued character of E05JBF
Related keywords: global optimization
E05JKF   22  nagf_glopt_bnd_mcs_optget_int
Get the setting of an integer valued of E05JBF
Related keywords: global optimizationminimization, simple bound constraints
E05JLF   22  nagf_glopt_bnd_mcs_optget_real
Get the setting of a real valued of E05JBF
Related keywords: global optimizationminimization, simple bound constraints
E05ZKF   23  nagf_glopt_optset
Option setting routine for E05SAF E05SBF E05UCF E05USF
Related keywords: global optimization
E05ZLF   23  nagf_glopt_optget
Option getting routine for E05SAF E05SBF E05UCF E05USF
Related keywords: global optimization
G02ZKF   23  nagf_correg_optset
Option setting routine for G02QGF
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionpolynomial regressionquantile regressionregression analysis
G02ZLF   23  nagf_correg_optget
Option getting routine for G02QGF
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionpolynomial regressionquantile regressionregression analysis
G05KFF   22  nagf_rand_init_repeat
Initializes a pseudorandom number generator to give a repeatable sequence
Related keywords: ACORNbig datadata analyticsmersenne twisterMRG32k3arandom number generatorsrandom numbersWichmann Hill
G05KGF   22  nagf_rand_init_nonrepeat
Initializes a pseudorandom number generator to give a non-repeatable sequence
Related keywords: ACORNbig datadata analyticsmersenne twisterMRG32k3arandom number generatorsrandom numbersWichmann Hill
G05KHF   22  nagf_rand_init_leapfrog
Primes a pseudorandom number generator for generating multiple streams using leap-frog
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
G05KJF   22  nagf_rand_init_skipahead
Primes a pseudorandom number generator for generating multiple streams using skip-ahead
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
G05KKF   23  nagf_rand_init_skipahead_power2
Primes a pseudorandom number generator for generating multiple streams using skip-ahead, skipping ahead a power of 2
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
G05XAF   24  nagf_rand_bb_init
Initializes the Brownian bridge generator
Related keywords: big databrownian bridgedata analyticsrandom number generators
G05XCF   24  nagf_rand_bb_inc_init
Initializes the generator which backs out the increments of sample paths generated by a Brownian bridge algorithm
Related keywords: big databrownian bridgedata analyticsrandom number generators
G05YMF   22  nagf_rand_quasi_uniform
Generates a uniform quasi-random number sequence
Related keywords: big datadata analyticsfinancelow-discrepancy sequencesquasi-random numbersrandom number generatorsrandom numbers
G05ZMF   24  nagf_rand_field_1d_user_setup
Setup for simulating one-dimensional random fields, user-defined variogram
Related keywords: big datadata analyticsrandom fieldsrandom number generatorsvariogram
G05ZNF   24  nagf_rand_field_1d_predef_setup
Setup for simulating one-dimensional random fields
Related keywords: big datadata analyticsrandom fieldsrandom number generatorsvariogram
G05ZQF   24  nagf_rand_field_2d_user_setup
Setup for simulating two-dimensional random fields, user-defined variogram
Related keywords: big datadata analyticsrandom fieldsrandom number generatorsvariogram
G05ZRF   24  nagf_rand_field_2d_predef_setup
Setup for simulating two-dimensional random fields, preset variogram
Related keywords: big datadata analyticsrandom fieldsrandom number generatorsvariogram
H02CCF   19  nagf_mip_iqp_dense_optfile
Read values for H02CBF from external file
Related keywords: integer quadratic programoperations research
H02CDF   19  nagf_mip_iqp_dense_optstr
Supply values to H02CBF
Related keywords: integer quadratic programoperations research
H02CFF   19  nagf_mip_iqp_sparse_optfile
Read values for H02CEF from external file
Related keywords: integer programmingmixed integer programmingoperations research
H02CGF   19  nagf_mip_iqp_sparse_optstr
Supply values to H02CEF
Related keywords: integer programmingoperations research
H02ZKF   25  nagf_mip_optset
Option setting routine for H02DAF
Related keywords: operations research
H02ZLF   25  nagf_mip_optget
Option getting routine for H02DAF
Related keywords: operations research
ordered observations G10ZAF   16  nagf_smooth_data_order
Reorder data to give ordered distinct observations
Related keywords: Smoothing in Statistics
ordinal scaling G03FCF   17  nagf_mv_multidimscal_ordinal
Performs non-metric (ordinal) multidimensional scaling
Related keywords: multivariate methodsnon-metric (ordinal) scaling
ordinary differential equations D02TLF   25  nagf_ode_bvp_coll_nlin_solve
Ordinary differential equations, general nonlinear boundary value problem, collocation technique (thread safe)
Related keywords: boundary value problemBVPdifferential equationsnonlinear mixed orderODE, ordinary differential equationstwo-point boundary value problem
orthogonalization F05 Chapter Introduction     Orthogonalization
orthogonal matrix, generation F08AFF   16  nagf_lapackeig_dorgqr
Forms all or part of orthogonal Q from Q R factorization determined by F08AEF F08BEF F08BFF
Related keywords: DORGQReigenproblemLAPACKLAPACKleast squaresorthogonal transformations QR factorization
F08AJF   16  nagf_lapackeig_dorglq
Forms all or part of orthogonal Q from L Q factorization determined by F08AHF
Related keywords: DORGLQeigenproblemLAPACKLAPACKleast squares LQ factorizationorthogonal transformations
F08CFF   22  nagf_lapackeig_dorgql
Form all or part of orthogonal Q from Q L factorization determined by F08CEF
Related keywords: DORGQLeigenproblemLAPACKLAPACKleast squaresorthogonal transformations QL factorization
F08CJF   22  nagf_lapackeig_dorgrq
Form all or part of orthogonal Q from R Q factorization determined by F08CHF
Related keywords: DORGRQeigenproblemLAPACKLAPACKleast squaresorthogonal transformationsRQ factorizations
F08FFF   16  nagf_lapackeig_dorgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF
Related keywords: DORGTReigenproblemLAPACKLAPACKleast squaresorthogonal transformations
F08GFF   16  nagf_lapackeig_dopgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF
Related keywords: DOPGTReigenproblemLAPACKLAPACKleast squaresorthogonal transformations
F08KFF   16  nagf_lapackeig_dorgbr
Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF
Related keywords: DORGBReigenproblemLAPACKLAPACKleast squaresorthogonal transformations
F08NFF   16  nagf_lapackeig_dorghr
Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF
Related keywords: DORGHReigenproblemLAPACKLAPACKleast squares
orthogonal transformations F08ACF   25  nagf_lapackeig_dgemqrt
Applies the orthogonal transformation determined by F08ABF
Related keywords: DGEMQRTeigenproblemexplicit blockingLAPACKleast squaresQR factorizationrecursive QR
F08AFF   16  nagf_lapackeig_dorgqr
Forms all or part of orthogonal Q from Q R factorization determined by F08AEF F08BEF F08BFF
Related keywords: DORGQReigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generation QR factorization
F08AGF   16  nagf_lapackeig_dormqr
Applies an orthogonal transformation determined by F08AEF F08BEF F08BFF
Related keywords: DORMQReigenproblemfinanceLAPACKLAPACKleast squares QR factorization
F08AJF   16  nagf_lapackeig_dorglq
Forms all or part of orthogonal Q from L Q factorization determined by F08AHF
Related keywords: DORGLQeigenproblemLAPACKLAPACKleast squares LQ factorizationorthogonal matrix, generation
F08AKF   16  nagf_lapackeig_dormlq
Applies the orthogonal transformation determined by F08AHF
Related keywords: DORMLQeigenproblemLAPACKLAPACKleast squares LQ factorization
F08BCF   25  nagf_lapackeig_dtpmqrt
Applies the orthogonal transformation determined by F08BBF
Related keywords: DTPMQRTeigenproblemexplicit blockingLAPACKleast squaresQR factorizationrecursive QR
F08BEF   16  nagf_lapackeig_dgeqpf
Q R factorization, with column pivoting, of real general rectangular matrix
Related keywords: DGEQPFeigenproblemfinanceLAPACKLAPACKleast squares QR factorizationreal, m by n matrix
F08BFF   22  nagf_lapackeig_dgeqp3
Q R factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
Related keywords: DGEQP3eigenproblemfinanceLAPACKLAPACKleast squares QR factorizationreal, m by n matrix
F08BHF   22  nagf_lapackeig_dtzrzf
Reduces a real upper trapezoidal matrix to upper triangular form
Related keywords: DTZRZFeigenproblemLAPACKLAPACKleast squaresmatrix, upper trapezoidalmatrix, upper triangularreal, trapezoidal matrix
F08BKF   22  nagf_lapackeig_dormrz
Applies the orthogonal transformation determined by F08BHF
Related keywords: DORMRZeigenproblemLAPACKLAPACKleast squares
F08CFF   22  nagf_lapackeig_dorgql
Form all or part of orthogonal Q from Q L factorization determined by F08CEF
Related keywords: DORGQLeigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generation QL factorization
F08CGF   22  nagf_lapackeig_dormql
Applies the orthogonal transformation determined by F08CEF
Related keywords: DORMQLeigenproblemLAPACKLAPACKleast squares QL factorization
F08CJF   22  nagf_lapackeig_dorgrq
Form all or part of orthogonal Q from R Q factorization determined by F08CHF
Related keywords: DORGRQeigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generationRQ factorizations
F08CKF   22  nagf_lapackeig_dormrq
Applies the orthogonal transformation determined by F08CHF
Related keywords: DORGRQeigenproblemLAPACKLAPACKleast squaresRQ factorizations
F08FEF   16  nagf_lapackeig_dsytrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
Related keywords: DSYTRDeigenproblemLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08FFF   16  nagf_lapackeig_dorgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF
Related keywords: DORGTReigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generation
F08FGF   16  nagf_lapackeig_dormtr
Applies the orthogonal transformation determined by F08FEF
Related keywords: DORMTReigenproblemLAPACKLAPACKleast squares
F08GAF   21  nagf_lapackeig_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Related keywords: DSPEVeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares QR algorithmreal, indefinite, symmetric matrix
F08GBF   21  nagf_lapackeig_dspevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Related keywords: DSPEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08GEF   16  nagf_lapackeig_dsptrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
Related keywords: DSPTRDeigenproblemLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08GFF   16  nagf_lapackeig_dopgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF
Related keywords: DOPGTReigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generation
F08GGF   16  nagf_lapackeig_dopmtr
Applies the orthogonal transformation determined by F08GEF
Related keywords: DOPMTReigenproblemLAPACKLAPACKleast squares
F08HEF   16  nagf_lapackeig_dsbtrd
Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
Related keywords: DSBTRDeigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, symmetric matrix
F08KEF   16  nagf_lapackeig_dgebrd
Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
Related keywords: DGEBRDeigenproblemLAPACKLAPACKleast squaresreal, m by n matrix
F08KFF   16  nagf_lapackeig_dorgbr
Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF
Related keywords: DORGBReigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generationorthogonal matrix, generation
F08KGF   16  nagf_lapackeig_dormbr
Applies the orthogonal transformations from reduction to bidiagonal form determined by F08KEF
Related keywords: DORMBReigenproblemLAPACKLAPACKleast squares
F08NAF   21  nagf_lapackeig_dgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
Related keywords: DGEEVeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares QR algorithmreal, nonsymmetric matrix
F08NBF   21  nagf_lapackeig_dgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGEEVXeigenproblemeigenvalueseigenvectorsfinanceforward errorLAPACKLAPACKleast squares QR algorithmreal, nonsymmetric matrix
F08NEF   16  nagf_lapackeig_dgehrd
Performs an orthogonal reduction of real general matrix to upper Hessenberg form
Related keywords: DGEHRDeigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08NGF   16  nagf_lapackeig_dormhr
Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF
Related keywords: DORMHReigenproblemLAPACKLAPACKleast squares
F08QFF   16  nagf_lapackeig_dtrexc
Reorders a Schur factorization of real matrix using orthogonal similarity transformation
Related keywords: DTREXCeigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form
F08QGF   16  nagf_lapackeig_dtrsen
Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
Related keywords: condition number, matrixDTREXCeigenproblemLAPACKLAPACKleast squaresSchur form
F08VEF   22  nagf_lapackeig_dggsvp
Produces orthogonal matrices that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
Related keywords: DGGSVPeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresreal, m by n matrixSVD, generalized
F08VGF   26  nagf_lapackeig_dggsvp3
Produces orthogonal matrices, using BLAS-3, that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
Related keywords: DGGSVP3eigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresreal, m by n matrixSVD, generalized
F08VSF   22  nagf_lapackeig_zggsvp
Produces unitary matrices that simultaneously reduce the complex, m by n , matrix A and the complex, p by n , matrix B to upper triangular form
Related keywords: complex, m by n matrixeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresSVD, generalizedZGGSVP
F08VUF   26  nagf_lapackeig_zggsvp3
Produces unitary matrices, using BLAS-3, that simultaneously reduce the complex, m by n , matrix A and the complex, p by n , matrix B to upper triangular form
Related keywords: complex, m by n matrixeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresSVD, generalizedZGGSVP3
F08WEF   20  nagf_lapackeig_dgghrd
Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Related keywords: DGGHRDeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08WFF   26  nagf_lapackeig_dgghd3
Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Related keywords: DGGHD3eigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08YFF   22  nagf_lapackeig_dtgexc
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
Related keywords: DTGEXCeigenproblemgeneralized Schur formLAPACKLAPACKleast squares
F08YGF   22  nagf_lapackeig_dtgsen
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Related keywords: condition number, matrixDTGSENeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrix
G03BAF   15  nagf_mv_rot_orthomax
Computes orthogonal rotations for loading matrix, generalized orthomax criterion
Related keywords: canonical variate analysisfactor analysismultivariate methodsorthomax criterion
orthomax criterion G03BAF   15  nagf_mv_rot_orthomax
Computes orthogonal rotations for loading matrix, generalized orthomax criterion
Related keywords: canonical variate analysisfactor analysismultivariate methodsorthogonal transformations
Osher's method, Euler equations D03PVF   17  nagf_pde_1d_parab_euler_osher
Osher's approximate Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
Related keywords: Euler equationsPDE, partial differential equationsRiemann solver, PDE
outlier detection E02GAF   nagf_fit_glin_l1sol
L 1 -approximation by general linear function
Related keywords: curve and surface fittingL1 approximation
E02GBF   nagf_fit_glinc_l1sol
L 1 -approximation by general linear function subject to linear inequality constraints
Related keywords: curve and surface fittingL1 approximation
G07GAF   23  nagf_univar_outlier_peirce_1var
Outlier detection using method of Peirce, raw data or single variance supplied
Related keywords: financePeirce outlier detectionunivariate estimation
G07GBF   23  nagf_univar_outlier_peirce_2var
Outlier detection using method of Peirce, two variances supplied
Related keywords: financePeirce outlier detectionunivariate estimation
output utilities X04 Chapter Introduction     Input/Output Utilities
Related keywords: input utilities
overdetermined linear equations F08AAF   21  nagf_lapackeig_dgels
Solves a real linear least squares problem of full rank
Related keywords: DGELSeigenproblemfinanceLAPACKLAPACKleast squareslinear least squares LQ decomposition QR factorizationreal, m by n matrixunderdetermined linear system
F08ANF   21  nagf_lapackeig_zgels
Solves a complex linear least problem of full rank
Related keywords: complex, m by n matrixeigenproblemfinanceLAPACKLAPACKleast squareslinear least squares LQ decomposition QR factorizationunderdetermined linear systemZGELS
Owen G05YNF   22  nagf_rand_quasi_init_scrambled
Initializes a scrambled quasi-random number generator
Related keywords: big datadata analyticsFaure–TezukafinanceNiederreiterrandom number generatorsrandom numbersscrambleSobol
Padé approximation E02RAF   nagf_fit_pade_app
Padé approximants
Related keywords: curve and surface fitting
E02RBF   nagf_fit_pade_eval
Evaluation of fitted rational function as computed by E02RAF
Related keywords: curve and surface fitting
pairs test for randomness G08EBF   14  nagf_nonpar_randtest_pairs
Performs the pairs (serial) test for randomness
Related keywords: nonparametric statisticsrandomness, tests for
Pal–Walker–Kahan ( QL or QR ) algorithm F08GCF   19  nagf_lapackeig_dspevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: divide-and-conquer methodDSPEVDeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08GQF   19  nagf_lapackeig_zhpevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: complex, Hermitian, indefinite matrixdivide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresZHPEVD
F08HCF   19  nagf_lapackeig_dsbevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: divide-and-conquer methodDSBEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, band, symmetric matrix
F08HQF   19  nagf_lapackeig_zhbevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
Related keywords: complex, band, Hermitian matrixdivide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandZHBEVD
F08JCF   19  nagf_lapackeig_dstevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
Related keywords: divide-and-conquer methodDSTEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
Pan's method G01JDF   15  nagf_stat_prob_chisq_lincomb
Computes lower tail probability for a linear combination of (central) χ 2 variables
Related keywords: chi-squared distributionfinanceImhof's methodlower tail probabilitySimple Calculations on Statistical Data
parabolic partial differential equation D03NCF   20  nagf_pde_1d_blackscholes_fd
Finite difference solution of the Black–Scholes equations
Related keywords: Black–Scholes option pricingone-dimensionalPDE, partial differential equations
D03NDF   20  nagf_pde_1d_blackscholes_closed
Analytic solution of the Black–Scholes equations
Related keywords: Black–Scholes option pricingPDE, partial differential equations
D03NEF   20  nagf_pde_1d_blackscholes_means
Compute average values for D03NDF
Related keywords: Black–Scholes option pricingPDE, partial differential equations
D03PCF   15  nagf_pde_1d_parab_fd_old
General system of parabolic PDEs, method of lines, finite differences, one space variable
Related keywords: method of linesPDE, partial differential equations
D03PDF   15  nagf_pde_1d_parab_coll_old
General system of parabolic PDEs, method of lines, Chebyshev C 0 collocation, one space variable
Related keywords: collocation methodmethod of linesPDE, partial differential equations
D03PEF   16  nagf_pde_1d_parab_keller
General system of first-order PDEs, method of lines, Keller box discretization, one space variable
Related keywords: Keller box discretizationmethod of linesPDE, partial differential equations
D03PHF   15  nagf_pde_1d_parab_dae_fd_old
General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable
Related keywords: DAE, differential algebraic equationsfinite difference discretizationmethod of linespartial differential equationsPDE, partial differential equations
D03PJF   15  nagf_pde_1d_parab_dae_coll_old
General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C 0 collocation, one space variable
Related keywords: DAE, differential algebraic equationsmethod of linespartial differential equationsPDE, partial differential equations
D03PPF   16  nagf_pde_1d_parab_remesh_fd_old
General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable
Related keywords: DAE, differential algebraic equationsmethod of linesone-dimensionalPDE, partial differential equations
D03PSF   17  nagf_pde_1d_parab_convdiff_remesh
General system of convection-diffusion PDEs, coupled DAEs, method of lines, upwind scheme, remeshing, one space variable
Related keywords: adaptive grid, PDEconvection-diffusion, PDEDAE, differential algebraic equationshyperbolic equationmethod of linesone-dimensionalPDE, partial differential equations
D03PYF   15  nagf_pde_1d_parab_coll_interp
PDEs, spatial interpolation with D03PDF or D03PJF
Related keywords: interpolationPDE, partial differential equations
D03PZF   15  nagf_pde_1d_parab_fd_interp
PDEs, spatial interpolation with D03PCF, D03PEF, D03PFF, D03PHF, D03PKF, D03PLF, D03PPF, D03PRF or D03PSF
Related keywords: interpolationPDE, partial differential equations
parameter estimates G08RAF   12  nagf_nonpar_rank_regsn
Regression using ranks, uncensored data
Related keywords: nonparametric statisticsregressionscoresvariance-covariance matrix
G08RBF   12  nagf_nonpar_rank_regsn_censored
Regression using ranks, right-censored data
Related keywords: nonparametric statisticsregressionscoresvariance-covariance matrix
G11CAF   19  nagf_contab_condl_logistic
Returns parameter estimates for the conditional analysis of stratified data
Related keywords: conditional logistic analysiscontingency table analysislogistic analysisstratified data
parameterized first order D02SAF   nagf_ode_bvp_shoot_genpar_algeq
Ordinary differential equations, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined
Related keywords: boundary value problemBVPODE, ordinary differential equationsshooting method, ODEtwo-point boundary value problem
Pareto distribution G07BFF   23  nagf_univar_estim_genpareto
Estimates parameter values of the generalized Pareto distribution
Related keywords: maximum likelihoodmomentsunivariate estimation
partial autocorrelation coefficients G13ACF   nagf_tsa_uni_autocorr_part
Univariate time series, partial autocorrelations from autocorrelations
Related keywords: autocorrelation coefficientsautoregressive parametersbig datadata analyticserror variance ratiosfinancetime seriestime series analysisunivariate time series
G13DBF   11  nagf_tsa_multi_autocorr_part
Multivariate time series, multiple squared partial autocorrelations
Related keywords: big datadata analyticsmultivariate time seriestime seriestime series analysis
partial autoregression matrices G13DPF   16  nagf_tsa_multi_regmat_partial
Multivariate time series, partial autoregression matrices
Related keywords: big datadata analyticsmultivariate time seriestime seriestime series analysis
partial correlation G02BYF   17  nagf_correg_corrmat_partial
Computes partial correlation/variance-covariance matrix from correlation/variance-covariance matrix computed by G02BXF
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
partial differential equations D03PFF   17  nagf_pde_1d_parab_convdiff
General system of convection-diffusion PDEs with source terms in conservative form, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable
Related keywords: convection-diffusion, PDEmethod of linesPDE, partial differential equations
D03PHF   15  nagf_pde_1d_parab_dae_fd_old
General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable
Related keywords: DAE, differential algebraic equationsfinite difference discretizationmethod of linesparabolic partial differential equationPDE, partial differential equations
D03PJF   15  nagf_pde_1d_parab_dae_coll_old
General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C 0 collocation, one space variable
Related keywords: DAE, differential algebraic equationsmethod of linesparabolic partial differential equationPDE, partial differential equations
D03PKF   16  nagf_pde_1d_parab_dae_keller
General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretization, one space variable
Related keywords: DAE, differential algebraic equationsKeller box discretizationmethod of linesPDE, partial differential equations
D03PLF   17  nagf_pde_1d_parab_convdiff_dae
General system of convection-diffusion PDEs with source terms in conservative form, coupled DAEs, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable
Related keywords: convection-diffusion, PDEDAE, differential algebraic equationsPDE, partial differential equations
partial lag G13DNF   15  nagf_tsa_multi_corrmat_partlag
Multivariate time series, sample partial lag correlation matrices, χ 2 statistics and significance levels
Related keywords: big datachi squared statisticsdata analyticsmultivariate time seriessignificancetime seriestime series analysis
partial least squares regression G02LAF   22  nagf_correg_pls_svd
Partial least squares (PLS) regression using singular value decomposition
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02LBF   22  nagf_correg_pls_wold
Partial least squares (PLS) regression using Wold's iterative method
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysisWold's iterative method
G02LCF   22  nagf_correg_pls_fit
PLS parameter estimates following partial least squares regression by G02LAF G02LBF
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02LDF   22  nagf_correg_pls_pred
PLS predictions based on parameter estimates from G02LCF
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
particle swarm algorithm E05SAF   23  nagf_glopt_bnd_pso
Global optimization using particle swarm algorithm (PSO), bound constraints only
Related keywords: global optimizationminimization, simple bound constraintsPSO, particle swarm algorithm
E05SBF   23  nagf_glopt_nlp_pso
Global optimization using particle swarm algorithm (PSO), comprehensive
Related keywords: global optimizationminimization, nonlinear constraintsPSO, particle swarm algorithm
Parzen lag window G13CAF   10  nagf_tsa_uni_spectrum_lag
Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: Bartlett lag windowbig datadata analyticsfinancerectangular lag windowsmoothingtime seriestime series analysisTukey lag windowunivariate time series
G13CCF   10  nagf_tsa_multi_spectrum_lag
Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: Bartlett lag windowbig datacross-spectrumdata analyticsfinancemultivariate time seriesrectangular lag windowsmoothingtime seriestime series analysisTukey lag window
Pascal distribution G05THF   22  nagf_rand_int_negbin
Generates a vector of pseudorandom integers from a negative binomial distribution
Related keywords: big datadata analyticsfinancenegative binomial distributionPolya distributionrandom integersrandom number generators
PDE, partial differential equations D03 Chapter Introduction     Partial Differential Equations
pdf G01KAF   23  nagf_stat_pdf_normal
Calculates the value for the probability density function of the Normal distribution at a chosen point
Related keywords: Gaussian distributionNormal distributionprobability density functionSimple Calculations on Statistical Data
G01KFF   23  nagf_stat_pdf_gamma
Calculates the value for the probability density function of the gamma distribution at a chosen point
Related keywords: gamma distributionprobability density functionSimple Calculations on Statistical Data
G01KKF   24  nagf_stat_pdf_gamma_vector
Computes a vector of values for the probability density function of the gamma distribution
Related keywords: gamma distributionprobability density functionSimple Calculations on Statistical Data
G01KQF   24  nagf_stat_pdf_normal_vector
Computes a vector of values for the probability density function of the Normal distribution
Related keywords: Gaussian distributionlogarithm, pdfNormal distributionprobability density functionSimple Calculations on Statistical Data
G01LBF   24  nagf_stat_pdf_multi_normal_vector
Computes a vector of values for the probability density function of the multivariate Normal distribution
Related keywords: Gaussian distributionlogarithm, pdfmultivariate Normal distributionNormal distributionprobability density functionSimple Calculations on Statistical Data
Pearson product moment correlation G02BAF   nagf_correg_coeffs_pearson
Pearson product-moment correlation coefficients, all variables, no missing values
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02BBF   nagf_correg_coeffs_pearson_miss_case
Pearson product-moment correlation coefficients, all variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinancemissing valuesnonlinear regressionpolynomial regressionregression analysis
G02BCF   nagf_correg_coeffs_pearson_miss_pair
Pearson product-moment correlation coefficients, all variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinancemissing valuesnonlinear regressionpolynomial regressionregression analysis
G02BGF   nagf_correg_coeffs_pearson_subset
Pearson product-moment correlation coefficients, subset of variables, no missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BHF   nagf_correg_coeffs_pearson_subset_miss_case
Pearson product-moment correlation coefficients, subset of variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BJF   nagf_correg_coeffs_pearson_subset_miss_pair
Pearson product-moment correlation coefficients, subset of variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviationsum of squares
G02BWF   14  nagf_correg_ssqmat_to_corrmat
Computes a correlation matrix from a sum of squares matrix
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02BXF   14  nagf_correg_corrmat
Computes (optionally weighted) correlation and covariance matrices
Related keywords: big datacorrelation analysisdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysisstandard deviationvariance-covariance matrix
Peirce outlier detection G07GAF   23  nagf_univar_outlier_peirce_1var
Outlier detection using method of Peirce, raw data or single variance supplied
Related keywords: financeoutlier detectionunivariate estimation
G07GBF   23  nagf_univar_outlier_peirce_2var
Outlier detection using method of Peirce, two variances supplied
Related keywords: financeoutlier detectionunivariate estimation
pelt G13NAF   25  nagf_tsa_cp_pelt
Change point detection, using the PELT algorithm
Related keywords: big datachange pointdata analyticstime seriestime series analysis
G13NBF   25  nagf_tsa_cp_pelt_user
Change points detection using the PELT algorithm, user supplied cost function
Related keywords: big datachange pointdata analyticstime seriestime series analysis
permutation F06QJF   13  nagf_blas_dgeap
Permute rows or columns, real rectangular matrix, permutations represented by an integer array
Related keywords: BLASlinear algebra support routinesreal, m by n matrix
F06QKF   13  nagf_blas_dgeapr
Permute rows or columns, real rectangular matrix, permutations represented by a real array
Related keywords: BLASlinear algebra support routinesreal, m by n matrix
F06VJF   13  nagf_blas_zgeap
Permute rows or columns, complex rectangular matrix, permutations represented by an integer array
Related keywords: BLAScomplex, m by n matrixlinear algebra support routines
F06VKF   13  nagf_blas_zgeapr
Permute rows or columns, complex rectangular matrix, permutations represented by a real array
Related keywords: BLAScomplex, m by n matrixlinear algebra support routines
F11YEF   25  nagf_sparse_sym_rcm
Reverse Cuthill–McKee reordering of a sparse symmetric matrix in CCS format
Related keywords: big datacomplex, symmetric matrixdata analyticslarge scale linear systemsreal, symmetric matrixsparsesparse matrix
G05NCF   22  nagf_rand_permute
Pseudorandom permutation of an integer vector
Related keywords: big datadata analyticsfinancerandom number generatorsrandom permutation
M01ZAF   12  nagf_sort_permute_invert
Invert a permutation
Related keywords: big datadata analyticsinvert permutationsearchingsorting
M01ZBF   12  nagf_sort_permute_check
Check validity of a permutation
Related keywords: big datadata analyticssearchingsorting
M01ZCF   12  nagf_sort_permute_decompose
Decompose a permutation into cycles
Related keywords: big datacyclesdata analyticssearchingsorting
permute G05PVF   25  nagf_rand_kfold_xyw
Permutes a matrix, vector, vector triplet into a form suitable for K -fold cross validation
Related keywords: big datacross-validationCVdata analyticsjacknifek-foldleave-one-outLOOrandom number generators
G05PWF   25  nagf_rand_subsamp_xyw
Permutes a matrix, vector, vector triplet into a form suitable for random sub-sampling validation
Related keywords: big datacross-validationdata analyticsrandom number generatorsresamplesub-sample
phase, time series G13CFF   10  nagf_tsa_multi_gain_bivar
Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra
Related keywords: big databivariate time seriescross-spectrumdata analyticsfinancegain, time seriesmultivariate time seriestime seriestime series analysis
pi, mathematical constant X01AAF   nagf_math_pi
Provides the mathematical constant π
Related keywords: mathematical constants
Plackett copula G05RGF   23  nagf_rand_copula_plackett_bivar
Generates a matrix of pseudorandom numbers from a bivariate Plackett copula
Related keywords: big datacopuladata analyticsrandom number generatorsrandom numbers
point probability G01SJF   24  nagf_stat_prob_binomial_vector
Computes a vector of probabilities for the binomial distribution
Related keywords: big databinomial distributionCDF, cumulative distribution functiondata analyticslower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01SKF   24  nagf_stat_prob_poisson_vector
Computes a vector of probabilities for the Poisson distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticslower tail probabilityPoisson distributionSimple Calculations on Statistical Dataupper tail probability
G01SLF   24  nagf_stat_prob_hypergeom_vector
Computes a vector of probabilities for the hypergeometric distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticshypergeometric distributionlower tail probabilitySimple Calculations on Statistical Dataupper tail probability
Poisson distribution G01BKF   13  nagf_stat_prob_poisson
Poisson distribution function
Related keywords: CDF, cumulative distribution functionfinanceSimple Calculations on Statistical Data
G01SKF   24  nagf_stat_prob_poisson_vector
Computes a vector of probabilities for the Poisson distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticslower tail probabilitypoint probabilitySimple Calculations on Statistical Dataupper tail probability
G05TJF   22  nagf_rand_int_poisson
Generates a vector of pseudorandom integers from a Poisson distribution
Related keywords: big datadata analyticsfinancerandom integersrandom number generators
G05TKF   22  nagf_rand_int_poisson_varmean
Generates a vector of pseudorandom integers from a Poisson distribution with varying mean
Related keywords: big datadata analyticsfinancerandom integersrandom number generators
G07ABF   15  nagf_univar_ci_poisson
Computes confidence interval for the parameter of a Poisson distribution
Related keywords: confidence intervalunivariate estimation
Polya distribution G05THF   22  nagf_rand_int_negbin
Generates a vector of pseudorandom integers from a negative binomial distribution
Related keywords: big datadata analyticsfinancenegative binomial distributionPascal distributionrandom integersrandom number generators
polygamma function S14AFF   20  nagf_specfun_psi_deriv_complex
Polygamma function ψ n z for complex z
Related keywords: approximations of special functionsderivatives, psi functiondigamma functionpsi functiontrigamma function
polynomial approximation E02ADF   nagf_fit_1dcheb_arb
Least squares curve fit, by polynomials, arbitrary data points
Related keywords: curve and surface fittingleast squares
E02AEF   nagf_fit_1dcheb_eval
Evaluation of fitted polynomial in one variable from Chebyshev series form (simplified parameter list)
Related keywords: curve and surface fitting
E02AFF   nagf_fit_1dcheb_glp
Least squares polynomial fit, special data points (including interpolation)
Related keywords: curve and surface fittingleast squares
E02AGF   nagf_fit_1dcheb_con
Least squares polynomial fit, values and derivatives may be constrained, arbitrary data points
Related keywords: curve and surface fittingleast squares
E02CAF   nagf_fit_2dcheb_lines
Least squares surface fit by polynomials, data on lines parallel to one independent coordinate axis
Related keywords: bivariate polynomial approximationChebyshev polynomial approximationcurve and surface fittingdata-on-lines polynomial approximationleast squarestwo-dimensional polynomial approximation
E02CBF   nagf_fit_2dcheb_eval
Evaluation of fitted polynomial in two variables
Related keywords: bivariate polynomial approximationChebyshev polynomial approximationcurve and surface fittingtwo-dimensional polynomial approximation
polynomial regression G02 Chapter Introduction     Correlation and Regression Analysis
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionregression analysis
pooled sample G08AJF   14  nagf_nonpar_prob_mwu_noties
Computes the exact probabilities for the Mann–Whitney U statistic, no ties in pooled sample
Related keywords: Mann–Whitney U statisticnonparametric statisticstail probabilities
G08AKF   14  nagf_nonpar_prob_mwu_ties
Computes the exact probabilities for the Mann–Whitney U statistic, ties in pooled sample
Related keywords: Mann–Whitney U statisticNeumann algorithmnonparametric statisticstail probabilities
precision X02BJF   12  nagf_machine_model_digits
The floating-point model parameter, p
Related keywords: floating-point modelmachine constants
predicted value G02GPF   22  nagf_correg_glm_predict
Computes a predicted value and its associated standard error based on a previously fitted generalized linear model
Related keywords: big datacorrelation analysisdata analyticsfinancegeneralized linear modelnonlinear regressionpolynomial regressionregression analysisstandard errors
pre-whitening, filtering G13BAF   10  nagf_tsa_multi_filter_arima
Multivariate time series, filtering (pre-whitening) by an ARIMA model
Related keywords: ARIMAbig datadata analyticsfilteringfinancemultivariate time seriestime seriestime series analysis
principal component analysis G03AAF   14  nagf_mv_prin_comp
Performs principal component analysis
Related keywords: big datadata analyticsfinancemultivariate methods
principal coordinate analysis G03FAF   17  nagf_mv_multidimscal_metric
Performs principal coordinate analysis, classical metric scaling
Related keywords: classical metric scalingmultivariate methods
print information E04RYF   26  nagf_opt_handle_print
Print information about a problem handle initialized by E04RAF
Related keywords: maximizing a functionminimizing a functionoptimization
print matrix X04CAF   14  nagf_file_print_matrix_real_gen
Print real general matrix (easy-to-use)
Related keywords: input utilitiesoutput utilities
X04CBF   14  nagf_file_print_matrix_real_gen_comp
Print real general matrix (comprehensive)
Related keywords: input utilitiesoutput utilities
X04CCF   14  nagf_file_print_matrix_real_packed
Print real packed triangular matrix (easy-to-use)
Related keywords: input utilitiesoutput utilities
X04CDF   14  nagf_file_print_matrix_real_packed_comp
Print real packed triangular matrix (comprehensive)
Related keywords: input utilitiesoutput utilities
X04CEF   14  nagf_file_print_matrix_real_band
Print real packed banded matrix (easy-to-use)
Related keywords: input utilitiesoutput utilities
X04CFF   14  nagf_file_print_matrix_real_band_comp
Print real packed banded matrix (comprehensive)
Related keywords: input utilitiesoutput utilities
X04DAF   14  nagf_file_print_matrix_complex_gen
Print complex general matrix (easy-to-use)
Related keywords: input utilitiesoutput utilities
X04DBF   14  nagf_file_print_matrix_complex_gen_comp
Print complex general matrix (comprehensive)
Related keywords: input utilitiesoutput utilities
X04DCF   14  nagf_file_print_matrix_complex_packed
Print complex packed triangular matrix (easy-to-use)
Related keywords: input utilitiesoutput utilities
X04DDF   14  nagf_file_print_matrix_complex_packed_comp
Print complex packed triangular matrix (comprehensive)
Related keywords: input utilitiesoutput utilities
X04DEF   14  nagf_file_print_matrix_complex_band
Print complex packed banded matrix (easy-to-use)
Related keywords: input utilitiesoutput utilities
X04DFF   14  nagf_file_print_matrix_complex_band_comp
Print complex packed banded matrix (comprehensive)
Related keywords: input utilitiesoutput utilities
X04EAF   14  nagf_file_print_matrix_integer
Print integer matrix (easy-to-use)
Related keywords: input utilitiesoutput utilities
X04EBF   14  nagf_file_print_matrix_integer_comp
Print integer matrix (comprehensive)
Related keywords: input utilitiesoutput utilities
probabilities G01EWF   25  nagf_stat_prob_dickey_fuller_unit
Computes probabilities for the Dickey–Fuller unit root test
Related keywords: Dickey–Fuller Simple Calculations on Statistical Datastatistical distribution functionsunit root
probability G01EAF   15  nagf_stat_prob_normal
Computes probabilities for the standard Normal distribution
Related keywords: CDF, cumulative distribution functionfinancelower tail probabilityNormal distributionSimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01EBF   14  nagf_stat_prob_students_t
Computes probabilities for Student's t -distribution
Related keywords: CDF, cumulative distribution functionfinancelower tail probabilitySimple Calculations on Statistical DataStudent's t -distributiontwo-tail probabilityupper tail probability
G01ECF   14  nagf_stat_prob_chisq
Computes probabilities for χ 2 distribution
Related keywords: CDF, cumulative distribution functionchi-squared distributionfinancelower tail probabilitySimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01EDF   14  nagf_stat_prob_f
Computes probabilities for F -distribution
Related keywords: CDF, cumulative distribution function F -distributionfinancelower tail probabilitySimple Calculations on Statistical Dataupper tail probabilityvariance-ratio distribution
G01EEF   14  nagf_stat_prob_beta
Computes upper and lower tail probabilities and probability density function for the beta distribution
Related keywords: beta distributionCDF, cumulative distribution functionfinancelower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01EFF   14  nagf_stat_prob_gamma
Computes probabilities for the gamma distribution
Related keywords: CDF, cumulative distribution functionfinancegamma distributionlower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01EMF   15  nagf_stat_prob_studentized_range
Computes probability for the Studentized range statistic
Related keywords: CDF, cumulative distribution functionfinanceSimple Calculations on Statistical DataStudentized range statistic
G01HCF   23  nagf_stat_prob_bivariate_students_t
Computes probabilities for the bivariate Student's t -distribution
Related keywords: bivariate Student's t -distributionSimple Calculations on Statistical DataStudent's t -distribution
G01HDF   24  nagf_stat_prob_multi_students_t
Computes the probability for the multivariate Student's t -distribution
Related keywords: multivariate Student's t -distributionSimple Calculations on Statistical DataStudent's t -distribution
G05TBF   22  nagf_rand_logical
Generates a vector of pseudorandom logical values
Related keywords: big datadata analyticsfinancerandom logicalsrandom number generators
G08CKF   23  nagf_nonpar_gofstat_anddar_normal
Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of a fully-unspecified Normal distribution
Related keywords: Anderson–Darling test statisticGaussian distributionnonparametric statisticsNormal distribution
G08CLF   23  nagf_nonpar_gofstat_anddar_exp
Calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of an unspecified exponential distribution
Related keywords: Anderson–Darling test statisticexponential distributionnonparametric statistics
probability density function G01KAF   23  nagf_stat_pdf_normal
Calculates the value for the probability density function of the Normal distribution at a chosen point
Related keywords: Gaussian distributionNormal distributionpdfSimple Calculations on Statistical Data
G01KFF   23  nagf_stat_pdf_gamma
Calculates the value for the probability density function of the gamma distribution at a chosen point
Related keywords: gamma distributionpdfSimple Calculations on Statistical Data
G01KKF   24  nagf_stat_pdf_gamma_vector
Computes a vector of values for the probability density function of the gamma distribution
Related keywords: gamma distributionpdfSimple Calculations on Statistical Data
G01KQF   24  nagf_stat_pdf_normal_vector
Computes a vector of values for the probability density function of the Normal distribution
Related keywords: Gaussian distributionlogarithm, pdfNormal distributionpdfSimple Calculations on Statistical Data
G01LBF   24  nagf_stat_pdf_multi_normal_vector
Computes a vector of values for the probability density function of the multivariate Normal distribution
Related keywords: Gaussian distributionlogarithm, pdfmultivariate Normal distributionNormal distributionpdfSimple Calculations on Statistical Data
probit G02GBF   14  nagf_correg_glm_binomial
Fits a generalized linear model with binomial errors
Related keywords: big datacorrelation analysisdata analyticsfinancegeneralized linear modellogistic regressionlogitnonlinear regressionpolynomial regressionregression analysis
Procrustes rotations G03BCF   15  nagf_mv_rot_procrustes
Computes Procrustes rotations
Related keywords: multivariate methods
product, matrices F01GAF   24  nagf_matop_real_gen_matrix_actexp
Action of a real matrix exponential on a real matrix
Related keywords: exponential, matrixinversionmatrix exponentialmatrix operationsreal, nonsymmetric matrix
F01GBF   24  nagf_matop_real_gen_matrix_actexp_rcomm
Action of a real matrix exponential on a real matrix (reverse communication)
Related keywords: exponential, matrixinversionmatrix exponentialmatrix operationsreal, nonsymmetric matrix
F01HAF   24  nagf_matop_complex_gen_matrix_actexp
Action of a complex matrix exponential on a complex matrix
Related keywords: complex, nonsymmetric matrixexponential, matrixinversionmatrix exponentialmatrix operations
F01HBF   24  nagf_matop_complex_gen_matrix_actexp_rcomm
Action of a complex matrix exponential on a complex matrix (reverse communication)
Related keywords: complex, nonsymmetric matrixexponential, matrixinversionmatrix exponentialmatrix operations
product-limit, Kaplan–Meier estimates G12AAF   15  nagf_surviv_kaplanmeier
Computes Kaplan–Meier (product-limit) estimates of survival probabilities
Related keywords: Kaplan–Meier estimatesurvival analysis
product-moment correlation coefficients G01ABF   nagf_stat_summary_2var
Means, corrected sums of squares and cross-products, etc., two variables, from raw data
Related keywords: cross-productsmaximum valuemeanminimum valueSimple Calculations on Statistical Datasum of squares
ProMax rotations G03BDF   22  nagf_mv_rot_promax
ProMax rotations
Related keywords: multivariate methods
pseudo-inverse F01BLF   nagf_matop_real_gen_pseudinv
Pseudo-inverse and rank of real m by n matrix m n
Related keywords: inversionmatrix, rankmatrix operationsreal, m by n matrix
pseudo-spectral method D02UEF   23  nagf_ode_bvp_ps_lin_solve
Solve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation
Related keywords: boundary value problemBVPGauss–Lobatto gridODE, ordinary differential equations
psi function S14ACF   14  nagf_specfun_polygamma
ψ x - ln x
Related keywords: approximations of special functionsfinance
S14ADF   14  nagf_specfun_polygamma_deriv
Scaled derivatives of ψ x
Related keywords: approximations of special functionsderivatives, psi functionfinance
S14AEF   20  nagf_specfun_psi_deriv_real
Polygamma function ψ n x for real x
Related keywords: approximations of special functionsderivatives, psi functionfinance
S14AFF   20  nagf_specfun_psi_deriv_complex
Polygamma function ψ n z for complex z
Related keywords: approximations of special functionsderivatives, psi functiondigamma functionpolygamma functiontrigamma function
PSO, particle swarm algorithm E05SAF   23  nagf_glopt_bnd_pso
Global optimization using particle swarm algorithm (PSO), bound constraints only
Related keywords: global optimizationminimization, simple bound constraintsparticle swarm algorithm
E05SBF   23  nagf_glopt_nlp_pso
Global optimization using particle swarm algorithm (PSO), comprehensive
Related keywords: global optimizationminimization, nonlinear constraintsparticle swarm algorithm
QAG D01AKF   nagf_quad_1d_fin_osc
One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQUADPACKquadraturequadrature, adaptive
D01ATF   13  nagf_quad_1d_fin_bad_vec
One-dimensional quadrature, adaptive, finite interval, variant of D01AJF efficient on vector machines
Related keywords: Gauss–Kronrod quadratureintegration, adaptiveQAGSQUADPACKquadraturequadrature, adaptivevectorized quadrature
QAGI D01AMF   nagf_quad_1d_inf
One-dimensional quadrature, adaptive, infinite or semi-infinite interval
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveintegration, infinite intervalQUADPACKquadraturequadrature, adaptive
QAGP D01ALF   nagf_quad_1d_fin_sing
One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQUADPACKquadraturequadrature, adaptive
QAGS D01AJF   nagf_quad_1d_fin_bad
One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQUADPACKquadraturequadrature, adaptive
D01ATF   13  nagf_quad_1d_fin_bad_vec
One-dimensional quadrature, adaptive, finite interval, variant of D01AJF efficient on vector machines
Related keywords: Gauss–Kronrod quadratureintegration, adaptiveQAGQUADPACKquadraturequadrature, adaptivevectorized quadrature
QAWC D01AQF   nagf_quad_1d_fin_wcauchy
One-dimensional quadrature, adaptive, finite interval, weight function 1 / x - c , Cauchy principal value (Hilbert transform)
Related keywords: Cauchy principal valuefinanceGauss–Kronrod quadratureHilbert transformintegration, adaptiveQUADPACKquadraturequadrature, adaptive
QAWFE D01ASF   13  nagf_quad_1d_inf_wtrig
One-dimensional quadrature, adaptive, semi-infinite interval, weight function cos ω x or sin ω x
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveintegration, infinite intervalQUADPACKquadraturequadrature, adaptivevectorized quadrature
QAWSE D01APF   nagf_quad_1d_fin_wsing
One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQUADPACKquadraturequadrature, adaptive
QFOUR D01ANF   nagf_quad_1d_fin_wtrig
One-dimensional quadrature, adaptive, finite interval, weight function cos ω x or sin ω x
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQUADPACKquadraturequadrature, adaptive
Qi and Sun algorithm G02AAF   22  nagf_correg_corrmat_nearest
Computes the nearest correlation matrix to a real square matrix, using the method of Qi and Sun
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsfinancenearest correlation matrixnonlinear regressionpolynomial regressionregression analysis
G02ABF   23  nagf_correg_corrmat_nearest_bounded
Computes the nearest correlation matrix to a real square matrix, augmenting G02AAF to incorporate weights and bounds
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsfinancenearest correlation matrixnonlinear regressionpolynomial regressionregression analysis
G02AEF   23  nagf_correg_corrmat_nearest_kfactor
Computes the nearest correlation matrix with k -factor structure to a real square matrix
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsfinance k -factor structurenearest correlation matrixnonlinear regressionpolynomial regressionregression analysis
G02AJF   24  nagf_correg_corrmat_h_weight
Computes the nearest correlation matrix to a real square matrix, using element-wise weighting
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsnearest correlation matrixnonlinear regressionpolynomial regressionregression analysis
QL algorithm F08JAF   21  nagf_lapackeig_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: DSTEVeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QR algorithmreal, symmetric, tridiagonal matrix
F08JEF   16  nagf_lapackeig_dsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit Q L or Q R algorithm
Related keywords: DSTEQReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QR algorithmreal, symmetric, tridiagonal matrix
F08JFF   16  nagf_lapackeig_dsterf
Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the Q L or Q R algorithm
Related keywords: DSTERFeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QR algorithmreal, symmetric, tridiagonal matrix
F08JHF   22  nagf_lapackeig_dstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
Related keywords: divide-and-conquer methodDSTEDCeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QR algorithmreal, symmetric, tridiagonal matrix
F08JVF   22  nagf_lapackeig_zstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares QR algorithmreal, symmetric, tridiagonal matrixZSTEDC
F08MEF   16  nagf_lapackeig_dbdsqr
Performs an SVD of real bidiagonal matrix reduced from real general matrix
Related keywords: DBDSQRdifferential qd algorithmeigenproblemLAPACKLAPACKleast squaresmatrix, band QR algorithmreal, bidiagonal matrixSVD, singular value decomposition
F08MSF   16  nagf_lapackeig_zbdsqr
Performs an SVD of real bidiagonal matrix reduced from complex general matrix
Related keywords: differential qd algorithmeigenproblemLAPACKLAPACKleast squaresmatrix, band QR algorithmreal, bidiagonal matrixSVD, singular value decompositionZBDSQR
QL factorization F08CEF   22  nagf_lapackeig_dgeqlf
Q L factorization of real general rectangular matrix
Related keywords: DGEQLFeigenproblemLAPACKLAPACKleast squaresreal, m by n matrix
F08CFF   22  nagf_lapackeig_dorgql
Form all or part of orthogonal Q from Q L factorization determined by F08CEF
Related keywords: DORGQLeigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generationorthogonal transformations
F08CGF   22  nagf_lapackeig_dormql
Applies the orthogonal transformation determined by F08CEF
Related keywords: DORMQLeigenproblemLAPACKLAPACKleast squaresorthogonal transformations
F08CSF   22  nagf_lapackeig_zgeqlf
Q L factorization of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresZGEQLF
F08CTF   22  nagf_lapackeig_zungql
Form all or part of unitary Q from Q L factorization determined by F08CSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary matrix, generationunitary transformationsZUNGQL
F08CUF   22  nagf_lapackeig_zunmql
Applies the unitary transformation determined by F08CSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformationsZUNMQL
QP E04RFF   26  nagf_opt_handle_set_quadobj
Define a linear or a quadratic objective function to a problem initialized by E04RAF
Related keywords: least squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimization
QP, quadratic programming E04MWF   26  nagf_opt_miqp_mps_write
Write MPS data file defining LP, QP, MILP or MIQP problem
Related keywords: linear programming,integerLP, linear programmingmaximizing a functionminimizing a functionMPS formatMPSX formatoptimizationservice routine
E04MXF   24  nagf_opt_miqp_mps_read
Read MPS data file defining LP, QP, MILP or MIQP problem
Related keywords: linear programming,integerLP, linear programmingmaximizing a functionminimizing a functionMPSX formatoptimizationservice routine
E04MZF   18  nagf_opt_qpconvex1_sparse_mps
Read MPS data file defining LP or QP problem, deprecated
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionMPSX formatoptimizationservice routine
E04NCF   12  nagf_opt_lsq_lincon_solve_old
Linear programming (LP) convex quadratic programming (QP) or linearly-constrained linear least squares problem, dense
Related keywords: active-setconvex optimizationdata fittingfinanceleast squaresmaximizing a functionminimizing a functionnonlinear least squaresoptimization
E04NDF   12  nagf_opt_lsq_lincon_option_file_old
Supply values for E04NCF from external file
Related keywords: convex optimizationleast squaresmaximizing a functionminimizing a functionoptimizationoptions, computational
E04NEF   12  nagf_opt_lsq_lincon_option_string_old
Supply values to E04NCF from a character string
Related keywords: least squaresmaximizing a functionminimizing a functionoptimizationoptions, computational
E04NFF   16  nagf_opt_qp_dense_solve_old
General (possibly non-convex) quadratic programming (QP), dense, active-set method
Related keywords: active-set methodfinancemaximizing a functionminimizing a functionoptimization
E04NGF   16  nagf_opt_qp_dense_option_file_old
Supply values for E04NFF from external file
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computational
E04NHF   16  nagf_opt_qp_dense_option_string_old
Supply values to E04NFF from a character string
Related keywords: maximizing a functionminimizing a functionoptimizationoptions, computational
E04NKF   18  nagf_opt_qpconvex1_sparse_solve_old
Linear programming (LP) or convex quadratic programming (QP), sparse, active-set method
Related keywords: financeLP, linear programmingmaximizing a functionminimizing a functionoptimizationservice routine
E04NLF   18  nagf_opt_qpconvex1_sparse_option_file_old
Supply values for E04NKF from external file
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationoptions, computational
E04NMF   18  nagf_opt_qpconvex1_sparse_option_string_old
Supply values to E04NKF from a character string
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationoptions, computational
E04NPF   21  nagf_opt_qpconvex2_sparse_init
Initialization routine for E04NQF
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationoptions, computational
E04NQF   21  nagf_opt_qpconvex2_sparse_solve
Linear programming (LP) or convex quadratic programming (QP), sparse, active-set method, recommended
Related keywords: active-set methodfinanceLP, linear programmingmaximizing a functionminimizing a functionoptimizationservice routinesparse convex QP prolem
E04NRF   21  nagf_opt_qpconvex2_sparse_option_file
Supply values for E04NQF from external file
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationoptions, computational
E04NSF   21  nagf_opt_qpconvex2_sparse_option_string
Set a single option for E04NQF from a character string
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationoptions, computational
E04NTF   21  nagf_opt_qpconvex2_sparse_option_integer_set
Set a single option for E04NQF from an integer argument
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationoptions, computational
E04NUF   21  nagf_opt_qpconvex2_sparse_option_double_set
Set a single option for E04NQF from a real argument
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationoptions, computational
E04NXF   21  nagf_opt_qpconvex2_sparse_option_integer_get
Get the setting of an integer valued option of E04NQF
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationoptions, computational
E04NYF   21  nagf_opt_qpconvex2_sparse_option_double_get
Get the setting of a real valued option of E04NQF
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionoptimizationoptions, computational
H02CBF   19  nagf_mip_iqp_dense
Integer QP problem (dense)
Related keywords: branch and boundfinanceinteger programminginteger quadratic programmixed integer programmingoperations research
H02CEF   19  nagf_mip_iqp_sparse
Integer LP or QP problem (sparse), using E04NKF
Related keywords: branch and boundfinanceinteger programminginteger quadratic programmixed integer programmingoperations research
QR algorithm F08GAF   21  nagf_lapackeig_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Related keywords: DSPEVeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresorthogonal transformationsreal, indefinite, symmetric matrix
F08HAF   21  nagf_lapackeig_dsbev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
Related keywords: DSBEVeigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, band, symmetric matrix
F08HNF   21  nagf_lapackeig_zhbev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
Related keywords: complex, band, Hermitian matrixeigenproblemLAPACKLAPACKleast squaresmatrix, bandunitary transformationsZHBEV
F08JAF   21  nagf_lapackeig_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: DSTEVeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithmreal, symmetric, tridiagonal matrix
F08JBF   21  nagf_lapackeig_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: bisection methodDSTEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
F08JEF   16  nagf_lapackeig_dsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit Q L or Q R algorithm
Related keywords: DSTEQReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithmreal, symmetric, tridiagonal matrix
F08JFF   16  nagf_lapackeig_dsterf
Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the Q L or Q R algorithm
Related keywords: DSTERFeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithmreal, symmetric, tridiagonal matrix
F08JHF   22  nagf_lapackeig_dstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
Related keywords: divide-and-conquer methodDSTEDCeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithmreal, symmetric, tridiagonal matrix
F08JSF   16  nagf_lapackeig_zsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit Q L or Q R algorithm
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, symmetric, tridiagonal matrixZSTEQR
F08JVF   22  nagf_lapackeig_zstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares QL algorithmreal, symmetric, tridiagonal matrixZSTEDC
F08MDF   22  nagf_lapackeig_dbdsdc
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
Related keywords: DBDSDCdivide-and-conquer methodeigenproblemLAPACKLAPACKleast squaresmatrix, bandreal, bidiagonal matrixSVD, singular value decomposition
F08MEF   16  nagf_lapackeig_dbdsqr
Performs an SVD of real bidiagonal matrix reduced from real general matrix
Related keywords: DBDSQRdifferential qd algorithmeigenproblemLAPACKLAPACKleast squaresmatrix, band QL algorithmreal, bidiagonal matrixSVD, singular value decomposition
F08MSF   16  nagf_lapackeig_zbdsqr
Performs an SVD of real bidiagonal matrix reduced from complex general matrix
Related keywords: differential qd algorithmeigenproblemLAPACKLAPACKleast squaresmatrix, band QL algorithmreal, bidiagonal matrixSVD, singular value decompositionZBDSQR
F08NAF   21  nagf_lapackeig_dgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
Related keywords: DGEEVeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresorthogonal transformationsreal, nonsymmetric matrix
F08NBF   21  nagf_lapackeig_dgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGEEVXeigenproblemeigenvalueseigenvectorsfinanceforward errorLAPACKLAPACKleast squaresorthogonal transformationsreal, nonsymmetric matrix
QR factorization F06QPF   13  nagf_blas_dutr1
Q R factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix
Related keywords: BLASlinear algebra support routinesrank k matrix updatesreal, triangular matrixrotation, elementary
F06QQF   13  nagf_blas_dutupd
Q R factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row
Related keywords: BLASlinear algebra support routinesrank k matrix updatesreal, triangular matrixrotation, elementary
F06QRF   13  nagf_blas_duhqr
Q R or R Q factorization by sequence of plane rotations, real upper Hessenberg matrix
Related keywords: BLASlinear algebra support routinesrank k matrix updatesreal, Hessenberg matrixrotation, elementaryRQ factorizations
F06QSF   13  nagf_blas_dusqr
Q R or R Q factorization by sequence of plane rotations, real upper spiked matrix
Related keywords: BLASlinear algebra support routinesrank k matrix updatesreal, nonsymmetric matrixrotation, elementaryRQ factorizations
F06QTF   13  nagf_blas_dutsqr
Q R factorization of U P or R Q factorization of P U , U real upper triangular, P a sequence of plane rotations
Related keywords: BLASlinear algebra support routinesrank k matrix updatesrotation, elementaryRQ factorizations
F06TPF   13  nagf_blas_zutr1
Q R factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix
Related keywords: BLAScomplex, triangular matrixlinear algebra support routinesrank k matrix updates
F06TQF   13  nagf_blas_zutupd
Q R factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row
Related keywords: BLAScomplex, triangular matrixlinear algebra support routinesrotation, elementary
F06TRF   13  nagf_blas_zuhqr
Q R or R Q factorization by sequence of plane rotations, complex upper Hessenberg matrix
Related keywords: BLAScomplex, Hessenberg matrixlinear algebra support routinesrotation, elementaryRQ factorizations
F06TSF   13  nagf_blas_zusqr
Q R or R Q factorization by sequence of plane rotations, complex upper spiked matrix
Related keywords: BLAScomplex, triangular matrixlinear algebra support routinesrotation, elementaryRQ factorizations
F06TTF   13  nagf_blas_zutsqr
Q R factorization of U P or R Q factorization of P U , U complex upper triangular, P a sequence of plane rotations
Related keywords: BLAScomplex, triangular matrixlinear algebra support routinesrotation, elementaryRQ factorizations
F08AAF   21  nagf_lapackeig_dgels
Solves a real linear least squares problem of full rank
Related keywords: DGELSeigenproblemfinanceLAPACKLAPACKleast squareslinear least squares LQ decompositionoverdetermined linear equationsreal, m by n matrixunderdetermined linear system
F08ABF   25  nagf_lapackeig_dgeqrt
Performs a Q R factorization of real general rectangular matrix, with explicit blocking
Related keywords: DGEQRTeigenproblemexplicit blockingLAPACKleast squaresreal, m by n matrixrecursive QR
F08ACF   25  nagf_lapackeig_dgemqrt
Applies the orthogonal transformation determined by F08ABF
Related keywords: DGEMQRTeigenproblemexplicit blockingLAPACKleast squaresorthogonal transformationsrecursive QR
F08AEF   16  nagf_lapackeig_dgeqrf
Performs a Q R factorization of real general rectangular matrix
Related keywords: DGEQRFeigenproblemfinanceLAPACKLAPACKleast squaresreal, m by n matrix
F08AFF   16  nagf_lapackeig_dorgqr
Forms all or part of orthogonal Q from Q R factorization determined by F08AEF F08BEF F08BFF
Related keywords: DORGQReigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generationorthogonal transformations
F08AGF   16  nagf_lapackeig_dormqr
Applies an orthogonal transformation determined by F08AEF F08BEF F08BFF
Related keywords: DORMQReigenproblemfinanceLAPACKLAPACKleast squaresorthogonal transformations
F08ANF   21  nagf_lapackeig_zgels
Solves a complex linear least problem of full rank
Related keywords: complex, m by n matrixeigenproblemfinanceLAPACKLAPACKleast squareslinear least squares LQ decompositionoverdetermined linear equationsunderdetermined linear systemZGELS
F08APF   25  nagf_lapackeig_zgeqrt
Performs a Q R factorization of complex general rectangular matrix using recursive algorithm
Related keywords: complex, m by n matrixeigenproblemexplicit blockingLAPACKleast squaresrecursive QRZGEQRT
F08AQF   25  nagf_lapackeig_zgemqrt
Applies the unitary transformation determined by F08APF
Related keywords: eigenproblemexplicit blockingLAPACKleast squaresrecursive QRunitary transformationsZGEMQRT
F08ASF   16  nagf_lapackeig_zgeqrf
Performs a Q R factorization of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresZGEQRF
F08ATF   16  nagf_lapackeig_zungqr
Forms all or part of unitary Q from Q R factorization determined by F08ASF F08BSF F08BTF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary matrix, generationunitary transformationsZUNGQR
F08AUF   16  nagf_lapackeig_zunmqr
Applies a unitary transformation determined by F08ASF F08BSF F08BTF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformationsZUNMQR
F08BBF   25  nagf_lapackeig_dtpqrt
Q R factorization of real general triangular-pentagonal matrix
Related keywords: DTPQRTeigenproblemexplicit blockingLAPACKleast squaresreal, triangular-pentagonal matrixrecursive QR
F08BCF   25  nagf_lapackeig_dtpmqrt
Applies the orthogonal transformation determined by F08BBF
Related keywords: DTPMQRTeigenproblemexplicit blockingLAPACKleast squaresorthogonal transformationsrecursive QR
F08BEF   16  nagf_lapackeig_dgeqpf
Q R factorization, with column pivoting, of real general rectangular matrix
Related keywords: DGEQPFeigenproblemfinanceLAPACKLAPACKleast squaresorthogonal transformationsreal, m by n matrix
F08BFF   22  nagf_lapackeig_dgeqp3
Q R factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
Related keywords: DGEQP3eigenproblemfinanceLAPACKLAPACKleast squaresorthogonal transformationsreal, m by n matrix
F08BPF   25  nagf_lapackeig_ztpqrt
Q R factorization of complex triangular-pentagonal matrix
Related keywords: complex, triangular-pentagonal matrixeigenproblemexplicit blockingLAPACKleast squaresrecursive QRZTPQRT
F08BQF   25  nagf_lapackeig_ztpmqrt
Applies the unitary transformation determined by F08BPF
Related keywords: eigenproblemexplicit blockingLAPACKleast squaresrecursive QRunitary transformationsZTPMQRT
F08BSF   16  nagf_lapackeig_zgeqpf
Q R factorization, with column pivoting, of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresZGEQPF
F08BTF   22  nagf_lapackeig_zgeqp3
Q R factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresZGEQP3
F08ZBF   21  nagf_lapackeig_dggglm
Solves a real general Gauss–Markov linear model (GLM) problem
Related keywords: DGGGLMeigenproblemGauss–Markov linear modelLAPACKLAPACKleast squaresreal, m by n matrix
F08ZEF   22  nagf_lapackeig_dggqrf
Computes a generalized Q R factorization of a real matrix pair
Related keywords: DGGQRFeigenproblemLAPACKLAPACKleast squaresreal, m by n matrix
F08ZSF   22  nagf_lapackeig_zggqrf
Computes a generalized Q R factorization of a complex matrix pair
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresZGGQRF
QUADPACK D01AJF   nagf_quad_1d_fin_bad
One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQAGSquadraturequadrature, adaptive
D01AKF   nagf_quad_1d_fin_osc
One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQAGquadraturequadrature, adaptive
D01ALF   nagf_quad_1d_fin_sing
One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQAGPquadraturequadrature, adaptive
D01AMF   nagf_quad_1d_inf
One-dimensional quadrature, adaptive, infinite or semi-infinite interval
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveintegration, infinite intervalQAGIquadraturequadrature, adaptive
D01ANF   nagf_quad_1d_fin_wtrig
One-dimensional quadrature, adaptive, finite interval, weight function cos ω x or sin ω x
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQFOURquadraturequadrature, adaptive
D01APF   nagf_quad_1d_fin_wsing
One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQAWSEquadraturequadrature, adaptive
D01AQF   nagf_quad_1d_fin_wcauchy
One-dimensional quadrature, adaptive, finite interval, weight function 1 / x - c , Cauchy principal value (Hilbert transform)
Related keywords: Cauchy principal valuefinanceGauss–Kronrod quadratureHilbert transformintegration, adaptiveQAWCquadraturequadrature, adaptive
D01ASF   13  nagf_quad_1d_inf_wtrig
One-dimensional quadrature, adaptive, semi-infinite interval, weight function cos ω x or sin ω x
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveintegration, infinite intervalQAWFEquadraturequadrature, adaptivevectorized quadrature
D01ATF   13  nagf_quad_1d_fin_bad_vec
One-dimensional quadrature, adaptive, finite interval, variant of D01AJF efficient on vector machines
Related keywords: Gauss–Kronrod quadratureintegration, adaptiveQAGQAGSquadraturequadrature, adaptivevectorized quadrature
quadratic polynomial C02AHF   14  nagf_zeros_quadratic_complex
All zeros of complex quadratic equation
Related keywords: root-findingzeros of polynomials
C02AJF   14  nagf_zeros_quadratic_real
All zeros of real quadratic equation
Related keywords: root-findingzeros of polynomials
quadrature D01 Chapter Introduction     Quadrature
quadrature, adaptive D01AHF   nagf_quad_1d_fin_well
One-dimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands
Related keywords: financeintegration, adaptivequadrature
D01AJF   nagf_quad_1d_fin_bad
One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQAGSQUADPACKquadrature
D01AKF   nagf_quad_1d_fin_osc
One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQAGQUADPACKquadrature
D01ALF   nagf_quad_1d_fin_sing
One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQAGPQUADPACKquadrature
D01AMF   nagf_quad_1d_inf
One-dimensional quadrature, adaptive, infinite or semi-infinite interval
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveintegration, infinite intervalQAGIQUADPACKquadrature
D01ANF   nagf_quad_1d_fin_wtrig
One-dimensional quadrature, adaptive, finite interval, weight function cos ω x or sin ω x
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQFOURQUADPACKquadrature
D01APF   nagf_quad_1d_fin_wsing
One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveQAWSEQUADPACKquadrature
D01AQF   nagf_quad_1d_fin_wcauchy
One-dimensional quadrature, adaptive, finite interval, weight function 1 / x - c , Cauchy principal value (Hilbert transform)
Related keywords: Cauchy principal valuefinanceGauss–Kronrod quadratureHilbert transformintegration, adaptiveQAWCQUADPACKquadrature
D01ASF   13  nagf_quad_1d_inf_wtrig
One-dimensional quadrature, adaptive, semi-infinite interval, weight function cos ω x or sin ω x
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveintegration, infinite intervalQAWFEQUADPACKquadraturevectorized quadrature
D01ATF   13  nagf_quad_1d_fin_bad_vec
One-dimensional quadrature, adaptive, finite interval, variant of D01AJF efficient on vector machines
Related keywords: Gauss–Kronrod quadratureintegration, adaptiveQAGQAGSQUADPACKquadraturevectorized quadrature
D01AUF   13  nagf_quad_1d_fin_osc_vec
One-dimensional quadrature, adaptive, finite interval, variant of D01AKF efficient on vector machines
Related keywords: financeintegration, adaptivequadrature
D01DAF   nagf_quad_2d_fin
Two-dimensional quadrature, finite region
Related keywords: financeintegration, multidimensionalquadrature
D01EAF   12  nagf_quad_md_adapt_multi
Multidimensional adaptive quadrature over hyper-rectangle, multiple integrands
Related keywords: integration, adaptiveintegration, multidimensionalquadraturevectorized quadrature
D01FCF   nagf_quad_md_adapt
Multidimensional adaptive quadrature over hyper-rectangle
Related keywords: financeintegration, adaptiveintegration, multidimensionalquadrature
D01RAF   24  nagf_quad_1d_gen_vec_multi_rcomm
One-dimensional quadrature, adaptive, finite interval, multiple integrands, vectorized abscissae, reverse communication
Related keywords: integration, adaptivequadrature
D01RCF   24  nagf_quad_1d_gen_vec_multi_dimreq
Determine required array dimensions for D01RAF
Related keywords: integration, adaptivequadrature
D01RGF   24  nagf_quad_1d_fin_gonnet_vec
One-dimensional quadrature, adaptive, finite interval, strategy due to Gonnet, allowing for badly behaved integrands
Related keywords: financeGonnet method, quadratureintegration, adaptivequadrature
quadrature, options D01ZKF   24  nagf_quad_opt_set
Option setting routine
Related keywords: integration, optionsoptions, computationalquadrature
D01ZLF   24  nagf_quad_opt_get
Option getting routine
Related keywords: integration, optionsoptions, computationalquadrature
quadrature non-adaptive D01ARF   10  nagf_quad_1d_indef
One-dimensional quadrature, non-adaptive, finite interval with provision for indefinite integrals
Related keywords: financequadrature
D01BDF   nagf_quad_1d_fin_smooth
One-dimensional quadrature, non-adaptive, finite interval
Related keywords: financeintegration, non-adaptivequadrature
D01FBF   nagf_quad_md_gauss
Multidimensional Gaussian quadrature over hyper-rectangle
Related keywords: financeintegration, multidimensionalintegration, non-adaptivequadrature
D01GAF   nagf_quad_1d_data
One-dimensional quadrature, integration of function defined by data values, Gill–Miller method
Related keywords: financeGill–Miller quadratureintegration, non-adaptivequadrature
D01GBF   10  nagf_quad_md_mcarlo
Multidimensional quadrature over hyper-rectangle, Monte–Carlo method
Related keywords: integration, multidimensionalMonte–Carlo methodquadrature
D01GCF   10  nagf_quad_md_numth
Multidimensional quadrature, general product region, number-theoretic method
Related keywords: integration, multidimensionalKorobov–Conroy method, numerical integrationnumerical integrationquadrature
D01GDF   14  nagf_quad_md_numth_vec
Multidimensional quadrature, general product region, number-theoretic method, variant of D01GCF efficient on vector machines
Related keywords: financeintegration, multidimensionalquadrature
D01JAF   10  nagf_quad_md_sphere_bad
Multidimensional quadrature over an n -sphere, allowing for badly behaved integrands
Related keywords: financeintegration, multidimensionalquadrature
D01PAF   10  nagf_quad_md_simplex
Multidimensional quadrature over an n -simplex
Related keywords: financeintegration, multidimensionalquadrature
D01UAF   24  nagf_quad_1d_gauss_vec
One-dimensional Gaussian quadrature, choice of weight functions (vectorized)
Related keywords: integration, non-adaptivequadrature
D01UBF   26  nagf_quad_1d_inf_exp_wt
Non-automatic routine to evaluate 0 exp - x 2 f x   d x
Related keywords: integration, non-adaptiveintegration, semi-infinite intervalquadrature
quantile regression G02QFF   23  nagf_correg_quantile_linreg_easy
Linear quantile regression, simple interface, independent, identically distributed (IID) errors
Related keywords: big datacorrelation analysisdata analyticsfinancelinear quantile regressionnonlinear regressionpolynomial regressionregression analysis
G02QGF   23  nagf_correg_quantile_linreg
Linear quantile regression, comprehensive interface
Related keywords: big datacorrelation analysisdata analyticsfinancelinear quantile regressionnonlinear regressionpolynomial regressionregression analysis
G02ZKF   23  nagf_correg_optset
Option setting routine for G02QGF
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionoptions, computationalpolynomial regressionregression analysis
G02ZLF   23  nagf_correg_optget
Option getting routine for G02QGF
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionoptions, computationalpolynomial regressionregression analysis
quantiles G01AMF   22  nagf_stat_quantiles
Find quantiles of an unordered vector, real numbers
Related keywords: financeSimple Calculations on Statistical Data
G01ANF   23  nagf_stat_quantiles_stream_fixed
Calculates approximate quantiles from a data stream of known size
Related keywords: big datadata analyticsdata streamSimple Calculations on Statistical Datastreaming
G01APF   23  nagf_stat_quantiles_stream_arbitrary
Calculates approximate quantiles from a data stream of unknown size
Related keywords: big datadata analyticsdata streamSimple Calculations on Statistical Datastreaming
quarter-wave C06RGF   25  nagf_sum_fft_qtrsine
Multiple discrete quarter-wave sine transforms, simple
Related keywords: Discrete Fourier TransformsFast Fourier TransformFFTFourier Transforms, realsine transformsummation of series
C06RHF   25  nagf_sum_fft_qtrcosine
Multiple discrete quarter-wave cosine transforms, simple
Related keywords: cosine transformDiscrete Fourier TransformsFast Fourier TransformFFTFourier Transforms, realsummation of series
quartic polynomials C02ALF   20  nagf_zeros_quartic_real
All zeros of real quartic equation
Related keywords: root-findingzeros of polynomials
C02ANF   20  nagf_zeros_quartic_complex
All zeros of complex quartic equation
Related keywords: root-findingzeros of polynomials
quasi-Newton E04DGF   12  nagf_opt_uncon_conjgrd_comp_old
Unconstrained minimum, preconditioned conjugate gradient algorithm, using first derivatives (comprehensive)
Related keywords: conjugate gradient methodfinancemaximizing a functionminimization, unconstrainedminimizing a functionNLPnonlinear programmingoptimization
quasi-Newton algorithm E04GBF   nagf_opt_lsq_uncon_quasi_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (comprehensive)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmdata fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationsum-of-squares minimization
E04GYF   18  nagf_opt_lsq_uncon_quasi_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmdata fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationsum-of-squares minimization
E04JYF   18  nagf_opt_bounds_quasi_func_easy
Bound constrained minimum, quasi-Newton algorithm, using function values only (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmfinancemaximizing a functionminimization, simple bound constraintsminimizing a functionNLPnonlinear programmingoptimization
E04KYF   18  nagf_opt_bounds_quasi_deriv_easy
Bound constrained minimum, quasi-Newton algorithm, using first derivatives (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmfinancemaximizing a functionminimization, simple bound constraintsminimizing a functionNLPnonlinear programmingoptimization
E04VHF   21  nagf_opt_nlp2_sparse_solve
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: financeLP, linear programmingmaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationsequential QP methodsimplex algorithmSQP
quasi-Newton approximation E04USF   14  nagf_opt_lsq_gencon_deriv_old
Minimum of a sum of squares, nonlinear constraints, dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: data fittingfinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear least squaresnonlinear programmingoptimizationsequential QP methodsum of squares
quasi-random numbers G05YJF   21  nagf_rand_quasi_normal
Generates a Normal quasi-random number sequence
Related keywords: big datadata analyticsFaure, quasi-random numbersGaussian distributionlow-discrepancy sequencesNiederreiter method, quasi-random numbersNormal distributionrandom number generatorsrandom numbersSobol, quasi-random numbers
G05YKF   21  nagf_rand_quasi_lognormal
Generates a log-normal quasi-random number sequence
Related keywords: big datadata analyticsFaure, quasi-random numberslog-normal distributionlow-discrepancy sequencesNiederreiter method, quasi-random numbersrandom number generatorsrandom numbersSobol, quasi-random numbers
G05YLF   22  nagf_rand_quasi_init
Initializes a quasi-random number generator
Related keywords: big datadata analyticsFaure, quasi-random numbersfinancelow-discrepancy sequencesNiederreiter method, quasi-random numbersrandom number generatorsrandom numbersrectangular distributionSobol, quasi-random numbersuniform distribution
G05YMF   22  nagf_rand_quasi_uniform
Generates a uniform quasi-random number sequence
Related keywords: big datadata analyticsfinancelow-discrepancy sequencesoptions, computationalrandom number generatorsrandom numbers
quicksort, double M01CAF   12  nagf_sort_realvec_sort
Sort a vector, real numbers
Related keywords: big datadata analyticssearchingsortsorting
quotient F06BLF   12  nagf_blas_ddiv
Compute quotient of two real scalars, with overflow flag
Related keywords: BLASlinear algebra support routines
QZ algorithm F08XSF   20  nagf_lapackeig_zhgeqz
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresZHGEQZ
R 2 values G02ECF   14  nagf_correg_linregm_rssq_stat
Calculates R 2 and C P values from residual sums of squares
Related keywords: big datacorrelation analysis C P valuesdata analyticsnonlinear regressionpolynomial regressionregression analysissum of squares
random correlation matrix G05PYF   22  nagf_rand_matrix_corr
Generates a random correlation matrix
Related keywords: big datadata analyticsfinancerandom number generators
random fields G05ZMF   24  nagf_rand_field_1d_user_setup
Setup for simulating one-dimensional random fields, user-defined variogram
Related keywords: big datadata analyticsoptions, computationalrandom number generatorsvariogram
G05ZNF   24  nagf_rand_field_1d_predef_setup
Setup for simulating one-dimensional random fields
Related keywords: big datadata analyticsoptions, computationalrandom number generatorsvariogram
G05ZPF   24  nagf_rand_field_1d_generate
Generates realizations of a one-dimensional random field
Related keywords: big datadata analyticsrandom number generators
G05ZQF   24  nagf_rand_field_2d_user_setup
Setup for simulating two-dimensional random fields, user-defined variogram
Related keywords: big datadata analyticsoptions, computationalrandom number generatorsvariogram
G05ZRF   24  nagf_rand_field_2d_predef_setup
Setup for simulating two-dimensional random fields, preset variogram
Related keywords: big datadata analyticsoptions, computationalrandom number generatorsvariogram
G05ZSF   24  nagf_rand_field_2d_generate
Generates realizations of a two-dimensional random field
Related keywords: big datadata analyticsrandom number generators
random integers G05TAF   22  nagf_rand_int_binomial
Generates a vector of pseudorandom integers from a binomial distribution
Related keywords: big databinomial distributiondata analyticsfinancerandom number generators
G05TCF   22  nagf_rand_int_geom
Generates a vector of pseudorandom integers from a geometric distribution
Related keywords: big datadata analyticsfinancegeometric distributionrandom number generators
G05TDF   22  nagf_rand_int_general
Generates a vector of pseudorandom integers from a general discrete distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticsdistribution functionfinancerandom number generators
G05TEF   22  nagf_rand_int_hypergeom
Generates a vector of pseudorandom integers from a hypergeometric distribution
Related keywords: big datadata analyticsfinancehypergeometric distributionrandom number generators
G05TFF   22  nagf_rand_int_log
Generates a vector of pseudorandom integers from a logarithmic distribution
Related keywords: big datadata analyticsfinancelogarithmic distributionrandom number generators
G05TGF   22  nagf_rand_int_multinomial
Generates a vector of pseudorandom integers from a multinomial distribution
Related keywords: big datadata analyticsfinancemultinomial distributionrandom number generators
G05THF   22  nagf_rand_int_negbin
Generates a vector of pseudorandom integers from a negative binomial distribution
Related keywords: big datadata analyticsfinancenegative binomial distributionPascal distributionPolya distributionrandom number generators
G05TJF   22  nagf_rand_int_poisson
Generates a vector of pseudorandom integers from a Poisson distribution
Related keywords: big datadata analyticsfinancePoisson distributionrandom number generators
G05TKF   22  nagf_rand_int_poisson_varmean
Generates a vector of pseudorandom integers from a Poisson distribution with varying mean
Related keywords: big datadata analyticsfinancePoisson distributionrandom number generators
G05TLF   22  nagf_rand_int_uniform
Generates a vector of pseudorandom integers from a uniform distribution
Related keywords: big datadata analyticsfinancerandom number generatorsrectangular distributionuniform distribution
randomized block design G04BBF   16  nagf_anova_random
Analysis of variance, randomized block or completely randomized design, treatment means and standard errors
Related keywords: analysis of varianceANOVAcompletely randomized designstandard errorstreatment means
random logicals G05TBF   22  nagf_rand_logical
Generates a vector of pseudorandom logical values
Related keywords: big datadata analyticsfinanceprobabilityrandom number generators
randomness, tests for G08EAF   14  nagf_nonpar_randtest_runs
Performs the runs up or runs down test for randomness
Related keywords: nonparametric statisticsruns up and runs down test for randomness
G08EBF   14  nagf_nonpar_randtest_pairs
Performs the pairs (serial) test for randomness
Related keywords: nonparametric statisticspairs test for randomness
G08ECF   14  nagf_nonpar_randtest_triplets
Performs the triplets test for randomness
Related keywords: nonparametric statisticstriplets test for randomness
G08EDF   14  nagf_nonpar_randtest_gaps
Performs the gaps test for randomness
Related keywords: gaps test for randomnessnonparametric statistics
random number generators G05 Chapter Introduction     Random Number Generators
Related keywords: big datadata analytics
random numbers G05KFF   22  nagf_rand_init_repeat
Initializes a pseudorandom number generator to give a repeatable sequence
Related keywords: ACORNbig datadata analyticsmersenne twisterMRG32k3aoptions, computationalrandom number generatorsWichmann Hill
G05KGF   22  nagf_rand_init_nonrepeat
Initializes a pseudorandom number generator to give a non-repeatable sequence
Related keywords: ACORNbig datadata analyticsmersenne twisterMRG32k3aoptions, computationalrandom number generatorsWichmann Hill
G05KHF   22  nagf_rand_init_leapfrog
Primes a pseudorandom number generator for generating multiple streams using leap-frog
Related keywords: big datadata analyticsfinanceoptions, computationalrandom number generators
G05KJF   22  nagf_rand_init_skipahead
Primes a pseudorandom number generator for generating multiple streams using skip-ahead
Related keywords: big datadata analyticsfinanceoptions, computationalrandom number generators
G05KKF   23  nagf_rand_init_skipahead_power2
Primes a pseudorandom number generator for generating multiple streams using skip-ahead, skipping ahead a power of 2
Related keywords: big datadata analyticsfinanceoptions, computationalrandom number generators
G05RCF   22  nagf_rand_copula_students_t
Generates a matrix of pseudorandom numbers from a Student's t -copula
Related keywords: big datacopuladata analyticsfinancerandom number generatorsstudent's t-copula
G05RDF   22  nagf_rand_copula_normal
Generates a matrix of pseudorandom numbers from a Gaussian copula
Related keywords: big datacopuladata analyticsfinanceGaussian copularandom number generators
G05REF   23  nagf_rand_copula_clayton_bivar
Generates a matrix of pseudorandom numbers from a bivariate Clayton/Cook–Johnson copula
Related keywords: big dataClayton/Cook–Johnson copulacopuladata analyticsrandom number generators
G05RFF   23  nagf_rand_copula_frank_bivar
Generates a matrix of pseudorandom numbers from a bivariate Frank copula
Related keywords: big datacopuladata analyticsFrank copularandom number generators
G05RGF   23  nagf_rand_copula_plackett_bivar
Generates a matrix of pseudorandom numbers from a bivariate Plackett copula
Related keywords: big datacopuladata analyticsPlackett copularandom number generators
G05RHF   23  nagf_rand_copula_clayton
Generates a matrix of pseudorandom numbers from a multivariate Clayton/Cook–Johnson copula
Related keywords: big dataClayton/Cook–Johnson copulacopuladata analyticsrandom number generators
G05RJF   23  nagf_rand_copula_frank
Generates a matrix of pseudorandom numbers from a multivariate Frank copula
Related keywords: big datacopuladata analyticsFrank copularandom number generators
G05RKF   23  nagf_rand_copula_gumbel
Generates a matrix of pseudorandom numbers from a Gumbel–Hougaard copula
Related keywords: big datacopuladata analyticsGumbel–Hougard copularandom number generators
G05RYF   22  nagf_rand_multivar_students_t
Generates a matrix of pseudorandom numbers from a multivariate Student's t -distribution
Related keywords: big datadata analyticsfinancemultivariate Student's t -distributionrandom number generatorsStudent's t -distribution
G05RZF   22  nagf_rand_multivar_normal
Generates a matrix of pseudorandom numbers from a multivariate Normal distribution
Related keywords: big datadata analyticsfinanceGaussian distributionmultivariate Normal distributionNormal distributionrandom number generators
G05SAF   22  nagf_rand_dist_uniform01
Generates a vector of pseudorandom numbers from a uniform distribution over 0 , 1
Related keywords: big datadata analyticsfinancerandom number generatorsrectangular distributionuniform distribution
G05SBF   22  nagf_rand_dist_beta
Generates a vector of pseudorandom numbers from a beta distribution
Related keywords: beta distributionbig datadata analyticsfinancerandom number generators
G05SCF   22  nagf_rand_dist_cauchy
Generates a vector of pseudorandom numbers from a Cauchy distribution
Related keywords: big dataCauchy distributiondata analyticsfinancerandom number generators
G05SDF   22  nagf_rand_dist_chisq
Generates a vector of pseudorandom numbers from a χ 2 distribution
Related keywords: big datachi-squared distributiondata analyticsfinancerandom number generators
G05SEF   22  nagf_rand_dist_dirichlet
Generates a vector of pseudorandom numbers from a Dirichlet distribution
Related keywords: big datadata analyticsDirichlet distributionfinancerandom number generators
G05SFF   22  nagf_rand_dist_exp
Generates a vector of pseudorandom numbers from an exponential distribution
Related keywords: big datadata analyticsexponential distributionfinancerandom number generators
G05SGF   22  nagf_rand_dist_expmix
Generates a vector of pseudorandom numbers from an exponential mix distribution
Related keywords: big datadata analyticsexponential distributionexponential mix distributionfinancerandom number generators
G05SHF   22  nagf_rand_dist_f
Generates a vector of pseudorandom numbers from an F -distribution
Related keywords: big datadata analytics F -distributionfinancerandom number generators
G05SJF   22  nagf_rand_dist_gamma
Generates a vector of pseudorandom numbers from a gamma distribution
Related keywords: big datadata analyticsfinancegamma distributionrandom number generators
G05SKF   22  nagf_rand_dist_normal
Generates a vector of pseudorandom numbers from a Normal distribution
Related keywords: big datadata analyticsfinanceGaussian distributionNormal distributionrandom number generators
G05SLF   22  nagf_rand_dist_logistic
Generates a vector of pseudorandom numbers from a logistic distribution
Related keywords: big datadata analyticsfinancelogistic distributionrandom number generators
G05SMF   22  nagf_rand_dist_lognormal
Generates a vector of pseudorandom numbers from a log-normal distribution
Related keywords: big datadata analyticsfinancelog-normal distributionrandom number generators
G05SNF   22  nagf_rand_dist_students_t
Generates a vector of pseudorandom numbers from a Student's t -distribution
Related keywords: big datadata analyticsfinancerandom number generatorsStudent's t -distribution
G05SPF   22  nagf_rand_dist_triangular
Generates a vector of pseudorandom numbers from a triangular distribution
Related keywords: big datadata analyticsfinancerandom number generatorstriangular distribution
G05SQF   22  nagf_rand_dist_uniform
Generates a vector of pseudorandom numbers from a uniform distribution over a , b
Related keywords: big datadata analyticsfinancerandom number generatorsrectangular distributionuniform distribution
G05SRF   22  nagf_rand_dist_vonmises
Generates a vector of pseudorandom numbers from a von Mises distribution
Related keywords: big datadata analyticsfinancerandom number generatorsvon Mises distribution
G05SSF   22  nagf_rand_dist_weibull
Generates a vector of pseudorandom numbers from a Weibull distribution
Related keywords: big datadata analyticsfinancerandom number generatorsWeibull distribution
G05YJF   21  nagf_rand_quasi_normal
Generates a Normal quasi-random number sequence
Related keywords: big datadata analyticsFaure, quasi-random numbersGaussian distributionlow-discrepancy sequencesNiederreiter method, quasi-random numbersNormal distributionquasi-random numbersrandom number generatorsSobol, quasi-random numbers
G05YKF   21  nagf_rand_quasi_lognormal
Generates a log-normal quasi-random number sequence
Related keywords: big datadata analyticsFaure, quasi-random numberslog-normal distributionlow-discrepancy sequencesNiederreiter method, quasi-random numbersquasi-random numbersrandom number generatorsSobol, quasi-random numbers
G05YLF   22  nagf_rand_quasi_init
Initializes a quasi-random number generator
Related keywords: big datadata analyticsFaure, quasi-random numbersfinancelow-discrepancy sequencesNiederreiter method, quasi-random numbersquasi-random numbersrandom number generatorsrectangular distributionSobol, quasi-random numbersuniform distribution
G05YMF   22  nagf_rand_quasi_uniform
Generates a uniform quasi-random number sequence
Related keywords: big datadata analyticsfinancelow-discrepancy sequencesoptions, computationalquasi-random numbersrandom number generators
G05YNF   22  nagf_rand_quasi_init_scrambled
Initializes a scrambled quasi-random number generator
Related keywords: big datadata analyticsFaure–TezukafinanceNiederreiterOwenrandom number generatorsscrambleSobol
random orthogonal matrix G05PXF   22  nagf_rand_matrix_orthog
Generates a random orthogonal matrix
Related keywords: big datadata analyticsfinancerandom number generators
random permutation G05NCF   22  nagf_rand_permute
Pseudorandom permutation of an integer vector
Related keywords: big datadata analyticsfinancepermutationrandom number generators
random sample G05NDF   22  nagf_rand_sample
Pseudorandom sample from an integer vector
Related keywords: big datadata analyticsfinancerandom number generatorssample, random
G05NEF   23  nagf_rand_sample_wgt
Pseudorandom sample, without replacement, unequal weights
Related keywords: big datadata analyticsrandom number generatorssample, random
random two-way table G05PZF   22  nagf_rand_matrix_2waytable
Generates a random two-way table
Related keywords: big datadata analyticsfinancerandom number generatorstwo-way contingency table
range G13AUF   14  nagf_tsa_uni_means
Computes quantities needed for range-mean or standard deviation-mean plot
Related keywords: big datadata analyticsfinancemeanrange-mean plotstandard deviationtime seriestime series analysis
range-mean plot G13AUF   14  nagf_tsa_uni_means
Computes quantities needed for range-mean or standard deviation-mean plot
Related keywords: big datadata analyticsfinancemeanrangestandard deviationtime seriestime series analysis
rank data M01DZF   12  nagf_sort_arbitrary_rank
Rank arbitrary data
Related keywords: big datadata analyticssearchingsorting
rank k matrix updates F06PMF   12  nagf_blas_dger
Rank-1 update, real rectangular matrix
Related keywords: BLASblas, real matricesdgerlinear algebra support routinesreal, m by n matrix
F06PPF   12  nagf_blas_dsyr
Rank-1 update, real symmetric matrix
Related keywords: BLASblas, real matricesdsyrlinear algebra support routinesreal, indefinite, symmetric matrix
F06PQF   12  nagf_blas_dspr
Rank-1 update, real symmetric packed matrix
Related keywords: BLASblas, real matricesdsprlinear algebra support routinesreal, indefinite, symmetric matrix
F06PRF   12  nagf_blas_dsyr2
Rank-2 update, real symmetric matrix
Related keywords: BLASblas, real matricesdsyr2linear algebra support routinesreal, indefinite, symmetric matrix
F06PSF   12  nagf_blas_dspr2
Rank-2 update, real symmetric packed matrix
Related keywords: BLASblas, real matricesdspr2linear algebra support routinesreal, indefinite, symmetric matrix
F06QPF   13  nagf_blas_dutr1
Q R factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix
Related keywords: BLASlinear algebra support routines QR factorizationreal, triangular matrixrotation, elementary
F06QQF   13  nagf_blas_dutupd
Q R factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row
Related keywords: BLASlinear algebra support routines QR factorizationreal, triangular matrixrotation, elementary
F06QRF   13  nagf_blas_duhqr
Q R or R Q factorization by sequence of plane rotations, real upper Hessenberg matrix
Related keywords: BLASlinear algebra support routines QR factorizationreal, Hessenberg matrixrotation, elementaryRQ factorizations
F06QSF   13  nagf_blas_dusqr
Q R or R Q factorization by sequence of plane rotations, real upper spiked matrix
Related keywords: BLASlinear algebra support routines QR factorizationreal, nonsymmetric matrixrotation, elementaryRQ factorizations
F06QTF   13  nagf_blas_dutsqr
Q R factorization of U P or R Q factorization of P U , U real upper triangular, P a sequence of plane rotations
Related keywords: BLASlinear algebra support routines QR factorizationrotation, elementaryRQ factorizations
F06SMF   12  nagf_blas_zgeru
Rank-1 update, complex rectangular matrix, unconjugated vector
Related keywords: BLASblas, complex matricescomplex, m by n matrixlinear algebra support routineszgeru
F06SNF   12  nagf_blas_zgerc
Rank-1 update, complex rectangular matrix, conjugated vector
Related keywords: BLASblas, complex matricescomplex, m by n matrixlinear algebra support routineszgerc
F06SPF   12  nagf_blas_zher
Rank-1 update, complex Hermitian matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian matrixlinear algebra support routineszher
F06SQF   12  nagf_blas_zhpr
Rank-1 update, complex Hermitian packed matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian matrixlinear algebra support routineszhpr
F06SRF   12  nagf_blas_zher2
Rank-2 update, complex Hermitian matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian matrixlinear algebra support routineszher2
F06SSF   12  nagf_blas_zhpr2
Rank-2 update, complex Hermitian packed matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian matrixlinear algebra support routineszhpr2
F06TBF   21  nagf_blas_zsyr
Rank-1 update, complex symmetric matrix
Related keywords: BLAScomplex, symmetric matrixlinear algebra support routines
F06TDF   21  nagf_blas_zspr
Rank-1 update, complex symmetric packed matrix
Related keywords: BLAScomplex, symmetric matrixlinear algebra support routines
F06TPF   13  nagf_blas_zutr1
Q R factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix
Related keywords: BLAScomplex, triangular matrixlinear algebra support routines QR factorization
F06WCF   23  nagf_blas_dsfrk
Rank- k update of a real symmetric matrix, Rectangular Full Packed format
Related keywords: BLASblas, real matricesdsfrklinear algebra support routinesreal, indefinite, symmetric matrix
F06WQF   23  nagf_blas_zhfrk
Rank- k update of a complex Hermitian matrix, Rectangular Full Packed format
Related keywords: BLASblas, complex matricescomplex, Hermitian, indefinite matrixlinear algebra support routineszherk
F06YRF   14  nagf_blas_dsyr2k
Rank- 2 k update of a real symmetric matrix
Related keywords: BLASblas, real matricesdsyr2klinear algebra support routinesreal, indefinite, symmetric matrix
F06ZPF   14  nagf_blas_zherk
Rank- k update of a complex Hermitian matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian, indefinite matrixlinear algebra support routineszherk
F06ZRF   14  nagf_blas_zher2k
Rank- 2 k update of a complex Hermitian matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian, indefinite matrixlinear algebra support routineszher2k
F06ZUF   14  nagf_blas_zsyrk
Rank- k update of a complex symmetric matrix
Related keywords: BLASblas, complex matricescomplex, symmetric matrixlinear algebra support routineszher2k
F06ZWF   14  nagf_blas_zsyr2k
Rank- 2 k update of a complex symmetric matrix
Related keywords: BLASblas, complex matricescomplex, symmetric matrixlinear algebra support routineszsyr2k
rank matrix M01DEF   12  nagf_sort_realmat_rank_rows
Rank rows of a matrix, real numbers
Related keywords: big datadata analyticssearchingsorting
M01DFF   12  nagf_sort_intmat_rank_rows
Rank rows of a matrix, integer numbers
Related keywords: big datadata analyticssearchingsorting
M01DJF   12  nagf_sort_realmat_rank_columns
Rank columns of a matrix, real numbers
Related keywords: big datadata analyticssearchingsorting
M01DKF   12  nagf_sort_intmat_rank_columns
Rank columns of a matrix, integer numbers
Related keywords: big datadata analyticssearchingsorting
rank scores G01DHF   15  nagf_stat_ranks_and_scores
Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores
Related keywords: Blom scoresexponential scoresfinanceSavage scoresSimple Calculations on Statistical DataTukey scoresvan der Waerden scores
rank statistics G12ABF   23  nagf_surviv_logrank
Computes rank statistics for comparing survival curves
Related keywords: log rank testsurvival analysis
rank vector M01DAF   12  nagf_sort_realvec_rank
Rank a vector, real numbers
Related keywords: big datadata analyticssearchingsorting
M01DBF   12  nagf_sort_intvec_rank
Rank a vector, integer numbers
Related keywords: big datadata analyticssearchingsorting
M01DCF   12  nagf_sort_charvec_rank
Rank a vector, character data
Related keywords: big datadata analyticssearchingsorting
M01EAF   12  nagf_sort_realvec_rank_rearrange
Rearrange a vector according to given ranks, real numbers
Related keywords: big datadata analyticsrearrange vectorsearchingsorting
M01EBF   12  nagf_sort_intvec_rank_rearrange
Rearrange a vector according to given ranks, integer numbers
Related keywords: big datadata analyticsrearrange vectorsearchingsorting
M01ECF   12  nagf_sort_charvec_rank_rearrange
Rearrange a vector according to given ranks, character data
Related keywords: big datadata analyticsrearrange vectorsearchingsorting
M01EDF   19  nagf_sort_cmplxvec_rank_rearrange
Rearrange a vector according to given ranks, complex numbers
Related keywords: big datadata analyticsrearrange vectorsearchingsorting
rational interpolant E01RAF   nagf_interp_1d_ratnl
Interpolating functions, rational interpolant, one variable
Related keywords: interpolationone-dimensional
E01RBF   nagf_interp_1d_ratnl_eval
Interpolated values, evaluate rational interpolant computed by E01RAF, one variable
Related keywords: interpolationone-dimensional
read X10CEF   26 
Read an integer scalar from the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationcallback data objectinteger scalar
X10CFF   26 
Read a real (working precision) scalar from the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationcallback data objectreal scalarworking precision
X10CJF   26 
Read a scalar of type nagad_a1w_w_rtype from the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationcallback dataobjectnagad_a1w_w_rtype
read record X04BBF   12  nagf_file_line_read
Read formatted record from external file
Related keywords: input utilitiesoutput utilities
real, almost block-diagonal matrix F01LHF   13  nagf_matop_real_gen_blkdiag_lu
L U factorization of real almost block diagonal matrix
Related keywords: inversionLU decompositionmatrix operations
F04LHF   13  nagf_linsys_real_blkdiag_fac_solve
Solution of real almost block diagonal simultaneous linear equations (coefficient matrix already factorized by F01LHF)
Related keywords: big datadata analyticslinear equationssimultaneous linear equations
real, band, m by n matrix F06PBF   12  nagf_blas_dgbmv
Matrix-vector product, real rectangular band matrix
Related keywords: BLASblas, real matricesdgbmvlinear algebra support routinesmatrix, bandmultiply, matrix
F06RBF   15  nagf_blas_dlangb
1 -norm, -norm, Frobenius norm, largest absolute element, real band matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesmatrix, bandnorm, matrix
F08LEF   19  nagf_lapackeig_dgbbrd
Performs a reduction of real rectangular band matrix to upper bidiagonal form
Related keywords: DGBBRDeigenproblemGivens rotationsLAPACKLAPACKleast squaresmatrix, band
F08LSF   19  nagf_lapackeig_zgbbrd
Reduction of complex rectangular band matrix to upper bidiagonal form
Related keywords: eigenproblemGivens rotationsLAPACKLAPACKleast squaresmatrix, bandZGBBRD
F16RBF   23  nagf_blast_dgb_norm
1 -norm, -norm, Frobenius norm, largest absolute element, real band matrix
Related keywords: 1-normabsolute valueabsolute valuebanded matrixFrobenius normfurther linear algebra support routinesinfinity-normmatrix, bandnorm, matrix
real, band, positive-definite, symmetric matrix F01BUF   nagf_matop_real_symm_posdef_fac
U L D L T U T factorization of real symmetric positive definite band matrix
Related keywords: decomposition, matrixinversionmatrix, bandmatrix operations U L D L T U T decomposition
F01BVF   nagf_matop_real_symm_posdef_geneig
Reduction to standard form, generalized real symmetric-definite banded eigenproblem
Related keywords: eigenproblem, generalizedgeneralized eigenprobleminversionmatrix, bandmatrix operations
F01MCF   nagf_matop_real_vband_posdef_fac
L D L T factorization of real symmetric positive definite variable-bandwidth matrix
Related keywords: inversion LDL T decompositionmatrix, bandmatrix operations
F03BHF   23  nagf_det_real_band_sym
Determinant of real symmetric positive definite banded matrix previously factorized by F07HDF
Related keywords: determinant
F04BFF   21  nagf_linsys_real_posdef_band_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite banded system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationssimultaneous linear equations
F04MCF   nagf_linsys_real_posdef_vband_solve
Solution of real symmetric positive definite variable-bandwidth simultaneous linear equations (coefficient matrix already factorized by F01MCF)
Related keywords: big datadata analyticslinear equationsmatrix, bandsimultaneous linear equations
F07HAF   21  nagf_lapacklin_dpbsv
Computes the solution to a real symmetric positive definite banded system of linear equations
Related keywords: Cholesky decompositionDPBSVLAPACKlinear equationsmatrix, band
F07HBF   21  nagf_lapacklin_dpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite banded system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixDPBSVXerror bound, matrixforward errorLAPACKlinear equationsmatrix, band
F07HDF   15  nagf_lapacklin_dpbtrf
Cholesky factorization of real symmetric positive definite band matrix
Related keywords: Cholesky decompositionDPBTRFfinanceLAPACKlinear equationsmatrix, band
F07HEF   15  nagf_lapacklin_dpbtrs
Solution of real symmetric positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HDF
Related keywords: Cholesky decompositionDPBTRSfinanceLAPACKlinear equationsmatrix, band
F07HFF   22  nagf_lapacklin_dpbequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite banded matrix and reduce its condition number
Related keywords: DPBEQUequilibrationLAPACKlinear equationsmatrix, bandscaling
F07HGF   15  nagf_lapacklin_dpbcon
Estimate condition number of real symmetric positive definite band matrix, matrix already factorized by F07HDF
Related keywords: condition number, matrixDPBCONLAPACKlinear equationsmatrix, band
F07HHF   15  nagf_lapacklin_dpbrfs
Refined solution with error bounds of real symmetric positive definite band system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositionDPBRFSforward errorLAPACKlinear equationsmatrix, band
F08UAF   21  nagf_lapackeig_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: DSBGVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, band
F08UBF   21  nagf_lapackeig_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
Related keywords: DSBGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, band
F08UCF   21  nagf_lapackeig_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodDSBGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, band
F08UEF   19  nagf_lapackeig_dsbgst
Performs a reduction of real symmetric-definite banded generalized eigenproblem A x = λ B x to standard form C y = λ y , such that C has the same bandwidth as A
Related keywords: DSBGSTeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, band
F08UFF   19  nagf_lapackeig_dpbstf
Computes a split Cholesky factorization of real symmetric positive definite band matrix A
Related keywords: Cholesky decompositionDPBSTFDSBGSTeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, band
real, band, symmetric matrix F06PDF   12  nagf_blas_dsbmv
Matrix-vector product, real symmetric band matrix
Related keywords: BLASblas, real matricesdsbmvlinear algebra support routinesmatrix, bandmultiply, matrix
F06REF   15  nagf_blas_dlansb
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric band matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesmatrix, bandnorm, matrix
F08HAF   21  nagf_lapackeig_dsbev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
Related keywords: DSBEVeigenproblemLAPACKLAPACKleast squaresmatrix, band QR algorithm
F08HBF   21  nagf_lapackeig_dsbevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
Related keywords: DSBEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band
F08HCF   19  nagf_lapackeig_dsbevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: divide-and-conquer methodDSBEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithm
F08HEF   16  nagf_lapackeig_dsbtrd
Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
Related keywords: DSBTRDeigenproblemLAPACKLAPACKleast squaresmatrix, bandorthogonal transformations
F12FFF   21  nagf_sparseig_real_symm_band_init
Initialization routine for (F12FGF) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric banded (standard or generalized) eigenproblem
Related keywords: big datadata analyticseigenproblem, initializationlarge scale eigenproblems
F12FGF   21  nagf_sparseig_real_symm_band_solve
Selected eigenvalues and, optionally, eigenvectors of a real symmetric banded eigenproblem, driver
Related keywords: big datadata analyticseigenproblem, bandedeigenvalueseigenvectorslarge scale eigenproblems
real, band, triangular matrix F06PGF   12  nagf_blas_dtbmv
Matrix-vector product, real triangular band matrix
Related keywords: BLASblas, real matricesdtbmvlinear algebra support routinesmatrix, bandmultiply, matrix
F06PKF   12  nagf_blas_dtbsv
System of equations, real triangular band matrix
Related keywords: BLASblas, real matricesdtbsvlinear algebra support routineslinear equationsmatrix, band
F06RLF   15  nagf_blas_dlantb
1 -norm, -norm, Frobenius norm, largest absolute element, real triangular band matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrix
F07VEF   15  nagf_lapacklin_dtbtrs
Solution of real band triangular system of linear equations, multiple right-hand sides
Related keywords: DTBTRSLAPACKlinear equationsmatrix, band
F07VGF   15  nagf_lapacklin_dtbcon
Estimate condition number of real band triangular matrix
Related keywords: condition number, matrixDTBCONLAPACKlinear equationsmatrix, band
F07VHF   15  nagf_lapacklin_dtbrfs
Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorDTBRFSerror bound, matrixforward errorLAPACKlinear equationsmatrix, band
real, band matrix F04BBF   21  nagf_linsys_real_band_solve
Computes the solution, estimated condition number and error-bound to a real banded system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationsmatrix, bandsimultaneous linear equations
F07BAF   21  nagf_lapacklin_dgbsv
Computes the solution to a real banded system of linear equations
Related keywords: DGBSVLAPACKlinear equations L U decompositionmatrix, band
F07BBF   21  nagf_lapacklin_dgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
Related keywords: backward errorcondition number, matrixDGBSVXerror bound, matrixforward errorLAPACKlinear equations L U decompositionmatrix, band
F07BDF   15  nagf_lapacklin_dgbtrf
L U factorization of real m by n band matrix
Related keywords: DGBTRFLAPACKlinear equations L U decompositionmatrix, band
F07BEF   15  nagf_lapacklin_dgbtrs
Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by F07BDF
Related keywords: DGBTRSLAPACKlinear equations L U decompositionmatrix, band
F07BFF   22  nagf_lapacklin_dgbequ
Computes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number
Related keywords: DGBEQUequilibrationLAPACKlinear equationsmatrix, bandscaling
F07BGF   15  nagf_lapacklin_dgbcon
Estimate condition number of real band matrix, matrix already factorized by F07BDF
Related keywords: condition number, matrixDGBCONLAPACKlinear equationsmatrix, band
F07BHF   15  nagf_lapacklin_dgbrfs
Refined solution with error bounds of real band system of linear equations, multiple right-hand sides
Related keywords: backward errorDGBRFSforward errorLAPACKlinear equations L U decompositionmatrix, band
F12AFF   21  nagf_sparseig_real_band_init
Initialization routine for (F12AGF) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded (standard or generalized) eigenproblem
Related keywords: big datadata analyticseigenproblem, initializationlarge scale eigenproblems
F12AGF   21  nagf_sparseig_real_band_solve
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded eigenproblem, driver
Related keywords: big datadata analyticseigenproblem, bandedeigenvalueseigenvectorslarge scale eigenproblems
real, bidiagonal matrix F08MDF   22  nagf_lapackeig_dbdsdc
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
Related keywords: DBDSDCdivide-and-conquer methodeigenproblemLAPACKLAPACKleast squaresmatrix, band QR algorithmSVD, singular value decomposition
F08MEF   16  nagf_lapackeig_dbdsqr
Performs an SVD of real bidiagonal matrix reduced from real general matrix
Related keywords: DBDSQRdifferential qd algorithmeigenproblemLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmSVD, singular value decomposition
F08MSF   16  nagf_lapackeig_zbdsqr
Performs an SVD of real bidiagonal matrix reduced from complex general matrix
Related keywords: differential qd algorithmeigenproblemLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmSVD, singular value decompositionZBDSQR
real, Hessenberg matrix F06QRF   13  nagf_blas_duhqr
Q R or R Q factorization by sequence of plane rotations, real upper Hessenberg matrix
Related keywords: BLASlinear algebra support routines QR factorizationrank k matrix updatesrotation, elementaryRQ factorizations
F06RMF   15  nagf_blas_dlanhs
1 -norm, -norm, Frobenius norm, largest absolute element, real upper Hessenberg matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrix
F08PKF   16  nagf_lapackeig_dhsein
Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
Related keywords: DHSEINeigenproblemeigenvectorsinverse iterationLAPACKLAPACKleast squares
F08XEF   20  nagf_lapackeig_dhgeqz
Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
Related keywords: DHGEQZeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squares
real, indefinite, symmetric matrix F01EDF   23  nagf_matop_real_symm_matrix_exp
Real symmetric matrix exponential
Related keywords: exponential, matrixfinanceinversionmatrix exponentialmatrix operations
F01EFF   23  nagf_matop_real_symm_matrix_fun
Function of a real symmetric matrix
Related keywords: financefunctions, matrixinversionmatrix functionsmatrix operations
F04BHF   21  nagf_linsys_real_symm_solve
Computes the solution, estimated condition number and error-bound to a real symmetric system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationssimultaneous linear equations
F04BJF   21  nagf_linsys_real_symm_packed_solve
Computes the solution, estimated condition number and error-bound to a real symmetric system of linear equations, packed storage
Related keywords: big datadata analyticsforward errorlinear equationssimultaneous linear equations
F06PCF   12  nagf_blas_dsymv
Matrix-vector product, real symmetric matrix
Related keywords: BLASblas, real matricesdsymvlinear algebra support routinesmultiply, matrix
F06PEF   12  nagf_blas_dspmv
Matrix-vector product, real symmetric packed matrix
Related keywords: BLASblas, real matricesdspmvlinear algebra support routinesmultiply, matrix
F06PPF   12  nagf_blas_dsyr
Rank-1 update, real symmetric matrix
Related keywords: BLASblas, real matricesdsyrlinear algebra support routinesrank k matrix updates
F06PQF   12  nagf_blas_dspr
Rank-1 update, real symmetric packed matrix
Related keywords: BLASblas, real matricesdsprlinear algebra support routinesrank k matrix updates
F06PRF   12  nagf_blas_dsyr2
Rank-2 update, real symmetric matrix
Related keywords: BLASblas, real matricesdsyr2linear algebra support routinesrank k matrix updates
F06PSF   12  nagf_blas_dspr2
Rank-2 update, real symmetric packed matrix
Related keywords: BLASblas, real matricesdspr2linear algebra support routinesrank k matrix updates
F06QMF   13  nagf_blas_dsysrc
Orthogonal similarity transformation of real symmetric matrix as a sequence of plane rotations
Related keywords: BLASlinear algebra support routinesrotation, elementary
F06RCF   15  nagf_blas_dlansy
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrix
F06RDF   15  nagf_blas_dlansp
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrix
F06WCF   23  nagf_blas_dsfrk
Rank- k update of a real symmetric matrix, Rectangular Full Packed format
Related keywords: BLASblas, real matricesdsfrklinear algebra support routinesrank k matrix updates
F06YCF   14  nagf_blas_dsymm
Matrix-matrix product, one real symmetric matrix, one real rectangular matrix
Related keywords: BLASblas, real matricesdsymmlinear algebra support routinesmultiply, matrixreal, m by n matrix
F06YPF   14  nagf_blas_dsyrk
Rank- k update of a real symmetric matrix
Related keywords: BLASblas, real matricesdsyrklinear algebra support routines
F06YRF   14  nagf_blas_dsyr2k
Rank- 2 k update of a real symmetric matrix
Related keywords: BLASblas, real matricesdsyr2klinear algebra support routinesrank k matrix updates
F07MAF   21  nagf_lapacklin_dsysv
Computes the solution to a real symmetric system of linear equations
Related keywords: diagonal pivoting methodDSYSVLAPACKLDLT decompositionlinear equations UDU T decompositiuon
F07MBF   21  nagf_lapacklin_dsysvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations
Related keywords: backward errordiagonal pivoting methodDSYSVXforward errorLAPACKLDLT decompositionlinear equations UDU T decompositiuon
F07MDF   15  nagf_lapacklin_dsytrf
Bunch–Kaufman factorization of real symmetric indefinite matrix
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodDSYTRFLAPACKlinear equations
F07MEF   15  nagf_lapacklin_dsytrs
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MDF
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodDSYTRSLAPACKlinear equations
F07MGF   15  nagf_lapacklin_dsycon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MDF
Related keywords: Bunch–Kaufman factorizationcondition number, matrixdiagonal pivoting methodDSYCONLAPACKlinear equations
F07MHF   15  nagf_lapacklin_dsyrfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides
Related keywords: backward errorBunch–Kaufman factorizationdiagonal pivoting methodDSYRFSforward errorLAPACKlinear equations
F07MJF   15  nagf_lapacklin_dsytri
Inverse of real symmetric indefinite matrix, matrix already factorized by F07MDF
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodDSYTRIinverse, matrixLAPACKlinear equations
F07PAF   21  nagf_lapacklin_dspsv
Computes the solution to a real symmetric system of linear equations, packed storage
Related keywords: diagonal pivoting methodDSPSVLAPACK LDL T decompositionlinear equations UDU T decomposition
F07PBF   21  nagf_lapacklin_dspsvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage. Error bounds and a condition estimate are also computed
Related keywords: backward errorcondition number, matrixdiagonal pivoting methodDSPSVXerror bound, matrixforward errorLAPACK LDL H decompositionlinear equations UDU H decomposition
F07PDF   15  nagf_lapacklin_dsptrf
Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodDSPTRFLAPACKlinear equations
F07PEF   15  nagf_lapacklin_dsptrs
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PDF, packed storage
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodDSPTRSLAPACKlinear equations
F07PGF   15  nagf_lapacklin_dspcon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage
Related keywords: Bunch–Kaufman factorizationcondition number, matrixdiagonal pivoting methodDSPCONLAPACKlinear equations
F07PHF   15  nagf_lapacklin_dsprfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorBunch–Kaufman factorizationdiagonal pivoting methodDSPRFSforward errorLAPACKlinear equations
F07PJF   15  nagf_lapacklin_dsptri
Inverse of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage
Related keywords: Bunch–Kaufman factorizationdiagonal pivoting methodDSPTRIinverse, matrixLAPACKlinear equations
F08FAF   21  nagf_lapackeig_dsyev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Related keywords: DSYEVeigenproblemeigenvalueseigenvectorsfinanceLAPACKLAPACKleast squares
F08FBF   21  nagf_lapackeig_dsyevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
Related keywords: DSYEVXeigenproblemeigenvalueseigenvectorsfinanceLAPACKLAPACKleast squares
F08FCF   19  nagf_lapackeig_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
Related keywords: divide-and-conquer methodDSYEVDeigenproblemeigenvalueseigenvectorsfinanceLAPACKLAPACKleast squares
F08FDF   21  nagf_lapackeig_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
Related keywords: dqds algorithmDSYEVReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresrelatively robust representations
F08FEF   16  nagf_lapackeig_dsytrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
Related keywords: DSYTRDeigenproblemLAPACKLAPACKleast squaresorthogonal transformations
F08FLF   22  nagf_lapackeig_ddisna
Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix
Related keywords: complex, Hermitian, indefinite matrixcondition number, matrixDDISNAeigenproblemeigenvectorsfinanceLAPACKLAPACKleast squares
F08GAF   21  nagf_lapackeig_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Related keywords: DSPEVeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresorthogonal transformations QR algorithm
F08GBF   21  nagf_lapackeig_dspevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
Related keywords: DSPEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresorthogonal transformations
F08GCF   19  nagf_lapackeig_dspevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: divide-and-conquer methodDSPEVDeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresPal–Walker–Kahan ( QL or QR ) algorithm
F08GEF   16  nagf_lapackeig_dsptrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
Related keywords: DSPTRDeigenproblemLAPACKLAPACKleast squaresorthogonal transformations
real, m by n matrix F01BLF   nagf_matop_real_gen_pseudinv
Pseudo-inverse and rank of real m by n matrix m n
Related keywords: inversionmatrix, rankmatrix operationspseudo-inverse
F01QJF   14  nagf_matop_real_gen_rq
R Q factorization of real m by n matrix m n
Related keywords: inversionmatrix operationsRQ factorizations
F02WGF   22  nagf_eigen_real_gen_partialsvd
Computes leading terms in the singular value decomposition of a real general matrix; also computes corresponding left and right singular vectors
Related keywords: big datadata analyticseigenvalueseigenvectorsSVD, singular value decomposition
F04AMF   nagf_linsys_real_gen_lsqsol
Least squares solution of m real equations in n unknowns, rank = n , m n using iterative refinement (Black Box)
Related keywords: big datadata analyticslinear equations, overdeterminedlinear least squaressimultaneous linear equations
F04JGF   nagf_linsys_real_gen_solve
Least squares (if rank = n ) or minimal least squares (if rank < n ) solution of m real equations in n unknowns, m n
Related keywords: big datadata analyticslinear equations, overdeterminedlinear least squaressimultaneous linear equations
F04QAF   11  nagf_linsys_real_gen_sparse_lsqsol
Sparse linear least squares problem, m real equations in n unknowns
Related keywords: big datadata analyticsleast squaresmatrix, sparseregressionridgesimultaneous linear equations
F04YAF   11  nagf_linsys_real_gen_lsq_covmat
Covariance matrix for linear least squares problems, m real equations in n unknowns
Related keywords: big datacovariance matrixdata analyticsleast squaressimultaneous linear equations
F04YDF   24  nagf_linsys_real_gen_norm_rcomm
Norm estimation (for use in condition estimation), real rectangular matrix
Related keywords: 1 -normbig datadata analyticsnorm, matrixsimultaneous linear equations
F06PAF   12  nagf_blas_dgemv
Matrix-vector product, real rectangular matrix
Related keywords: BLASblas, real matricesdgemvfinancelinear algebra support routinesmultiply, matrix
F06PMF   12  nagf_blas_dger
Rank-1 update, real rectangular matrix
Related keywords: BLASblas, real matricesdgerlinear algebra support routinesrank k matrix updates
F06QFF   13  nagf_blas_dmcopy
Matrix copy, real rectangular or trapezoidal matrix
Related keywords: BLAScopy, vectors and matriceselementary arithmeticfinancelinear algebra support routinesreal, trapezoidal matrix
F06QHF   13  nagf_blas_dmload
Matrix initialization, real rectangular matrix
Related keywords: BLASelementary arithmeticfinancelinear algebra support routines
F06QJF   13  nagf_blas_dgeap
Permute rows or columns, real rectangular matrix, permutations represented by an integer array
Related keywords: BLASlinear algebra support routinespermutation
F06QKF   13  nagf_blas_dgeapr
Permute rows or columns, real rectangular matrix, permutations represented by a real array
Related keywords: BLASlinear algebra support routinespermutation
F06QXF   13  nagf_blas_dgesrc
Apply sequence of plane rotations, real rectangular matrix
Related keywords: BLASlinear algebra support routinesrotation, elementary
F06RAF   15  nagf_blas_dlange
1 -norm, -norm, Frobenius norm, largest absolute element, real general matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrix
F06YAF   14  nagf_blas_dgemm
Matrix-matrix product, two real rectangular matrices
Related keywords: BLASblas, real matricesdgemmfinancelinear algebra support routinesmultiply, matrix
F06YCF   14  nagf_blas_dsymm
Matrix-matrix product, one real symmetric matrix, one real rectangular matrix
Related keywords: BLASblas, real matricesdsymmlinear algebra support routinesmultiply, matrixreal, indefinite, symmetric matrix
F06YFF   14  nagf_blas_dtrmm
Matrix-matrix product, one real triangular matrix, one real rectangular matrix
Related keywords: BLASblas, real matricesdsymmlinear algebra support routinesmultiply, matrixreal, triangular matrix
F07ADF   15  nagf_lapacklin_dgetrf
L U factorization of real m by n matrix
Related keywords: DGETRFfinanceLAPACKlinear equations L U decomposition
F08AAF   21  nagf_lapackeig_dgels
Solves a real linear least squares problem of full rank
Related keywords: DGELSeigenproblemfinanceLAPACKLAPACKleast squareslinear least squares LQ decompositionoverdetermined linear equations QR factorizationunderdetermined linear system
F08ABF   25  nagf_lapackeig_dgeqrt
Performs a Q R factorization of real general rectangular matrix, with explicit blocking
Related keywords: DGEQRTeigenproblemexplicit blockingLAPACKleast squaresQR factorizationrecursive QR
F08AEF   16  nagf_lapackeig_dgeqrf
Performs a Q R factorization of real general rectangular matrix
Related keywords: DGEQRFeigenproblemfinanceLAPACKLAPACKleast squares QR factorization
F08AHF   16  nagf_lapackeig_dgelqf
Performs a L Q factorization of real general rectangular matrix
Related keywords: DGELQFeigenproblemLAPACKLAPACKleast squares LQ factorization
F08BAF   21  nagf_lapackeig_dgelsy
Computes the minimum-norm solution to a real linear least squares problem
Related keywords: DGELSYeigenproblemfinanceLAPACKLAPACKleast squareslinear least squaresminimal least squares
F08BEF   16  nagf_lapackeig_dgeqpf
Q R factorization, with column pivoting, of real general rectangular matrix
Related keywords: DGEQPFeigenproblemfinanceLAPACKLAPACKleast squaresorthogonal transformations QR factorization
F08BFF   22  nagf_lapackeig_dgeqp3
Q R factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
Related keywords: DGEQP3eigenproblemfinanceLAPACKLAPACKleast squaresorthogonal transformations QR factorization
F08CEF   22  nagf_lapackeig_dgeqlf
Q L factorization of real general rectangular matrix
Related keywords: DGEQLFeigenproblemLAPACKLAPACKleast squares QL factorization
F08CHF   22  nagf_lapackeig_dgerqf
R Q factorization of real general rectangular matrix
Related keywords: DGERQFeigenproblemLAPACKLAPACKleast squaresRQ factorizations
F08KAF   21  nagf_lapackeig_dgelss
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
Related keywords: DGELSSeigenproblemLAPACKLAPACKleast squareslinear least squaresminimal least squaresSVD, singular value decomposition
F08KCF   21  nagf_lapackeig_dgelsd
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
Related keywords: DGELSDdivide-and-conquer methodeigenproblemfinanceLAPACKLAPACKleast squareslinear least squaresminimal least squaresSVD, singular value decomposition
F08KEF   16  nagf_lapackeig_dgebrd
Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
Related keywords: DGEBRDeigenproblemLAPACKLAPACKleast squaresorthogonal transformations
F08VEF   22  nagf_lapackeig_dggsvp
Produces orthogonal matrices that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
Related keywords: DGGSVPeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresorthogonal transformationsSVD, generalized
F08VGF   26  nagf_lapackeig_dggsvp3
Produces orthogonal matrices, using BLAS-3, that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
Related keywords: DGGSVP3eigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresorthogonal transformationsSVD, generalized
F08ZAF   21  nagf_lapackeig_dgglse
Solves the real linear equality-constrained least squares (LSE) problem
Related keywords: DGGLSEeigenproblemLAPACKLAPACKleast squareslinear least squaresRQ factorizations
F08ZBF   21  nagf_lapackeig_dggglm
Solves a real general Gauss–Markov linear model (GLM) problem
Related keywords: DGGGLMeigenproblemGauss–Markov linear modelLAPACKLAPACKleast squares QR factorization
F08ZEF   22  nagf_lapackeig_dggqrf
Computes a generalized Q R factorization of a real matrix pair
Related keywords: DGGQRFeigenproblemLAPACKLAPACKleast squares QR factorization
F08ZFF   22  nagf_lapackeig_dggrqf
Computes a generalized R Q factorization of a real matrix pair
Related keywords: DGGRQFeigenproblemLAPACKLAPACKleast squaresRQ factorizations
real, nonsymmetric matrix F01CKF   nagf_matop_real_gen_matmul
Multiplication of real matrices
Related keywords: inversionmatrix operationsmultiply, matrix
F01CRF   nagf_matop_real_gen_trans_inplace
Transposition of a real matrix
Related keywords: inversionmatrix operationstranspose, matrix
F01CTF   14  nagf_matop_real_addsub
Sum or difference of two real matrices, optional scaling and transposition
Related keywords: inversionmatrix operationssum, matrixtranspose, matrix
F01ECF   22  nagf_matop_real_gen_matrix_exp
Real matrix exponential
Related keywords: exponential, matrixinversionmatrix exponentialmatrix operations
F01EJF   24  nagf_matop_real_gen_matrix_log
Real matrix logarithm
Related keywords: inversionlogarithm, matrixmatrix logarithmmatrix operations
F01EKF   24  nagf_matop_real_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm)
Related keywords: cosh, matrixcosine, matrixexponential, matrixfunctions, matrixinversionmatrix operationssine, matrixsinh, matrix
F01ELF   24  nagf_matop_real_gen_matrix_fun_num
Function of a real matrix (using numerical differentiation)
Related keywords: functions, matrixinversionmatrix functionsmatrix operations
F01EMF   24  nagf_matop_real_gen_matrix_fun_usd
Function of a real matrix (using user-supplied derivatives)
Related keywords: functions, matrixinversionmatrix functionsmatrix operations
F01ENF   25  nagf_matop_real_gen_matrix_sqrt
Real matrix square root
Related keywords: inversionmatrix operations
F01GAF   24  nagf_matop_real_gen_matrix_actexp
Action of a real matrix exponential on a real matrix
Related keywords: exponential, matrixinversionmatrix exponentialmatrix operationsproduct, matrices
F01GBF   24  nagf_matop_real_gen_matrix_actexp_rcomm
Action of a real matrix exponential on a real matrix (reverse communication)
Related keywords: exponential, matrixinversionmatrix exponentialmatrix operationsproduct, matrices
F01JAF   24  nagf_matop_real_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix
Related keywords: condition number, matrixcosh, matrixcosine, matrixexponential, matrixinversionlogarithm, matrixmatrix operationssine, matrixsinh, matrix
F01JBF   24  nagf_matop_real_gen_matrix_cond_num
Condition number for a function of a real matrix (using numerical differentiation)
Related keywords: condition number, matrixinversionmatrix functionsmatrix operations
F01JCF   24  nagf_matop_real_gen_matrix_cond_usd
Condition number for a function of a real matrix (using user-supplied derivatives)
Related keywords: condition number, matrixinversionmatrix functionsmatrix operations
F01JDF   25  nagf_matop_real_gen_matrix_cond_sqrt
Condition number for square root of real matrix
Related keywords: condition numberinversionmatrix operations
F01JGF   25  nagf_matop_real_gen_matrix_cond_exp
Condition number for real matrix exponential
Related keywords: condition numberinversionmatrix operations
F01JHF   25  nagf_matop_real_gen_matrix_frcht_exp
Fréchet derivative of real matrix exponential
Related keywords: Fréchet derivativeinversionmatrix operations
F01JJF   25  nagf_matop_real_gen_matrix_cond_log
Condition number for real matrix logarithm
Related keywords: condition numberinversionmatrix operations
F01JKF   25  nagf_matop_real_gen_matrix_frcht_log
Fréchet derivative of real matrix logarithm
Related keywords: Fréchet derivativeinversionmatrix operations
F01ZAF   14  nagf_matop_real_tri_pack
Convert real matrix between packed triangular and square storage formats
Related keywords: convert matrix storage formatsinversionmatrix operations
F01ZCF   14  nagf_matop_real_band_pack
Convert real matrix between packed banded and rectangular storage formats
Related keywords: convert matrix storage formatsinversionmatrix operations
F02ECF   17  nagf_eigen_real_gen_eigsys
Selected eigenvalues and eigenvectors of real nonsymmetric matrix (Black Box)
Related keywords: big datadata analyticseigenvalueseigenvectors
F03BAF   23  nagf_det_real_gen
Determinant of real matrix, matrix already factorized by F07ADF
Related keywords: determinant
F04BAF   21  nagf_linsys_real_square_solve
Computes the solution, estimated condition number and error-bound to a real system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationssimultaneous linear equations
F06QSF   13  nagf_blas_dusqr
Q R or R Q factorization by sequence of plane rotations, real upper spiked matrix
Related keywords: BLASlinear algebra support routines QR factorizationrank k matrix updatesrotation, elementaryRQ factorizations
F07AAF   21  nagf_lapacklin_dgesv
Computes the solution to a real system of linear equations
Related keywords: DGESVfinanceLAPACKlinear equations L U decomposition
F07ABF   21  nagf_lapacklin_dgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
Related keywords: backward errorcondition number, matrixDGESVXerror bound, matrixfinanceforward errorLAPACKlinear equations L U decomposition
F07ACF   22  nagf_lapacklin_dsgesv
Computes the solution to a real system of linear equations using mixed precision arithmetic
Related keywords: DSGESVLAPACKlinear equationsmixed-precision
F07AEF   15  nagf_lapacklin_dgetrs
Solution of real system of linear equations, multiple right-hand sides, matrix already factorized by F07ADF
Related keywords: DGETRSLAPACKlinear equations L U decomposition
F07AFF   22  nagf_lapacklin_dgeequ
Computes row and column scalings intended to equilibrate a general real matrix and reduce its condition number
Related keywords: DGEEQUequilibrationLAPACKlinear equationsscaling
F07AGF   15  nagf_lapacklin_dgecon
Estimate condition number of real matrix, matrix already factorized by F07ADF
Related keywords: condition number, matrixDGECONLAPACKlinear equations L U decomposition
F07AHF   15  nagf_lapacklin_dgerfs
Refined solution with error bounds of real system of linear equations, multiple right-hand sides
Related keywords: backward errorDGERFSerror bound, matrixforward errorLAPACKlinear equations L U decomposition
F07AJF   15  nagf_lapacklin_dgetri
Inverse of real matrix, matrix already factorized by F07ADF
Related keywords: DGETRIfinanceinverse, matrixLAPACKlinear equations L U decomposition
F08KBF   21  nagf_lapackeig_dgesvd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
Related keywords: DGESVDeigenproblemfinanceLAPACKLAPACKleast squaresSVD, singular value decomposition
F08KDF   21  nagf_lapackeig_dgesdd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
Related keywords: DGESDDdivide-and-conquer methodeigenproblemfinanceLAPACKLAPACKleast squaresSVD, singular value decomposition
F08KHF   23  nagf_lapackeig_dgejsv
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
Related keywords: DGEJSVeigenproblemJacobi methodLAPACKLAPACKleast squaressingular value decomposition
F08KJF   23  nagf_lapackeig_dgesvj
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
Related keywords: DGESVJeigenproblemJacobi methodLAPACKLAPACKleast squaressingular value decomposition
F08NAF   21  nagf_lapackeig_dgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
Related keywords: DGEEVeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresorthogonal transformations QR algorithm
F08NBF   21  nagf_lapackeig_dgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGEEVXeigenproblemeigenvalueseigenvectorsfinanceforward errorLAPACKLAPACKleast squaresorthogonal transformations QR algorithm
F08NEF   16  nagf_lapackeig_dgehrd
Performs an orthogonal reduction of real general matrix to upper Hessenberg form
Related keywords: DGEHRDeigenproblemLAPACKLAPACKleast squaresorthogonal transformations
F08NHF   16  nagf_lapackeig_dgebal
Balances a real general matrix
Related keywords: balancingDGEBALeigenproblemLAPACKLAPACKleast squares
F08NJF   16  nagf_lapackeig_dgebak
Transforms eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF
Related keywords: balancingDGEBAKeigenproblemeigenvectorsLAPACKLAPACKleast squares
F08PAF   21  nagf_lapackeig_dgees
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
Related keywords: DGEESeigenproblemeigenvaluesLAPACKLAPACKleast squaresSchur formSchur vectors
F08PBF   21  nagf_lapackeig_dgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: condition number, matrixDGEESeigenproblemeigenvaluesLAPACKLAPACKleast squaresSchur formSchur vectors
F08PEF   16  nagf_lapackeig_dhseqr
Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
Related keywords: DHSEQReigenproblemeigenvaluesLAPACKLAPACKleast squaresSchur form
F08PPF   21  nagf_lapackeig_zgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also computes a reciprocal condition number for the average of the selected eigenvalues and for the right invariant subspace corresponding to these eigenvalues
Related keywords: condition number, matrixeigenproblemeigenvaluesLAPACKLAPACKleast squaresSchur formSchur vectorsZGEESX
F08QFF   16  nagf_lapackeig_dtrexc
Reorders a Schur factorization of real matrix using orthogonal similarity transformation
Related keywords: DTREXCeigenproblemLAPACKLAPACKleast squaresorthogonal transformationsSchur form
F08VAF   21  nagf_lapackeig_dggsvd
Computes the generalized singular value decomposition of a real matrix pair
Related keywords: DGGSVDeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresSVD, generalized
F08VCF   26  nagf_lapackeig_dggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair
Related keywords: DGGSVD3eigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresSVD, generalized
F08WAF   21  nagf_lapackeig_dggev
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: DGGEVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
F08WBF   21  nagf_lapackeig_dggevx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcondition number, matrixDGGEVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsfinanceforward errorgeneralized eigenproblemLAPACKLAPACKleast squares
F08WCF   26  nagf_lapackeig_dggev3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: DGGEVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
F08WEF   20  nagf_lapackeig_dgghrd
Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Related keywords: DGGHRDeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresorthogonal transformations
F08WFF   26  nagf_lapackeig_dgghd3
Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
Related keywords: DGGHD3eigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresorthogonal transformations
F08XAF   21  nagf_lapackeig_dgges
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: DGGESeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresSchur form, generalizedSchur vectors
F08XBF   21  nagf_lapackeig_dggesx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: condition number, matrixDGGESXeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresSchur form, generalizedSchur vectors
F08XCF   26  nagf_lapackeig_dgges3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: DGGES3eigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresSchur form, generalizedSchur vectors
F08YGF   22  nagf_lapackeig_dtgsen
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Related keywords: condition number, matrixDTGSENeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresorthogonal transformations
F08YLF   22  nagf_lapackeig_dtgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
Related keywords: condition number, matrixDTGSNAeigenproblemgeneralized Schur formLAPACKLAPACKleast squares
real, orthogonal matrix F08RAF   25  nagf_lapackeig_dorcsd
Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
Related keywords: complete CS decompositionDORCSDeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squares
real, positive-definite, symmetric, Toeplitz matrix F04FEF   15  nagf_linsys_real_toeplitz_yule
Solution of the Yule–Walker equations for real symmetric positive definite Toeplitz matrix, one right-hand side
Related keywords: big datadata analyticssimultaneous linear equationsToeplitz matrixYule–Walker equations
F04FFF   15  nagf_linsys_real_toeplitz_solve
Solution of real symmetric positive definite Toeplitz system, one right-hand side
Related keywords: big datadata analyticssimultaneous linear equationsToeplitz matrix
F04MEF   15  nagf_linsys_real_toeplitz_yule_update
Update solution of the Yule–Walker equations for real symmetric positive definite Toeplitz matrix
Related keywords: big datadata analyticssimultaneous linear equationsToeplitz matrixYule–Walker equations
F04MFF   15  nagf_linsys_real_toeplitz_update
Update solution of real symmetric positive definite Toeplitz system
Related keywords: big datadata analyticssimultaneous linear equationsToeplitz matrix
real, positive-definite, symmetric, tridiagonal matrix F04BGF   21  nagf_linsys_real_posdef_tridiag_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite tridiagonal system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationssimultaneous linear equations
F07JAF   21  nagf_lapacklin_dptsv
Computes the solution to a real symmetric positive definite tridiagonal system of linear equations
Related keywords: Cholesky decompositionDPTSVLAPACKlinear equationsmatrix, band
F07JBF   21  nagf_lapacklin_dptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixDPTSVXerror bound, matrixforward errorLAPACKlinear equationsmatrix, band
F07JDF   22  nagf_lapacklin_dpttrf
Computes the LDL T factorization of a real symmetric positive definite tridiagonal matrix
Related keywords: Cholesky decompositionDPTTRFLAPACKlinear equationsmatrix, band
F07JEF   22  nagf_lapacklin_dpttrs
Solves a real symmetric positive definite tridiagonal system using the LDL T factorization computed by F07JDF
Related keywords: Cholesky decompositionDPTTRSLAPACKlinear equationsmatrix, band
F07JGF   22  nagf_lapacklin_dptcon
Computes the reciprocal of the condition number of a real symmetric positive definite tridiagonal system using the LDL T factorization computed by F07JDF
Related keywords: condition number, matrixDPTCONLAPACKlinear equationsmatrix, band
F07JHF   22  nagf_lapacklin_dptrfs
Refined solution with error bounds of real symmetric positive definite tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositionDPTRFSforward errorLAPACKlinear equationsmatrix, band
real, positive-definite, symmetric matrix F01ABF   nagf_matop_real_symm_posdef_inv
Inverse of real symmetric positive definite matrix using iterative refinement
Related keywords: inverse, matrixinversionmatrix inversematrix operations
F01ADF   nagf_matop_real_symm_posdef_inv_noref
Inverse of real symmetric positive definite matrix
Related keywords: inverse, matrixinversionmatrix inversematrix operations
F03BFF   23  nagf_det_real_sym
Determinant of real symmetric positive definite matrix
Related keywords: determinant
F04BDF   21  nagf_linsys_real_posdef_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationssimultaneous linear equations
F04BEF   21  nagf_linsys_real_posdef_packed_solve
Computes the solution, estimated condition number and error-bound to a real symmetric positive definite system of linear equations, packed storage
Related keywords: big datadata analyticsforward errorlinear equationssimultaneous linear equations
F07FAF   21  nagf_lapacklin_dposv
Computes the solution to a real symmetric positive definite system of linear equations
Related keywords: Cholesky decompositionDPOSVfinanceLAPACKlinear equations
F07FBF   21  nagf_lapacklin_dposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations
Related keywords: backward errorCholesky decompositioncondition number, matrixDPOSVXerror bound, matrixfinanceforward errorLAPACKlinear equations
F07FCF   23  nagf_lapacklin_dsposv
Computes the solution to a real symmetric positive definite system of linear equations using mixed precision arithmetic
Related keywords: Cholesky decompositionDSPOSVLAPACKlinear equationsmixed-precision
F07FDF   15  nagf_lapacklin_dpotrf
Cholesky factorization of real symmetric positive definite matrix
Related keywords: Cholesky decompositionDPOTRFfinanceLAPACKlinear equations
F07FEF   15  nagf_lapacklin_dpotrs
Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FDF
Related keywords: Cholesky decompositionDPOTRSfinanceLAPACKlinear equations
F07FFF   22  nagf_lapacklin_dpoequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number
Related keywords: DPOEQUequilibrationLAPACKlinear equationsscaling
F07FGF   15  nagf_lapacklin_dpocon
Estimate condition number of real symmetric positive definite matrix, matrix already factorized by F07FDF
Related keywords: condition number, matrixDPOCONLAPACKlinear equations
F07FHF   15  nagf_lapacklin_dporfs
Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositionDPORFSforward errorLAPACKlinear equations
F07FJF   15  nagf_lapacklin_dpotri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07FDF
Related keywords: Cholesky decompositionDPOTRIfinanceinverse, matrixLAPACKlinear equations
F07GAF   21  nagf_lapacklin_dppsv
Computes the solution to a real symmetric positive definite system of linear equations, packed storage
Related keywords: Cholesky decompositionDPPSVLAPACKlinear equations
F07GBF   21  nagf_lapacklin_dppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations, packed storage
Related keywords: backward errorCholesky decompositioncondition number, matrixDPPSVXerror bound, matrixforward errorLAPACKlinear equations
F07GDF   15  nagf_lapacklin_dpptrf
Cholesky factorization of real symmetric positive definite matrix, packed storage
Related keywords: Cholesky decompositionDPPTRFLAPACKlinear equations
F07GEF   15  nagf_lapacklin_dpptrs
Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GDF, packed storage
Related keywords: Cholesky decompositionDPPTRSLAPACKlinear equations
F07GFF   22  nagf_lapacklin_dppequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number, packed storage
Related keywords: DPPEQUequilibrationLAPACKlinear equationsscaling
F07GGF   15  nagf_lapacklin_dppcon
Estimate condition number of real symmetric positive definite matrix, matrix already factorized by F07GDF, packed storage
Related keywords: Cholesky decompositioncondition number, matrixDPPCONLAPACKlinear equations
F07GHF   15  nagf_lapacklin_dpprfs
Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorCholesky decompositionDPPRFSforward errorLAPACKlinear equations
F07GJF   15  nagf_lapacklin_dpptri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07GDF, packed storage
Related keywords: Cholesky decompositionDPPTRIinverse, matrixLAPACKlinear equations
F07WDF   23  nagf_lapacklin_dpftrf
Cholesky factorization of real symmetric positive definite matrix, Rectangular Full Packed format
Related keywords: Cholesky decompositionDPFTRFLAPACKlinear equations
F07WEF   23  nagf_lapacklin_dpftrs
Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by F07WDF, Rectangular Full Packed format
Related keywords: Cholesky decompositionDPFTRSLAPACKlinear equations
F07WJF   23  nagf_lapacklin_dpftri
Inverse of real symmetric positive definite matrix, matrix already factorized by F07WDF, Rectangular Full Packed format
Related keywords: Cholesky decompositionDPETRIinverse, matrixLAPACKlinear equations
F08SAF   21  nagf_lapackeig_dsygv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Related keywords: DSYGVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
F08SBF   21  nagf_lapackeig_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
Related keywords: DSYGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
F08SCF   21  nagf_lapackeig_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
Related keywords: divide-and-conquer methodDSYGVDeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
F08SEF   16  nagf_lapackeig_dsygst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , B factorized by F07FDF
Related keywords: DSYGSTeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squares
F08TAF   21  nagf_lapackeig_dspgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Related keywords: DSPGVeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
F08TBF   21  nagf_lapackeig_dspgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
Related keywords: DSPGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
F08TCF   21  nagf_lapackeig_dspgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: divide-and-conquer methodDSPGVXeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
F08TEF   16  nagf_lapackeig_dspgst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , packed storage, B factorized by F07GDF
Related keywords: DSPGVXeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squares
real, positive-semidefinite, symmetric matrix F07KDF   23  nagf_lapacklin_dpstrf
Cholesky factorization, with complete pivoting, of a real, symmetric, positive semidefinite matrix
Related keywords: Cholesky decompositionDPSTRFLAPACKlinear equations
real, quasi-triangular matrix F01EPF   25  nagf_matop_real_tri_matrix_sqrt
Real upper quasi-triangular matrix square root
Related keywords: inversionmatrix operations
F08QHF   16  nagf_lapackeig_dtrsyl
Solves the real Sylvester matrix equation A X + X B = C , A and B are upper quasi-triangular or transposes
Related keywords: DTRSYLeigenproblemLAPACKLAPACKleast squaresSylvester equation
F08QKF   16  nagf_lapackeig_dtrevc
Computes left and right eigenvectors of real upper quasi-triangular matrix
Related keywords: DTREVCeigenproblemeigenvectorsLAPACKLAPACKleast squares
F08QLF   16  nagf_lapackeig_dtrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
Related keywords: condition number, matrixDTRSNAeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares
F08YHF   22  nagf_lapackeig_dtgsyl
Solves the real-valued, generalized, quasi-trangular, Sylvester equation
Related keywords: DTGSYLeigenproblemLAPACKLAPACKleast squaresSylvester equation
real, sparse, symmetric matrix F02FJF   11  nagf_eigen_real_symm_sparse_eigsys
Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box)
Related keywords: big datadata analyticseigenvalueseigenvectorsmatrix, sparse
F02FKF   25  nagf_eigen_real_symm_sparse_arnoldi
Selected eigenvalues and eigenvectors of a real symmetric sparse matrix
Related keywords: big datadata analyticseigenproblemeigenvalueseigenvalueseigenvectorseigenvectorslarge scale eigenproblemsmatrix, sparsesparse eigenproblem
F11DKF   20  nagf_sparse_real_gen_precon_jacobi
Real, sparse, symmetric or nonsymmetric, linear systems, line Jacobi preconditioner
Related keywords: big datadata analyticsJacobi preconditioninglarge scale linear systemslinear equations, pre-conditionersreal, sparse matrix
F11GDF   20  nagf_sparse_real_symm_basic_setup
Real sparse symmetric linear systems, setup for F11GEF
Related keywords: big datadata analyticslarge scale linear systemslinear equations, iterative method, setup
F11GEF   20  nagf_sparse_real_symm_basic_solver
Real sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos method or the MINRES algorithm
Related keywords: big dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodMINRES, iterative linear equation solver
F11GFF   20  nagf_sparse_real_symm_basic_diag
Real sparse symmetric linear systems, diagnostic for F11GEF
Related keywords: big datadata analyticslarge scale linear systemslinear equations, iterative method, diagnostic
F11JAF   17  nagf_sparse_real_symm_precon_ichol
Real sparse symmetric matrix, incomplete Cholesky factorization
Related keywords: big datadata analyticsincomplete Cholesky factorizationlarge scale linear systemslinear equations, pre-conditioners
F11JBF   17  nagf_sparse_real_symm_precon_ichol_solve
Solution of linear system involving incomplete Cholesky preconditioning matrix generated by F11JAF
Related keywords: big datadata analyticsincomplete Cholesky factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative method
F11JCF   17  nagf_sparse_real_symm_solve_ichol
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JAF (Black Box)
Related keywords: big dataCGS, conjugate gradient methoddata analyticsincomplete Cholesky factorizationiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemslinear equations, iterative method
F11JDF   17  nagf_sparse_real_symm_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse symmetric matrix
Related keywords: big datadata analyticslarge scale linear systemslinear equations, pre-conditionersSSOR method, symmetric successive over-relaxation
F11JEF   17  nagf_sparse_real_symm_solve_jacssor
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsJacobi preconditioningLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodSSOR method, symmetric successive over-relaxation
F11XEF   17  nagf_sparse_real_symm_matvec
Real sparse symmetric matrix-vector multiply
Related keywords: big datadata analyticslarge scale linear systemsmultiply, matrix
F11ZBF   17  nagf_sparse_real_symm_sort
Real sparse symmetric matrix reorder routine
Related keywords: big datadata analyticslarge scale linear systemsmatrix, reorder
F12FAF   21  nagf_sparseig_real_symm_init
Initialization routine for (F12FBF) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse (standard or generalized) eigenproblem
Related keywords: big datadata analyticseigenproblem, initializationlarge scale eigenproblems
F12FBF   21  nagf_sparseig_real_symm_iter
Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, reverse communication
Related keywords: big datadata analyticseigenvalueseigenvectorslarge scale eigenproblemssparse eigenproblem
F12FCF   21  nagf_sparseig_real_symm_proc
Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, postprocessing for F12FBF
Related keywords: big datadata analyticslarge scale eigenproblemssparse eigenproblem, postprocessing
F12FDF   21  nagf_sparseig_real_symm_option
Set a single option from a string (F12FBF/F12FCF/F12FGF)
Related keywords: big datadata analyticslarge scale eigenproblemssparse eigenproblem, options
F12FEF   21  nagf_sparseig_real_symm_monit
Provides monitoring information for F12FBF
Related keywords: big datadata analyticslarge scale eigenproblemssparse eigenproblem, monitoring
real, sparse matrix F01BRF   nagf_matop_real_gen_sparse_lu
L U factorization of real sparse matrix
Related keywords: inversionLU decompositionmatrix operationssparse linear equations
F01BSF   nagf_matop_real_gen_sparse_lu_reuse
L U factorization of real sparse matrix with known sparsity pattern
Related keywords: inversionLU decompositionmatrix operationssparse linear equations
F02EKF   24  nagf_eigen_real_gen_sparse_arnoldi
Selected eigenvalues and eigenvectors of a real sparse general matrix
Related keywords: big datadata analyticseigenvalueseigenvectorslarge scale eigenproblemsmatrix, sparse
F04AXF   nagf_linsys_real_sparse_fac_solve
Solution of real sparse simultaneous linear equations (coefficient matrix already factorized)
Related keywords: big datadata analyticslinear equationsmatrix, sparsesimultaneous linear equations
F11BDF   19  nagf_sparse_real_gen_basic_setup
Real sparse nonsymmetric linear systems, setup for F11BEF
Related keywords: big datadata analyticslarge scale linear systemslinear equations, iterative method, setup
F11BEF   19  nagf_sparse_real_gen_basic_solver
Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11BFF   19  nagf_sparse_real_gen_basic_diag
Real sparse nonsymmetric linear systems, diagnostic for F11BEF
Related keywords: big datadata analyticslarge scale linear systemslinear equations, iterative method, diagnostic
F11DAF   18  nagf_sparse_real_gen_precon_ilu
Real sparse nonsymmetric linear systems, incomplete L U factorization
Related keywords: big datadata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, pre-conditioners
F11DBF   18  nagf_sparse_real_gen_precon_ilu_solve
Solution of linear system involving incomplete L U preconditioning matrix generated by F11DAF
Related keywords: big datadata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative method
F11DCF   18  nagf_sparse_real_gen_solve_ilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DAF
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DDF   18  nagf_sparse_real_gen_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse nonsymmetric matrix
Related keywords: big datadata analyticslarge scale linear systemslinear equations, pre-conditionersSSOR method, successive over-relaxation
F11DEF   18  nagf_sparse_real_gen_solve_jacssor
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsJacobi preconditioninglarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodSSOR method, symmetric successive over-relaxationTFQMR, transpose-free quasi-minimal residual method
F11DFF   24  nagf_sparse_real_gen_precon_bdilu
Real sparse nonsymmetric linear system, incomplete L U factorization of local or overlapping diagonal blocks
Related keywords: additive Schwarz preconditionerbig datadata analyticsincomplete L U factorizationlarge scale linear systemslinear equations, pre-conditioners
F11DGF   24  nagf_sparse_real_gen_solve_bdilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DFF
Related keywords: additive Schwarz preconditionerBi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DKF   20  nagf_sparse_real_gen_precon_jacobi
Real, sparse, symmetric or nonsymmetric, linear systems, line Jacobi preconditioner
Related keywords: big datadata analyticsJacobi preconditioninglarge scale linear systemslinear equations, pre-conditionersreal, sparse, symmetric matrix
F11MDF   21  nagf_sparse_direct_real_gen_setup
Real sparse nonsymmetric linear systems, setup for F11MEF
Related keywords: big datadata analyticslarge scale linear systemslinear equations, direct method, setup
F11MEF   21  nagf_sparse_direct_real_gen_lu
L U factorization of real sparse matrix
Related keywords: big datadata analyticsdiscretised systemlarge scale linear systemsLU decompositionsparse linear system
F11MFF   21  nagf_sparse_direct_real_gen_solve
Solution of real sparse simultaneous linear equations (coefficient matrix already factorized)
Related keywords: big datadata analyticsdiscretised systemlarge scale linear systemslinear equationssparse linear system
F11MGF   21  nagf_sparse_direct_real_gen_cond
Estimate condition number of real matrix, matrix already factorized by F11MEF
Related keywords: big datacondition number, matrixdata analyticslarge scale linear systems
F11MHF   21  nagf_sparse_direct_real_gen_refine
Refined solution with error bounds of real system of linear equations, multiple right-hand sides
Related keywords: backward errorbig datadata analyticsforward errorlarge scale linear systemslinear equations
F11MKF   21  nagf_sparse_direct_real_gen_matmul
Real sparse nonsymmetric matrix-matrix multiply, compressed column storage
Related keywords: big datadata analyticslarge scale linear systemsmultiply, matrix
F11MLF   21  nagf_sparse_direct_real_gen_norm
1 -norm, -norm, largest absolute element, real, square, sparse matrix
Related keywords: 1-normabsolute valuebig datadata analyticsinfinity-normlarge scale linear systemsnorm, matrix
F11MMF   21  nagf_sparse_direct_real_gen_diag
Real sparse nonsymmetric linear systems, diagnostic for F11MEF
Related keywords: big datadata analyticslarge scale linear systemslinear equations
F11XAF   18  nagf_sparse_real_gen_matvec
Real, sparse, nonsymmetric matrix-vector multiply
Related keywords: big datadata analyticslarge scale linear systemsmultiply, matrix
F11ZAF   18  nagf_sparse_real_gen_sort
Real sparse nonsymmetric matrix reorder routine
Related keywords: big datadata analyticslarge scale linear systemsmatrix, reorder
F12AAF   21  nagf_sparseig_real_init
Initialization routine for (F12ABF) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse (standard or generalized) eigenproblem
Related keywords: big datadata analyticseigenproblemeigenproblem, initializationlarge scale eigenproblems
F12ABF   21  nagf_sparseig_real_iter
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, reverse communication
Related keywords: big datadata analyticseigenproblemeigenvalueseigenvectorslarge scale eigenproblemssparse eigenproblem
F12ACF   21  nagf_sparseig_real_proc
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, postprocessing for F12ABF
Related keywords: big datadata analyticseigenproblemeigenvalueseigenvectorslarge scale eigenproblemssparse eigenproblem
F12ADF   21  nagf_sparseig_real_option
Set a single option from a string (F12ABF/F12ACF/F12AGF)
Related keywords: big datadata analyticslarge scale eigenproblemssparse eigenproblem, options
F12AEF   21  nagf_sparseig_real_monit
Provides monitoring information for F12ABF
Related keywords: big datadata analyticseigenproblemlarge scale eigenproblemsmonitoring informationsparse eigenproblems, monitoring
real, symmetric, tridiagonal matrix F06RPF   21  nagf_blas_dlanst
1 -norm, -norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesmatrix, bandnorm, matrix
F08JAF   21  nagf_lapackeig_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: DSTEVeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithm
F08JBF   21  nagf_lapackeig_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
Related keywords: bisection methodDSTEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QR algorithm
F08JCF   19  nagf_lapackeig_dstevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
Related keywords: divide-and-conquer methodDSTEVXeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithm
F08JDF   21  nagf_lapackeig_dstevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
Related keywords: dqds algorithmDSTEVReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandrelatively robust representations
F08JEF   16  nagf_lapackeig_dsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit Q L or Q R algorithm
Related keywords: DSTEQReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithm
F08JFF   16  nagf_lapackeig_dsterf
Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the Q L or Q R algorithm
Related keywords: DSTERFeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithm
F08JGF   16  nagf_lapackeig_dpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
Related keywords: DPTEQReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band
F08JHF   22  nagf_lapackeig_dstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
Related keywords: divide-and-conquer methodDSTEDCeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithm
F08JJF   16  nagf_lapackeig_dstebz
Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection
Related keywords: bisection methodDSTEBZeigenproblemeigenvaluesLAPACKLAPACKleast squaresmatrix, band
F08JKF   16  nagf_lapackeig_dstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
Related keywords: DSTEINeigenproblemeigenvectorsinverse iterationLAPACKLAPACKleast squaresmatrix, band
F08JLF   22  nagf_lapackeig_dstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
Related keywords: dqds algorithmDSTEGReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandrelatively robust representations
F08JSF   16  nagf_lapackeig_zsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit Q L or Q R algorithm
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares QR algorithmZSTEQR
F08JUF   16  nagf_lapackeig_zpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACK LDL H decompositionleast squaresZPTEQR
F08JVF   22  nagf_lapackeig_zstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares QL algorithm QR algorithmZSTEDC
F08JXF   16  nagf_lapackeig_zstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
Related keywords: eigenproblemeigenvectorsinverse iterationLAPACKLAPACKleast squaresmatrix, bandZSTEIN
F08JYF   22  nagf_lapackeig_zstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
Related keywords: dqds algorithmeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandrelatively robust representationsZSTEGR
real, symmetric matrix F06WAF   23  nagf_blas_dlansf
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format
Related keywords: 1-normBLASBLASblas, real matricesdlansfFrobenius norminfinity-normlinear algebra support routineslinear algebra support routines;
F11YEF   25  nagf_sparse_sym_rcm
Reverse Cuthill–McKee reordering of a sparse symmetric matrix in CCS format
Related keywords: big datacomplex, symmetric matrixdata analyticslarge scale linear systemspermutationsparsesparse matrix
real, trapezoidal matrix F01QGF   14  nagf_matop_real_trapez_rq
R Q factorization of real m by n upper trapezoidal matrix m n
Related keywords: inversionmatrix operationsRQ factorizations
F06QFF   13  nagf_blas_dmcopy
Matrix copy, real rectangular or trapezoidal matrix
Related keywords: BLAScopy, vectors and matriceselementary arithmeticfinancelinear algebra support routinesreal, m by n matrix
F06RJF   15  nagf_blas_dlantr
1 -norm, -norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrixreal, triangular matrix
F08BHF   22  nagf_lapackeig_dtzrzf
Reduces a real upper trapezoidal matrix to upper triangular form
Related keywords: DTZRZFeigenproblemLAPACKLAPACKleast squaresmatrix, upper trapezoidalmatrix, upper triangularorthogonal transformations
F08YEF   22  nagf_lapackeig_dtgsja
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
Related keywords: DTGSJAeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresreal, triangular matrixSVD, generalized
real, triangular matrix F01VAF   23  nagf_matop_dtrttp
Copies a real triangular matrix from full format to packed format
Related keywords: DTRTTPfinanceinversionLAPACKmatrix operations
F01VCF   23  nagf_matop_dtpttr
Copies a real triangular matrix from packed format to full format
Related keywords: DTPTTRfinanceinversionLAPACKmatrix operations
F01VEF   23  nagf_matop_dtrttf
Copies a real triangular matrix from full format to Rectangular Full Packed format
Related keywords: DTRTTPfinanceinversionLAPACKmatrix operations
F01VGF   23  nagf_matop_dtfttr
Copies a real triangular matrix from Rectangular Full Packed format to full format
Related keywords: DTFTTRfinanceinversionLAPACKmatrix operations
F01VJF   23  nagf_matop_dtpttf
Copies a real triangular matrix from packed format to Rectangular Full Packed format
Related keywords: DTPTTFfinanceinversionLAPACKmatrix operations
F01VLF   23  nagf_matop_dtfttp
Copies a real triangular matrix from Rectangular Full Packed format to packed format
Related keywords: DTFTTPfinanceinversionLAPACKmatrix operations
F02WUF   14  nagf_eigen_real_triang_svd
SVD of real upper triangular matrix (Black Box)
Related keywords: big datadata analyticseigenvalueseigenvectorsSVD, singular value decomposition
F06PFF   12  nagf_blas_dtrmv
Matrix-vector product, real triangular matrix
Related keywords: BLASblas, real matricesdtrmvlinear algebra support routinesmultiply, matrix
F06PHF   12  nagf_blas_dtpmv
Matrix-vector product, real triangular packed matrix
Related keywords: BLASblas, real matricesdtpmvlinear algebra support routinesmultiply, matrix
F06PJF   12  nagf_blas_dtrsv
System of equations, real triangular matrix
Related keywords: BLASblas, real matricesdtrsvfinancelinear algebra support routineslinear equations
F06PLF   12  nagf_blas_dtpsv
System of equations, real triangular packed matrix
Related keywords: BLASblas, real matricesdtpsvlinear algebra support routineslinear equations
F06QPF   13  nagf_blas_dutr1
Q R factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix
Related keywords: BLASlinear algebra support routines QR factorizationrank k matrix updatesrotation, elementary
F06QQF   13  nagf_blas_dutupd
Q R factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row
Related keywords: BLASlinear algebra support routines QR factorizationrank k matrix updatesrotation, elementary
F06QVF   13  nagf_blas_dutsrh
Compute upper Hessenberg matrix by sequence of plane rotations, real upper triangular matrix
Related keywords: BLASlinear algebra support routinesrotation, elementary
F06QWF   13  nagf_blas_dutsrs
Compute upper spiked matrix by sequence of plane rotations, real upper triangular matrix
Related keywords: BLASlinear algebra support routinesrotation, elementary
F06RJF   15  nagf_blas_dlantr
1 -norm, -norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrixreal, trapezoidal matrix
F06RKF   15  nagf_blas_dlantp
1 -norm, -norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesnorm, matrix
F06WBF   23  nagf_blas_dtfsm
Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix, Rectangular Full Packed format
Related keywords: BLASBLASblas, real matricesdtfsmlinear algebra support routineslinear algebra support routines;linear equations
F06YFF   14  nagf_blas_dtrmm
Matrix-matrix product, one real triangular matrix, one real rectangular matrix
Related keywords: BLASblas, real matricesdsymmlinear algebra support routinesmultiply, matrixreal, m by n matrix
F06YJF   14  nagf_blas_dtrsm
Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix
Related keywords: BLASblas, real matricesfinancelinear algebra support routineslinear equations
F07TEF   15  nagf_lapacklin_dtrtrs
Solution of real triangular system of linear equations, multiple right-hand sides
Related keywords: DTRTRSfinanceLAPACKlinear equations
F07TGF   15  nagf_lapacklin_dtrcon
Estimate condition number of real triangular matrix
Related keywords: condition number, matrixDTRCONLAPACKlinear equations
F07THF   15  nagf_lapacklin_dtrrfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorDTRRFSerror bound, matrixfinanceforward errorLAPACKlinear equations
F07TJF   15  nagf_lapacklin_dtrtri
Inverse of real triangular matrix
Related keywords: DTRTRIfinanceinverse, matrixLAPACKlinear equations
F07UEF   15  nagf_lapacklin_dtptrs
Solution of real triangular system of linear equations, multiple right-hand sides, packed storage
Related keywords: DTPTRSLAPACKlinear equations
F07UGF   15  nagf_lapacklin_dtpcon
Estimate condition number of real triangular matrix, packed storage
Related keywords: condition number, matrixDTPCONLAPACKlinear equations
F07UHF   15  nagf_lapacklin_dtprfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorDTPRFSerror bound, matrixforward errorLAPACKlinear equations
F07UJF   15  nagf_lapacklin_dtptri
Inverse of real triangular matrix, packed storage
Related keywords: DTPTRIinverse, matrixLAPACKlinear equations
F07WKF   23  nagf_lapacklin_dtftri
Inverse of real triangular matrix, Rectangular Full Packed format
Related keywords: DTFTRIinverse, matrixLAPACKlinear equations
F08YEF   22  nagf_lapackeig_dtgsja
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
Related keywords: DTGSJAeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresreal, trapezoidal matrixSVD, generalized
real, triangular-pentagonal matrix F08BBF   25  nagf_lapackeig_dtpqrt
Q R factorization of real general triangular-pentagonal matrix
Related keywords: DTPQRTeigenproblemexplicit blockingLAPACKleast squaresQR factorizationrecursive QR
real, tridiagonal matrix F04BCF   21  nagf_linsys_real_tridiag_solve
Computes the solution, estimated condition number and error-bound to a real tridiagonal system of linear equations
Related keywords: big datadata analyticsforward errorlinear equationsmatrix, bandsimultaneous linear equations
F04LEF   11  nagf_linsys_real_tridiag_fac_solve
Solution of real tridiagonal simultaneous linear equations (coefficient matrix already factorized by F01LEF)
Related keywords: big datadata analyticslinear equationsmatrix, bandsimultaneous linear equations
F06RNF   21  nagf_blas_dlangt
1 -norm, -norm, Frobenius norm, largest absolute element, real tridiagonal matrix
Related keywords: 1-normBLASFrobenius norminfinity-normlinear algebra support routinesmatrix, bandnorm, matrix
F07CAF   21  nagf_lapacklin_dgtsv
Computes the solution to a real tridiagonal system of linear equations
Related keywords: DGTSVfinanceLAPACKlinear equations L U decompositionmatrix, band
F07CBF   21  nagf_lapacklin_dgtsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
Related keywords: backward errorcondition number, matrixDGTSVXerror bound, matrixforward errorLAPACKlinear equations L U decompositionmatrix, band
F07CDF   22  nagf_lapacklin_dgttrf
L U factorization of real tridiagonal matrix
Related keywords: DGTTRFfinanceLAPACKlinear equations L U decompositionmatrix, band
F07CEF   22  nagf_lapacklin_dgttrs
Solves a real tridiagonal system of linear equations using the L U factorization computed by F07CDF
Related keywords: DGTTRSfinanceLAPACKlinear equations L U decompositionmatrix, band
F07CGF   22  nagf_lapacklin_dgtcon
Estimates the reciprocal of the condition number of a real tridiagonal matrix using the L U factorization computed by F07CDF
Related keywords: condition number, matrixDGTCONLAPACKlinear equations L U decompositionmatrix, band
F07CHF   22  nagf_lapacklin_dgtrfs
Refined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorDGTCONforward errorLAPACKlinear equations L U decompositionmatrix, band
real scalar X10BFF   26 
Write a real (working precision) scalar to the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationcallback data objectworking precisionwrite
X10CFF   26 
Read a real (working precision) scalar from the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationcallback data objectreadworking precision
rearrange vector M01EAF   12  nagf_sort_realvec_rank_rearrange
Rearrange a vector according to given ranks, real numbers
Related keywords: big datadata analyticsrank vectorsearchingsorting
M01EBF   12  nagf_sort_intvec_rank_rearrange
Rearrange a vector according to given ranks, integer numbers
Related keywords: big datadata analyticsrank vectorsearchingsorting
M01ECF   12  nagf_sort_charvec_rank_rearrange
Rearrange a vector according to given ranks, character data
Related keywords: big datadata analyticsrank vectorsearchingsorting
M01EDF   19  nagf_sort_cmplxvec_rank_rearrange
Rearrange a vector according to given ranks, complex numbers
Related keywords: big datadata analyticsrank vectorsearchingsorting
rectangular D03EDF   12  nagf_pde_2d_ellip_mgrid
Elliptic PDE, solution of finite difference equations by a multigrid technique
Related keywords: elliptic partial differential equationsmultigrid methodPDE, partial differential equationstwo-dimensional
rectangular distribution G05SAF   22  nagf_rand_dist_uniform01
Generates a vector of pseudorandom numbers from a uniform distribution over 0 , 1
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbersuniform distribution
G05SQF   22  nagf_rand_dist_uniform
Generates a vector of pseudorandom numbers from a uniform distribution over a , b
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbersuniform distribution
G05TLF   22  nagf_rand_int_uniform
Generates a vector of pseudorandom integers from a uniform distribution
Related keywords: big datadata analyticsfinancerandom integersrandom number generatorsuniform distribution
G05YLF   22  nagf_rand_quasi_init
Initializes a quasi-random number generator
Related keywords: big datadata analyticsFaure, quasi-random numbersfinancelow-discrepancy sequencesNiederreiter method, quasi-random numbersquasi-random numbersrandom number generatorsrandom numbersSobol, quasi-random numbersuniform distribution
rectangular lag window G13CAF   10  nagf_tsa_uni_spectrum_lag
Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: Bartlett lag windowbig datadata analyticsfinanceParzen lag windowsmoothingtime seriestime series analysisTukey lag windowunivariate time series
G13CCF   10  nagf_tsa_multi_spectrum_lag
Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: Bartlett lag windowbig datacross-spectrumdata analyticsfinancemultivariate time seriesParzen lag windowsmoothingtime seriestime series analysisTukey lag window
recursion coefficients D01TEF   26  nagf_quad_1d_gauss_recm
Generates recursion coefficients needed by D01TDF to calculate a Gaussian quadrature rule
Related keywords: abscissaecubatureGaussianGolubGolub and Welschintegrationnon-adaptivequadratureWelsch
recursive QR F08ABF   25  nagf_lapackeig_dgeqrt
Performs a Q R factorization of real general rectangular matrix, with explicit blocking
Related keywords: DGEQRTeigenproblemexplicit blockingLAPACKleast squaresQR factorizationreal, m by n matrix
F08ACF   25  nagf_lapackeig_dgemqrt
Applies the orthogonal transformation determined by F08ABF
Related keywords: DGEMQRTeigenproblemexplicit blockingLAPACKleast squaresorthogonal transformationsQR factorization
F08APF   25  nagf_lapackeig_zgeqrt
Performs a Q R factorization of complex general rectangular matrix using recursive algorithm
Related keywords: complex, m by n matrixeigenproblemexplicit blockingLAPACKleast squaresQR factorizationZGEQRT
F08AQF   25  nagf_lapackeig_zgemqrt
Applies the unitary transformation determined by F08APF
Related keywords: eigenproblemexplicit blockingLAPACKleast squaresQR factorizationunitary transformationsZGEMQRT
F08BBF   25  nagf_lapackeig_dtpqrt
Q R factorization of real general triangular-pentagonal matrix
Related keywords: DTPQRTeigenproblemexplicit blockingLAPACKleast squaresQR factorizationreal, triangular-pentagonal matrix
F08BCF   25  nagf_lapackeig_dtpmqrt
Applies the orthogonal transformation determined by F08BBF
Related keywords: DTPMQRTeigenproblemexplicit blockingLAPACKleast squaresorthogonal transformationsQR factorization
F08BPF   25  nagf_lapackeig_ztpqrt
Q R factorization of complex triangular-pentagonal matrix
Related keywords: complex, triangular-pentagonal matrixeigenproblemexplicit blockingLAPACKleast squaresQR factorizationZTPQRT
F08BQF   25  nagf_lapackeig_ztpmqrt
Applies the unitary transformation determined by F08BPF
Related keywords: eigenproblemexplicit blockingLAPACKleast squaresQR factorizationunitary transformationsZTPMQRT
regression F04QAF   11  nagf_linsys_real_gen_sparse_lsqsol
Sparse linear least squares problem, m real equations in n unknowns
Related keywords: big datadata analyticsleast squaresmatrix, sparsereal, m by n matrixridgesimultaneous linear equations
G02CAF   nagf_correg_linregs_const
Simple linear regression with constant term, no missing values
Related keywords: big datacorrelation analysisdata analyticsfinancelinear regressionnonlinear regressionpolynomial regressionregression analysis
G02CBF   nagf_correg_linregs_noconst
Simple linear regression without constant term, no missing values
Related keywords: big datacorrelation analysisdata analyticsfinancelinear regressionnonlinear regressionpolynomial regressionregression analysis
G02CCF   nagf_correg_linregs_const_miss
Simple linear regression with constant term, missing values
Related keywords: big datacorrelation analysisdata analyticsfinancelinear regressionmissing valuesnonlinear regressionpolynomial regressionregression analysis
G02CDF   nagf_correg_linregs_noconst_miss
Simple linear regression without constant term, missing values
Related keywords: big datacorrelation analysisdata analyticsfinancelinear regressionmissing valuesnonlinear regressionpolynomial regressionregression analysis
G02DCF   14  nagf_correg_linregm_obs_edit
Add/delete an observation to/from a general linear regression model
Related keywords: big datacorrelation analysisdata analyticsfinancelinear regressionnonlinear regressionpolynomial regressionregression analysisstandard errorsvariance-covariance matrix
G02DDF   14  nagf_correg_linregm_update
Estimates of linear parameters and general linear regression model from updated model
Related keywords: big datacorrelation analysisdata analyticsfinancelinear regressionnonlinear regressionpolynomial regressionregression analysis
G02HAF   13  nagf_correg_robustm
Robust regression, standard M -estimates
Related keywords: Andrew's sine wavebig datacorrelation analysisdata analyticsfinanceHampel's piecewise linear functionHuber type regressionKrasker–Welsch weightsMallows type regressionMaronna's weights M -estimatesnonlinear regressionpolynomial regressionregression analysisrobust regressionScheppe type regressionTukey's bi-weight
G08RAF   12  nagf_nonpar_rank_regsn
Regression using ranks, uncensored data
Related keywords: nonparametric statisticsparameter estimatesscoresvariance-covariance matrix
G08RBF   12  nagf_nonpar_rank_regsn_censored
Regression using ranks, right-censored data
Related keywords: nonparametric statisticsparameter estimatesscoresvariance-covariance matrix
G22YAF   26  nagf_blgm_lm_formula
Specify a linear model via a formula string
Related keywords: specification
G22YCF   26  nagf_blgm_lm_design_matrix
Construct a design matrix from a linear model specified using G22YAF
Related keywords: design matrix
G22YDF   26  nagf_blgm_lm_submodel
Construct a vector indicating which columns of a design matrix to include in a submodel specified using G22YAF
Related keywords: design matrix
regression analysis G02 Chapter Introduction     Correlation and Regression Analysis
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionpolynomial regression
relatively robust representations F08FDF   21  nagf_lapackeig_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
Related keywords: dqds algorithmDSYEVReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresreal, indefinite, symmetric matrix
F08FRF   21  nagf_lapackeig_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresunitary transformationsZHEEVR
F08JDF   21  nagf_lapackeig_dstevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
Related keywords: dqds algorithmDSTEVReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
F08JLF   22  nagf_lapackeig_dstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
Related keywords: dqds algorithmDSTEGReigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
F08JYF   22  nagf_lapackeig_zstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
Related keywords: dqds algorithmeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrixZSTEGR
reliability G04GAF   26  nagf_anova_icc
Intraclass correlation (ICC) for assessing rater reliability
Related keywords: analysis of varianceICCinterraterintraclassintrarater
REML, Restricted Maximum Likelihood G02JAF   21  nagf_correg_mixeff_reml
Linear mixed effects regression using Restricted Maximum Likelihood (REML)
Related keywords: big datacorrelation analysisdata analyticsfinancemaximum likelihoodmixed effects regressionnonlinear regressionpolynomial regressionregression analysis
G02JDF   23  nagf_correg_mixeff_hier_reml
Hierarchical mixed effects regression using Restricted Maximum Likelihood (REML)
Related keywords: big datacorrelation analysisdata analyticshierarchical mixed effects regressionmixed effects regressionnonlinear regressionpolynomial regressionregression analysis
remove X10ABF   26 
Remove a configuration data object
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationconfiguration data object
Renka and Cline method E01EAF   25  nagf_interp_2d_triangulate
Triangulation of two-dimensional scattered grid, method of Renka and Cline
Related keywords: interpolationScattered dataTriangulation
E01EBF   25  nagf_interp_2d_triang_bary_eval
Barycentric interpolation on function values provided on a two-dimensional scattered grid
Related keywords: Barycentric interpolationBilinear interpolationfinanceinterpolationInterpolationScattered dataScattered data interpolationTriangulation
E01SAF   13  nagf_interp_2d_scat
Interpolating functions, method of Renka and Cline, two variables
Related keywords: interpolation
E01SBF   13  nagf_interp_2d_scat_eval
Interpolated values, evaluate interpolant computed by E01SAF, two variables
Related keywords: interpolation
resample G05PWF   25  nagf_rand_subsamp_xyw
Permutes a matrix, vector, vector triplet into a form suitable for random sub-sampling validation
Related keywords: big datacross-validationdata analyticspermuterandom number generatorssub-sample
residual correlations G03CAF   15  nagf_mv_factor
Computes maximum likelihood estimates of the parameters of a factor analysis model, factor loadings, communalities and residual correlations
Related keywords: communalities, maximum likelihoodfactor analysisfactor loadingsmaximum likelihoodmultivariate methods
RGMRES, restarted generalized minimum residual method F11BEF   19  nagf_sparse_real_gen_basic_solver
Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixTFQMR, transpose-free quasi-minimal residual method
F11BSF   19  nagf_sparse_complex_gen_basic_solver
Complex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodTFQMR, transpose-free quasi-minimal residual method
F11DCF   18  nagf_sparse_real_gen_solve_ilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DAF
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixTFQMR, transpose-free quasi-minimal residual method
F11DEF   18  nagf_sparse_real_gen_solve_jacssor
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsJacobi preconditioninglarge scale linear systemslinear equations, iterative methodreal, sparse matrixSSOR method, symmetric successive over-relaxationTFQMR, transpose-free quasi-minimal residual method
F11DGF   24  nagf_sparse_real_gen_solve_bdilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DFF
Related keywords: additive Schwarz preconditionerBi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixTFQMR, transpose-free quasi-minimal residual method
F11DQF   19  nagf_sparse_complex_gen_solve_ilu
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DNF (Black Box)
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodTFQMR, transpose-free quasi-minimal residual method
F11DSF   19  nagf_sparse_complex_gen_solve_jacssor
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsiterative methods, linear equationsJacobi preconditioninglarge scale linear systemslinear equations, iterative methodSSOR method, symmetric successive over-relaxationTFQMR, transpose-free quasi-minimal residual method
F11DUF   24  nagf_sparse_complex_gen_solve_bdilu
Solution of complex, sparse, non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DTF
Related keywords: additive Schwarz preconditionerBi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodTFQMR, transpose-free quasi-minimal residual method
ridge F04QAF   11  nagf_linsys_real_gen_sparse_lsqsol
Sparse linear least squares problem, m real equations in n unknowns
Related keywords: big datadata analyticsleast squaresmatrix, sparsereal, m by n matrixregressionsimultaneous linear equations
ridge regression G02KAF   22  nagf_correg_ridge_opt
Ridge regression, optimizing a ridge regression parameter
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02KBF   22  nagf_correg_ridge
Ridge regression using a number of supplied ridge regression parameters
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
Riemann solver, PDE D03PUF   17  nagf_pde_1d_parab_euler_roe
Roe's approximate Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
Related keywords: Euler equationsPDE, partial differential equationsRoe's method
D03PVF   17  nagf_pde_1d_parab_euler_osher
Osher's approximate Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
Related keywords: Euler equationsOsher's method, Euler equationsPDE, partial differential equations
D03PWF   18  nagf_pde_1d_parab_euler_hll
Modified HLL Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
Related keywords: Euler equationsHarten–Lax-van Leer solvermodified HLL solverPDE, partial differential equations
D03PXF   18  nagf_pde_1d_parab_euler_exact
Exact Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
Related keywords: Euler equationsPDE, partial differential equations
risk sets G12ZAF   19  nagf_surviv_coxmodel_risksets
Creates the risk sets associated with the Cox proportional hazards model for fixed covariates
Related keywords: Cox proportional hazard modelsurvival analysis
RK23 D02PEF   24  nagf_ode_ivp_rkts_range
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output
Related keywords: first-order systemIVP, initial value problemNonstiffODE, ordinary differential equationsRK45RK78Runge–Kutta–Merson
D02PFF   24  nagf_ode_ivp_rkts_onestep
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step
Related keywords: first-order systemIVP, initial value problemNonstiffODE, ordinary differential equationsRK45RK78Runge–Kutta–Merson
D02PGF   26  nagf_ode_ivp_rk_step_revcomm
Ordinary differential equations, initial value problem, Runge–Kutta method, integration by reverse communication
Related keywords: IVP, initial value problemODE, ordinary differential equationsRK45RK78Runge–Kutta–Merson
RK45 D02BJF   18  nagf_ode_ivp_rk_zero_simple
Ordinary differential equations, initial value problem, Runge–Kutta method, until function of solution is zero, integration over range with intermediate output (simple driver)
Related keywords: initial value problemIVP, initial value problemODE, ordinary differential equationsRunge–Kutta–Merson, ODE
D02PEF   24  nagf_ode_ivp_rkts_range
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output
Related keywords: first-order systemIVP, initial value problemNonstiffODE, ordinary differential equationsRK23RK78Runge–Kutta–Merson
D02PFF   24  nagf_ode_ivp_rkts_onestep
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step
Related keywords: first-order systemIVP, initial value problemNonstiffODE, ordinary differential equationsRK23RK78Runge–Kutta–Merson
D02PGF   26  nagf_ode_ivp_rk_step_revcomm
Ordinary differential equations, initial value problem, Runge–Kutta method, integration by reverse communication
Related keywords: IVP, initial value problemODE, ordinary differential equationsRK23RK78Runge–Kutta–Merson
RK78 D02PEF   24  nagf_ode_ivp_rkts_range
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output
Related keywords: first-order systemIVP, initial value problemNonstiffODE, ordinary differential equationsRK23RK45Runge–Kutta–Merson
D02PFF   24  nagf_ode_ivp_rkts_onestep
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step
Related keywords: first-order systemIVP, initial value problemNonstiffODE, ordinary differential equationsRK23RK45Runge–Kutta–Merson
D02PGF   26  nagf_ode_ivp_rk_step_revcomm
Ordinary differential equations, initial value problem, Runge–Kutta method, integration by reverse communication
Related keywords: IVP, initial value problemODE, ordinary differential equationsRK23RK45Runge–Kutta–Merson
robust estimation G02HLF   14  nagf_correg_robustm_corr_user_deriv
Calculates a robust estimation of a covariance matrix, user-supplied weight function plus derivatives
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02HMF   14  nagf_correg_robustm_corr_user
Calculates a robust estimation of a covariance matrix, user-supplied weight function
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G07DAF   13  nagf_univar_robust_1var_median
Robust estimation, median, median absolute deviation, robust standard deviation
Related keywords: meanmedianstandard deviationunivariate estimation
G07DBF   13  nagf_univar_robust_1var_mestim
Robust estimation, M -estimates for location and scale parameters, standard weight functions
Related keywords: location, robust estimation M -estimatesscale parametersunivariate estimation
G07DCF   13  nagf_univar_robust_1var_mestim_wgt
Robust estimation, M -estimates for location and scale parameters, user-defined weight functions
Related keywords: location, robust estimation M -estimatesscale parametersunivariate estimation
G07EAF   16  nagf_univar_robust_1var_ci
Robust confidence intervals, one-sample
Related keywords: confidence intervalunivariate estimation
G07EBF   16  nagf_univar_robust_2var_ci
Robust confidence intervals, two-sample
Related keywords: confidence intervalunivariate estimation
robust regression G02HAF   13  nagf_correg_robustm
Robust regression, standard M -estimates
Related keywords: Andrew's sine wavebig datacorrelation analysisdata analyticsfinanceHampel's piecewise linear functionHuber type regressionKrasker–Welsch weightsMallows type regressionMaronna's weights M -estimatesnonlinear regressionpolynomial regressionregressionregression analysisScheppe type regressionTukey's bi-weight
G02HBF   13  nagf_correg_robustm_wts
Robust regression, compute weights for use with G02HDF
Related keywords: big databounded influencecorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
G02HDF   13  nagf_correg_robustm_user
Robust regression, compute regression with user-supplied functions and weights
Related keywords: big databounded influencecorrelation analysisdata analyticsfinanceiterative weighted least squares M -estimatesnonlinear regressionpolynomial regressionregression analysis
G02HFF   13  nagf_correg_robustm_user_varmat
Robust regression, variance-covariance matrix following G02HDF
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysisvariance-covariance matrix
Roe's method D03PUF   17  nagf_pde_1d_parab_euler_roe
Roe's approximate Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF
Related keywords: Euler equationsPDE, partial differential equationsRiemann solver, PDE
root-finding C02AFF   14  nagf_zeros_poly_complex
All zeros of complex polynomial, modified Laguerre's method
Related keywords: Laguerre's methodzeros of polynomials
C02AGF   13  nagf_zeros_poly_real
All zeros of real polynomial, modified Laguerre's method
Related keywords: Laguerre's methodzeros of polynomials
C02AHF   14  nagf_zeros_quadratic_complex
All zeros of complex quadratic equation
Related keywords: quadratic polynomialzeros of polynomials
C02AJF   14  nagf_zeros_quadratic_real
All zeros of real quadratic equation
Related keywords: quadratic polynomialzeros of polynomials
C02AKF   20  nagf_zeros_cubic_real
All zeros of real cubic equation
Related keywords: cubic polynomialzeros of polynomials
C02ALF   20  nagf_zeros_quartic_real
All zeros of real quartic equation
Related keywords: quartic polynomialszeros of polynomials
C02AMF   20  nagf_zeros_cubic_complex
All zeros of complex cubic equation
Related keywords: cubic polynomialzeros of polynomials
C02ANF   20  nagf_zeros_quartic_complex
All zeros of complex quartic equation
Related keywords: quartic polynomialszeros of polynomials
C05AUF   23  nagf_roots_contfn_brent_interval
Zero of continuous function, Brent algorithm, from a given starting value, binary search for interval
Related keywords: Brent algorithmfinanceroots of transcendental equationszeros of transcendental functions
C05AVF   nagf_roots_contfn_interval_rcomm
Binary search for interval containing zero of continuous function (reverse communication)
Related keywords: financeroots of transcendental equationszeros of transcendental functions
C05AWF   23  nagf_roots_contfn_cntin
Zero of continuous function, continuation method, from a given starting value
Related keywords: financeroots of transcendental equationszeros of transcendental functions
C05AXF   nagf_roots_contfn_cntin_rcomm
Zero of continuous function, continuation method, from a given starting value (reverse communication)
Related keywords: financeroots of transcendental equationszeros of transcendental functions
C05AYF   23  nagf_roots_contfn_brent
Zero of continuous function in a given interval, Brent algorithm
Related keywords: Brent algorithmfinanceroots of transcendental equationszeros of transcendental functions
C05AZF   nagf_roots_contfn_brent_rcomm
Zero of continuous function in a given interval, Brent algorithm (reverse communication)
Related keywords: Brent algorithmfinanceroots of transcendental equationszeros of transcendental functions
C05MDF   26  nagf_roots_sys_func_aa_rcomm
Solution of a system of nonlinear equations using Anderson acceleration (reverse communication)
Related keywords: Anderson accelerationroots of transcendental equationszeros of transcendental functions
C05QBF   23  nagf_roots_sys_func_easy
Solution of a system of nonlinear equations using function values only (easy-to-use)
Related keywords: financeroots of transcendental equationszeros of transcendental functions
C05QCF   23  nagf_roots_sys_func_expert
Solution of a system of nonlinear equations using function values only (comprehensive)
Related keywords: financeroots of transcendental equationszeros of transcendental functions
C05QDF   23  nagf_roots_sys_func_rcomm
Solution of a system of nonlinear equations using function values only (reverse communication)
Related keywords: financeroots of transcendental equationszeros of transcendental functions
C05QSF   23  nagf_roots_sparsys_func_easy
Solution of a sparse system of nonlinear equations using function values only (easy-to-use)
Related keywords: discretised systemroots of transcendental equationssparse nonlinear systemzeros of transcendental functions
C05RBF   23  nagf_roots_sys_deriv_easy
Solution of a system of nonlinear equations using first derivatives (easy-to-use)
Related keywords: financeroots of transcendental equationszeros of transcendental functions
C05RCF   23  nagf_roots_sys_deriv_expert
Solution of a system of nonlinear equations using first derivatives (comprehensive)
Related keywords: financeroots of transcendental equationszeros of transcendental functions
C05RDF   23  nagf_roots_sys_deriv_rcomm
Solution of a system of nonlinear equations using first derivatives (reverse communication)
Related keywords: financeroots of transcendental equationszeros of transcendental functions
roots of transcendental equations C05 Chapter Introduction     Roots of One or More Transcendental Equations
rotation, elementary F06AAF   12  nagf_blas_drotg
Generate real plane rotation
Related keywords: BLASblas, real matricesdrotglinear algebra support routines
F06BAF   12  nagf_blas_drotgc
Generate real plane rotation, storing tangent
Related keywords: BLASlinear algebra support routines
F06BEF   12  nagf_blas_drotj
Generate real Jacobi plane rotation
Related keywords: BLASJacobi methodlinear algebra support routines
F06BHF   12  nagf_blas_drot2
Apply real similarity rotation to 2 by 2 symmetric matrix
Related keywords: BLASlinear algebra support routines
F06CAF   12  nagf_blas_zrotgc
Generate complex plane rotation, storing tangent, real cosine
Related keywords: BLASlinear algebra support routines
F06CBF   12  nagf_blas_zrotgs
Generate complex plane rotation, storing tangent, real sine
Related keywords: BLASlinear algebra support routines
F06CHF   12  nagf_blas_zrot2
Apply complex similarity rotation to 2 by 2 Hermitian matrix
Related keywords: BLASlinear algebra support routines
F06EPF   12  nagf_blas_drot
Apply real plane rotation
Related keywords: BLASblas, real matricesdrotlinear algebra support routines
F06EXF   14  nagf_blas_droti
Apply plane rotation to a real sparse and a full vector
Related keywords: BLASblas, real matricesdrotilinear algebra support routines
F06FPF   12  nagf_blas_drots
Apply real symmetric plane rotation to two vectors
Related keywords: BLASlinear algebra support routines
F06FQF   12  nagf_blas_dsrotg
Generate sequence of real plane rotations
Related keywords: BLASlinear algebra support routines
F06HMF   21  nagf_blas_zrot
Apply plane rotation with real cosine and complex sine
Related keywords: BLASblas, complex matriceslinear algebra support routineszrot
F06HPF   12  nagf_blas_zcrot
Apply complex plane rotation
Related keywords: BLASlinear algebra support routines
F06HQF   12  nagf_blas_zsrotg
Generate sequence of complex plane rotations
Related keywords: BLASlinear algebra support routines
F06KPF   12  nagf_blas_zdrot
Apply real plane rotation to two complex vectors
Related keywords: BLASlinear algebra support routineszdrot
F06QMF   13  nagf_blas_dsysrc
Orthogonal similarity transformation of real symmetric matrix as a sequence of plane rotations
Related keywords: BLASlinear algebra support routinesreal, indefinite, symmetric matrix
F06QPF   13  nagf_blas_dutr1
Q R factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix
Related keywords: BLASlinear algebra support routines QR factorizationrank k matrix updatesreal, triangular matrix
F06QQF   13  nagf_blas_dutupd
Q R factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row
Related keywords: BLASlinear algebra support routines QR factorizationrank k matrix updatesreal, triangular matrix
F06QRF   13  nagf_blas_duhqr
Q R or R Q factorization by sequence of plane rotations, real upper Hessenberg matrix
Related keywords: BLASlinear algebra support routines QR factorizationrank k matrix updatesreal, Hessenberg matrixRQ factorizations
F06QSF   13  nagf_blas_dusqr
Q R or R Q factorization by sequence of plane rotations, real upper spiked matrix
Related keywords: BLASlinear algebra support routines QR factorizationrank k matrix updatesreal, nonsymmetric matrixRQ factorizations
F06QTF   13  nagf_blas_dutsqr
Q R factorization of U P or R Q factorization of P U , U real upper triangular, P a sequence of plane rotations
Related keywords: BLASlinear algebra support routines QR factorizationrank k matrix updatesRQ factorizations
F06QVF   13  nagf_blas_dutsrh
Compute upper Hessenberg matrix by sequence of plane rotations, real upper triangular matrix
Related keywords: BLASlinear algebra support routinesreal, triangular matrix
F06QWF   13  nagf_blas_dutsrs
Compute upper spiked matrix by sequence of plane rotations, real upper triangular matrix
Related keywords: BLASlinear algebra support routinesreal, triangular matrix
F06QXF   13  nagf_blas_dgesrc
Apply sequence of plane rotations, real rectangular matrix
Related keywords: BLASlinear algebra support routinesreal, m by n matrix
F06TMF   13  nagf_blas_zhesrc
Unitary similarity transformation of Hermitian matrix as a sequence of plane rotations
Related keywords: BLAScomplex, Hermitian matrixlinear algebra support routines
F06TQF   13  nagf_blas_zutupd
Q R factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row
Related keywords: BLAScomplex, triangular matrixlinear algebra support routines QR factorization
F06TRF   13  nagf_blas_zuhqr
Q R or R Q factorization by sequence of plane rotations, complex upper Hessenberg matrix
Related keywords: BLAScomplex, Hessenberg matrixlinear algebra support routines QR factorizationRQ factorizations
F06TSF   13  nagf_blas_zusqr
Q R or R Q factorization by sequence of plane rotations, complex upper spiked matrix
Related keywords: BLAScomplex, triangular matrixlinear algebra support routines QR factorizationRQ factorizations
F06TTF   13  nagf_blas_zutsqr
Q R factorization of U P or R Q factorization of P U , U complex upper triangular, P a sequence of plane rotations
Related keywords: BLAScomplex, triangular matrixlinear algebra support routines QR factorizationRQ factorizations
F06TVF   13  nagf_blas_zutsrh
Compute upper Hessenberg matrix by sequence of plane rotations, complex upper triangular matrix
Related keywords: BLAScomplex, triangular matrixlinear algebra support routines
F06TWF   13  nagf_blas_zutsrs
Compute upper spiked matrix by sequence of plane rotations, complex upper triangular matrix
Related keywords: BLAScomplex, triangular matrixlinear algebra support routines
F06TXF   13  nagf_blas_zgesrc
Apply sequence of plane rotations, complex rectangular matrix, real cosine and complex sine
Related keywords: BLAScomplex, m by n matrixlinear algebra support routines
F06TYF   13  nagf_blas_zgesrs
Apply sequence of plane rotations, complex rectangular matrix, complex cosine and real sine
Related keywords: BLAScomplex, m by n matrixlinear algebra support routines
F06VXF   13  nagf_blas_zsgesr
Apply sequence of plane rotations, complex rectangular matrix, real cosine and sine
Related keywords: BLAScomplex, m by n matrixlinear algebra support routines
RQ factorizations F01QGF   14  nagf_matop_real_trapez_rq
R Q factorization of real m by n upper trapezoidal matrix m n
Related keywords: inversionmatrix operationsreal, trapezoidal matrix
F01QJF   14  nagf_matop_real_gen_rq
R Q factorization of real m by n matrix m n
Related keywords: inversionmatrix operationsreal, m by n matrix
F01QKF   14  nagf_matop_real_gen_rq_formq
Operations with orthogonal matrices, form rows of Q , after R Q factorization by F01QJF
Related keywords: inversionmatrix operations
F01RGF   14  nagf_matop_complex_trapez_rq
R Q factorization of complex m by n upper trapezoidal matrix m n
Related keywords: complex, trapezoidal matrixinversionmatrix operations
F01RJF   14  nagf_matop_complex_gen_rq
R Q factorization of complex m by n matrix m n
Related keywords: complex, m by n matrixinversionmatrix operations
F01RKF   14  nagf_matop_complex_gen_rq_formq
Operations with unitary matrices, form rows of Q , after R Q factorization by F01RJF
Related keywords: inversionmatrix operations
F06QRF   13  nagf_blas_duhqr
Q R or R Q factorization by sequence of plane rotations, real upper Hessenberg matrix
Related keywords: BLASlinear algebra support routines QR factorizationrank k matrix updatesreal, Hessenberg matrixrotation, elementary
F06QSF   13  nagf_blas_dusqr
Q R or R Q factorization by sequence of plane rotations, real upper spiked matrix
Related keywords: BLASlinear algebra support routines QR factorizationrank k matrix updatesreal, nonsymmetric matrixrotation, elementary
F06QTF   13  nagf_blas_dutsqr
Q R factorization of U P or R Q factorization of P U , U real upper triangular, P a sequence of plane rotations
Related keywords: BLASlinear algebra support routines QR factorizationrank k matrix updatesrotation, elementary
F06TRF   13  nagf_blas_zuhqr
Q R or R Q factorization by sequence of plane rotations, complex upper Hessenberg matrix
Related keywords: BLAScomplex, Hessenberg matrixlinear algebra support routines QR factorizationrotation, elementary
F06TSF   13  nagf_blas_zusqr
Q R or R Q factorization by sequence of plane rotations, complex upper spiked matrix
Related keywords: BLAScomplex, triangular matrixlinear algebra support routines QR factorizationrotation, elementary
F06TTF   13  nagf_blas_zutsqr
Q R factorization of U P or R Q factorization of P U , U complex upper triangular, P a sequence of plane rotations
Related keywords: BLAScomplex, triangular matrixlinear algebra support routines QR factorizationrotation, elementary
F08CHF   22  nagf_lapackeig_dgerqf
R Q factorization of real general rectangular matrix
Related keywords: DGERQFeigenproblemLAPACKLAPACKleast squaresreal, m by n matrix
F08CJF   22  nagf_lapackeig_dorgrq
Form all or part of orthogonal Q from R Q factorization determined by F08CHF
Related keywords: DORGRQeigenproblemLAPACKLAPACKleast squaresorthogonal matrix, generationorthogonal transformations
F08CKF   22  nagf_lapackeig_dormrq
Applies the orthogonal transformation determined by F08CHF
Related keywords: DORGRQeigenproblemLAPACKLAPACKleast squaresorthogonal transformations
F08CVF   22  nagf_lapackeig_zgerqf
R Q factorization of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresZGERQF
F08CWF   22  nagf_lapackeig_zungrq
Form all or part of unitary Q from R Q factorization determined by F08CVF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary matrix, generationunitary transformationsZUNGRQ
F08CXF   22  nagf_lapackeig_zunmrq
Applies the unitary transformation determined by F08CVF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformationsZUNMRQ
F08ZAF   21  nagf_lapackeig_dgglse
Solves the real linear equality-constrained least squares (LSE) problem
Related keywords: DGGLSEeigenproblemLAPACKLAPACKleast squareslinear least squaresreal, m by n matrix
F08ZFF   22  nagf_lapackeig_dggrqf
Computes a generalized R Q factorization of a real matrix pair
Related keywords: DGGRQFeigenproblemLAPACKLAPACKleast squaresreal, m by n matrix
F08ZNF   21  nagf_lapackeig_zgglse
Solves the complex linear equality-constrained least squares (LSE) problem
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squareslinear least squaresZGGLSE
F08ZTF   22  nagf_lapackeig_zggrqf
Computes a generalized R Q factorization of a complex matrix pair
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresZGGRQF
Runge–Kutta–Merson D02PEF   24  nagf_ode_ivp_rkts_range
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output
Related keywords: first-order systemIVP, initial value problemNonstiffODE, ordinary differential equationsRK23RK45RK78
D02PFF   24  nagf_ode_ivp_rkts_onestep
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step
Related keywords: first-order systemIVP, initial value problemNonstiffODE, ordinary differential equationsRK23RK45RK78
D02PGF   26  nagf_ode_ivp_rk_step_revcomm
Ordinary differential equations, initial value problem, Runge–Kutta method, integration by reverse communication
Related keywords: IVP, initial value problemODE, ordinary differential equationsRK23RK45RK78
D02PHF   26  nagf_ode_ivp_rk_interp_setup
Set up interpolant by reverse communication for solution and derivative evaluations at points within the range of the last integration step taken by D02PGF
Related keywords: first-order systeminterpolationIVP, initial value problemNonstiffODE, ordinary differential equations
D02PJF   26  nagf_ode_ivp_rk_interp_eval
Evaluate interpolant, set up using D02PQF, to approximate solution and/or solution derivatives at a point within the range of the last integration step taken by D02PGF
Related keywords: interpolationIVP, initial value problemODE, ordinary differential equations
D02PQF   24  nagf_ode_ivp_rkts_setup
Ordinary differential equations, initial value problem, setup for D02PEF D02PFF
Related keywords: IVP, initial value problemODE, ordinary differential equations
D02PRF   24  nagf_ode_ivp_rkts_reset_tend
Ordinary differential equations, initial value problem, resets end of range for D02PFF
Related keywords: IVP, initial value problemODE, ordinary differential equations
D02PSF   24  nagf_ode_ivp_rkts_interp
Ordinary differential equations, initial value problem, interpolation for D02PFF
Related keywords: interpolationIVP, initial value problemODE, ordinary differential equations
D02PTF   24  nagf_ode_ivp_rkts_diag
Ordinary differential equations, initial value problem, integration diagnostics for D02PEF D02PFF
Related keywords: IVP, initial value problemODE, ordinary differential equations
D02PUF   24  nagf_ode_ivp_rkts_errass
Ordinary differential equations, initial value problem, error assessment diagnostics for D02PEF D02PFF
Related keywords: IVP, initial value problemODE, ordinary differential equations
Runge–Kutta–Merson, ODE D02BGF   nagf_ode_ivp_rkm_val_simple
Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until a component attains given value (simple driver)
Related keywords: initial value problemIVP, initial value problemODE, ordinary differential equations
D02BHF   nagf_ode_ivp_rkm_zero_simple
Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until function of solution is zero (simple driver)
Related keywords: initial value problemIVP, initial value problemODE, ordinary differential equations
D02BJF   18  nagf_ode_ivp_rk_zero_simple
Ordinary differential equations, initial value problem, Runge–Kutta method, until function of solution is zero, integration over range with intermediate output (simple driver)
Related keywords: initial value problemIVP, initial value problemODE, ordinary differential equationsRK45
Runge–Kutta–Nystrom, ODE D02LAF   13  nagf_ode_ivp_2nd_rkn
Second-order ordinary differential equations, initial value problem, Runge–Kutta–Nystrom method
Related keywords: initial value problemIVP, initial value problemODE, ordinary differential equations
D02LXF   13  nagf_ode_ivp_2nd_rkn_setup
Second-order ordinary differential equations, initial value problem, setup for D02LAF
Related keywords: initial value problemIVP, initial value problemODE, ordinary differential equations
D02LYF   13  nagf_ode_ivp_2nd_rkn_diag
Second-order ordinary differential equations, initial value problem, diagnostics for D02LAF
Related keywords: initial value problemIVP, initial value problemODE, ordinary differential equations
D02LZF   13  nagf_ode_ivp_2nd_rkn_interp
Second-order ordinary differential equations, initial value problem, interpolation for D02LAF
Related keywords: initial value problemIVP, initial value problemODE, ordinary differential equations
running median G10CAF   16  nagf_smooth_data_runningmedian
Compute smoothed data sequence using running median smoothers
Related keywords: smoothingSmoothing in StatisticsTukey's smoothing
runs up and runs down test for randomness G08EAF   14  nagf_nonpar_randtest_runs
Performs the runs up or runs down test for randomness
Related keywords: nonparametric statisticsrandomness, tests for
Sag–Szekeres method D01FDF   10  nagf_quad_md_sphere
Multidimensional quadrature, Sag–Szekeres method, general product region or n -sphere
Related keywords: integration, multidimensionalquadrature
sample, random G05NDF   22  nagf_rand_sample
Pseudorandom sample from an integer vector
Related keywords: big datadata analyticsfinancerandom number generatorsrandom sample
G05NEF   23  nagf_rand_sample_wgt
Pseudorandom sample, without replacement, unequal weights
Related keywords: big datadata analyticsrandom number generatorsrandom sample
Savage scores G01DHF   15  nagf_stat_ranks_and_scores
Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores
Related keywords: Blom scoresexponential scoresfinancerank scoresSimple Calculations on Statistical DataTukey scoresvan der Waerden scores
scalar product X03AAF   nagf_dot_real_prec
Real inner product added to initial value, basic/additional precision
Related keywords: additional precision accumulationdot productextended precision accumulationinner productinner products
X03ABF   nagf_dot_complex_prec
Complex inner product added to initial value, basic/additional precision
Related keywords: additional precision accumulationdot productextended precision accumulationinner productinner products
scale parameters G07DBF   13  nagf_univar_robust_1var_mestim
Robust estimation, M -estimates for location and scale parameters, standard weight functions
Related keywords: location, robust estimation M -estimatesrobust estimationunivariate estimation
G07DCF   13  nagf_univar_robust_1var_mestim_wgt
Robust estimation, M -estimates for location and scale parameters, user-defined weight functions
Related keywords: location, robust estimation M -estimatesrobust estimationunivariate estimation
scaling F07AFF   22  nagf_lapacklin_dgeequ
Computes row and column scalings intended to equilibrate a general real matrix and reduce its condition number
Related keywords: DGEEQUequilibrationLAPACKlinear equationsreal, nonsymmetric matrix
F07ATF   22  nagf_lapacklin_zgeequ
Computes row and column scalings intended to equilibrate a general complex matrix and reduce its condition number
Related keywords: complex, nonsymmetric matrixequilibrationLAPACKlinear equationsZGEEQU
F07BFF   22  nagf_lapacklin_dgbequ
Computes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number
Related keywords: DGBEQUequilibrationLAPACKlinear equationsmatrix, bandreal, band matrix
F07BTF   22  nagf_lapacklin_zgbequ
Computes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number
Related keywords: complex, band matrixequilibrationLAPACKlinear equationsmatrix, bandZGBEQU
F07FFF   22  nagf_lapacklin_dpoequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number
Related keywords: DPOEQUequilibrationLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07FTF   22  nagf_lapacklin_zpoequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number
Related keywords: complex, Hermitian, positive-definite matrixequilibrationLAPACKlinear equationsZPOEQU
F07GFF   22  nagf_lapacklin_dppequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number, packed storage
Related keywords: DPPEQUequilibrationLAPACKlinear equationsreal, positive-definite, symmetric matrix
F07GTF   22  nagf_lapacklin_zppequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number, packed storage
Related keywords: complex, Hermitian, positive-definite matrixequilibrationLAPACKlinear equationsZPPEQU
F07HFF   22  nagf_lapacklin_dpbequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite banded matrix and reduce its condition number
Related keywords: DPBEQUequilibrationLAPACKlinear equationsmatrix, bandreal, band, positive-definite, symmetric matrix
F07HTF   22  nagf_lapacklin_zpbequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite banded matrix and reduce its condition number
Related keywords: complex, band, Hermitian, positive-definite matrixequilibrationLAPACKlinear equationsmatrix, bandZPBEQU
scattered data E02DDF   13  nagf_fit_2dspline_sctr
Least squares surface fit by bicubic splines with automatic knot placement, scattered data
Related keywords: bicubic splinesB-splinescurve and surface fittingleast squaressmoothing
E02JDF   24  nagf_fit_2dspline_ts_sctr
Spline approximation to a set of scattered data using a two-stage approximation method
Related keywords: curve and surface fittingsplinetwo-dimensional spline approximation
E02JEF   24  nagf_fit_2dspline_ts_evalv
Evaluation at a vector of points of a spline computed by E02JDF
Related keywords: curve and surface fittingsplinetwo-dimensional spline approximation
E02JFF   24  nagf_fit_2dspline_ts_evalm
Evaluation at a mesh of points of a spline computed by E02JDF
Related keywords: curve and surface fittinggridded datasplinetwo-dimensional spline approximation
Scattered data E01EAF   25  nagf_interp_2d_triangulate
Triangulation of two-dimensional scattered grid, method of Renka and Cline
Related keywords: interpolationRenka and Cline methodTriangulation
E01EBF   25  nagf_interp_2d_triang_bary_eval
Barycentric interpolation on function values provided on a two-dimensional scattered grid
Related keywords: Barycentric interpolationBilinear interpolationfinanceinterpolationInterpolationRenka and Cline methodScattered data interpolationTriangulation
Scattered data interpolation E01EBF   25  nagf_interp_2d_triang_bary_eval
Barycentric interpolation on function values provided on a two-dimensional scattered grid
Related keywords: Barycentric interpolationBilinear interpolationfinanceinterpolationInterpolationRenka and Cline methodScattered dataTriangulation
Scheppe type regression G02HAF   13  nagf_correg_robustm
Robust regression, standard M -estimates
Related keywords: Andrew's sine wavebig datacorrelation analysisdata analyticsfinanceHampel's piecewise linear functionHuber type regressionKrasker–Welsch weightsMallows type regressionMaronna's weights M -estimatesnonlinear regressionpolynomial regressionregressionregression analysisrobust regressionTukey's bi-weight
Schur form F08PAF   21  nagf_lapackeig_dgees
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
Related keywords: DGEESeigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur vectors
F08PBF   21  nagf_lapackeig_dgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: condition number, matrixDGEESeigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur vectors
F08PEF   16  nagf_lapackeig_dhseqr
Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
Related keywords: DHSEQReigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08PNF   21  nagf_lapackeig_zgees
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenvaluesLAPACKLAPACKleast squaresSchur vectorsZGEES
F08PPF   21  nagf_lapackeig_zgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also computes a reciprocal condition number for the average of the selected eigenvalues and for the right invariant subspace corresponding to these eigenvalues
Related keywords: condition number, matrixeigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur vectorsZGEESX
F08PSF   16  nagf_lapackeig_zhseqr
Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
Related keywords: complex, Hessenberg matrixeigenproblemeigenvaluesLAPACKLAPACKleast squaresZHSEQR
F08QFF   16  nagf_lapackeig_dtrexc
Reorders a Schur factorization of real matrix using orthogonal similarity transformation
Related keywords: DTREXCeigenproblemLAPACKLAPACKleast squaresorthogonal transformationsreal, nonsymmetric matrix
F08QGF   16  nagf_lapackeig_dtrsen
Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
Related keywords: condition number, matrixDTREXCeigenproblemLAPACKLAPACKleast squaresorthogonal transformations
F08QTF   16  nagf_lapackeig_ztrexc
Reorders a Schur factorization of complex matrix using unitary similarity transformation
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformationsZTREXC
F08QUF   16  nagf_lapackeig_ztrsen
Reorders a Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
Related keywords: condition number, matrixeigenproblemLAPACKLAPACKleast squaresZTRSEN
Schur form, generalized F08XAF   21  nagf_lapackeig_dgges
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: DGGESeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur vectors
F08XBF   21  nagf_lapackeig_dggesx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: condition number, matrixDGGESXeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur vectors
F08XCF   26  nagf_lapackeig_dgges3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: DGGES3eigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur vectors
Schur vectors F08PAF   21  nagf_lapackeig_dgees
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
Related keywords: DGEESeigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form
F08PBF   21  nagf_lapackeig_dgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: condition number, matrixDGEESeigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form
F08PNF   21  nagf_lapackeig_zgees
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenvaluesLAPACKLAPACKleast squaresSchur formZGEES
F08PPF   21  nagf_lapackeig_zgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also computes a reciprocal condition number for the average of the selected eigenvalues and for the right invariant subspace corresponding to these eigenvalues
Related keywords: condition number, matrixeigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur formZGEESX
F08XAF   21  nagf_lapackeig_dgges
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: DGGESeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form, generalized
F08XBF   21  nagf_lapackeig_dggesx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: condition number, matrixDGGESXeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form, generalized
F08XCF   26  nagf_lapackeig_dgges3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: DGGES3eigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur form, generalized
F08XNF   21  nagf_lapackeig_zgges
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresZGGES
F08XPF   21  nagf_lapackeig_zggesx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresZGGES
F08XQF   26  nagf_lapackeig_zgges3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresZGGES3
score patterns G11SAF   12  nagf_contab_binary
Contingency table, latent variable model for binary data
Related keywords: contingency table analysisfactor scoreslatent variable modeltheta scores
scores G08RAF   12  nagf_nonpar_rank_regsn
Regression using ranks, uncensored data
Related keywords: nonparametric statisticsparameter estimatesregressionvariance-covariance matrix
G08RBF   12  nagf_nonpar_rank_regsn_censored
Regression using ranks, right-censored data
Related keywords: nonparametric statisticsparameter estimatesregressionvariance-covariance matrix
scramble G05YNF   22  nagf_rand_quasi_init_scrambled
Initializes a scrambled quasi-random number generator
Related keywords: big datadata analyticsFaure–TezukafinanceNiederreiterOwenrandom number generatorsrandom numbersSobol
SDP E04RAF   26  nagf_opt_handle_init
Initialization of a handle for the NAG optimization modelling suite for problems, such as, linear programming (LP), quadratic programming (QP), nonlinear programming (NLP), least squares (LSQ) problems, linear semidefinite programming (SDP) or SDP with bilinear matrix inequalities (BMI-SDP)
Related keywords: initializationleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationsemidefinite programming
E04RDF   26  nagf_opt_sdp_read_sdpa
A reader of sparse SDPA data files for linear SDP problems
Related keywords: least squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationsemidefinite programmingservice routine
E04SVF   26  nagf_opt_handle_solve_pennon
Run the Pennon solver on a compatible problem initialized by E04RAF and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI)
Related keywords: bilinear matrix inequalityBMIgeneralized augmented Lagrangian methodLagrangianleast squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionmonitoring informationoptimizationoptimizationsemidefinite programming
searching M01 Chapter Introduction     Sorting and Searching
Related keywords: big datadata analyticssorting
seasonal differencing G13AAF   nagf_tsa_uni_diff
Univariate time series, seasonal and non-seasonal differencing
Related keywords: big datadata analyticsdifferencing, time seriesfinancenon-seasonal differencingtime seriestime series analysisunivariate time series
semidefinite programming E04RAF   26  nagf_opt_handle_init
Initialization of a handle for the NAG optimization modelling suite for problems, such as, linear programming (LP), quadratic programming (QP), nonlinear programming (NLP), least squares (LSQ) problems, linear semidefinite programming (SDP) or SDP with bilinear matrix inequalities (BMI-SDP)
Related keywords: initializationleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationSDP
E04RDF   26  nagf_opt_sdp_read_sdpa
A reader of sparse SDPA data files for linear SDP problems
Related keywords: least squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationSDPservice routine
E04SVF   26  nagf_opt_handle_solve_pennon
Run the Pennon solver on a compatible problem initialized by E04RAF and defined by other routines from the suite, such as, semidefinite programming (SDP) and SDP with bilinear matrix inequalities (BMI)
Related keywords: bilinear matrix inequalityBMIgeneralized augmented Lagrangian methodLagrangianleast squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionmonitoring informationoptimizationoptimizationSDP
sequence, accelerate C06BAF   10  nagf_sum_accelerate
Acceleration of convergence of sequence, Shanks' transformation and epsilon algorithm
Related keywords: epsilon algorithmShanks' transformation, epsilon algorithmsummation of series
sequential QP method E04UCF   12  nagf_opt_nlp1_solve_old
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: densefinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationSQP
E04UFF   18  nagf_opt_nlp1_rcomm_old
Nonlinear programming (NLP), dense, active-set, SQP method, using function values and optionally first derivatives (reverse communication, comprehensive)
Related keywords: densefinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationSQP
E04UGF   19  nagf_opt_nlp1_sparse_solve_old
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives
Related keywords: financemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationSQP
E04USF   14  nagf_opt_lsq_gencon_deriv_old
Minimum of a sum of squares, nonlinear constraints, dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: data fittingfinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear least squaresnonlinear programmingoptimizationquasi-Newton approximationsum of squares
E04VHF   21  nagf_opt_nlp2_sparse_solve
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: financeLP, linear programmingmaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton algorithmsimplex algorithmSQP
E04WDF   21  nagf_opt_nlp2_solve
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: densefinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationSQP
E05UCF   24  nagf_glopt_nlp_multistart_sqp
Global optimization using multi-start, nonlinear constraints
Related keywords: financeglobal optimizationminimization, nonlinear constraintsmulti-start algorithm
E05USF   24  nagf_glopt_nlp_multistart_sqp_lsq
Global optimization of a sum of squares problem using multi-start, nonlinear constraints
Related keywords: financeglobal optimizationmulti-start algorithmsum of squares
service routine E04HCF   nagf_opt_check_deriv
Check user's routine for calculating first derivatives of function
Related keywords: check derivativefinancemaximizing a functionminimization, unconstrainedminimizing a functionoptimization
E04HDF   nagf_opt_check_deriv2
Check user's routine for calculating second derivatives of function
Related keywords: check derivativefinancemaximizing a functionminimization, unconstrainedminimizing a functionoptimization
E04MWF   26  nagf_opt_miqp_mps_write
Write MPS data file defining LP, QP, MILP or MIQP problem
Related keywords: linear programming,integerLP, linear programmingmaximizing a functionminimizing a functionMPS formatMPSX formatoptimizationQP, quadratic programming
E04MXF   24  nagf_opt_miqp_mps_read
Read MPS data file defining LP, QP, MILP or MIQP problem
Related keywords: linear programming,integerLP, linear programmingmaximizing a functionminimizing a functionMPSX formatoptimizationQP, quadratic programming
E04MZF   18  nagf_opt_qpconvex1_sparse_mps
Read MPS data file defining LP or QP problem, deprecated
Related keywords: LP, linear programmingmaximizing a functionminimizing a functionMPSX formatoptimizationQP, quadratic programming
E04NKF   18  nagf_opt_qpconvex1_sparse_solve_old
Linear programming (LP) or convex quadratic programming (QP), sparse, active-set method
Related keywords: financeLP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programming
E04NQF   21  nagf_opt_qpconvex2_sparse_solve
Linear programming (LP) or convex quadratic programming (QP), sparse, active-set method, recommended
Related keywords: active-set methodfinanceLP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programmingsparse convex QP prolem
E04RDF   26  nagf_opt_sdp_read_sdpa
A reader of sparse SDPA data files for linear SDP problems
Related keywords: least squares fittinglinear matrix inequalityLMImatrix constraintsmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionoptimizationoptimizationSDPsemidefinite programming
E04YAF   nagf_opt_lsq_check_deriv
Check user's routine for calculating Jacobian of first derivatives
Related keywords: financeJacobian estimationmaximizing a functionminimizing a functionoptimization
E04YBF   nagf_opt_lsq_check_hessian
Check user's routine for calculating Hessian of a sum of squares
Related keywords: financeHessian estimationmaximizing a functionminimizing a functionoptimization
E04YCF   11  nagf_opt_lsq_uncon_covariance
Covariance matrix for nonlinear least squares problem (unconstrained)
Related keywords: covariance matrixmaximizing a functionminimizing a functionnonlinear least squaresoptimization
set X10ACF   26 
Set the algorithmic mode
Related keywords: adjoint derivativesAD utility operationsalgorithmic modeautomatic differentiation
X10BCF   26 
Set the callback algorithmic mode
Related keywords: adjoint derivativesAD utility operationsautomatic differentiationcallback algorithmic mode
set information E04RXF   26  nagf_opt_handle_set_get_real
Retrieve or write a piece of information in a problem handle initialized by E04RAF
Related keywords: get informationmaximizing a functionminimizing a functionoptimization
seven-point stencil D03UBF   nagf_pde_3d_ellip_fd_iter
Elliptic PDE, solution of finite difference equations by SIP, seven-point three-dimensional molecule, one iteration
Related keywords: elliptic partial differential equationsPDE, partial differential equationsStone's strongly implicit procedure
Shanks' transformation, epsilon algorithm C06BAF   10  nagf_sum_accelerate
Acceleration of convergence of sequence, Shanks' transformation and epsilon algorithm
Related keywords: epsilon algorithmsequence, acceleratesummation of series
Shapiro and Wilk's W test for Normality G01DDF   12  nagf_stat_test_shapiro_wilk
Shapiro and Wilk's W test for Normality
Related keywords: financeSimple Calculations on Statistical DataW test for Normality
Shepard method E01SGF   18  nagf_interp_2d_scat_shep
Interpolating functions, modified Shepard's method, two variables
Related keywords: interpolation
E01SHF   18  nagf_interp_2d_scat_shep_eval
Interpolated values, evaluate interpolant computed by E01SGF, function and first derivatives, two variables
Related keywords: interpolation
E01TGF   18  nagf_interp_3d_scat_shep
Interpolating functions, modified Shepard's method, three variables
Related keywords: interpolation
E01THF   18  nagf_interp_3d_scat_shep_eval
Interpolated values, evaluate interpolant computed by E01TGF, function and first derivatives, three variables
Related keywords: interpolation
E01TKF   23  nagf_interp_4d_scat_shep
Interpolating functions, modified Shepard's method, four variables
Related keywords: interpolation
E01TLF   23  nagf_interp_4d_scat_shep_eval
Interpolated values, evaluate interpolant computed by E01TKF, function and first derivatives, four variables
Related keywords: interpolation
E01TMF   23  nagf_interp_5d_scat_shep
Interpolating functions, modified Shepard's method, five variables
Related keywords: interpolation
E01TNF   23  nagf_interp_5d_scat_shep_eval
Interpolated values, evaluate interpolant computed by E01TMF, function and first derivatives, five variables
Related keywords: interpolation
E01ZMF   24  nagf_interp_nd_scat_shep
Interpolating function, modified Shepard's method, d dimensions
Related keywords: interpolation
E01ZNF   24  nagf_interp_nd_scat_shep_eval
Interpolated values, evaluate interpolant computed by E01ZMF, function and first derivatives, d dimensions
Related keywords: interpolation
shifted logarithmic function S01BAF   14  nagf_specfun_log_shifted
ln 1 + x
Related keywords: approximations of special functionsfinancelogarithmic function
shooting method, ODE D02AGF   nagf_ode_bvp_shoot_genpar_intern
Ordinary differential equations, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined
Related keywords: boundary value problemBVPODE, ordinary differential equations
D02HAF   nagf_ode_bvp_shoot_bval
Ordinary differential equations, boundary value problem, shooting and matching, boundary values to be determined
Related keywords: boundary value problemBVPODE, ordinary differential equations
D02HBF   nagf_ode_bvp_shoot_genpar
Ordinary differential equations, boundary value problem, shooting and matching, general parameters to be determined
Related keywords: boundary value problemBVPODE, ordinary differential equations
D02SAF   nagf_ode_bvp_shoot_genpar_algeq
Ordinary differential equations, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined
Related keywords: boundary value problemBVPODE, ordinary differential equationsparameterized first ordertwo-point boundary value problem
shortest path H03ADF   18  nagf_mip_shortestpath
Shortest path problem, Dijkstra's algorithm
Related keywords: Dijkstra's algorithm, shortest pathoperations research
H03BBF   25  nagf_mip_tsp_simann
Travelling Salesman Problem, simulated annealing
Related keywords: operations researchsimulated annealingTravelling Salesman ProblemTSP
shrinkage G02APF   26  nagf_correg_corrmat_target
Computes a correlation matrix from an approximate one using a specified target matrix
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticselementwise weightsnearest correlation matrixnonlinear regressionpolynomial regressionregression analysisshrinking method
shrinking method G02ANF   25  nagf_correg_corrmat_shrinking
Computes a correlation matrix from an approximate matrix with fixed submatrix
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticsnearest correlation matrixnonlinear regressionpolynomial regressionregression analysis
G02APF   26  nagf_correg_corrmat_target
Computes a correlation matrix from an approximate one using a specified target matrix
Related keywords: big datacorrelation analysiscorrelation matrixdata analyticselementwise weightsnearest correlation matrixnonlinear regressionpolynomial regressionregression analysisshrinkage
signed rank test G08AGF   14  nagf_nonpar_test_wilcoxon
Performs the Wilcoxon one-sample (matched pairs) signed rank test
Related keywords: nonparametric statisticsWilcoxon signed rank test
significance G01EPF   15  nagf_stat_prob_durbin_watson
Computes bounds for the significance of a Durbin–Watson statistic
Related keywords: CDF, cumulative distribution functionDurbin–Watson statisticfinanceSimple Calculations on Statistical Data
G01SAF   24  nagf_stat_prob_normal_vector
Computes a vector of probabilities for the standard Normal distribution
Related keywords: big dataCDF, cumulative distribution functionconfidence intervaldata analyticsGaussian distributionlower tail probabilityNormal distributionSimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01SBF   24  nagf_stat_prob_students_t_vector
Computes a vector of probabilities for the Student's t -distribution
Related keywords: big dataCDF, cumulative distribution functionconfidence intervaldata analyticslower tail probabilitySimple Calculations on Statistical DataStudent's t -distributiontwo-tail probabilityupper tail probability
G02FCF   15  nagf_correg_linregm_stat_durbwat
Computes Durbin–Watson test statistic
Related keywords: big datacorrelation analysisdata analyticsDurbin–Watson statisticfinancenonlinear regressionpolynomial regressionregression analysis
G13ASF   13  nagf_tsa_uni_arima_resid
Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF
Related keywords: ARMAautocorrelation functionbig dataBox–Jenkins modelsBox–Ljung portmanteau statisticdata analyticsfinancestandard errorstime seriestime series analysisunivariate time series
G13DNF   15  nagf_tsa_multi_corrmat_partlag
Multivariate time series, sample partial lag correlation matrices, χ 2 statistics and significance levels
Related keywords: big datachi squared statisticsdata analyticsmultivariate time seriespartial lagtime seriestime series analysis
sign test G08AAF   nagf_nonpar_test_sign
Sign test on two paired samples
Related keywords: nonparametric statistics
Simple Calculations on Statistical Data G01 Chapter Introduction     Simple Calculations on Statistical Data
simple incremental method D06AAF   20  nagf_mesh_2d_gen_inc
Generates a two-dimensional mesh using a simple incremental method
Related keywords: mesh generationtriangular mesh
simplex algorithm E04CBF   22  nagf_opt_uncon_simplex
Unconstrained minimum, Nelder–Mead simplex algorithm, using function values only
Related keywords: derivative-free minimizationfinancemaximizing a functionminimization, unconstrainedminimizing a functionNelder–Mead algorithmNLPnonlinear programmingoptimization
E04VHF   21  nagf_opt_nlp2_sparse_solve
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: financeLP, linear programmingmaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton algorithmsequential QP methodSQP
simulated annealing H03BBF   25  nagf_mip_tsp_simann
Travelling Salesman Problem, simulated annealing
Related keywords: operations researchshortest pathTravelling Salesman ProblemTSP
simultaneous linear equations F04 Chapter Introduction     Simultaneous Linear Equations
Related keywords: big datadata analytics
sine, matrix F01EKF   24  nagf_matop_real_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm)
Related keywords: cosh, matrixcosine, matrixexponential, matrixfunctions, matrixinversionmatrix operationsreal, nonsymmetric matrixsinh, matrix
F01FKF   24  nagf_matop_complex_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm)
Related keywords: complex, nonsymmetric matrixcosh, matrixcosine, matrixexponential, matrixfunctions, matrixinversionmatrix operationssinh, matrix
F01JAF   24  nagf_matop_real_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix
Related keywords: condition number, matrixcosh, matrixcosine, matrixexponential, matrixinversionlogarithm, matrixmatrix operationsreal, nonsymmetric matrixsinh, matrix
F01KAF   24  nagf_matop_complex_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix
Related keywords: complex, nonsymmetric matrixcondition number, matrixcosh, matrixcosine, matrixexponential, matrixinversionlogarithm, matrixmatrix operationssinh, matrix
sine integral S13ADF   nagf_specfun_integral_sin
Sine integral Si x
Related keywords: approximations of special functionsfinancesine integral, Si x
sine integral, Si x S13ADF   nagf_specfun_integral_sin
Sine integral Si x
Related keywords: approximations of special functionsfinancesine integral
sine transform C06RAF   19  nagf_sum_fft_real_sine_simple
Discrete sine transform (easy-to-use)
Related keywords: summation of series
C06RCF   19  nagf_sum_fft_real_qtrsine_simple
Discrete quarter-wave sine transform (easy-to-use)
Related keywords: summation of series
C06REF   25  nagf_sum_fft_sine
Multiple discrete sine transforms, simple
Related keywords: Discrete Fourier TransformsFast Fourier TransformFFTFourier Transforms, realsummation of series
C06RGF   25  nagf_sum_fft_qtrsine
Multiple discrete quarter-wave sine transforms, simple
Related keywords: Discrete Fourier TransformsFast Fourier TransformFFTFourier Transforms, realquarter-wavesummation of series
singular value decomposition F08KHF   23  nagf_lapackeig_dgejsv
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
Related keywords: DGEJSVeigenproblemJacobi methodLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08KJF   23  nagf_lapackeig_dgesvj
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
Related keywords: DGESVJeigenproblemJacobi methodLAPACKLAPACKleast squaresreal, nonsymmetric matrix
sinh, matrix F01EKF   24  nagf_matop_real_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm)
Related keywords: cosh, matrixcosine, matrixexponential, matrixfunctions, matrixinversionmatrix operationsreal, nonsymmetric matrixsine, matrix
F01FKF   24  nagf_matop_complex_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm)
Related keywords: complex, nonsymmetric matrixcosh, matrixcosine, matrixexponential, matrixfunctions, matrixinversionmatrix operationssine, matrix
F01JAF   24  nagf_matop_real_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix
Related keywords: condition number, matrixcosh, matrixcosine, matrixexponential, matrixinversionlogarithm, matrixmatrix operationsreal, nonsymmetric matrixsine, matrix
F01KAF   24  nagf_matop_complex_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix
Related keywords: complex, nonsymmetric matrixcondition number, matrixcosh, matrixcosine, matrixexponential, matrixinversionlogarithm, matrixmatrix operationssine, matrix
skewness G01ADF   nagf_stat_summary_freq
Mean, variance, skewness, kurtosis, etc., one variable, from frequency table
Related keywords: financekurtosismeanSimple Calculations on Statistical Datastandard deviation
G01ATF   24  nagf_stat_summary_onevar
Computes univariate summary information: mean, variance, skewness, kurtosis
Related keywords: big datadata analyticsdata streamkurtosismaximum valuemeanminimum valueSimple Calculations on Statistical Datastandard deviationstreaming
smallest floating-point number X02AKF   12  nagf_machine_real_smallest
The smallest positive model number
Related keywords: machine constants
smoothing D06CAF   20  nagf_mesh_2d_smooth_bary
Uses a barycentering technique to smooth a given mesh
Related keywords: barycenteringbarycentricmesh generation
E02BEF   13  nagf_fit_1dspline_auto
Least squares cubic spline curve fit, automatic knot placement
Related keywords: B-splinescubic splinescurve and surface fittingleast squares
E02DCF   13  nagf_fit_2dspline_grid
Least squares surface fit by bicubic splines with automatic knot placement, data on rectangular grid
Related keywords: bicubic splinesB-splinescurve and surface fittingleast squarestwo-dimensional spline approximation
E02DDF   13  nagf_fit_2dspline_sctr
Least squares surface fit by bicubic splines with automatic knot placement, scattered data
Related keywords: bicubic splinesB-splinescurve and surface fittingleast squaresscattered data
G10ABF   16  nagf_smooth_fit_spline
Fit cubic smoothing spline, smoothing parameter given
Related keywords: Smoothing in Statisticsspline
G10ACF   16  nagf_smooth_fit_spline_parest
Fit cubic smoothing spline, smoothing parameter estimated
Related keywords: Smoothing in Statisticsspline
G10CAF   16  nagf_smooth_data_runningmedian
Compute smoothed data sequence using running median smoothers
Related keywords: running medianSmoothing in StatisticsTukey's smoothing
G13CAF   10  nagf_tsa_uni_spectrum_lag
Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: Bartlett lag windowbig datadata analyticsfinanceParzen lag windowrectangular lag windowtime seriestime series analysisTukey lag windowunivariate time series
G13CBF   10  nagf_tsa_uni_spectrum_daniell
Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window
Related keywords: big dataDaniell windowdata analyticsfinancespectral smoothingtime seriestime series analysistrapezium frequency windowunivariate time series
G13CCF   10  nagf_tsa_multi_spectrum_lag
Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: Bartlett lag windowbig datacross-spectrumdata analyticsfinancemultivariate time seriesParzen lag windowrectangular lag windowtime seriestime series analysisTukey lag window
G13CDF   10  nagf_tsa_multi_spectrum_daniell
Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window
Related keywords: big datacross-spectrumDaniell windowdata analyticsfinancemultivariate time seriesspectral smoothingtime seriestime series analysistrapezium frequency window
Smoothing in Statistics G10 Chapter Introduction     Smoothing in Statistics
sn, Jacobian elliptic functions S21CAF   15  nagf_specfun_jacellip_real
Jacobian elliptic functions sn, cn and dn of real argument
Related keywords: approximations of special functionscn, Jacobian elliptic functiondn, Jacobian elliptic functionelliptic functionsfinanceJacobian elliptic functions
S21CBF   20  nagf_specfun_jacellip_complex
Jacobian elliptic functions sn, cn and dn of complex argument
Related keywords: approximations of special functionscn, Jacobian elliptic functiondn, Jacobian elliptic functionelliptic functionsfinanceJacobian elliptic functions
Sobol G05YNF   22  nagf_rand_quasi_init_scrambled
Initializes a scrambled quasi-random number generator
Related keywords: big datadata analyticsFaure–TezukafinanceNiederreiterOwenrandom number generatorsrandom numbersscramble
Sobol, quasi-random numbers G05YJF   21  nagf_rand_quasi_normal
Generates a Normal quasi-random number sequence
Related keywords: big datadata analyticsFaure, quasi-random numbersGaussian distributionlow-discrepancy sequencesNiederreiter method, quasi-random numbersNormal distributionquasi-random numbersrandom number generatorsrandom numbers
G05YKF   21  nagf_rand_quasi_lognormal
Generates a log-normal quasi-random number sequence
Related keywords: big datadata analyticsFaure, quasi-random numberslog-normal distributionlow-discrepancy sequencesNiederreiter method, quasi-random numbersquasi-random numbersrandom number generatorsrandom numbers
G05YLF   22  nagf_rand_quasi_init
Initializes a quasi-random number generator
Related keywords: big datadata analyticsFaure, quasi-random numbersfinancelow-discrepancy sequencesNiederreiter method, quasi-random numbersquasi-random numbersrandom number generatorsrandom numbersrectangular distributionuniform distribution
sort E02ZAF   nagf_fit_2dspline_sort
Sort two-dimensional data into panels for fitting bicubic splines
Related keywords: curve and surface fittinggridded datatwo-dimensional spline approximation
M01CAF   12  nagf_sort_realvec_sort
Sort a vector, real numbers
Related keywords: big datadata analyticsquicksort, doublesearchingsorting
M01CBF   12  nagf_sort_intvec_sort
Sort a vector, integer numbers
Related keywords: big datadata analyticssearchingsorting
M01CCF   12  nagf_sort_charvec_sort
Sort a vector, character data
Related keywords: big datadata analyticssearchingsorting
sorting M01 Chapter Introduction     Sorting and Searching
Related keywords: big datadata analyticssearching
sparse D01ESF   25  nagf_quad_md_sgq_multi_vec
Multi-dimensional quadrature using sparse grids
Related keywords: automaticmultidimensionalmultiple integrandsquadraturevectorized
F11YEF   25  nagf_sparse_sym_rcm
Reverse Cuthill–McKee reordering of a sparse symmetric matrix in CCS format
Related keywords: big datacomplex, symmetric matrixdata analyticslarge scale linear systemspermutationreal, symmetric matrixsparse matrix
sparse convex QP prolem E04NQF   21  nagf_opt_qpconvex2_sparse_solve
Linear programming (LP) or convex quadratic programming (QP), sparse, active-set method, recommended
Related keywords: active-set methodfinanceLP, linear programmingmaximizing a functionminimizing a functionoptimizationQP, quadratic programmingservice routine
sparse eigenproblem F02FKF   25  nagf_eigen_real_symm_sparse_arnoldi
Selected eigenvalues and eigenvectors of a real symmetric sparse matrix
Related keywords: big datadata analyticseigenproblemeigenvalueseigenvalueseigenvectorseigenvectorslarge scale eigenproblemsmatrix, sparsereal, sparse, symmetric matrix
F12ABF   21  nagf_sparseig_real_iter
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, reverse communication
Related keywords: big datadata analyticseigenproblemeigenvalueseigenvectorslarge scale eigenproblemsreal, sparse matrix
F12ACF   21  nagf_sparseig_real_proc
Selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse eigenproblem, postprocessing for F12ABF
Related keywords: big datadata analyticseigenproblemeigenvalueseigenvectorslarge scale eigenproblemsreal, sparse matrix
F12APF   21  nagf_sparseig_complex_iter
Selected eigenvalues and, optionally, eigenvectors of a complex sparse eigenproblem, reverse communication
Related keywords: big datacomplex, sparse matrixdata analyticseigenvalueseigenvectorslarge scale eigenproblemssparse generalized eigenproblem
F12FBF   21  nagf_sparseig_real_symm_iter
Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, reverse communication
Related keywords: big datadata analyticseigenvalueseigenvectorslarge scale eigenproblemsreal, sparse, symmetric matrix
sparse eigenproblem, monitoring F12FEF   21  nagf_sparseig_real_symm_monit
Provides monitoring information for F12FBF
Related keywords: big datadata analyticslarge scale eigenproblemsreal, sparse, symmetric matrix
sparse eigenproblem, options F12ADF   21  nagf_sparseig_real_option
Set a single option from a string (F12ABF/F12ACF/F12AGF)
Related keywords: big datadata analyticslarge scale eigenproblemsreal, sparse matrix
F12ARF   21  nagf_sparseig_complex_option
Set a single option from a string (F12APF/F12AQF)
Related keywords: big datacomplex, sparse matrixdata analyticslarge scale eigenproblems
F12FDF   21  nagf_sparseig_real_symm_option
Set a single option from a string (F12FBF/F12FCF/F12FGF)
Related keywords: big datadata analyticslarge scale eigenproblemsreal, sparse, symmetric matrix
sparse eigenproblem, postprocessing F12AQF   21  nagf_sparseig_complex_proc
Selected eigenvalues and, optionally, eigenvectors of a complex sparse eigenproblem, postprocessing for F12APF
Related keywords: big datacomplex, sparse matrixdata analyticslarge scale eigenproblems
F12FCF   21  nagf_sparseig_real_symm_proc
Selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse eigenproblem, postprocessing for F12FBF
Related keywords: big datadata analyticslarge scale eigenproblemsreal, sparse, symmetric matrix
sparse eigenproblems, monitoring F12AEF   21  nagf_sparseig_real_monit
Provides monitoring information for F12ABF
Related keywords: big datadata analyticseigenproblemlarge scale eigenproblemsmonitoring informationreal, sparse matrix
F12ASF   21  nagf_sparseig_complex_monit
Provides monitoring information for F12APF
Related keywords: big datacomplex, sparse matrixdata analyticseigenproblemlarge scale eigenproblemsmonitoring information
sparse generalized eigenproblem F12APF   21  nagf_sparseig_complex_iter
Selected eigenvalues and, optionally, eigenvectors of a complex sparse eigenproblem, reverse communication
Related keywords: big datacomplex, sparse matrixdata analyticseigenvalueseigenvectorslarge scale eigenproblemssparse eigenproblem
sparse linear equations F01BRF   nagf_matop_real_gen_sparse_lu
L U factorization of real sparse matrix
Related keywords: inversionLU decompositionmatrix operationsreal, sparse matrix
F01BSF   nagf_matop_real_gen_sparse_lu_reuse
L U factorization of real sparse matrix with known sparsity pattern
Related keywords: inversionLU decompositionmatrix operationsreal, sparse matrix
F11JQF   19  nagf_sparse_complex_herm_solve_ilu
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JNF (Black Box)
Related keywords: big datacomplex, Hermitian, sparse matrixconjugate gradient methoddata analyticsiterative methods, linear equationsLanczos method, linear equationslarge scale linear systemslinear equations, iterative method
F11JRF   19  nagf_sparse_complex_herm_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse Hermitian matrix
Related keywords: big datacomplex, Hermitian, sparse matrixdata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodSSOR method, symmetric successive over-relaxation
F11JSF   19  nagf_sparse_complex_herm_solve_jacssor
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big datacomplex, Hermitian, sparse matrixconjugate gradient methoddata analyticsiterative methods, linear equationsJacobi methodLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodSSOR method, symmetric successive over-relaxation
sparse linear system F11MEF   21  nagf_sparse_direct_real_gen_lu
L U factorization of real sparse matrix
Related keywords: big datadata analyticsdiscretised systemlarge scale linear systemsLU decompositionreal, sparse matrix
F11MFF   21  nagf_sparse_direct_real_gen_solve
Solution of real sparse simultaneous linear equations (coefficient matrix already factorized)
Related keywords: big datadata analyticsdiscretised systemlarge scale linear systemslinear equationsreal, sparse matrix
sparse matrix F11YEF   25  nagf_sparse_sym_rcm
Reverse Cuthill–McKee reordering of a sparse symmetric matrix in CCS format
Related keywords: big datacomplex, symmetric matrixdata analyticslarge scale linear systemspermutationreal, symmetric matrixsparse
sparse nonlinear system C05QSF   23  nagf_roots_sparsys_func_easy
Solution of a sparse system of nonlinear equations using function values only (easy-to-use)
Related keywords: discretised systemroot-findingroots of transcendental equationszeros of transcendental functions
sparsity pattern D06CBF   20  nagf_mesh_2d_sparsity
Generates a sparsity pattern of a Finite Element matrix associated with a given mesh
Related keywords: finite elementmesh generation
sparsity structure E04VJF   21  nagf_opt_nlp2_sparse_jacobian
Determine the pattern of nonzeros in the Jacobian matrix for E04VHF
Related keywords: financemaximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationSQP
Spearman's rank correlation coefficients G02BNF   nagf_correg_coeffs_kspearman_overwrite
Kendall/Spearman non-parametric rank correlation coefficients, no missing values, overwriting input data
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinanceKendall's tau correlation coefficientnonlinear regressionpolynomial regressionregression analysis
G02BPF   nagf_correg_coeffs_kspearman_miss_case_overwrite
Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinanceKendall's tau correlation coefficientmissing valuesnonlinear regressionpolynomial regressionregression analysis
G02BQF   nagf_correg_coeffs_kspearman
Kendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinanceKendall's tau correlation coefficientnonlinear regressionpolynomial regressionregression analysis
G02BRF   nagf_correg_coeffs_kspearman_miss_case
Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinanceKendall's tau correlation coefficientmissing valuesnonlinear regressionpolynomial regressionregression analysis
G02BSF   nagf_correg_coeffs_kspearman_miss_pair
Kendall/Spearman non-parametric rank correlation coefficients, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation coefficientsdata analyticsfinanceKendall's tau correlation coefficientmissing valuesnonlinear regressionpolynomial regressionregression analysis
specification G22YAF   26  nagf_blgm_lm_formula
Specify a linear model via a formula string
Related keywords: regression
spectral smoothing G13CBF   10  nagf_tsa_uni_spectrum_daniell
Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window
Related keywords: big dataDaniell windowdata analyticsfinancesmoothingtime seriestime series analysistrapezium frequency windowunivariate time series
G13CDF   10  nagf_tsa_multi_spectrum_daniell
Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window
Related keywords: big datacross-spectrumDaniell windowdata analyticsfinancemultivariate time seriessmoothingtime seriestime series analysistrapezium frequency window
spline E02JDF   24  nagf_fit_2dspline_ts_sctr
Spline approximation to a set of scattered data using a two-stage approximation method
Related keywords: curve and surface fittingscattered datatwo-dimensional spline approximation
E02JEF   24  nagf_fit_2dspline_ts_evalv
Evaluation at a vector of points of a spline computed by E02JDF
Related keywords: curve and surface fittingscattered datatwo-dimensional spline approximation
E02JFF   24  nagf_fit_2dspline_ts_evalm
Evaluation at a mesh of points of a spline computed by E02JDF
Related keywords: curve and surface fittinggridded datascattered datatwo-dimensional spline approximation
G10ABF   16  nagf_smooth_fit_spline
Fit cubic smoothing spline, smoothing parameter given
Related keywords: smoothingSmoothing in Statistics
G10ACF   16  nagf_smooth_fit_spline_parest
Fit cubic smoothing spline, smoothing parameter estimated
Related keywords: smoothingSmoothing in Statistics
Split Cholesky factorization F08UTF   19  nagf_lapackeig_zpbstf
Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandZPBSTF
SQP E04UCF   12  nagf_opt_nlp1_solve_old
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: densefinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationsequential QP method
E04UDF   12  nagf_opt_nlp1_option_file_old
Supply values for E04UCF or E04UFF from external file
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationoptions, computational
E04UEF   12  nagf_opt_nlp1_option_string_old
Supply values to E04UCF or E04UFF from a character string
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationoptions, computational
E04UFF   18  nagf_opt_nlp1_rcomm_old
Nonlinear programming (NLP), dense, active-set, SQP method, using function values and optionally first derivatives (reverse communication, comprehensive)
Related keywords: densefinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationsequential QP method
E04UGF   19  nagf_opt_nlp1_sparse_solve_old
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives
Related keywords: financemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationsequential QP method
E04UHF   19  nagf_opt_nlp1_sparse_option_file_old
Supply values for E04UGF from external file
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationoptions, computational
E04UJF   19  nagf_opt_nlp1_sparse_option_string_old
Supply values to E04UGF from a character string
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationoptions, computational
E04UQF   14  nagf_opt_lsq_gencon_deriv_option_file_old
Supply values for E04USF from external file
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationoptions, computationalsum of squares
E04URF   14  nagf_opt_lsq_gencon_deriv_option_string_old
Supply values to E04USF from a character string
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationoptions, computationalsum of squares
E04VGF   21  nagf_opt_nlp2_sparse_init
Initialization routine for E04VHF
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationoptions, computational
E04VHF   21  nagf_opt_nlp2_sparse_solve
Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives, recommended
Related keywords: financeLP, linear programmingmaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationquasi-Newton algorithmsequential QP methodsimplex algorithm
E04VJF   21  nagf_opt_nlp2_sparse_jacobian
Determine the pattern of nonzeros in the Jacobian matrix for E04VHF
Related keywords: financemaximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationsparsity structure
E04VKF   21  nagf_opt_nlp2_sparse_option_file
Supply values for E04VHF from external file
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationoptions, computational
E04VLF   21  nagf_opt_nlp2_sparse_option_string
Set a single option for E04VHF from a character string
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationoptions, computational
E04VMF   21  nagf_opt_nlp2_sparse_option_integer_set
Set a single option for E04VHF from an integer argument
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationoptions, computational
E04VNF   21  nagf_opt_nlp2_sparse_option_double_set
Set a single option for E04VHF from a real argument
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationoptions, computational
E04VRF   21  nagf_opt_nlp2_sparse_option_integer_get
Get the setting of an integer valued option of E04VHF
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationoptions, computational
E04VSF   21  nagf_opt_nlp2_sparse_option_double_get
Get the setting of a real valued option of E04VHF
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionoptimizationoptions, computational
E04WDF   21  nagf_opt_nlp2_solve
Nonlinear programming (NLP), dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: densefinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationsequential QP method
E04WEF   21  nagf_opt_nlp2_option_file
Supply values for E04WDF from external file
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationoptions, computational
E04WFF   21  nagf_opt_nlp2_option_string
Set a single option for E04WDF from a character string
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationoptions, computational
E04WGF   21  nagf_opt_nlp2_option_integer_set
Set a single option for E04WDF from an integer argument
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationoptions, computational
E04WHF   21  nagf_opt_nlp2_option_double_set
Set a single option for E04WDF from a real argument
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationoptions, computational
E04WKF   21  nagf_opt_nlp2_option_integer_get
Get the setting of an integer valued option of E04WDF
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationoptions, computational
E04WLF   21  nagf_opt_nlp2_option_double_get
Get the setting of a real valued option of E04WDF
Related keywords: maximizing a functionminimizing a functionNLPnonlinear programmingoptimizationoptions, computational
SQP, sequential quadratic programming H02DAF   25  nagf_mip_sqp
Mixed integer nonlinear programming
Related keywords: integer programminginteger quadratic programmixed integer programmingnonlinear programmingoperations research
squared coherency G13CEF   10  nagf_tsa_multi_spectrum_bivar
Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra
Related keywords: big databivariate spectracoherency, squared, time seriescross amplitude spectrumdata analyticsfinancemultivariate time seriestime seriestime series analysis
square root, complex A02AAF   nagf_complex_sqrt
Square root of complex number
Related keywords: complex arithmetic
SSOR method, successive over-relaxation F11DDF   18  nagf_sparse_real_gen_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse nonsymmetric matrix
Related keywords: big datadata analyticslarge scale linear systemslinear equations, pre-conditionersreal, sparse matrix
SSOR method, symmetric successive over-relaxation F11DEF   18  nagf_sparse_real_gen_solve_jacssor
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsJacobi preconditioninglarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11DRF   19  nagf_sparse_complex_gen_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse non-Hermitian matrix
Related keywords: big datacomplex, sparse matrixdata analyticslarge scale linear systemslinear equations, pre-conditioners
F11DSF   19  nagf_sparse_complex_gen_solve_jacssor
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsiterative methods, linear equationsJacobi preconditioninglarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodTFQMR, transpose-free quasi-minimal residual method
F11JDF   17  nagf_sparse_real_symm_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse symmetric matrix
Related keywords: big datadata analyticslarge scale linear systemslinear equations, pre-conditionersreal, sparse, symmetric matrix
F11JEF   17  nagf_sparse_real_symm_solve_jacssor
Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsJacobi preconditioningLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse, symmetric matrix
F11JRF   19  nagf_sparse_complex_herm_precon_ssor_solve
Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse Hermitian matrix
Related keywords: big datacomplex, Hermitian, sparse matrixdata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodsparse linear equations
F11JSF   19  nagf_sparse_complex_herm_solve_jacssor
Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: big datacomplex, Hermitian, sparse matrixconjugate gradient methoddata analyticsiterative methods, linear equationsJacobi methodLanczos method, linear equationslarge scale linear systemslinear equations, iterative methodsparse linear equations
standard deviation G01ADF   nagf_stat_summary_freq
Mean, variance, skewness, kurtosis, etc., one variable, from frequency table
Related keywords: financekurtosismeanSimple Calculations on Statistical Dataskewness
G01ATF   24  nagf_stat_summary_onevar
Computes univariate summary information: mean, variance, skewness, kurtosis
Related keywords: big datadata analyticsdata streamkurtosismaximum valuemeanminimum valueSimple Calculations on Statistical Dataskewnessstreaming
G01WAF   24  nagf_stat_moving_average
Computes the mean and standard deviation using a rolling window
Related keywords: big datadata analyticsdata streammeanmoving averageSimple Calculations on Statistical Datastreaming
G02BDF   nagf_correg_coeffs_zero
Correlation-like coefficients (about zero), all variables, no missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysissum of squares
G02BEF   nagf_correg_coeffs_zero_miss_case
Correlation-like coefficients (about zero), all variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysissum of squares
G02BFF   nagf_correg_coeffs_zero_miss_pair
Correlation-like coefficients (about zero), all variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysissum of squares
G02BGF   nagf_correg_coeffs_pearson_subset
Pearson product-moment correlation coefficients, subset of variables, no missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeannonlinear regressionPearson product moment correlationpolynomial regressionregression analysissum of squares
G02BHF   nagf_correg_coeffs_pearson_subset_miss_case
Pearson product-moment correlation coefficients, subset of variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionPearson product moment correlationpolynomial regressionregression analysissum of squares
G02BJF   nagf_correg_coeffs_pearson_subset_miss_pair
Pearson product-moment correlation coefficients, subset of variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionPearson product moment correlationpolynomial regressionregression analysissum of squares
G02BKF   nagf_correg_coeffs_zero_subset
Correlation-like coefficients (about zero), subset of variables, no missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysissum of squares
G02BLF   nagf_correg_coeffs_zero_subset_miss_case
Correlation-like coefficients (about zero), subset of variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysissum of squares
G02BMF   nagf_correg_coeffs_zero_subset_miss_pair
Correlation-like coefficients (about zero), subset of variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysissum of squares
G02BXF   14  nagf_correg_corrmat
Computes (optionally weighted) correlation and covariance matrices
Related keywords: big datacorrelation analysisdata analyticsfinancemeannonlinear regressionPearson product moment correlationpolynomial regressionregression analysisvariance-covariance matrix
G07DAF   13  nagf_univar_robust_1var_median
Robust estimation, median, median absolute deviation, robust standard deviation
Related keywords: meanmedianrobust estimationunivariate estimation
G13AJF   10  nagf_tsa_uni_arima_forcecast
Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model
Related keywords: big datadata analyticsfinanceforecastingtime seriestime series analysisunivariate time series
G13AUF   14  nagf_tsa_uni_means
Computes quantities needed for range-mean or standard deviation-mean plot
Related keywords: big datadata analyticsfinancemeanrangerange-mean plottime seriestime series analysis
standard errors G02DCF   14  nagf_correg_linregm_obs_edit
Add/delete an observation to/from a general linear regression model
Related keywords: big datacorrelation analysisdata analyticsfinancelinear regressionnonlinear regressionpolynomial regressionregressionregression analysisvariance-covariance matrix
G02DKF   14  nagf_correg_linregm_constrain
Estimates and standard errors of parameters of a general linear regression model for given constraints
Related keywords: big datacorrelation analysisdata analyticsfinancelinear regressionnonlinear regressionpolynomial regressionregression analysis
G02GKF   14  nagf_correg_glm_constrain
Estimates and standard errors of parameters of a general linear model for given constraints
Related keywords: big datacorrelation analysisdata analyticsfinancegeneralized linear modelnonlinear regressionpolynomial regressionregression analysis
G02GPF   22  nagf_correg_glm_predict
Computes a predicted value and its associated standard error based on a previously fitted generalized linear model
Related keywords: big datacorrelation analysisdata analyticsfinancegeneralized linear modelnonlinear regressionpolynomial regressionpredicted valueregression analysis
G04BBF   16  nagf_anova_random
Analysis of variance, randomized block or completely randomized design, treatment means and standard errors
Related keywords: analysis of varianceANOVAcompletely randomized designrandomized block designtreatment means
G04BCF   17  nagf_anova_rowcol
Analysis of variance, general row and column design, treatment means and standard errors
Related keywords: analysis of varianceANOVAtreatment means
G04CAF   16  nagf_anova_factorial
Analysis of variance, complete factorial design, treatment means and standard errors
Related keywords: analysis of varianceANOVAfactorial designtreatment means
G13ASF   13  nagf_tsa_uni_arima_resid
Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF
Related keywords: ARMAautocorrelation functionbig dataBox–Jenkins modelsBox–Ljung portmanteau statisticdata analyticsfinancesignificancetime seriestime series analysisunivariate time series
G13CGF   10  nagf_tsa_multi_noise_bivar
Multivariate time series, noise spectrum, bounds, impulse response function and its standard error
Related keywords: big datadata analyticsfinanceimpulse response functionmultivariate time seriesnoise spectrumtime seriestime series analysis
G13DDF   22  nagf_tsa_multi_varma_estimate
Multivariate time series, estimation of VARMA model
Related keywords: big datacorrelation matrixdata analyticsfinancemaximum likelihoodmultivariate time seriestime seriestime series analysisVARMA, vector autoregressive moving average model
G13DJF   15  nagf_tsa_multi_varma_forecast
Multivariate time series, forecasts and their standard errors
Related keywords: big datadata analyticsfinanceforecastingmultivariate time seriestime seriestime series analysis
G13DKF   15  nagf_tsa_multi_varma_update
Multivariate time series, updates forecasts and their standard errors
Related keywords: big datadata analyticsfinanceforecastingmultivariate time seriestime seriestime series analysis
standardized residuals G02FAF   14  nagf_correg_linregm_stat_resinf
Calculates standardized residuals and influence statistics
Related keywords: big datacorrelation analysisdata analyticsfinanceinfluence statisticsnonlinear regressionpolynomial regressionregression analysis
standardized values G03ZAF   15  nagf_mv_z_scores
Produces standardized values ( z -scores) for a data matrix
Related keywords: multivariate methodsz-scores
stationary C09DAF   25  nagf_wav_1d_mxolap_fwd
One-dimensional maximal overlap discrete wavelet transform (MODWT)
Related keywords: discretemaximal-overlapwavelet transforms
C09DBF   25  nagf_wav_1d_mxolap_inv
One-dimensional inverse maximal overlap discrete wavelet transform (IMODWT)
Related keywords: discreteinversemaximal-overlapwavelet transforms
C09DCF   25  nagf_wav_1d_mxolap_multi_fwd
One-dimensional multi-level maximal overlap discrete wavelet transform (MODWT)
Related keywords: discretemaximal-overlapmulti-levelwavelet transforms
C09DDF   25  nagf_wav_1d_mxolap_multi_inv
One-dimensional inverse multi-level maximal overlap discrete wavelet transform (IMODWT)
Related keywords: discreteinversemaximal-overlapmulti-levelwavelet transforms
statistical distribution functions G01EWF   25  nagf_stat_prob_dickey_fuller_unit
Computes probabilities for the Dickey–Fuller unit root test
Related keywords: Dickey–Fuller probabilitiesSimple Calculations on Statistical Dataunit root
stem stem and leaf plot G01ARF   14  nagf_stat_plot_stem_leaf
Constructs a stem and leaf plot
Related keywords: Simple Calculations on Statistical Data
stepping stone algorithm H03ABF   nagf_mip_transportation
Transportation problem, modified stepping stone method
Related keywords: operations researchtransportation problem
stepwise linear regression G02EFF   21  nagf_correg_linregm_fit_stepwise
Stepwise linear regression
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysis
stiff differential equations D02EJF   12  nagf_ode_ivp_bdf_zero_simple
Ordinary differential equations, stiff initial value problem, backward differentiation formulae method, until function of solution is zero, intermediate output (simple driver)
Related keywords: backward difference formulaBDF, backward differentiation formulainitial value problemIVP, initial value problemODE, ordinary differential equations
D02MCF   22  nagf_ode_dae_dassl_cont
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method continuation for D02NEF
Related keywords: DAE, differential algebraic equationsDASSL, ordinary differential equationsimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equations
D02MVF   14  nagf_ode_ivp_stiff_dassl
Ordinary differential equations, initial value problem, DASSL method, setup for d02m–n routines
Related keywords: DASSL, ordinary differential equationsimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equations
D02MWF   22  nagf_ode_dae_dassl_setup
Implicit ordinary differential equations/DAEs, initial value problem, setup for D02NEF
Related keywords: DASSL, ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equations
D02NBF   12  nagf_ode_ivp_stiff_exp_fulljac
Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
Related keywords: backward difference formulainitial value problemIVP, initial value problemJacobianODE, ordinary differential equations
D02NCF   12  nagf_ode_ivp_stiff_exp_bandjac
Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulainitial value problemJacobianODE, ordinary differential equations
D02NDF   12  nagf_ode_ivp_stiff_exp_sparjac
Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulainitial value problemIVP, initial value problemODE, ordinary differential equations
D02NGF   12  nagf_ode_ivp_stiff_imp_fulljac
Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulaimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemJacobianODE, ordinary differential equations
D02NHF   12  nagf_ode_ivp_stiff_imp_bandjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulaimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemJacobianODE, ordinary differential equations
D02NJF   12  nagf_ode_ivp_stiff_imp_sparjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formuladiscretised systemimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemJacobianODEODE, ordinary differential equations
D02NMF   12  nagf_ode_ivp_stiff_exp_revcom
Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
Related keywords: backward difference formulaBDF, backward differentiation formulainitial value problemIVP, initial value problemODE, ordinary differential equations
D02NNF   12  nagf_ode_ivp_stiff_imp_revcom
Implicit/algebraic ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
Related keywords: backward difference formulaimplicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equations
D02NPF   22  nagf_ode_dae_dassl_linalg
Implicit ordinary differential equations/DAEs, initial value problem linear algebra setup routine for D02NEF
Related keywords: implicit algebraic ordinary differential equationsinitial value problemIVP, initial value problemODE, ordinary differential equations
D02NRF   12  nagf_ode_ivp_stiff_sparjac_enq
Ordinary differential equations, initial value problem, for use with d02m–n routines, sparse Jacobian, enquiry routine
Related keywords: initial value problemODE, ordinary differential equations
D02NSF   12  nagf_ode_ivp_stiff_fulljac_setup
Ordinary differential equations, initial value problem, for use with d02m–n routines, full Jacobian, linear algebra set up
Related keywords: initial value problemODE, ordinary differential equations
D02NTF   12  nagf_ode_ivp_stiff_bandjac_setup
Ordinary differential equations, initial value problem, for use with d02m–n routines, banded Jacobian, linear algebra set up
Related keywords: initial value problemODE, ordinary differential equations
D02NUF   12  nagf_ode_ivp_stiff_sparjac_setup
Ordinary differential equations, initial value problem, for use with d02m–n routines, sparse Jacobian, linear algebra set up
Related keywords: initial value problemODE, ordinary differential equations
D02NVF   12  nagf_ode_ivp_stiff_bdf
Ordinary differential equations, initial value problem, backward differentiation formulae method, setup for d02m–n routines
Related keywords: backward difference formulainitial value problemODE, ordinary differential equations
D02NWF   12  nagf_ode_ivp_stiff_blend
Ordinary differential equations, initial value problem, Blend method, setup for d02m–n routines
Related keywords: Blend methodinitial value problemODE, ordinary differential equations
D02NXF   12  nagf_ode_ivp_stiff_sparjac_diag
Ordinary differential equations, initial value problem, sparse Jacobian, linear algebra diagnostics, for use with d02m–n routines
Related keywords: initial value problemODE, ordinary differential equations
D02NYF   12  nagf_ode_ivp_stiff_integ_diag
Ordinary differential equations, initial value problem, integrator diagnostics, for use with d02m–n routines
Related keywords: initial value problemODE, ordinary differential equations
D02NZF   12  nagf_ode_ivp_stiff_contin
Ordinary differential equations, initial value problem, setup for continuation calls to integrator, for use with d02m–n routines
Related keywords: initial value problemODE, ordinary differential equations
stochastic volatility S30NCF   25  nagf_specfun_opt_heston_term
Heston's model option pricing with term structure
Related keywords: approximations of special functionsEuropeanfinanceHestonterm structure
Stone's strongly implicit procedure D03EBF   nagf_pde_2d_ellip_fd
Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, iterate to convergence
Related keywords: elliptic partial differential equationsLaplace's equationPDE, partial differential equations
D03ECF   nagf_pde_3d_ellip_fd
Elliptic PDE, solution of finite difference equations by SIP for seven-point three-dimensional molecule, iterate to convergence
Related keywords: cuboidelliptic partial differential equationsLaplace's equationPDE, partial differential equations
D03UAF   nagf_pde_2d_ellip_fd_iter
Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, one iteration
Related keywords: elliptic partial differential equationsfive-point stencilPDE, partial differential equations
D03UBF   nagf_pde_3d_ellip_fd_iter
Elliptic PDE, solution of finite difference equations by SIP, seven-point three-dimensional molecule, one iteration
Related keywords: elliptic partial differential equationsPDE, partial differential equationsseven-point stencil
stop at roots D02CJF   13  nagf_ode_ivp_adams_zero_simple
Ordinary differential equations, initial value problem, Adams' method, until function of solution is zero, intermediate output (simple driver)
Related keywords: Adams' methodfirst-order systeminitial value problemIVP, initial value problemNonstiffODE, ordinary differential equations
stratified data G11CAF   19  nagf_contab_condl_logistic
Returns parameter estimates for the conditional analysis of stratified data
Related keywords: conditional logistic analysiscontingency table analysislogistic analysisparameter estimates
streaming G01ANF   23  nagf_stat_quantiles_stream_fixed
Calculates approximate quantiles from a data stream of known size
Related keywords: big datadata analyticsdata streamquantilesSimple Calculations on Statistical Data
G01APF   23  nagf_stat_quantiles_stream_arbitrary
Calculates approximate quantiles from a data stream of unknown size
Related keywords: big datadata analyticsdata streamquantilesSimple Calculations on Statistical Data
G01ATF   24  nagf_stat_summary_onevar
Computes univariate summary information: mean, variance, skewness, kurtosis
Related keywords: big datadata analyticsdata streamkurtosismaximum valuemeanminimum valueSimple Calculations on Statistical Dataskewnessstandard deviation
G01AUF   24  nagf_stat_summary_onevar_combine
Combines multiple sets of summary information, for use after G01ATF
Related keywords: big datadata analyticsdata streamSimple Calculations on Statistical Datasummary information
G01WAF   24  nagf_stat_moving_average
Computes the mean and standard deviation using a rolling window
Related keywords: big datadata analyticsdata streammeanmoving averageSimple Calculations on Statistical Datastandard deviation
G02BZF   24  nagf_correg_ssqmat_combine
Combines two sums of squares matrices, for use after G02BUF
Related keywords: big datacorrelation analysiscross-productsdata analyticsdata streammeannonlinear regressionpolynomial regressionregression analysissum of squares
G13MEF   24  nagf_tsa_inhom_iema
Computes the iterated exponential moving average for a univariate inhomogeneous time series
Related keywords: big datadata analyticsdata streamexponential moving averagemoving averagetime seriestime series analysisunivariate time series
G13MFF   24  nagf_tsa_inhom_iema_all
Computes the iterated exponential moving average for a univariate inhomogeneous time series, intermediate results are also returned
Related keywords: big datadata analyticsdata streamexponential moving averagemoving averagetime seriestime series analysisunivariate time series
G13MGF   24  nagf_tsa_inhom_ma
Computes the exponential moving average for a univariate inhomogeneous time series
Related keywords: big datadata analyticsdata streamexponential moving averagemoving averagetime seriestime series analysisunivariate time series
Struve function S17GAF   26  nagf_specfun_struve_h0
Struve function of order 0 , H 0 x
Related keywords: approximations of special functions H 0 x , Struve function
S17GBF   26  nagf_specfun_struve_h1
Struve function of order 1 , H 1 x
Related keywords: approximations of special functions H 1 x , Struve function
student's t-copula G05RCF   22  nagf_rand_copula_students_t
Generates a matrix of pseudorandom numbers from a Student's t -copula
Related keywords: big datacopuladata analyticsfinancerandom number generatorsrandom numbers
Student's t -distribution G01EBF   14  nagf_stat_prob_students_t
Computes probabilities for Student's t -distribution
Related keywords: CDF, cumulative distribution functionfinancelower tail probabilityprobabilitySimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01FBF   14  nagf_stat_inv_cdf_students_t
Computes deviates for Student's t -distribution
Related keywords: deviatesfinanceinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G01GBF   14  nagf_stat_prob_students_t_noncentral
Computes probabilities for the non-central Student's t -distribution
Related keywords: financelower tail probabilitySimple Calculations on Statistical Data
G01HCF   23  nagf_stat_prob_bivariate_students_t
Computes probabilities for the bivariate Student's t -distribution
Related keywords: bivariate Student's t -distributionprobabilitySimple Calculations on Statistical Data
G01HDF   24  nagf_stat_prob_multi_students_t
Computes the probability for the multivariate Student's t -distribution
Related keywords: multivariate Student's t -distributionprobabilitySimple Calculations on Statistical Data
G01SBF   24  nagf_stat_prob_students_t_vector
Computes a vector of probabilities for the Student's t -distribution
Related keywords: big dataCDF, cumulative distribution functionconfidence intervaldata analyticslower tail probabilitysignificanceSimple Calculations on Statistical Datatwo-tail probabilityupper tail probability
G01TBF   24  nagf_stat_inv_cdf_students_t_vector
Computes a vector of deviates for Student's t -distribution
Related keywords: big datadata analyticsdeviatesinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
G05RYF   22  nagf_rand_multivar_students_t
Generates a matrix of pseudorandom numbers from a multivariate Student's t -distribution
Related keywords: big datadata analyticsfinancemultivariate Student's t -distributionrandom number generatorsrandom numbers
G05SNF   22  nagf_rand_dist_students_t
Generates a vector of pseudorandom numbers from a Student's t -distribution
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
Studentized range statistic G01EMF   15  nagf_stat_prob_studentized_range
Computes probability for the Studentized range statistic
Related keywords: CDF, cumulative distribution functionfinanceprobabilitySimple Calculations on Statistical Data
G01FMF   15  nagf_stat_inv_cdf_studentized_range
Computes deviates for the Studentized range statistic
Related keywords: deviatesfinanceinverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
Sturm–Liouville equations D02KAF   nagf_ode_sl2_reg_finite
Second-order Sturm–Liouville problem, regular system, finite range, eigenvalue only
Related keywords: boundary value problemBVPeigenproblemODE, ordinary differential equations
D02KDF   nagf_ode_sl2_breaks_vals
Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points
Related keywords: boundary value problemBVPeigenproblemgeneralODE, ordinary differential equations
D02KEF   nagf_ode_sl2_breaks_funs
Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points
Related keywords: boundary value problemBVPeigenproblemODE, ordinary differential equations
sub-sample G05PWF   25  nagf_rand_subsamp_xyw
Permutes a matrix, vector, vector triplet into a form suitable for random sub-sampling validation
Related keywords: big datacross-validationdata analyticspermuterandom number generatorsresample
subsetting, best H05AAF   24  nagf_mip_best_subset_given_size_revcomm
Best n subsets of size p (reverse communication)
Related keywords: best subsetoperations research
H05ABF   24  nagf_mip_best_subset_given_size
Best n subsets of size p (direct communication)
Related keywords: best subsetoperations research
sum, matrix F01CTF   14  nagf_matop_real_addsub
Sum or difference of two real matrices, optional scaling and transposition
Related keywords: inversionmatrix operationsreal, nonsymmetric matrixtranspose, matrix
F01CWF   14  nagf_matop_complex_addsub
Sum or difference of two complex matrices, optional scaling and transposition
Related keywords: complex, nonsymmetric matrixinversionmatrix operationstranspose, matrix
sum, vector F16DLF   22  nagf_blast_isum
Sum elements of integer vector
Related keywords: further linear algebra support routines
F16ECF   24  nagf_blast_daxpby
Real weighted vector addition
Related keywords: blasblas_daxpbyfurther linear algebra support routines
F16EHF   22  nagf_blast_dwaxpby
Real weighted vector addition preserving input
Related keywords: blasblas_dwaxpbyfurther linear algebra support routines
F16ELF   22  nagf_blast_dsum
Sum elements of real vector
Related keywords: blasblas_dsumfurther linear algebra support routines
F16GCF   24  nagf_blast_zaxpby
Complex weighted vector addition
Related keywords: blasblas_zaxpbyfurther linear algebra support routines
F16GHF   22  nagf_blast_zwaxpby
Complex weighted vector addition preserving input
Related keywords: blasblas_zwaxpbyfurther linear algebra support routines
F16GLF   22  nagf_blast_zsum
Sum elements of complex vector
Related keywords: blasblas_zsumfurther linear algebra support routines
summary information G01AUF   24  nagf_stat_summary_onevar_combine
Combines multiple sets of summary information, for use after G01ATF
Related keywords: big datadata analyticsdata streamSimple Calculations on Statistical Datastreaming
summation of series C06 Chapter Introduction     Summation of Series
C06SAF   26  nagf_sum_fast_gauss
Multidimensional fast Gauss transform
Related keywords: Fast Gauss Transform
sum of squares E04FFF   26  nagf_opt_handle_solve_dfls
Derivative-free (DFO) solver for a nonlinear least squares objective function with bounded variables
Related keywords: calibrationdata fittingderivative-free optimizationDFODFOmaximizing a functionminimizing a functionnonlinear least squaresnonlinear least squaresoptimizationoptimization
E04RMF   26  nagf_opt_handle_set_nlnls
Define a nonlinear least squares objective function to a problem initialized by E04RAF
Related keywords: calibrationdata fittingderivative-free optimizationDFOleast squares fittingmaximizationmaximizing a functionminimizing a functionminimizing or maximizing a functionNLPnonlinear least squaresoptimizationoptimizationoptimization
E04UQF   14  nagf_opt_lsq_gencon_deriv_option_file_old
Supply values for E04USF from external file
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationoptions, computationalSQP
E04URF   14  nagf_opt_lsq_gencon_deriv_option_string_old
Supply values to E04USF from a character string
Related keywords: maximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear programmingoptimizationoptions, computationalSQP
E04USF   14  nagf_opt_lsq_gencon_deriv_old
Minimum of a sum of squares, nonlinear constraints, dense, active-set SQP method, using function values and optionally first derivatives
Related keywords: data fittingfinancemaximizing a functionminimization, nonlinear constraintsminimizing a functionNLPnonlinear least squaresnonlinear programmingoptimizationquasi-Newton approximationsequential QP method
E05USF   24  nagf_glopt_nlp_multistart_sqp_lsq
Global optimization of a sum of squares problem using multi-start, nonlinear constraints
Related keywords: financeglobal optimizationmulti-start algorithmsequential QP method
G01ABF   nagf_stat_summary_2var
Means, corrected sums of squares and cross-products, etc., two variables, from raw data
Related keywords: cross-productsmaximum valuemeanminimum valueproduct-moment correlation coefficientsSimple Calculations on Statistical Data
G02BDF   nagf_correg_coeffs_zero
Correlation-like coefficients (about zero), all variables, no missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysisstandard deviation
G02BEF   nagf_correg_coeffs_zero_miss_case
Correlation-like coefficients (about zero), all variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviation
G02BFF   nagf_correg_coeffs_zero_miss_pair
Correlation-like coefficients (about zero), all variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviation
G02BGF   nagf_correg_coeffs_pearson_subset
Pearson product-moment correlation coefficients, subset of variables, no missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeannonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviation
G02BHF   nagf_correg_coeffs_pearson_subset_miss_case
Pearson product-moment correlation coefficients, subset of variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviation
G02BJF   nagf_correg_coeffs_pearson_subset_miss_pair
Pearson product-moment correlation coefficients, subset of variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviation
G02BKF   nagf_correg_coeffs_zero_subset
Correlation-like coefficients (about zero), subset of variables, no missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysisstandard deviation
G02BLF   nagf_correg_coeffs_zero_subset_miss_case
Correlation-like coefficients (about zero), subset of variables, casewise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviation
G02BMF   nagf_correg_coeffs_zero_subset_miss_pair
Correlation-like coefficients (about zero), subset of variables, pairwise treatment of missing values
Related keywords: big datacorrelation analysiscorrelation-like coefficientscross-productsdata analyticsfinancemeanmissing valuesnonlinear regressionpolynomial regressionregression analysisstandard deviation
G02BTF   14  nagf_correg_ssqmat_update
Update a weighted sum of squares matrix with a new observation
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysis
G02BUF   14  nagf_correg_ssqmat
Computes a weighted sum of squares matrix
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysisWest's WV2 algorithm
G02BZF   24  nagf_correg_ssqmat_combine
Combines two sums of squares matrices, for use after G02BUF
Related keywords: big datacorrelation analysiscross-productsdata analyticsdata streammeannonlinear regressionpolynomial regressionregression analysisstreaming
G02EAF   14  nagf_correg_linregm_rssq
Computes residual sums of squares for all possible linear regressions for a set of independent variables
Related keywords: big datacorrelation analysisdata analyticsnonlinear regressionpolynomial regressionregression analysis
G02ECF   14  nagf_correg_linregm_rssq_stat
Calculates R 2 and C P values from residual sums of squares
Related keywords: big datacorrelation analysis C P valuesdata analyticsnonlinear regressionpolynomial regression R 2 valuesregression analysis
G04DAF   17  nagf_anova_contrasts
Computes sum of squares for contrast between means
Related keywords: analysis of variancedesign of experimentsexperimental design
sum-of-squares minimization E04FCF   nagf_opt_lsq_uncon_mod_func_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (comprehensive)
Related keywords: data fittingderivative-free minimizationfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimization
E04FYF   18  nagf_opt_lsq_uncon_mod_func_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using function values only (easy-to-use)
Related keywords: data fittingderivative-free minimizationfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimization
E04GBF   nagf_opt_lsq_uncon_quasi_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (comprehensive)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmdata fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationquasi-Newton algorithm
E04GDF   nagf_opt_lsq_uncon_mod_deriv_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (comprehensive)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimization
E04GYF   18  nagf_opt_lsq_uncon_quasi_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use)
Related keywords: BFGS, Broyden, Fletcher, Goldfarb and Shanno algorithmdata fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionnonlinear least squaresoptimizationquasi-Newton algorithm
E04GZF   18  nagf_opt_lsq_uncon_mod_deriv_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using first derivatives (easy-to-use)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimization
E04HEF   nagf_opt_lsq_uncon_mod_deriv2_comp
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimization
E04HYF   18  nagf_opt_lsq_uncon_mod_deriv2_easy
Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use)
Related keywords: data fittingfinanceGauss–Newton optimizationmaximizing a functionminimization, unconstrainedminimizing a functionNewton algorithmnonlinear least squaresoptimization
supremum norm E02GCF   nagf_fit_glin_linf
L -approximation by general linear function
Related keywords: curve and surface fittingL(infinity) approximation
surface fitting E02ALF   25  nagf_fit_1d_minimax_polynomial
Minimax curve fit by polynomials
Related keywords: curve and surface fittingminimax
survival analysis G12 Chapter Introduction     Survival Analysis
SVD, generalized F08VAF   21  nagf_lapackeig_dggsvd
Computes the generalized singular value decomposition of a real matrix pair
Related keywords: DGGSVDeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08VCF   26  nagf_lapackeig_dggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair
Related keywords: DGGSVD3eigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08VEF   22  nagf_lapackeig_dggsvp
Produces orthogonal matrices that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
Related keywords: DGGSVPeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresorthogonal transformationsreal, m by n matrix
F08VGF   26  nagf_lapackeig_dggsvp3
Produces orthogonal matrices, using BLAS-3, that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
Related keywords: DGGSVP3eigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresorthogonal transformationsreal, m by n matrix
F08VNF   21  nagf_lapackeig_zggsvd
Computes the generalized singular value decomposition of a complex matrix pair
Related keywords: complex, nonsymmetric matrixeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresZGGSVD
F08VQF   26  nagf_lapackeig_zggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair
Related keywords: complex, nonsymmetric matrixeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresZGGSVD3
F08VSF   22  nagf_lapackeig_zggsvp
Produces unitary matrices that simultaneously reduce the complex, m by n , matrix A and the complex, p by n , matrix B to upper triangular form
Related keywords: complex, m by n matrixeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresorthogonal transformationsZGGSVP
F08VUF   26  nagf_lapackeig_zggsvp3
Produces unitary matrices, using BLAS-3, that simultaneously reduce the complex, m by n , matrix A and the complex, p by n , matrix B to upper triangular form
Related keywords: complex, m by n matrixeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresorthogonal transformationsZGGSVP3
F08YEF   22  nagf_lapackeig_dtgsja
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
Related keywords: DTGSJAeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresreal, trapezoidal matrixreal, triangular matrix
SVD, singular value decomposition F02WGF   22  nagf_eigen_real_gen_partialsvd
Computes leading terms in the singular value decomposition of a real general matrix; also computes corresponding left and right singular vectors
Related keywords: big datadata analyticseigenvalueseigenvectorsreal, m by n matrix
F02WUF   14  nagf_eigen_real_triang_svd
SVD of real upper triangular matrix (Black Box)
Related keywords: big datadata analyticseigenvalueseigenvectorsreal, triangular matrix
F02XUF   13  nagf_eigen_complex_triang_svd
SVD of complex upper triangular matrix (Black Box)
Related keywords: big datacomplex, triangular matrixdata analyticseigenvalueseigenvectors
F08KAF   21  nagf_lapackeig_dgelss
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
Related keywords: DGELSSeigenproblemLAPACKLAPACKleast squareslinear least squaresminimal least squaresreal, m by n matrix
F08KBF   21  nagf_lapackeig_dgesvd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
Related keywords: DGESVDeigenproblemfinanceLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08KCF   21  nagf_lapackeig_dgelsd
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
Related keywords: DGELSDdivide-and-conquer methodeigenproblemfinanceLAPACKLAPACKleast squareslinear least squaresminimal least squaresreal, m by n matrix
F08KDF   21  nagf_lapackeig_dgesdd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
Related keywords: DGESDDdivide-and-conquer methodeigenproblemfinanceLAPACKLAPACKleast squaresreal, nonsymmetric matrix
F08KNF   21  nagf_lapackeig_zgelss
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squareslinear least squaresminimal least squaresZGELSS
F08KPF   21  nagf_lapackeig_zgesvd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
Related keywords: complex, nonsymmetric matrixeigenproblemfinanceLAPACKLAPACKleast squaresZGESVD
F08KQF   21  nagf_lapackeig_zgelsd
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
Related keywords: complex, m by n matrixdivide-and-conquer methodeigenproblemLAPACKLAPACKleast squareslinear least squaresminimal least squaresZGELSD
F08KRF   21  nagf_lapackeig_zgesdd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
Related keywords: complex, nonsymmetric matrixdivide-and-conquer methodeigenproblemLAPACKLAPACKleast squaresZGESDD
F08MDF   22  nagf_lapackeig_dbdsdc
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
Related keywords: DBDSDCdivide-and-conquer methodeigenproblemLAPACKLAPACKleast squaresmatrix, band QR algorithmreal, bidiagonal matrix
F08MEF   16  nagf_lapackeig_dbdsqr
Performs an SVD of real bidiagonal matrix reduced from real general matrix
Related keywords: DBDSQRdifferential qd algorithmeigenproblemLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, bidiagonal matrix
F08MSF   16  nagf_lapackeig_zbdsqr
Performs an SVD of real bidiagonal matrix reduced from complex general matrix
Related keywords: differential qd algorithmeigenproblemLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, bidiagonal matrixZBDSQR
S x , Fresnel Integral S20ACF   nagf_specfun_fresnel_s
Fresnel integral S x
Related keywords: approximations of special functionsfinanceFresnel integral
S20AQF   24  nagf_specfun_fresnel_s_vector
Fresnel integral vectorized S x
Related keywords: approximations of special functionsFresnel integral
Sylvester equation F08QHF   16  nagf_lapackeig_dtrsyl
Solves the real Sylvester matrix equation A X + X B = C , A and B are upper quasi-triangular or transposes
Related keywords: DTRSYLeigenproblemLAPACKLAPACKleast squaresreal, quasi-triangular matrix
F08QVF   16  nagf_lapackeig_ztrsyl
Solves the complex Sylvester matrix equation A X + X B = C , A and B are upper triangular or conjugate-transposes
Related keywords: complex, triangular matrixeigenproblemLAPACKLAPACKleast squaresZTRSYL
F08YHF   22  nagf_lapackeig_dtgsyl
Solves the real-valued, generalized, quasi-trangular, Sylvester equation
Related keywords: DTGSYLeigenproblemLAPACKLAPACKleast squaresreal, quasi-triangular matrix
F08YVF   22  nagf_lapackeig_ztgsyl
Solves the complex generalized Sylvester equation
Related keywords: complex, triangular matrixeigenproblemLAPACKLAPACKleast squaresZTGSYL
table G11BAF   17  nagf_contab_tabulate_stat
Computes multiway table from set of classification factors using selected statistic
Related keywords: classification variablecontingency table analysisfactor variable
G11BBF   17  nagf_contab_tabulate_percentile
Computes multiway table from set of classification factors using given percentile/quantile
Related keywords: classification variablecontingency table analysisfactor variable
tail probabilities G08AHF   14  nagf_nonpar_test_mwu
Performs the Mann–Whitney U test on two independent samples
Related keywords: Mann–Whitney U statisticnonparametric statistics
G08AJF   14  nagf_nonpar_prob_mwu_noties
Computes the exact probabilities for the Mann–Whitney U statistic, no ties in pooled sample
Related keywords: Mann–Whitney U statisticnonparametric statisticspooled sample
G08AKF   14  nagf_nonpar_prob_mwu_ties
Computes the exact probabilities for the Mann–Whitney U statistic, ties in pooled sample
Related keywords: Mann–Whitney U statisticNeumann algorithmnonparametric statisticspooled sample
tangent, circular F06BCF   12  nagf_blas_dcsg
Recover cosine and sine from given real tangent
Related keywords: BLASlinear algebra support routines
S07AAF   nagf_specfun_tan
tan x
Related keywords: approximations of special functionscircular tangentfinance tan x
term structure S30NCF   25  nagf_specfun_opt_heston_term
Heston's model option pricing with term structure
Related keywords: approximations of special functionsEuropeanfinanceHestonstochastic volatility
test statistic G03DAF   15  nagf_mv_discrim
Computes test statistic for equality of within-group covariance matrices and matrices for discriminant analysis
Related keywords: discriminant analysismultivariate methods
G13ABF   nagf_tsa_uni_autocorr
Univariate time series, sample autocorrelation function
Related keywords: autocorrelation coefficientsbig datadata analyticsfinancemeantime seriestime series analysisunivariate time seriesvariance
TFQMR, transpose-free quasi-minimal residual method F11BEF   19  nagf_sparse_real_gen_basic_solver
Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual method
F11BSF   19  nagf_sparse_complex_gen_basic_solver
Complex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual method
F11DCF   18  nagf_sparse_real_gen_solve_ilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DAF
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual method
F11DEF   18  nagf_sparse_real_gen_solve_jacssor
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box)
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsiterative methods, linear equationsJacobi preconditioninglarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual methodSSOR method, symmetric successive over-relaxation
F11DGF   24  nagf_sparse_real_gen_solve_bdilu
Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DFF
Related keywords: additive Schwarz preconditionerBi-CGSTABbig dataCGS, conjugate gradient methoddata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodreal, sparse matrixRGMRES, restarted generalized minimum residual method
F11DQF   19  nagf_sparse_complex_gen_solve_ilu
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DNF (Black Box)
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual method
F11DSF   19  nagf_sparse_complex_gen_solve_jacssor
Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box
Related keywords: Bi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsiterative methods, linear equationsJacobi preconditioninglarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual methodSSOR method, symmetric successive over-relaxation
F11DUF   24  nagf_sparse_complex_gen_solve_bdilu
Solution of complex, sparse, non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, incomplete L U block diagonal preconditioner computed by F11DTF
Related keywords: additive Schwarz preconditionerBi-CGSTABbig dataCGS, conjugate gradient methodcomplex, sparse matrixdata analyticsincomplete L U factorizationiterative methods, linear equationslarge scale linear systemslinear equations, iterative methodRGMRES, restarted generalized minimum residual method
theta, Jacobian theta functions S21CCF   20  nagf_specfun_jactheta_real
Jacobian theta functions θ k x , q of real argument
Related keywords: approximations of special functionsfinanceJacobian theta functions
theta scores G11SAF   12  nagf_contab_binary
Contingency table, latent variable model for binary data
Related keywords: contingency table analysisfactor scoreslatent variable modelscore patterns
thread X06 Chapter Introduction     OpenMP Utilities
Related keywords: constants and utilitiesopenMP
X06AAF   25  nagf_omp_set_num_threads
Sets the number of threads for OpenMP parallel regions
Related keywords: constants and utilitiesconstants and utilitiesopenMPopenMP
X06ABF   25  nagf_omp_get_num_threads
The number of OpenMP threads in the current team
Related keywords: constants and utilitiesconstants and utilitiesopenMPopenMP
X06ACF   25  nagf_omp_get_max_threads
An upper bound on the number of threads in the next parallel region
Related keywords: constants and utilitiesconstants and utilitiesopenMPopenMP
X06ADF   25  nagf_omp_get_thread_num
The OpenMP thread number of the calling thread
Related keywords: constants and utilitiesconstants and utilitiesopenMPopenMP
X06AFF   25  nagf_omp_in_parallel
Tests for an active OpenMP parallel region
Related keywords: constants and utilitiesconstants and utilitiesopenMPopenMP
X06AGF   25  nagf_omp_set_nested
Enables or disables nested OpenMP parallelism
Related keywords: constants and utilitiesconstants and utilitiesopenMPopenMP
X06AHF   25  nagf_omp_get_nested
Tests the status of nested OpenMP parallelism
Related keywords: constants and utilitiesconstants and utilitiesopenMPopenMP
X06XAF   26  nagf_omp_using_threaded_impl
Tests whether a threaded NAG Library is being used
Related keywords: constants and utilitiesconstants and utilitiesopenMPopenMP
three-dimensional C09FYF   25  nagf_wav_3d_coeff_ext
Three-dimensional discrete wavelet transform coefficient extraction
Related keywords: coefficientsextractwaveletwavelet transforms
C09FZF   25  nagf_wav_3d_coeff_ins
Three-dimensional discrete wavelet transform coefficient insertion
Related keywords: coefficientsinsertwaveletwavelet transforms
time X05AAF   14  nagf_time_date_array
Return date and time as an array of integers
Related keywords: data and time utilitiesdate and time
X05ABF   14  nagf_time_date_array_string
Convert array of integers representing date and time to character string
Related keywords: data and time utilitiesdate and time
X05ACF   14  nagf_time_date_string_compare
Compare two character strings representing date and time
Related keywords: data and time utilitiesdate and time
time, cpu X05BAF   14  nagf_time_cpu
Return the CPU time
Related keywords: CPU timedata and time utilities
time series G05PDF   22  nagf_rand_times_garch_asym1
Generates a realization of a time series from a GARCH process with asymmetry of the form ε t - 1 + γ 2
Related keywords: big datadata analyticsfinanceGARCHrandom number generators
G05PEF   22  nagf_rand_times_garch_asym2
Generates a realization of a time series from a GARCH process with asymmetry of the form ε t - 1 + γ ε t - 1 2
Related keywords: big datadata analyticsfinanceGARCHrandom number generators
G05PFF   22  nagf_rand_times_garch_gjr
Generates a realization of a time series from an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsfinanceGARCHrandom number generators
G05PGF   22  nagf_rand_times_garch_exp
Generates a realization of a time series from an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsEGARCHfinancerandom number generators
G05PHF   22  nagf_rand_times_arma
Generates a realization of a time series from an ARMA model
Related keywords: ARMAbig datadata analyticsfinancerandom number generators
G05PJF   22  nagf_rand_times_mv_varma
Generates a realization of a multivariate time series from a VARMA model
Related keywords: big datadata analyticsfinancerandom number generatorsVARMA, vector autoregressive moving average model
G05PMF   22  nagf_rand_times_smooth_exp
Generates a realization of a time series from an exponential smoothing model
Related keywords: big datadata analyticsexponential smoothingfinancerandom number generators
G13AAF   nagf_tsa_uni_diff
Univariate time series, seasonal and non-seasonal differencing
Related keywords: big datadata analyticsdifferencing, time seriesfinancenon-seasonal differencingseasonal differencingtime series analysisunivariate time series
G13ABF   nagf_tsa_uni_autocorr
Univariate time series, sample autocorrelation function
Related keywords: autocorrelation coefficientsbig datadata analyticsfinancemeantest statistictime series analysisunivariate time seriesvariance
G13ACF   nagf_tsa_uni_autocorr_part
Univariate time series, partial autocorrelations from autocorrelations
Related keywords: autocorrelation coefficientsautoregressive parametersbig datadata analyticserror variance ratiosfinancepartial autocorrelation coefficientstime series analysisunivariate time series
G13ADF   nagf_tsa_uni_arima_prelim
Univariate time series, preliminary estimation, seasonal ARIMA model
Related keywords: ARIMAbig datadata analyticsfinancetime series analysisunivariate time series
G13AEF   nagf_tsa_uni_arima_estim
Univariate time series, estimation, seasonal ARIMA model (comprehensive)
Related keywords: ARIMAbig datadata analyticstime series analysisunivariate time series
G13AFF   nagf_tsa_uni_arima_estim_easy
Univariate time series, estimation, seasonal ARIMA model (easy-to-use)
Related keywords: ARIMAbig datadata analyticsfinancetime series analysisunivariate time series
G13AGF   nagf_tsa_uni_arima_update
Univariate time series, update state set for forecasting
Related keywords: big datadata analyticsfinanceforecastingtime series analysisunivariate time series
G13AHF   nagf_tsa_uni_arima_forecast_state
Univariate time series, forecasting from state set
Related keywords: big datadata analyticsfinanceforecastingtime series analysisunivariate time series
G13AJF   10  nagf_tsa_uni_arima_forcecast
Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model
Related keywords: big datadata analyticsfinanceforecastingstandard deviationtime series analysisunivariate time series
G13AMF   22  nagf_tsa_uni_smooth_exp
Univariate time series, exponential smoothing
Related keywords: big dataBrowns Exponentialdata analyticsexponential smoothingfinanceHolt WinterLinear Holttime series analysisunivariate time series
G13ASF   13  nagf_tsa_uni_arima_resid
Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF
Related keywords: ARMAautocorrelation functionbig dataBox–Jenkins modelsBox–Ljung portmanteau statisticdata analyticsfinancesignificancestandard errorstime series analysisunivariate time series
G13AUF   14  nagf_tsa_uni_means
Computes quantities needed for range-mean or standard deviation-mean plot
Related keywords: big datadata analyticsfinancemeanrangerange-mean plotstandard deviationtime series analysis
G13BAF   10  nagf_tsa_multi_filter_arima
Multivariate time series, filtering (pre-whitening) by an ARIMA model
Related keywords: ARIMAbig datadata analyticsfilteringfinancemultivariate time seriespre-whitening, filteringtime series analysis
G13BBF   11  nagf_tsa_multi_filter_transf
Multivariate time series, filtering by a transfer function model
Related keywords: big datadata analyticsfilteringfinancemultivariate time seriestime series analysis
G13BCF   10  nagf_tsa_multi_xcorr
Multivariate time series, cross-correlations
Related keywords: big datacross-correlationdata analyticsfinancemultivariate time seriestime series analysis
G13BDF   11  nagf_tsa_multi_transf_prelim
Multivariate time series, preliminary estimation of transfer function model
Related keywords: big datadata analyticsfinancemultivariate time seriestime series analysis
G13BEF   11  nagf_tsa_multi_inputmod_estim
Multivariate time series, estimation of multi-input model
Related keywords: ARIMAbig datadata analyticsexact likelihoodfinancemarginal likelihoodmultivariate time seriesnonlinear least squarestime series analysisunivariate time series
G13BGF   11  nagf_tsa_multi_inputmod_update
Multivariate time series, update state set for forecasting from multi-input model
Related keywords: big datadata analyticsfinanceforecastingmultivariate time seriestime series analysis
G13BHF   11  nagf_tsa_multi_inputmod_forecast_state
Multivariate time series, forecasting from state set of multi-input model
Related keywords: big datadata analyticsforecastingmultivariate time seriestime series analysis
G13BJF   11  nagf_tsa_multi_inputmod_forecast
Multivariate time series, state set and forecasts from fully specified multi-input model
Related keywords: big datadata analyticsfinanceforecastingmultivariate time seriestime series analysis
G13CAF   10  nagf_tsa_uni_spectrum_lag
Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: Bartlett lag windowbig datadata analyticsfinanceParzen lag windowrectangular lag windowsmoothingtime series analysisTukey lag windowunivariate time series
G13CBF   10  nagf_tsa_uni_spectrum_daniell
Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window
Related keywords: big dataDaniell windowdata analyticsfinancesmoothingspectral smoothingtime series analysistrapezium frequency windowunivariate time series
G13CCF   10  nagf_tsa_multi_spectrum_lag
Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: Bartlett lag windowbig datacross-spectrumdata analyticsfinancemultivariate time seriesParzen lag windowrectangular lag windowsmoothingtime series analysisTukey lag window
G13CDF   10  nagf_tsa_multi_spectrum_daniell
Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window
Related keywords: big datacross-spectrumDaniell windowdata analyticsfinancemultivariate time seriessmoothingspectral smoothingtime series analysistrapezium frequency window
G13CEF   10  nagf_tsa_multi_spectrum_bivar
Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra
Related keywords: big databivariate spectracoherency, squared, time seriescross amplitude spectrumdata analyticsfinancemultivariate time seriessquared coherencytime series analysis
G13CFF   10  nagf_tsa_multi_gain_bivar
Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra
Related keywords: big databivariate time seriescross-spectrumdata analyticsfinancegain, time seriesmultivariate time seriesphase, time seriestime series analysis
G13CGF   10  nagf_tsa_multi_noise_bivar
Multivariate time series, noise spectrum, bounds, impulse response function and its standard error
Related keywords: big datadata analyticsfinanceimpulse response functionmultivariate time seriesnoise spectrumstandard errorstime series analysis
G13DBF   11  nagf_tsa_multi_autocorr_part
Multivariate time series, multiple squared partial autocorrelations
Related keywords: big datadata analyticsmultivariate time seriespartial autocorrelation coefficientstime series analysis
G13DDF   22  nagf_tsa_multi_varma_estimate
Multivariate time series, estimation of VARMA model
Related keywords: big datacorrelation matrixdata analyticsfinancemaximum likelihoodmultivariate time seriesstandard errorstime series analysisVARMA, vector autoregressive moving average model
G13DJF   15  nagf_tsa_multi_varma_forecast
Multivariate time series, forecasts and their standard errors
Related keywords: big datadata analyticsfinanceforecastingmultivariate time seriesstandard errorstime series analysis
G13DKF   15  nagf_tsa_multi_varma_update
Multivariate time series, updates forecasts and their standard errors
Related keywords: big datadata analyticsfinanceforecastingmultivariate time seriesstandard errorstime series analysis
G13DLF   15  nagf_tsa_multi_diff
Multivariate time series, differences and/or transforms
Related keywords: big datadata analyticsfinancemultivariate time seriestime series analysisVARMA, vector autoregressive moving average model
G13DMF   15  nagf_tsa_multi_corrmat_cross
Multivariate time series, sample cross-correlation or cross-covariance matrices
Related keywords: big datacross-correlationcross-covariancedata analyticsmultivariate time seriestime series analysis
G13DNF   15  nagf_tsa_multi_corrmat_partlag
Multivariate time series, sample partial lag correlation matrices, χ 2 statistics and significance levels
Related keywords: big datachi squared statisticsdata analyticsmultivariate time seriespartial lagsignificancetime series analysis
G13DPF   16  nagf_tsa_multi_regmat_partial
Multivariate time series, partial autoregression matrices
Related keywords: big datadata analyticsmultivariate time seriespartial autoregression matricestime series analysis
G13DSF   13  nagf_tsa_multi_varma_diag
Multivariate time series, diagnostic checking of residuals, following G13DDF
Related keywords: big datadata analyticsmultivariate time seriestime series analysis
G13DXF   15  nagf_tsa_uni_arma_roots
Calculates the zeros of a vector autoregressive (or moving average) operator
Related keywords: big datadata analyticsfinancetime series analysisVARMA, vector autoregressive moving average model
G13EJF   25  nagf_tsa_kalman_unscented_state_revcom
Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise (reverse communication)
Related keywords: big datadata analyticsfiltertime series analysistransformUKFunscentedUT
G13EKF   25  nagf_tsa_kalman_unscented_state
Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise
Related keywords: big datadata analyticsfiltertime series analysisUKFunscented
G13FAF   20  nagf_tsa_uni_garch_asym1_estim
Univariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the form ε t - 1 + γ 2
Related keywords: big datadata analyticsfinanceGARCHtime series analysisunivariate time series
G13FBF   20  nagf_tsa_uni_garch_asym1_forecast
Univariate time series, forecast function for either a symmetric GARCH process or a GARCH process with asymmetry of the form ε t - 1 + γ 2
Related keywords: big datadata analyticsfinanceforecastingGARCHtime series analysisunivariate time series
G13FCF   20  nagf_tsa_uni_garch_asym2_estim
Univariate time series, parameter estimation for a GARCH process with asymmetry of the form ε t - 1 + γ ε t - 1 2
Related keywords: big datadata analyticsfinanceGARCHtime series analysisunivariate time series
G13FDF   20  nagf_tsa_uni_garch_asym2_forecast
Univariate time series, forecast function for a GARCH process with asymmetry of the form ε t - 1 + γ ε t - 1 2
Related keywords: big datadata analyticsfinanceforecastingGARCHtime series analysisunivariate time series
G13FEF   20  nagf_tsa_uni_garch_gjr_estim
Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsfinanceGARCHGJR GARCH processGlosten, Jagannathan and Runkle processtime series analysisunivariate time series
G13FFF   20  nagf_tsa_uni_garch_gjr_forecast
Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsfinanceforecastingGARCHGJR GARCH processGlosten, Jagannathan and Runkle processtime series analysisunivariate time series
G13FGF   20  nagf_tsa_uni_garch_exp_estim
Univariate time series, parameter estimation for an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsEGARCHexponential GARCHfinanceGARCHtime series analysisunivariate time series
G13FHF   20  nagf_tsa_uni_garch_exp_forecast
Univariate time series, forecast function for an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsEGARCHexponential GARCHfinanceforecastingGARCHtime series analysisunivariate time series
G13MEF   24  nagf_tsa_inhom_iema
Computes the iterated exponential moving average for a univariate inhomogeneous time series
Related keywords: big datadata analyticsdata streamexponential moving averagemoving averagestreamingtime series analysisunivariate time series
G13MFF   24  nagf_tsa_inhom_iema_all
Computes the iterated exponential moving average for a univariate inhomogeneous time series, intermediate results are also returned
Related keywords: big datadata analyticsdata streamexponential moving averagemoving averagestreamingtime series analysisunivariate time series
G13MGF   24  nagf_tsa_inhom_ma
Computes the exponential moving average for a univariate inhomogeneous time series
Related keywords: big datadata analyticsdata streamexponential moving averagemoving averagestreamingtime series analysisunivariate time series
G13NAF   25  nagf_tsa_cp_pelt
Change point detection, using the PELT algorithm
Related keywords: big datachange pointdata analyticspelttime series analysis
G13NBF   25  nagf_tsa_cp_pelt_user
Change points detection using the PELT algorithm, user supplied cost function
Related keywords: big datachange pointdata analyticspelttime series analysis
G13NDF   25  nagf_tsa_cp_binary
Change point detection, using binary segmentation
Related keywords: big databinary segmentationchange pointdata analyticstime series analysis
G13NEF   25  nagf_tsa_cp_binary_user
Change point detection, using binary segmentation, user supplied cost function
Related keywords: big databinary segmentationchange pointdata analyticstime series analysis
time series analysis G13 Chapter Introduction     Time Series Analysis
Related keywords: big datadata analytics
Toeplitz matrix F04FEF   15  nagf_linsys_real_toeplitz_yule
Solution of the Yule–Walker equations for real symmetric positive definite Toeplitz matrix, one right-hand side
Related keywords: big datadata analyticsreal, positive-definite, symmetric, Toeplitz matrixsimultaneous linear equationsYule–Walker equations
F04FFF   15  nagf_linsys_real_toeplitz_solve
Solution of real symmetric positive definite Toeplitz system, one right-hand side
Related keywords: big datadata analyticsreal, positive-definite, symmetric, Toeplitz matrixsimultaneous linear equations
F04MEF   15  nagf_linsys_real_toeplitz_yule_update
Update solution of the Yule–Walker equations for real symmetric positive definite Toeplitz matrix
Related keywords: big datadata analyticsreal, positive-definite, symmetric, Toeplitz matrixsimultaneous linear equationsYule–Walker equations
F04MFF   15  nagf_linsys_real_toeplitz_update
Update solution of real symmetric positive definite Toeplitz system
Related keywords: big datadata analyticsreal, positive-definite, symmetric, Toeplitz matrixsimultaneous linear equations
transform G13EJF   25  nagf_tsa_kalman_unscented_state_revcom
Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise (reverse communication)
Related keywords: big datadata analyticsfiltertime seriestime series analysisUKFunscentedUT
transportation problem H03ABF   nagf_mip_transportation
Transportation problem, modified stepping stone method
Related keywords: operations researchstepping stone algorithm
transpose, matrix F01CRF   nagf_matop_real_gen_trans_inplace
Transposition of a real matrix
Related keywords: inversionmatrix operationsreal, nonsymmetric matrix
F01CTF   14  nagf_matop_real_addsub
Sum or difference of two real matrices, optional scaling and transposition
Related keywords: inversionmatrix operationsreal, nonsymmetric matrixsum, matrix
F01CWF   14  nagf_matop_complex_addsub
Sum or difference of two complex matrices, optional scaling and transposition
Related keywords: complex, nonsymmetric matrixinversionmatrix operationssum, matrix
trapezium frequency window G13CBF   10  nagf_tsa_uni_spectrum_daniell
Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window
Related keywords: big dataDaniell windowdata analyticsfinancesmoothingspectral smoothingtime seriestime series analysisunivariate time series
G13CDF   10  nagf_tsa_multi_spectrum_daniell
Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window
Related keywords: big datacross-spectrumDaniell windowdata analyticsfinancemultivariate time seriessmoothingspectral smoothingtime seriestime series analysis
Travelling Salesman Problem H03BBF   25  nagf_mip_tsp_simann
Travelling Salesman Problem, simulated annealing
Related keywords: operations researchshortest pathsimulated annealingTSP
treatment means G04BBF   16  nagf_anova_random
Analysis of variance, randomized block or completely randomized design, treatment means and standard errors
Related keywords: analysis of varianceANOVAcompletely randomized designrandomized block designstandard errors
G04BCF   17  nagf_anova_rowcol
Analysis of variance, general row and column design, treatment means and standard errors
Related keywords: analysis of varianceANOVAstandard errors
G04CAF   16  nagf_anova_factorial
Analysis of variance, complete factorial design, treatment means and standard errors
Related keywords: analysis of varianceANOVAfactorial designstandard errors
triangular distribution G05SPF   22  nagf_rand_dist_triangular
Generates a vector of pseudorandom numbers from a triangular distribution
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
triangularization, mesh generation D03MAF   nagf_pde_2d_triangulate
Triangulation of plane region
Related keywords: mesh generationPDE, partial differential equations
triangular mesh D06AAF   20  nagf_mesh_2d_gen_inc
Generates a two-dimensional mesh using a simple incremental method
Related keywords: mesh generationsimple incremental method
D06ABF   20  nagf_mesh_2d_gen_delaunay
Generates a two-dimensional mesh using a Delaunay–Voronoi process
Related keywords: Delaunay–Voronoi processmesh generation
D06ACF   20  nagf_mesh_2d_gen_front
Generates a two-dimensional mesh using an Advancing-front method
Related keywords: Advancing-front methodmesh generation
Triangulation E01EAF   25  nagf_interp_2d_triangulate
Triangulation of two-dimensional scattered grid, method of Renka and Cline
Related keywords: interpolationRenka and Cline methodScattered data
E01EBF   25  nagf_interp_2d_triang_bary_eval
Barycentric interpolation on function values provided on a two-dimensional scattered grid
Related keywords: Barycentric interpolationBilinear interpolationfinanceinterpolationInterpolationRenka and Cline methodScattered dataScattered data interpolation
trigamma function S14AFF   20  nagf_specfun_psi_deriv_complex
Polygamma function ψ n z for complex z
Related keywords: approximations of special functionsderivatives, psi functiondigamma functionpolygamma functionpsi function
trimmed mean G07DDF   14  nagf_univar_robust_1var_trimmed
Computes a trimmed and winsorized mean of a single sample with estimates of their variance
Related keywords: univariate estimationvariancewinsorized mean
triplets test for randomness G08ECF   14  nagf_nonpar_randtest_triplets
Performs the triplets test for randomness
Related keywords: nonparametric statisticsrandomness, tests for
TSP H03BBF   25  nagf_mip_tsp_simann
Travelling Salesman Problem, simulated annealing
Related keywords: operations researchshortest pathsimulated annealingTravelling Salesman Problem
t-test statistic G07CAF   15  nagf_univar_ttest_2normal
Computes t -test statistic for a difference in means between two Normal populations, confidence interval
Related keywords: confidence intervalGaussian distributionNormal distributionunivariate estimation
Tukey's bi-weight G02HAF   13  nagf_correg_robustm
Robust regression, standard M -estimates
Related keywords: Andrew's sine wavebig datacorrelation analysisdata analyticsfinanceHampel's piecewise linear functionHuber type regressionKrasker–Welsch weightsMallows type regressionMaronna's weights M -estimatesnonlinear regressionpolynomial regressionregressionregression analysisrobust regressionScheppe type regression
Tukey's smoothing G10CAF   16  nagf_smooth_data_runningmedian
Compute smoothed data sequence using running median smoothers
Related keywords: running mediansmoothingSmoothing in Statistics
Tukey lag window G13CAF   10  nagf_tsa_uni_spectrum_lag
Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: Bartlett lag windowbig datadata analyticsfinanceParzen lag windowrectangular lag windowsmoothingtime seriestime series analysisunivariate time series
G13CCF   10  nagf_tsa_multi_spectrum_lag
Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: Bartlett lag windowbig datacross-spectrumdata analyticsfinancemultivariate time seriesParzen lag windowrectangular lag windowsmoothingtime seriestime series analysis
Tukey scores G01DHF   15  nagf_stat_ranks_and_scores
Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores
Related keywords: Blom scoresexponential scoresfinancerank scoresSavage scoresSimple Calculations on Statistical Datavan der Waerden scores
two-dimensional C09EYF   25  nagf_wav_2d_coeff_ext
Two-dimensional discrete wavelet transform coefficient extraction
Related keywords: coefficientsextractwaveletwavelet transforms
C09EZF   25  nagf_wav_2d_coeff_ins
Two-dimensional discrete wavelet transform coefficient insertion
Related keywords: coefficientsinsertwaveletwavelet transforms
D03EDF   12  nagf_pde_2d_ellip_mgrid
Elliptic PDE, solution of finite difference equations by a multigrid technique
Related keywords: elliptic partial differential equationsmultigrid methodPDE, partial differential equationsrectangular
E01DAF   14  nagf_interp_2d_spline_grid
Interpolating functions, fitting bicubic spline, data on rectangular grid
Related keywords: bicubic splinefinanceinterpolation
two-dimensional PDE D03RAF   18  nagf_pde_2d_gen_order2_rectangle
General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region
Related keywords: mesh refinementmethod of linesPDE, partial differential equations
D03RBF   18  nagf_pde_2d_gen_order2_rectilinear
General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectilinear region
Related keywords: mesh refinementmethod of linesPDE, partial differential equations
D03RZF   18  nagf_pde_2d_gen_order2_rectilinear_extractgrid
Extract grid data from D03RBF
Related keywords: grid extractionmesh refinementmethod of linesPDE, partial differential equations
two-dimensional polynomial approximation E02CAF   nagf_fit_2dcheb_lines
Least squares surface fit by polynomials, data on lines parallel to one independent coordinate axis
Related keywords: bivariate polynomial approximationChebyshev polynomial approximationcurve and surface fittingdata-on-lines polynomial approximationleast squarespolynomial approximation
E02CBF   nagf_fit_2dcheb_eval
Evaluation of fitted polynomial in two variables
Related keywords: bivariate polynomial approximationChebyshev polynomial approximationcurve and surface fittingpolynomial approximation
two-dimensional spline approximation E02DAF   nagf_fit_2dspline_panel
Least squares surface fit, bicubic splines
Related keywords: bicubic splinesB-splinescurve and surface fittingknotsleast squares
E02DCF   13  nagf_fit_2dspline_grid
Least squares surface fit by bicubic splines with automatic knot placement, data on rectangular grid
Related keywords: bicubic splinesB-splinescurve and surface fittingleast squaressmoothing
E02JDF   24  nagf_fit_2dspline_ts_sctr
Spline approximation to a set of scattered data using a two-stage approximation method
Related keywords: curve and surface fittingscattered dataspline
E02JEF   24  nagf_fit_2dspline_ts_evalv
Evaluation at a vector of points of a spline computed by E02JDF
Related keywords: curve and surface fittingscattered dataspline
E02JFF   24  nagf_fit_2dspline_ts_evalm
Evaluation at a mesh of points of a spline computed by E02JDF
Related keywords: curve and surface fittinggridded datascattered dataspline
E02ZAF   nagf_fit_2dspline_sort
Sort two-dimensional data into panels for fitting bicubic splines
Related keywords: curve and surface fittinggridded datasort
two-point boundary value problem D02SAF   nagf_ode_bvp_shoot_genpar_algeq
Ordinary differential equations, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined
Related keywords: boundary value problemBVPODE, ordinary differential equationsparameterized first ordershooting method, ODE
D02TLF   25  nagf_ode_bvp_coll_nlin_solve
Ordinary differential equations, general nonlinear boundary value problem, collocation technique (thread safe)
Related keywords: boundary value problemBVPdifferential equationsnonlinear mixed orderODE, ordinary differential equationsordinary differential equations
two-tail probability G01EAF   15  nagf_stat_prob_normal
Computes probabilities for the standard Normal distribution
Related keywords: CDF, cumulative distribution functionfinancelower tail probabilityNormal distributionprobabilitySimple Calculations on Statistical Dataupper tail probability
G01EBF   14  nagf_stat_prob_students_t
Computes probabilities for Student's t -distribution
Related keywords: CDF, cumulative distribution functionfinancelower tail probabilityprobabilitySimple Calculations on Statistical DataStudent's t -distributionupper tail probability
G01ECF   14  nagf_stat_prob_chisq
Computes probabilities for χ 2 distribution
Related keywords: CDF, cumulative distribution functionchi-squared distributionfinancelower tail probabilityprobabilitySimple Calculations on Statistical Dataupper tail probability
G01SAF   24  nagf_stat_prob_normal_vector
Computes a vector of probabilities for the standard Normal distribution
Related keywords: big dataCDF, cumulative distribution functionconfidence intervaldata analyticsGaussian distributionlower tail probabilityNormal distributionsignificanceSimple Calculations on Statistical Dataupper tail probability
G01SBF   24  nagf_stat_prob_students_t_vector
Computes a vector of probabilities for the Student's t -distribution
Related keywords: big dataCDF, cumulative distribution functionconfidence intervaldata analyticslower tail probabilitysignificanceSimple Calculations on Statistical DataStudent's t -distributionupper tail probability
two-way analysis of variance G04AGF   nagf_anova_hier2
Two-way analysis of variance, hierarchical classification, subgroups of unequal size
Related keywords: analysis of varianceANOVAhierarchical classification
two-way contingency table G01AFF   nagf_stat_contingency_table
Two-way contingency table analysis, with χ 2 /Fisher's exact test
Related keywords: chi-squared distributioncontingency tablefinanceFisher's exact testSimple Calculations on Statistical DataYates' correction
G05PZF   22  nagf_rand_matrix_2waytable
Generates a random two-way table
Related keywords: big datadata analyticsfinancerandom number generatorsrandom two-way table
UDU H decomposition F07MNF   21  nagf_lapacklin_zhesv
Computes the solution to a complex Hermitian system of linear equations
Related keywords: complex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACK LDL H decompositionlinear equationsZHESV
F07MPF   21  nagf_lapacklin_zhesvx
Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations
Related keywords: backward errorcomplex, Hermitian, indefinite matrixdiagonal pivoting methodforward errorLAPACK LDL H decompositionlinear equationsZHESVX
F07NNF   21  nagf_lapacklin_zsysv
Computes the solution to a complex symmetric system of linear equations
Related keywords: complex, symmetric matrixdiagonal pivoting methodLAPACK LDL H decompositionlinear equationsZSYSV
F07NPF   21  nagf_lapacklin_zsysvx
Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations
Related keywords: backward errorcomplex, symmetric matrixdiagonal pivoting methodforward errorLAPACK LDL H decompositionlinear equationsZSYSVX
F07PAF   21  nagf_lapacklin_dspsv
Computes the solution to a real symmetric system of linear equations, packed storage
Related keywords: diagonal pivoting methodDSPSVLAPACK LDL T decompositionlinear equationsreal, indefinite, symmetric matrix
F07PBF   21  nagf_lapacklin_dspsvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage. Error bounds and a condition estimate are also computed
Related keywords: backward errorcondition number, matrixdiagonal pivoting methodDSPSVXerror bound, matrixforward errorLAPACK LDL H decompositionlinear equationsreal, indefinite, symmetric matrix
F07PNF   21  nagf_lapacklin_zhpsv
Computes the solution to a complex Hermitian system of linear equations, packed storage
Related keywords: complex, Hermitian, indefinite matrixdiagonal pivoting methodinverse, matrixLAPACK LDL H decompositionlinear equationsZHPSV
F07PPF   21  nagf_lapacklin_zhpsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, Hermitian, system of linear equations, error bounds and condition estimates. Packed storage
Related keywords: backward errorcomplex, Hermitian, indefinite matrixdiagonal pivoting methodforward errorinverse, matrixLAPACK LDL H decompositionlinear equationsZHPSVX
F07QNF   21  nagf_lapacklin_zspsv
Computes the solution to a complex symmetric system of linear equations, packed storage
Related keywords: complex, symmetric matrixdiagonal pivoting methodLAPACK LDL T decompositionlinear equationsZSPSV
F07QPF   21  nagf_lapacklin_zspsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, symmetric, system of linear equations, error bounds and condition estimates. Packed storage
Related keywords: backward errorcomplex, symmetric matrixdiagonal pivoting methodforward errorLAPACK LDL T decompositionlinear equationsZSPSVX
UDU T decompositiuon F07MAF   21  nagf_lapacklin_dsysv
Computes the solution to a real symmetric system of linear equations
Related keywords: diagonal pivoting methodDSYSVLAPACKLDLT decompositionlinear equationsreal, indefinite, symmetric matrix
F07MBF   21  nagf_lapacklin_dsysvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations
Related keywords: backward errordiagonal pivoting methodDSYSVXforward errorLAPACKLDLT decompositionlinear equationsreal, indefinite, symmetric matrix
UKF G13EJF   25  nagf_tsa_kalman_unscented_state_revcom
Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise (reverse communication)
Related keywords: big datadata analyticsfiltertime seriestime series analysistransformunscentedUT
G13EKF   25  nagf_tsa_kalman_unscented_state
Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise
Related keywords: big datadata analyticsfiltertime seriestime series analysisunscented
U L D L T U T decomposition F01BUF   nagf_matop_real_symm_posdef_fac
U L D L T U T factorization of real symmetric positive definite band matrix
Related keywords: decomposition, matrixinversionmatrix, bandmatrix operationsreal, band, positive-definite, symmetric matrix
underdetermined linear system F08AAF   21  nagf_lapackeig_dgels
Solves a real linear least squares problem of full rank
Related keywords: DGELSeigenproblemfinanceLAPACKLAPACKleast squareslinear least squares LQ decompositionoverdetermined linear equations QR factorizationreal, m by n matrix
F08ANF   21  nagf_lapackeig_zgels
Solves a complex linear least problem of full rank
Related keywords: complex, m by n matrixeigenproblemfinanceLAPACKLAPACKleast squareslinear least squares LQ decompositionoverdetermined linear equations QR factorizationZGELS
uniform distribution G05SAF   22  nagf_rand_dist_uniform01
Generates a vector of pseudorandom numbers from a uniform distribution over 0 , 1
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbersrectangular distribution
G05SQF   22  nagf_rand_dist_uniform
Generates a vector of pseudorandom numbers from a uniform distribution over a , b
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbersrectangular distribution
G05TLF   22  nagf_rand_int_uniform
Generates a vector of pseudorandom integers from a uniform distribution
Related keywords: big datadata analyticsfinancerandom integersrandom number generatorsrectangular distribution
G05YLF   22  nagf_rand_quasi_init
Initializes a quasi-random number generator
Related keywords: big datadata analyticsFaure, quasi-random numbersfinancelow-discrepancy sequencesNiederreiter method, quasi-random numbersquasi-random numbersrandom number generatorsrandom numbersrectangular distributionSobol, quasi-random numbers
unitary matrix, generation F08ATF   16  nagf_lapackeig_zungqr
Forms all or part of unitary Q from Q R factorization determined by F08ASF F08BSF F08BTF
Related keywords: eigenproblemLAPACKLAPACKleast squares QR factorizationunitary transformationsZUNGQR
F08AWF   16  nagf_lapackeig_zunglq
Forms all or part of unitary Q from L Q factorization determined by F08AVF
Related keywords: eigenproblemLAPACKLAPACKleast squares LQ factorizationunitary transformationsZUNGLQ
F08CTF   22  nagf_lapackeig_zungql
Form all or part of unitary Q from Q L factorization determined by F08CSF
Related keywords: eigenproblemLAPACKLAPACKleast squares QL factorizationunitary transformationsZUNGQL
F08CWF   22  nagf_lapackeig_zungrq
Form all or part of unitary Q from R Q factorization determined by F08CVF
Related keywords: eigenproblemLAPACKLAPACKleast squaresRQ factorizationsunitary transformationsZUNGRQ
F08FTF   16  nagf_lapackeig_zungtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformationsZUNGTR
F08GTF   16  nagf_lapackeig_zupgtr
Generates a unitary transformation matrix from reduction to tridiagonal form determined by F08GSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformationsZUPGTR
F08KTF   16  nagf_lapackeig_zungbr
Generates unitary transformation matrices from the reduction to bidiagonal form determined by F08KSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformationsZUNGBR
F08NTF   16  nagf_lapackeig_zunghr
Generates a unitary transformation matrix from reduction to Hessenberg form determined by F08NSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresZUNGHR
unitary transformations F08AQF   25  nagf_lapackeig_zgemqrt
Applies the unitary transformation determined by F08APF
Related keywords: eigenproblemexplicit blockingLAPACKleast squaresQR factorizationrecursive QRZGEMQRT
F08ATF   16  nagf_lapackeig_zungqr
Forms all or part of unitary Q from Q R factorization determined by F08ASF F08BSF F08BTF
Related keywords: eigenproblemLAPACKLAPACKleast squares QR factorizationunitary matrix, generationZUNGQR
F08AUF   16  nagf_lapackeig_zunmqr
Applies a unitary transformation determined by F08ASF F08BSF F08BTF
Related keywords: eigenproblemLAPACKLAPACKleast squares QR factorizationZUNMQR
F08AWF   16  nagf_lapackeig_zunglq
Forms all or part of unitary Q from L Q factorization determined by F08AVF
Related keywords: eigenproblemLAPACKLAPACKleast squares LQ factorizationunitary matrix, generationZUNGLQ
F08AXF   16  nagf_lapackeig_zunmlq
Applies the unitary transformation determined by F08AVF
Related keywords: eigenproblemLAPACKLAPACKleast squares LQ factorizationZUNMLQ
F08BQF   25  nagf_lapackeig_ztpmqrt
Applies the unitary transformation determined by F08BPF
Related keywords: eigenproblemexplicit blockingLAPACKleast squaresQR factorizationrecursive QRZTPMQRT
F08BXF   22  nagf_lapackeig_zunmrz
Applies the unitary transformation determined by F08BVF
Related keywords: eigenproblemLAPACKLAPACKleast squaresZUNMRZ
F08CTF   22  nagf_lapackeig_zungql
Form all or part of unitary Q from Q L factorization determined by F08CSF
Related keywords: eigenproblemLAPACKLAPACKleast squares QL factorizationunitary matrix, generationZUNGQL
F08CUF   22  nagf_lapackeig_zunmql
Applies the unitary transformation determined by F08CSF
Related keywords: eigenproblemLAPACKLAPACKleast squares QL factorizationZUNMQL
F08CWF   22  nagf_lapackeig_zungrq
Form all or part of unitary Q from R Q factorization determined by F08CVF
Related keywords: eigenproblemLAPACKLAPACKleast squaresRQ factorizationsunitary matrix, generationZUNGRQ
F08CXF   22  nagf_lapackeig_zunmrq
Applies the unitary transformation determined by F08CVF
Related keywords: eigenproblemLAPACKLAPACKleast squaresRQ factorizationsZUNMRQ
F08FRF   21  nagf_lapackeig_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresrelatively robust representationsZHEEVR
F08FSF   16  nagf_lapackeig_zhetrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
Related keywords: complex, Hermitian, indefinite matrixeigenproblemLAPACKLAPACKleast squaresZHETRD
F08FTF   16  nagf_lapackeig_zungtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary matrix, generationZUNGTR
F08FUF   16  nagf_lapackeig_zunmtr
Applies the unitary transformation matrix determined by F08FSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresZUNMTR
F08GSF   16  nagf_lapackeig_zhptrd
Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
Related keywords: complex, Hermitian, indefinite matrixeigenproblemLAPACKLAPACKleast squaresZHPTRD
F08GTF   16  nagf_lapackeig_zupgtr
Generates a unitary transformation matrix from reduction to tridiagonal form determined by F08GSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary matrix, generationZUPGTR
F08GUF   16  nagf_lapackeig_zupmtr
Applies the unitary transformation matrix determined by F08GSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresZUPGTR
F08HNF   21  nagf_lapackeig_zhbev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
Related keywords: complex, band, Hermitian matrixeigenproblemLAPACKLAPACKleast squaresmatrix, band QR algorithmZHBEV
F08HPF   21  nagf_lapackeig_zhbevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
Related keywords: complex, band, Hermitian matrixeigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBEVX
F08HSF   16  nagf_lapackeig_zhbtrd
Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
Related keywords: complex, band, Hermitian matrixeigenproblemLAPACKLAPACKleast squaresmatrix, bandZHBTRD
F08KSF   16  nagf_lapackeig_zgebrd
Performs a unitary reduction of complex general rectangular matrix to bidiagonal form
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresZGEBRD
F08KTF   16  nagf_lapackeig_zungbr
Generates unitary transformation matrices from the reduction to bidiagonal form determined by F08KSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary matrix, generationZUNGBR
F08KUF   16  nagf_lapackeig_zunmbr
Applies the unitary transformations from reduction to bidiagonal form determined by F08KSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresZUNMBR
F08NSF   16  nagf_lapackeig_zgehrd
Performs a unitary reduction of complex general matrix to upper Hessenberg form
Related keywords: complex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresZGEHRD
F08NUF   16  nagf_lapackeig_zunmhr
Applies the unitary transformation matrix from reduction to Hessenberg form determined by F08NSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresZUNMHR
F08QTF   16  nagf_lapackeig_ztrexc
Reorders a Schur factorization of complex matrix using unitary similarity transformation
Related keywords: eigenproblemLAPACKLAPACKleast squaresSchur formZTREXC
F08WSF   20  nagf_lapackeig_zgghrd
Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
Related keywords: complex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresZGGHRD
F08WTF   26  nagf_lapackeig_zgghd3
Performs, using BLAS-3, a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
Related keywords: complex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresZGGHD3
F08YTF   22  nagf_lapackeig_ztgexc
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
Related keywords: complex, nonsymmetric matrixeigenproblemgeneralized Schur formLAPACKLAPACKleast squaresZTGEXC
F08YUF   22  nagf_lapackeig_ztgsen
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresZTGEXC
unit root G01EWF   25  nagf_stat_prob_dickey_fuller_unit
Computes probabilities for the Dickey–Fuller unit root test
Related keywords: Dickey–Fuller probabilitiesSimple Calculations on Statistical Datastatistical distribution functions
G13AWF   25  nagf_tsa_uni_dickey_fuller_unit
Computes (augmented) Dickey–Fuller unit root test statistic
Related keywords: big datadata analyticsDickey–Fullertime series analysis
univariate estimation G07 Chapter Introduction     Univariate Estimation
univariate minimization E04ABF   nagf_opt_one_var_func_old
Minimum, function of one variable, using function values only
Related keywords: derivative-free minimizationfinancemaximizing a functionminimization, unconstrainedminimizing a functionNLPnonlinear programmingone-dimensional quadratic interpolationoptimization
univariate time series G13AAF   nagf_tsa_uni_diff
Univariate time series, seasonal and non-seasonal differencing
Related keywords: big datadata analyticsdifferencing, time seriesfinancenon-seasonal differencingseasonal differencingtime seriestime series analysis
G13ABF   nagf_tsa_uni_autocorr
Univariate time series, sample autocorrelation function
Related keywords: autocorrelation coefficientsbig datadata analyticsfinancemeantest statistictime seriestime series analysisvariance
G13ACF   nagf_tsa_uni_autocorr_part
Univariate time series, partial autocorrelations from autocorrelations
Related keywords: autocorrelation coefficientsautoregressive parametersbig datadata analyticserror variance ratiosfinancepartial autocorrelation coefficientstime seriestime series analysis
G13ADF   nagf_tsa_uni_arima_prelim
Univariate time series, preliminary estimation, seasonal ARIMA model
Related keywords: ARIMAbig datadata analyticsfinancetime seriestime series analysis
G13AEF   nagf_tsa_uni_arima_estim
Univariate time series, estimation, seasonal ARIMA model (comprehensive)
Related keywords: ARIMAbig datadata analyticstime seriestime series analysis
G13AFF   nagf_tsa_uni_arima_estim_easy
Univariate time series, estimation, seasonal ARIMA model (easy-to-use)
Related keywords: ARIMAbig datadata analyticsfinancetime seriestime series analysis
G13AGF   nagf_tsa_uni_arima_update
Univariate time series, update state set for forecasting
Related keywords: big datadata analyticsfinanceforecastingtime seriestime series analysis
G13AHF   nagf_tsa_uni_arima_forecast_state
Univariate time series, forecasting from state set
Related keywords: big datadata analyticsfinanceforecastingtime seriestime series analysis
G13AJF   10  nagf_tsa_uni_arima_forcecast
Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model
Related keywords: big datadata analyticsfinanceforecastingstandard deviationtime seriestime series analysis
G13AMF   22  nagf_tsa_uni_smooth_exp
Univariate time series, exponential smoothing
Related keywords: big dataBrowns Exponentialdata analyticsexponential smoothingfinanceHolt WinterLinear Holttime seriestime series analysis
G13ASF   13  nagf_tsa_uni_arima_resid
Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF
Related keywords: ARMAautocorrelation functionbig dataBox–Jenkins modelsBox–Ljung portmanteau statisticdata analyticsfinancesignificancestandard errorstime seriestime series analysis
G13BEF   11  nagf_tsa_multi_inputmod_estim
Multivariate time series, estimation of multi-input model
Related keywords: ARIMAbig datadata analyticsexact likelihoodfinancemarginal likelihoodmultivariate time seriesnonlinear least squarestime seriestime series analysis
G13CAF   10  nagf_tsa_uni_spectrum_lag
Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window
Related keywords: Bartlett lag windowbig datadata analyticsfinanceParzen lag windowrectangular lag windowsmoothingtime seriestime series analysisTukey lag window
G13CBF   10  nagf_tsa_uni_spectrum_daniell
Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window
Related keywords: big dataDaniell windowdata analyticsfinancesmoothingspectral smoothingtime seriestime series analysistrapezium frequency window
G13FAF   20  nagf_tsa_uni_garch_asym1_estim
Univariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the form ε t - 1 + γ 2
Related keywords: big datadata analyticsfinanceGARCHtime seriestime series analysis
G13FBF   20  nagf_tsa_uni_garch_asym1_forecast
Univariate time series, forecast function for either a symmetric GARCH process or a GARCH process with asymmetry of the form ε t - 1 + γ 2
Related keywords: big datadata analyticsfinanceforecastingGARCHtime seriestime series analysis
G13FCF   20  nagf_tsa_uni_garch_asym2_estim
Univariate time series, parameter estimation for a GARCH process with asymmetry of the form ε t - 1 + γ ε t - 1 2
Related keywords: big datadata analyticsfinanceGARCHtime seriestime series analysis
G13FDF   20  nagf_tsa_uni_garch_asym2_forecast
Univariate time series, forecast function for a GARCH process with asymmetry of the form ε t - 1 + γ ε t - 1 2
Related keywords: big datadata analyticsfinanceforecastingGARCHtime seriestime series analysis
G13FEF   20  nagf_tsa_uni_garch_gjr_estim
Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsfinanceGARCHGJR GARCH processGlosten, Jagannathan and Runkle processtime seriestime series analysis
G13FFF   20  nagf_tsa_uni_garch_gjr_forecast
Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
Related keywords: big datadata analyticsfinanceforecastingGARCHGJR GARCH processGlosten, Jagannathan and Runkle processtime seriestime series analysis
G13FGF   20  nagf_tsa_uni_garch_exp_estim
Univariate time series, parameter estimation for an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsEGARCHexponential GARCHfinanceGARCHtime seriestime series analysis
G13FHF   20  nagf_tsa_uni_garch_exp_forecast
Univariate time series, forecast function for an exponential GARCH (EGARCH) process
Related keywords: big datadata analyticsEGARCHexponential GARCHfinanceforecastingGARCHtime seriestime series analysis
G13MEF   24  nagf_tsa_inhom_iema
Computes the iterated exponential moving average for a univariate inhomogeneous time series
Related keywords: big datadata analyticsdata streamexponential moving averagemoving averagestreamingtime seriestime series analysis
G13MFF   24  nagf_tsa_inhom_iema_all
Computes the iterated exponential moving average for a univariate inhomogeneous time series, intermediate results are also returned
Related keywords: big datadata analyticsdata streamexponential moving averagemoving averagestreamingtime seriestime series analysis
G13MGF   24  nagf_tsa_inhom_ma
Computes the exponential moving average for a univariate inhomogeneous time series
Related keywords: big datadata analyticsdata streamexponential moving averagemoving averagestreamingtime seriestime series analysis
unscented G13EJF   25  nagf_tsa_kalman_unscented_state_revcom
Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise (reverse communication)
Related keywords: big datadata analyticsfiltertime seriestime series analysistransformUKFUT
G13EKF   25  nagf_tsa_kalman_unscented_state
Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise
Related keywords: big datadata analyticsfiltertime seriestime series analysisUKF
upper tail probability G01EAF   15  nagf_stat_prob_normal
Computes probabilities for the standard Normal distribution
Related keywords: CDF, cumulative distribution functionfinancelower tail probabilityNormal distributionprobabilitySimple Calculations on Statistical Datatwo-tail probability
G01EBF   14  nagf_stat_prob_students_t
Computes probabilities for Student's t -distribution
Related keywords: CDF, cumulative distribution functionfinancelower tail probabilityprobabilitySimple Calculations on Statistical DataStudent's t -distributiontwo-tail probability
G01ECF   14  nagf_stat_prob_chisq
Computes probabilities for χ 2 distribution
Related keywords: CDF, cumulative distribution functionchi-squared distributionfinancelower tail probabilityprobabilitySimple Calculations on Statistical Datatwo-tail probability
G01EDF   14  nagf_stat_prob_f
Computes probabilities for F -distribution
Related keywords: CDF, cumulative distribution function F -distributionfinancelower tail probabilityprobabilitySimple Calculations on Statistical Datavariance-ratio distribution
G01EEF   14  nagf_stat_prob_beta
Computes upper and lower tail probabilities and probability density function for the beta distribution
Related keywords: beta distributionCDF, cumulative distribution functionfinancelower tail probabilityprobabilitySimple Calculations on Statistical Data
G01EFF   14  nagf_stat_prob_gamma
Computes probabilities for the gamma distribution
Related keywords: CDF, cumulative distribution functionfinancegamma distributionlower tail probabilityprobabilitySimple Calculations on Statistical Data
G01EYF   14  nagf_stat_prob_kolmogorov1
Computes probabilities for the one-sample Kolmogorov–Smirnov distribution
Related keywords: financeKolmogorov–Smirnov distributionSimple Calculations on Statistical Data
G01EZF   14  nagf_stat_prob_kolmogorov2
Computes probabilities for the two-sample Kolmogorov–Smirnov distribution
Related keywords: financeKolmogorov–Smirnov distributionSimple Calculations on Statistical Data
G01HBF   15  nagf_stat_prob_multi_normal
Computes probabilities for the multivariate Normal distribution
Related keywords: central probabilityfinancelower tail probabilitymultivariate Normal distributionNormal distributionSimple Calculations on Statistical Data
G01SAF   24  nagf_stat_prob_normal_vector
Computes a vector of probabilities for the standard Normal distribution
Related keywords: big dataCDF, cumulative distribution functionconfidence intervaldata analyticsGaussian distributionlower tail probabilityNormal distributionsignificanceSimple Calculations on Statistical Datatwo-tail probability
G01SBF   24  nagf_stat_prob_students_t_vector
Computes a vector of probabilities for the Student's t -distribution
Related keywords: big dataCDF, cumulative distribution functionconfidence intervaldata analyticslower tail probabilitysignificanceSimple Calculations on Statistical DataStudent's t -distributiontwo-tail probability
G01SCF   24  nagf_stat_prob_chisq_vector
Computes a vector of probabilities for χ 2 distribution
Related keywords: big dataCDF, cumulative distribution functionchi-squared distributiondata analyticslower tail probabilitySimple Calculations on Statistical Data
G01SDF   24  nagf_stat_prob_f_vector
Computes a vector of probabilities for F -distribution
Related keywords: big dataCDF, cumulative distribution functiondata analytics F -distributionlower tail probabilitySimple Calculations on Statistical Datavariance-ratio distribution
G01SEF   24  nagf_stat_prob_beta_vector
Computes a vector of probabilities for the beta distribution
Related keywords: beta distributionbig dataCDF, cumulative distribution functiondata analyticslower tail probabilitySimple Calculations on Statistical Data
G01SFF   24  nagf_stat_prob_gamma_vector
Computes a vector of probabilities for the gamma distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticsgamma distributionlower tail probabilitySimple Calculations on Statistical Data
G01SJF   24  nagf_stat_prob_binomial_vector
Computes a vector of probabilities for the binomial distribution
Related keywords: big databinomial distributionCDF, cumulative distribution functiondata analyticslower tail probabilitypoint probabilitySimple Calculations on Statistical Data
G01SKF   24  nagf_stat_prob_poisson_vector
Computes a vector of probabilities for the Poisson distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticslower tail probabilitypoint probabilityPoisson distributionSimple Calculations on Statistical Data
G01SLF   24  nagf_stat_prob_hypergeom_vector
Computes a vector of probabilities for the hypergeometric distribution
Related keywords: big dataCDF, cumulative distribution functiondata analyticshypergeometric distributionlower tail probabilitypoint probabilitySimple Calculations on Statistical Data
UT G13EJF   25  nagf_tsa_kalman_unscented_state_revcom
Combined time and measurement update, one iteration of the Unscented Kalman Filter for a nonlinear state space model, with additive noise (reverse communication)
Related keywords: big datadata analyticsfiltertime seriestime series analysistransformUKFunscented
van der Waerden scores G01DHF   15  nagf_stat_ranks_and_scores
Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores
Related keywords: Blom scoresexponential scoresfinancerank scoresSavage scoresSimple Calculations on Statistical DataTukey scores
variance G07DDF   14  nagf_univar_robust_1var_trimmed
Computes a trimmed and winsorized mean of a single sample with estimates of their variance
Related keywords: trimmed meanunivariate estimationwinsorized mean
G13ABF   nagf_tsa_uni_autocorr
Univariate time series, sample autocorrelation function
Related keywords: autocorrelation coefficientsbig datadata analyticsfinancemeantest statistictime seriestime series analysisunivariate time series
variance-covariance matrix G01DCF   12  nagf_stat_normal_scores_var
Normal scores, approximate variance-covariance matrix
Related keywords: covariance matrixfinanceNormal scoresSimple Calculations on Statistical Data
G02BXF   14  nagf_correg_corrmat
Computes (optionally weighted) correlation and covariance matrices
Related keywords: big datacorrelation analysisdata analyticsfinancemeannonlinear regressionPearson product moment correlationpolynomial regressionregression analysisstandard deviation
G02DCF   14  nagf_correg_linregm_obs_edit
Add/delete an observation to/from a general linear regression model
Related keywords: big datacorrelation analysisdata analyticsfinancelinear regressionnonlinear regressionpolynomial regressionregressionregression analysisstandard errors
G02HFF   13  nagf_correg_robustm_user_varmat
Robust regression, variance-covariance matrix following G02HDF
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpolynomial regressionregression analysisrobust regression
G08RAF   12  nagf_nonpar_rank_regsn
Regression using ranks, uncensored data
Related keywords: nonparametric statisticsparameter estimatesregressionscores
G08RBF   12  nagf_nonpar_rank_regsn_censored
Regression using ranks, right-censored data
Related keywords: nonparametric statisticsparameter estimatesregressionscores
variance-ratio distribution G01EDF   14  nagf_stat_prob_f
Computes probabilities for F -distribution
Related keywords: CDF, cumulative distribution function F -distributionfinancelower tail probabilityprobabilitySimple Calculations on Statistical Dataupper tail probability
G01GDF   14  nagf_stat_prob_f_noncentral
Computes probabilities for the non-central F -distribution
Related keywords: F -distributionfinancelower tail probabilitySimple Calculations on Statistical Data
G01SDF   24  nagf_stat_prob_f_vector
Computes a vector of probabilities for F -distribution
Related keywords: big dataCDF, cumulative distribution functiondata analytics F -distributionlower tail probabilitySimple Calculations on Statistical Dataupper tail probability
G01TDF   24  nagf_stat_inv_cdf_f_vector
Computes a vector of deviates for F -distribution
Related keywords: big datadata analyticsdeviates F -distributioninverse CDFinverse cumulative distribution functionSimple Calculations on Statistical Data
variogram G05ZMF   24  nagf_rand_field_1d_user_setup
Setup for simulating one-dimensional random fields, user-defined variogram
Related keywords: big datadata analyticsoptions, computationalrandom fieldsrandom number generators
G05ZNF   24  nagf_rand_field_1d_predef_setup
Setup for simulating one-dimensional random fields
Related keywords: big datadata analyticsoptions, computationalrandom fieldsrandom number generators
G05ZQF   24  nagf_rand_field_2d_user_setup
Setup for simulating two-dimensional random fields, user-defined variogram
Related keywords: big datadata analyticsoptions, computationalrandom fieldsrandom number generators
G05ZRF   24  nagf_rand_field_2d_predef_setup
Setup for simulating two-dimensional random fields, preset variogram
Related keywords: big datadata analyticsoptions, computationalrandom fieldsrandom number generators
VARMA, vector autoregressive moving average model G05PJF   22  nagf_rand_times_mv_varma
Generates a realization of a multivariate time series from a VARMA model
Related keywords: big datadata analyticsfinancerandom number generatorstime series
G13DDF   22  nagf_tsa_multi_varma_estimate
Multivariate time series, estimation of VARMA model
Related keywords: big datacorrelation matrixdata analyticsfinancemaximum likelihoodmultivariate time seriesstandard errorstime seriestime series analysis
G13DLF   15  nagf_tsa_multi_diff
Multivariate time series, differences and/or transforms
Related keywords: big datadata analyticsfinancemultivariate time seriestime seriestime series analysis
G13DXF   15  nagf_tsa_uni_arma_roots
Calculates the zeros of a vector autoregressive (or moving average) operator
Related keywords: big datadata analyticsfinancetime seriestime series analysis
Vavilov density function G01MUF   21  nagf_stat_pdf_vavilov
Vavilov density function ϕ V λ ; κ , β 2
Related keywords: financeSimple Calculations on Statistical Data
G01ZUF   21  nagf_stat_init_vavilov
Initialization routine for G01MUF and G01EUF
Related keywords: financeSimple Calculations on Statistical Data
Vavilov distribution G01EUF   21  nagf_stat_prob_vavilov
Vavilov distribution function
Related keywords: financeSimple Calculations on Statistical Data
vectorized D01ESF   25  nagf_quad_md_sgq_multi_vec
Multi-dimensional quadrature using sparse grids
Related keywords: automaticmultidimensionalmultiple integrandsquadraturesparse
vectorized quadrature D01ASF   13  nagf_quad_1d_inf_wtrig
One-dimensional quadrature, adaptive, semi-infinite interval, weight function cos ω x or sin ω x
Related keywords: financeGauss–Kronrod quadratureintegration, adaptiveintegration, infinite intervalQAWFEQUADPACKquadraturequadrature, adaptive
D01ATF   13  nagf_quad_1d_fin_bad_vec
One-dimensional quadrature, adaptive, finite interval, variant of D01AJF efficient on vector machines
Related keywords: Gauss–Kronrod quadratureintegration, adaptiveQAGQAGSQUADPACKquadraturequadrature, adaptive
D01EAF   12  nagf_quad_md_adapt_multi
Multidimensional adaptive quadrature over hyper-rectangle, multiple integrands
Related keywords: integration, adaptiveintegration, multidimensionalquadraturequadrature, adaptive
Volterra integral equations D05BAF   14  nagf_inteq_volterra2
Nonlinear Volterra convolution equation, second kind
Related keywords: integral equations
D05BDF   16  nagf_inteq_abel2_weak
Nonlinear convolution Volterra–Abel equation, second kind, weakly singular
Related keywords: integral equations
D05BEF   16  nagf_inteq_abel1_weak
Nonlinear convolution Volterra–Abel equation, first kind, weakly singular
Related keywords: integral equations
D05BWF   16  nagf_inteq_volterra_weights
Generate weights for use in solving Volterra equations
Related keywords: integral equationsweights and abscissae
von Mises distribution G01ERF   16  nagf_stat_prob_vonmises
Computes probability for von Mises distribution
Related keywords: CDF, cumulative distribution functionfinancelower tail probabilitySimple Calculations on Statistical Data
G05SRF   22  nagf_rand_dist_vonmises
Generates a vector of pseudorandom numbers from a von Mises distribution
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
wavelet C09EYF   25  nagf_wav_2d_coeff_ext
Two-dimensional discrete wavelet transform coefficient extraction
Related keywords: coefficientsextracttwo-dimensionalwavelet transforms
C09EZF   25  nagf_wav_2d_coeff_ins
Two-dimensional discrete wavelet transform coefficient insertion
Related keywords: coefficientsinserttwo-dimensionalwavelet transforms
C09FYF   25  nagf_wav_3d_coeff_ext
Three-dimensional discrete wavelet transform coefficient extraction
Related keywords: coefficientsextractthree-dimensionalwavelet transforms
C09FZF   25  nagf_wav_3d_coeff_ins
Three-dimensional discrete wavelet transform coefficient insertion
Related keywords: coefficientsinsertthree-dimensionalwavelet transforms
wavelet continuous C09BAF   23  nagf_wav_1d_cont
One-dimensional real continuous wavelet transform
Related keywords: derivative of a Gaussian waveletMexican hat waveletMorlet waveletwaveletswavelets, one-dimensionalwavelet transforms
wavelets C09AAF   22  nagf_wav_1d_init
One-dimensional wavelet filter initialization
Related keywords: biorthogonal waveletDaubechies waveletHaar waveletwavelets, one-dimensionalwavelet transforms
C09ABF   23  nagf_wav_2d_init
Two-dimensional wavelet filter initialization
Related keywords: biorthogonal waveletDaubechies waveletHaar waveletwavelets, two-dimensionalwavelet transforms
C09ACF   24  nagf_wav_3d_init
Three-dimensional wavelet filter initialization
Related keywords: biorthogonal waveletDaubechies waveletHaar waveletwavelets, three-dimensionalwavelet transforms
C09BAF   23  nagf_wav_1d_cont
One-dimensional real continuous wavelet transform
Related keywords: derivative of a Gaussian waveletMexican hat waveletMorlet waveletwavelet continuouswavelets, one-dimensionalwavelet transforms
C09CAF   22  nagf_wav_1d_sngl_fwd
One-dimensional discrete wavelet transform
Related keywords: discrete transformfinancewavelets, one-dimensionalwavelet transforms
C09CBF   22  nagf_wav_1d_sngl_inv
One-dimensional inverse discrete wavelet transform
Related keywords: discrete transformfinancewavelets, one-dimensionalwavelet transforms
C09CCF   22  nagf_wav_1d_multi_fwd
One-dimensional multi-level discrete wavelet transform
Related keywords: financemulti-level discrete transformwavelets, one-dimensionalwavelet transforms
C09CDF   22  nagf_wav_1d_multi_inv
One-dimensional inverse multi-level discrete wavelet transform
Related keywords: financemulti-level discrete transformwavelets, one-dimensionalwavelet transforms
C09EAF   23  nagf_wav_2d_sngl_fwd
Two-dimensional discrete wavelet transform
Related keywords: discrete transformwavelets, two-dimensionalwavelet transforms
C09EBF   23  nagf_wav_2d_sngl_inv
Two-dimensional inverse discrete wavelet transform
Related keywords: discrete transformwavelets, two-dimensionalwavelet transforms
C09ECF   23  nagf_wav_2d_multi_fwd
Two-dimensional multi-level discrete wavelet transform
Related keywords: discrete transformmulti-level discrete transformwavelets, two-dimensionalwavelet transforms
C09EDF   23  nagf_wav_2d_multi_inv
Two-dimensional inverse multi-level discrete wavelet transform
Related keywords: discrete transformmulti-level discrete transformwavelets, two-dimensionalwavelet transforms
C09FAF   24  nagf_wav_3d_sngl_fwd
Three-dimensional discrete wavelet transform
Related keywords: discrete transformwavelets, three-dimensionalwavelet transforms
C09FBF   24  nagf_wav_3d_sngl_inv
Three-dimensional inverse discrete wavelet transform
Related keywords: discrete transformwavelets, three-dimensionalwavelet transforms
C09FCF   24  nagf_wav_3d_multi_fwd
Three-dimensional multi-level discrete wavelet transform
Related keywords: discrete transformmulti-level discrete transformwavelets, three-dimensionalwavelet transforms
C09FDF   24  nagf_wav_3d_mxolap_multi_inv
Three-dimensional inverse multi-level discrete wavelet transform
Related keywords: discrete transformmulti-level discrete transformwavelets, three-dimensionalwavelet transforms
wavelets, one-dimensional C09AAF   22  nagf_wav_1d_init
One-dimensional wavelet filter initialization
Related keywords: biorthogonal waveletDaubechies waveletHaar waveletwaveletswavelet transforms
C09BAF   23  nagf_wav_1d_cont
One-dimensional real continuous wavelet transform
Related keywords: derivative of a Gaussian waveletMexican hat waveletMorlet waveletwavelet continuouswaveletswavelet transforms
C09CAF   22  nagf_wav_1d_sngl_fwd
One-dimensional discrete wavelet transform
Related keywords: discrete transformfinancewaveletswavelet transforms
C09CBF   22  nagf_wav_1d_sngl_inv
One-dimensional inverse discrete wavelet transform
Related keywords: discrete transformfinancewaveletswavelet transforms
C09CCF   22  nagf_wav_1d_multi_fwd
One-dimensional multi-level discrete wavelet transform
Related keywords: financemulti-level discrete transformwaveletswavelet transforms
C09CDF   22  nagf_wav_1d_multi_inv
One-dimensional inverse multi-level discrete wavelet transform
Related keywords: financemulti-level discrete transformwaveletswavelet transforms
wavelets, three-dimensional C09ACF   24  nagf_wav_3d_init
Three-dimensional wavelet filter initialization
Related keywords: biorthogonal waveletDaubechies waveletHaar waveletwaveletswavelet transforms
C09FAF   24  nagf_wav_3d_sngl_fwd
Three-dimensional discrete wavelet transform
Related keywords: discrete transformwaveletswavelet transforms
C09FBF   24  nagf_wav_3d_sngl_inv
Three-dimensional inverse discrete wavelet transform
Related keywords: discrete transformwaveletswavelet transforms
C09FCF   24  nagf_wav_3d_multi_fwd
Three-dimensional multi-level discrete wavelet transform
Related keywords: discrete transformmulti-level discrete transformwaveletswavelet transforms
C09FDF   24  nagf_wav_3d_mxolap_multi_inv
Three-dimensional inverse multi-level discrete wavelet transform
Related keywords: discrete transformmulti-level discrete transformwaveletswavelet transforms
wavelets, two-dimensional C09ABF   23  nagf_wav_2d_init
Two-dimensional wavelet filter initialization
Related keywords: biorthogonal waveletDaubechies waveletHaar waveletwaveletswavelet transforms
C09EAF   23  nagf_wav_2d_sngl_fwd
Two-dimensional discrete wavelet transform
Related keywords: discrete transformwaveletswavelet transforms
C09EBF   23  nagf_wav_2d_sngl_inv
Two-dimensional inverse discrete wavelet transform
Related keywords: discrete transformwaveletswavelet transforms
C09ECF   23  nagf_wav_2d_multi_fwd
Two-dimensional multi-level discrete wavelet transform
Related keywords: discrete transformmulti-level discrete transformwaveletswavelet transforms
C09EDF   23  nagf_wav_2d_multi_inv
Two-dimensional inverse multi-level discrete wavelet transform
Related keywords: discrete transformmulti-level discrete transformwaveletswavelet transforms
wavelet transforms C09 Chapter Introduction   22  Wavelet Transforms
Weeks method C06LBF   14  nagf_sum_invlaplace_weeks
Inverse Laplace transform, modified Weeks' method
Related keywords: inverse Laplace transformLaplace transformsummation of series
Weibull distribution G05SSF   22  nagf_rand_dist_weibull
Generates a vector of pseudorandom numbers from a Weibull distribution
Related keywords: big datadata analyticsfinancerandom number generatorsrandom numbers
G07BEF   15  nagf_univar_estim_weibull
Computes maximum likelihood estimates for parameters of the Weibull distribution
Related keywords: maximum likelihoodunivariate estimation
weights and abscissae D01BCF   nagf_quad_1d_gauss_wgen
Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule
Related keywords: abscissaecubaturefinanceintegration, non-adaptivequadrature
D01TBF   24  nagf_quad_1d_gauss_wres
Pre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule
Related keywords: abscissaequadrature
D01TDF   26  nagf_quad_1d_gauss_wrec
Calculation of weights and abscissae for Gaussian quadrature rules, method of Golub and Welsch
Related keywords: abscissaecubatureGaussianGolubGolub and Welschintegrationnon-adaptivequadratureWelsch
D02UYF   23  nagf_ode_bvp_ps_lin_quad_weights
Clenshaw–Curtis quadrature weights for integration using computed Chebyshev coefficients
Related keywords: Chebyshev series approximationClenshaw–Curtis quadratureODE, ordinary differential equations
D05BWF   16  nagf_inteq_volterra_weights
Generate weights for use in solving Volterra equations
Related keywords: integral equationsVolterra integral equations
D05BYF   16  nagf_inteq_abel_weak_weights
Generate weights for use in solving weakly singular Abel-type equations
Related keywords: integral equations
Welsch D01TDF   26  nagf_quad_1d_gauss_wrec
Calculation of weights and abscissae for Gaussian quadrature rules, method of Golub and Welsch
Related keywords: abscissaecubatureGaussianGolubGolub and Welschintegrationnon-adaptivequadratureweights and abscissae
D01TEF   26  nagf_quad_1d_gauss_recm
Generates recursion coefficients needed by D01TDF to calculate a Gaussian quadrature rule
Related keywords: abscissaecubatureGaussianGolubGolub and Welschintegrationnon-adaptivequadraturerecursion coefficients
West's WV2 algorithm G02BUF   14  nagf_correg_ssqmat
Computes a weighted sum of squares matrix
Related keywords: big datacorrelation analysiscross-productsdata analyticsfinancemeannonlinear regressionpolynomial regressionregression analysissum of squares
Wichmann Hill G05KFF   22  nagf_rand_init_repeat
Initializes a pseudorandom number generator to give a repeatable sequence
Related keywords: ACORNbig datadata analyticsmersenne twisterMRG32k3aoptions, computationalrandom number generatorsrandom numbers
G05KGF   22  nagf_rand_init_nonrepeat
Initializes a pseudorandom number generator to give a non-repeatable sequence
Related keywords: ACORNbig datadata analyticsmersenne twisterMRG32k3aoptions, computationalrandom number generatorsrandom numbers
Wiener process G05XBF   24  nagf_rand_bb
Generate paths for a free or non-free Wiener process using the Brownian bridge algorithm
Related keywords: big databrownian bridgedata analyticsrandom number generators
Wilcoxon signed rank test G08AGF   14  nagf_nonpar_test_wilcoxon
Performs the Wilcoxon one-sample (matched pairs) signed rank test
Related keywords: nonparametric statisticssigned rank test
winsorized mean G07DDF   14  nagf_univar_robust_1var_trimmed
Computes a trimmed and winsorized mean of a single sample with estimates of their variance
Related keywords: trimmed meanunivariate estimationvariance
Wold's iterative method G02LBF   22  nagf_correg_pls_wold
Partial least squares (PLS) regression using Wold's iterative method
Related keywords: big datacorrelation analysisdata analyticsfinancenonlinear regressionpartial least squares regressionpolynomial regressionregression analysis
working precision X10BEF   26 
Write an integer (working precision) scalar to the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationcallback data ojbectinteger scalarwrite
X10BFF   26 
Write a real (working precision) scalar to the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationcallback data objectreal scalarwrite
X10CFF   26 
Read a real (working precision) scalar from the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationcallback data objectreadreal scalar
write X10BEF   26 
Write an integer (working precision) scalar to the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationcallback data ojbectinteger scalarworking precision
X10BFF   26 
Write a real (working precision) scalar to the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationcallback data objectreal scalarworking precision
X10BJF   26 
Write a scalar of type nagad_a1w_w_rtype to the callback data object
Related keywords: adjoint derivativesAD scalarAD utility operationsautomatic differentiationcallback data objectnagad_a1w_w_rtype
write record X04BAF   12  nagf_file_line_write
Write formatted record to external file
Related keywords: input utilitiesoutput utilities
W test for Normality G01DDF   12  nagf_stat_test_shapiro_wilk
Shapiro and Wilk's W test for Normality
Related keywords: financeShapiro and Wilk's W test for NormalitySimple Calculations on Statistical Data
tan x S07AAF   nagf_specfun_tan
tan x
Related keywords: approximations of special functionscircular tangentfinancetangent, circular
S10AAF   nagf_specfun_tanh
tanh x
Related keywords: approximations of special functionsfinancehyperbolic tangent
S10ACF   nagf_specfun_cosh
cosh x
Related keywords: approximations of special functionsfinancehyperbolic cosine
ber x , Kelvin function S19AAF   11  nagf_specfun_kelvin_ber
Kelvin function ber x
Related keywords: approximations of special functionsfinanceKelvin functions
S19ABF   11  nagf_specfun_kelvin_bei
Kelvin function bei x
Related keywords: approximations of special functionsfinanceKelvin functions
S19ACF   11  nagf_specfun_kelvin_ker
Kelvin function ker x
Related keywords: approximations of special functionsfinanceKelvin functions
S19ADF   11  nagf_specfun_kelvin_kei
Kelvin function kei x
Related keywords: approximations of special functionsfinanceKelvin functions
S19ANF   24  nagf_specfun_kelvin_ber_vector
Kelvin function vectorized ber x
Related keywords: approximations of special functionsKelvin functions
S19APF   24  nagf_specfun_kelvin_bei_vector
Kelvin function vectorized bei x
Related keywords: approximations of special functionsKelvin functions
S19AQF   24  nagf_specfun_kelvin_ker_vector
Kelvin function vectorized ker x
Related keywords: approximations of special functionsKelvin functions
S19ARF   24  nagf_specfun_kelvin_kei_vector
Kelvin function vectorized kei x
Related keywords: approximations of special functionsKelvin functions
Y 0 x , Bessel function S17ACF   nagf_specfun_bessel_y0_real
Bessel function Y 0 x
Related keywords: approximations of special functionsBessel functionfinance
S17AQF   24  nagf_specfun_bessel_y0_real_vector
Bessel function vectorized Y 0 x
Related keywords: approximations of special functionsBessel function
Y 1 x , Bessel function S17ADF   nagf_specfun_bessel_y1_real
Bessel function Y 1 x
Related keywords: approximations of special functionsBessel functionfinance
S17ARF   24  nagf_specfun_bessel_y1_real_vector
Bessel function vectorized Y 1 x
Related keywords: approximations of special functionsBessel function
Yates' correction G01AFF   nagf_stat_contingency_table
Two-way contingency table analysis, with χ 2 /Fisher's exact test
Related keywords: chi-squared distributioncontingency tablefinanceFisher's exact testSimple Calculations on Statistical Datatwo-way contingency table
Yule–Walker equations F04FEF   15  nagf_linsys_real_toeplitz_yule
Solution of the Yule–Walker equations for real symmetric positive definite Toeplitz matrix, one right-hand side
Related keywords: big datadata analyticsreal, positive-definite, symmetric, Toeplitz matrixsimultaneous linear equationsToeplitz matrix
F04MEF   15  nagf_linsys_real_toeplitz_yule_update
Update solution of the Yule–Walker equations for real symmetric positive definite Toeplitz matrix
Related keywords: big datadata analyticsreal, positive-definite, symmetric, Toeplitz matrixsimultaneous linear equationsToeplitz matrix
zaxpy F06GCF   12  nagf_blas_zaxpy
Add scalar times complex vector to complex vector
Related keywords: BLASblas, complex matriceselementary arithmeticlinear algebra support routines
zaxpyi F06GTF   14  nagf_blas_zaxpyi
Add scalar times complex sparse vector to a full vector
Related keywords: BLASblas, complex matricesinner productlinear algebra support routines
ZBDSQR F08MSF   16  nagf_lapackeig_zbdsqr
Performs an SVD of real bidiagonal matrix reduced from complex general matrix
Related keywords: differential qd algorithmeigenproblemLAPACKLAPACKleast squaresmatrix, band QL algorithm QR algorithmreal, bidiagonal matrixSVD, singular value decomposition
ZCGESV F07AQF   22  nagf_lapacklin_zcgesv
Computes the solution to a complex system of linear equations using mixed precision arithmetic
Related keywords: complex, nonsymmetric matrixLAPACKlinear equationsmixed-precision
zcopy F06GFF   12  nagf_blas_zcopy
Copy complex vector
Related keywords: BLASblas, complex matriceselementary arithmeticlinear algebra support routines
ZCPOSV F07FQF   23  nagf_lapacklin_zcposv
Computes the solution to a complex Hermitian positive definite system of linear equations using mixed precision arithmetic
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixLAPACKlinear equationsmixed-precision
zdotc F06GBF   12  nagf_blas_zdotc
Dot product of two complex vectors, conjugated
Related keywords: BLASblas, complex matricesinner productlinear algebra support routines
zdotci F06GSF   14  nagf_blas_zdotci
Dot product of a complex sparse and a full vector, conjugated
Related keywords: BLASblas, complex matricesinner productlinear algebra support routines
zdotu F06GAF   12  nagf_blas_zdotu
Dot product of two complex vectors, unconjugated
Related keywords: BLASblas, complex matricesinner productlinear algebra support routines
zdotui F06GRF   14  nagf_blas_zdotui
Dot product of a complex sparse and a full vector, unconjugated
Related keywords: BLASblas, complex matricesinner productlinear algebra support routines
zdrot F06KPF   12  nagf_blas_zdrot
Apply real plane rotation to two complex vectors
Related keywords: BLASlinear algebra support routinesrotation, elementary
zdscal F06JDF   12  nagf_blas_zdscal
Multiply complex vector by real scalar
Related keywords: BLASblas, complex matriceselementary arithmeticlinear algebra support routines
zeros of bessel functions S17ALF   20  nagf_specfun_bessel_zeros
Zeros of Bessel functions J α x , J α x , Y α x or Y α x
Related keywords: approximations of special functionsBessel functionfinance
zeros of polynomials C02 Chapter Introduction     Zeros of Polynomials
zeros of transcendental functions C05AUF   23  nagf_roots_contfn_brent_interval
Zero of continuous function, Brent algorithm, from a given starting value, binary search for interval
Related keywords: Brent algorithmfinanceroot-findingroots of transcendental equations
C05AVF   nagf_roots_contfn_interval_rcomm
Binary search for interval containing zero of continuous function (reverse communication)
Related keywords: financeroot-findingroots of transcendental equations
C05AWF   23  nagf_roots_contfn_cntin
Zero of continuous function, continuation method, from a given starting value
Related keywords: financeroot-findingroots of transcendental equations
C05AXF   nagf_roots_contfn_cntin_rcomm
Zero of continuous function, continuation method, from a given starting value (reverse communication)
Related keywords: financeroot-findingroots of transcendental equations
C05AYF   23  nagf_roots_contfn_brent
Zero of continuous function in a given interval, Brent algorithm
Related keywords: Brent algorithmfinanceroot-findingroots of transcendental equations
C05AZF   nagf_roots_contfn_brent_rcomm
Zero of continuous function in a given interval, Brent algorithm (reverse communication)
Related keywords: Brent algorithmfinanceroot-findingroots of transcendental equations
C05MDF   26  nagf_roots_sys_func_aa_rcomm
Solution of a system of nonlinear equations using Anderson acceleration (reverse communication)
Related keywords: Anderson accelerationroot-findingroots of transcendental equations
C05QBF   23  nagf_roots_sys_func_easy
Solution of a system of nonlinear equations using function values only (easy-to-use)
Related keywords: financeroot-findingroots of transcendental equations
C05QCF   23  nagf_roots_sys_func_expert
Solution of a system of nonlinear equations using function values only (comprehensive)
Related keywords: financeroot-findingroots of transcendental equations
C05QDF   23  nagf_roots_sys_func_rcomm
Solution of a system of nonlinear equations using function values only (reverse communication)
Related keywords: financeroot-findingroots of transcendental equations
C05QSF   23  nagf_roots_sparsys_func_easy
Solution of a sparse system of nonlinear equations using function values only (easy-to-use)
Related keywords: discretised systemroot-findingroots of transcendental equationssparse nonlinear system
C05RBF   23  nagf_roots_sys_deriv_easy
Solution of a system of nonlinear equations using first derivatives (easy-to-use)
Related keywords: financeroot-findingroots of transcendental equations
C05RCF   23  nagf_roots_sys_deriv_expert
Solution of a system of nonlinear equations using first derivatives (comprehensive)
Related keywords: financeroot-findingroots of transcendental equations
C05RDF   23  nagf_roots_sys_deriv_rcomm
Solution of a system of nonlinear equations using first derivatives (reverse communication)
Related keywords: financeroot-findingroots of transcendental equations
ZGBBRD F08LSF   19  nagf_lapackeig_zgbbrd
Reduction of complex rectangular band matrix to upper bidiagonal form
Related keywords: eigenproblemGivens rotationsLAPACKLAPACKleast squaresmatrix, bandreal, band, m by n matrix
ZGBEQU F07BTF   22  nagf_lapacklin_zgbequ
Computes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number
Related keywords: complex, band matrixequilibrationLAPACKlinear equationsmatrix, bandscaling
F07BUF   15  nagf_lapacklin_zgbcon
Estimate condition number of complex band matrix, matrix already factorized by F07BRF
Related keywords: complex, band matrixcondition number, matrixLAPACKlinear equationsmatrix, band
zgbmv F06SBF   12  nagf_blas_zgbmv
Matrix-vector product, complex rectangular band matrix
Related keywords: BLASblas, complex matricescomplex, band, m by n matrixlinear algebra support routinesmatrix, bandmultiply, matrix
ZGBRFS F07BVF   15  nagf_lapacklin_zgbrfs
Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, band matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, band
ZGBSV F07BNF   21  nagf_lapacklin_zgbsv
Computes the solution to a complex banded system of linear equations
Related keywords: complex, band matrixLAPACKlinear equations L U decompositionmatrix, band
ZGBSVX F07BPF   21  nagf_lapacklin_zgbsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
Related keywords: backward errorcomplex, band matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equations L U decompositionmatrix, band
F07BRF   15  nagf_lapacklin_zgbtrf
L U factorization of complex m by n band matrix
Related keywords: complex, m by n matrixLAPACKlinear equations L U decompositionmatrix, band
ZGBTRS F07BSF   15  nagf_lapacklin_zgbtrs
Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by F07BRF
Related keywords: complex, band matrixLAPACKlinear equations L U decompositionmatrix, band
ZGEBAK F08NWF   16  nagf_lapackeig_zgebak
Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF
Related keywords: balancingcomplex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squares
ZGEBAL F08NVF   16  nagf_lapackeig_zgebal
Balances a complex general matrix
Related keywords: balancingcomplex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squares
ZGEBRD F08KSF   16  nagf_lapackeig_zgebrd
Performs a unitary reduction of complex general rectangular matrix to bidiagonal form
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresunitary transformations
ZGECON F07AUF   15  nagf_lapacklin_zgecon
Estimate condition number of complex matrix, matrix already factorized by F07ARF
Related keywords: complex, nonsymmetric matrixcondition number, matrixLAPACKlinear equations
ZGEEQU F07ATF   22  nagf_lapacklin_zgeequ
Computes row and column scalings intended to equilibrate a general complex matrix and reduce its condition number
Related keywords: complex, nonsymmetric matrixequilibrationLAPACKlinear equationsscaling
ZGEES F08PNF   21  nagf_lapackeig_zgees
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenvaluesLAPACKLAPACKleast squaresSchur formSchur vectors
ZGEESX F08PPF   21  nagf_lapackeig_zgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also computes a reciprocal condition number for the average of the selected eigenvalues and for the right invariant subspace corresponding to these eigenvalues
Related keywords: condition number, matrixeigenproblemeigenvaluesLAPACKLAPACKleast squaresreal, nonsymmetric matrixSchur formSchur vectors
ZGEHRD F08NSF   16  nagf_lapackeig_zgehrd
Performs a unitary reduction of complex general matrix to upper Hessenberg form
Related keywords: complex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresunitary transformations
ZGELQF F08AVF   16  nagf_lapackeig_zgelqf
Performs a L Q factorization of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squares LQ factorization
ZGELS F08ANF   21  nagf_lapackeig_zgels
Solves a complex linear least problem of full rank
Related keywords: complex, m by n matrixeigenproblemfinanceLAPACKLAPACKleast squareslinear least squares LQ decompositionoverdetermined linear equations QR factorizationunderdetermined linear system
ZGELSD F08KQF   21  nagf_lapackeig_zgelsd
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
Related keywords: complex, m by n matrixdivide-and-conquer methodeigenproblemLAPACKLAPACKleast squareslinear least squaresminimal least squaresSVD, singular value decomposition
ZGELSS F08KNF   21  nagf_lapackeig_zgelss
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squareslinear least squaresminimal least squaresSVD, singular value decomposition
ZGELSY F08BNF   21  nagf_lapackeig_zgelsy
Computes the minimum-norm solution to a complex linear least squares problem
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squareslinear least squaresminimal least squares
zgemm F06ZAF   14  nagf_blas_zgemm
Matrix-matrix product, two complex rectangular matrices
Related keywords: BLASblas, complex matricescomplex, m by n matrixlinear algebra support routinesmultiply, matrix
F06ZCF   14  nagf_blas_zhemm
Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian, indefinite matrixcomplex, m by n matrixlinear algebra support routinesmultiply, matrix
ZGEMQRT F08AQF   25  nagf_lapackeig_zgemqrt
Applies the unitary transformation determined by F08APF
Related keywords: eigenproblemexplicit blockingLAPACKleast squaresQR factorizationrecursive QRunitary transformations
zgemv F06SAF   12  nagf_blas_zgemv
Matrix-vector product, complex rectangular matrix
Related keywords: BLASblas, complex matricescomplex, m by n matrixlinear algebra support routinesmultiply, matrix
ZGEQLF F08CSF   22  nagf_lapackeig_zgeqlf
Q L factorization of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squares QL factorization
ZGEQP3 F08BTF   22  nagf_lapackeig_zgeqp3
Q R factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squares QR factorization
ZGEQPF F08BSF   16  nagf_lapackeig_zgeqpf
Q R factorization, with column pivoting, of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squares QR factorization
ZGEQRF F08ASF   16  nagf_lapackeig_zgeqrf
Performs a Q R factorization of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squares QR factorization
ZGEQRT F08APF   25  nagf_lapackeig_zgeqrt
Performs a Q R factorization of complex general rectangular matrix using recursive algorithm
Related keywords: complex, m by n matrixeigenproblemexplicit blockingLAPACKleast squaresQR factorizationrecursive QR
zgerc F06SNF   12  nagf_blas_zgerc
Rank-1 update, complex rectangular matrix, conjugated vector
Related keywords: BLASblas, complex matricescomplex, m by n matrixlinear algebra support routinesrank k matrix updates
ZGERFS F07AVF   15  nagf_lapacklin_zgerfs
Refined solution with error bounds of complex system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, nonsymmetric matrixforward errorLAPACKlinear equations
ZGERQF F08CVF   22  nagf_lapackeig_zgerqf
R Q factorization of complex general rectangular matrix
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresRQ factorizations
zgeru F06SMF   12  nagf_blas_zgeru
Rank-1 update, complex rectangular matrix, unconjugated vector
Related keywords: BLASblas, complex matricescomplex, m by n matrixlinear algebra support routinesrank k matrix updates
ZGESDD F08KRF   21  nagf_lapackeig_zgesdd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
Related keywords: complex, nonsymmetric matrixdivide-and-conquer methodeigenproblemLAPACKLAPACKleast squaresSVD, singular value decomposition
ZGESV F07ANF   21  nagf_lapacklin_zgesv
Computes the solution to a complex system of linear equations
Related keywords: complex, nonsymmetric matrixLAPACKlinear equations L U decomposition
ZGESVD F08KPF   21  nagf_lapackeig_zgesvd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
Related keywords: complex, nonsymmetric matrixeigenproblemfinanceLAPACKLAPACKleast squaresSVD, singular value decomposition
ZGESVX F07APF   21  nagf_lapacklin_zgesvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
Related keywords: backward errorcomplex, nonsymmetric matrixcondition number, matrixerror bound, matrixfinanceforward errorLAPACKlinear equations L U decomposition
ZGETRF F07ARF   15  nagf_lapacklin_zgetrf
L U factorization of complex m by n matrix
Related keywords: complex, m by n matrixfinanceLAPACKlinear equations L U decomposition
ZGETRI F07AWF   15  nagf_lapacklin_zgetri
Inverse of complex matrix, matrix already factorized by F07ARF
Related keywords: complex, nonsymmetric matrixinverse, matrixLAPACKlinear equations
ZGETRS F07ASF   15  nagf_lapacklin_zgetrs
Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by F07ARF
Related keywords: complex, nonsymmetric matrixfinanceLAPACKlinear equations L U decomposition
ZGGBAL F08WVF   20  nagf_lapackeig_zggbal
Balances a pair of complex, square, matrices
Related keywords: balancingcomplex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squares
F08WWF   20  nagf_lapackeig_zggbak
Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF
Related keywords: balancingcomplex, nonsymmetric matrixeigenproblemeigenvectorsLAPACKLAPACKleast squares
ZGGES F08XNF   21  nagf_lapackeig_zgges
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresSchur vectors
F08XPF   21  nagf_lapackeig_zggesx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresSchur vectors
ZGGES3 F08XQF   26  nagf_lapackeig_zgges3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresSchur vectors
ZGGEV F08WNF   21  nagf_lapackeig_zggev
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
ZGGEV3 F08WQF   26  nagf_lapackeig_zggev3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
Related keywords: complex, nonsymmetric matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
ZGGEVX F08WPF   21  nagf_lapackeig_zggevx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
Related keywords: balancingcomplex, nonsymmetric matrixcondition number, matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsfinanceforward errorgeneralized eigenproblemLAPACKLAPACKleast squares
ZGGGLM F08ZPF   21  nagf_lapackeig_zggglm
Solves a complex general Gauss–Markov linear model (GLM) problem
Related keywords: complex, m by n matrixeigenproblemGauss–Markov linear modelLAPACKLAPACKleast squares
ZGGHD3 F08WTF   26  nagf_lapackeig_zgghd3
Performs, using BLAS-3, a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
Related keywords: complex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresunitary transformations
ZGGHRD F08WSF   20  nagf_lapackeig_zgghrd
Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
Related keywords: complex, nonsymmetric matrixeigenproblemLAPACKLAPACKleast squaresunitary transformations
ZGGLSE F08ZNF   21  nagf_lapackeig_zgglse
Solves the complex linear equality-constrained least squares (LSE) problem
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squareslinear least squaresRQ factorizations
ZGGQRF F08ZSF   22  nagf_lapackeig_zggqrf
Computes a generalized Q R factorization of a complex matrix pair
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squares QR factorization
ZGGRQF F08ZTF   22  nagf_lapackeig_zggrqf
Computes a generalized R Q factorization of a complex matrix pair
Related keywords: complex, m by n matrixeigenproblemLAPACKLAPACKleast squaresRQ factorizations
ZGGSVD F08VNF   21  nagf_lapackeig_zggsvd
Computes the generalized singular value decomposition of a complex matrix pair
Related keywords: complex, nonsymmetric matrixeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresSVD, generalized
ZGGSVD3 F08VQF   26  nagf_lapackeig_zggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair
Related keywords: complex, nonsymmetric matrixeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresSVD, generalized
ZGGSVP F08VSF   22  nagf_lapackeig_zggsvp
Produces unitary matrices that simultaneously reduce the complex, m by n , matrix A and the complex, p by n , matrix B to upper triangular form
Related keywords: complex, m by n matrixeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresorthogonal transformationsSVD, generalized
ZGGSVP3 F08VUF   26  nagf_lapackeig_zggsvp3
Produces unitary matrices, using BLAS-3, that simultaneously reduce the complex, m by n , matrix A and the complex, p by n , matrix B to upper triangular form
Related keywords: complex, m by n matrixeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squaresorthogonal transformationsSVD, generalized
ZGTCON F07CUF   22  nagf_lapacklin_zgtcon
Estimates the reciprocal of the condition number of a complex tridiagonal matrix using the L U factorization computed by F07CDF
Related keywords: complex, tridiagonal matrixcondition number, matrixLAPACKlinear equations L U decompositionmatrix, band
zgthr F06GUF   14  nagf_blas_zgthr
Gather complex sparse vector
Related keywords: BLASblas, complex matriceselementary arithmeticlinear algebra support routines
zgthrz F06GVF   14  nagf_blas_zgthrz
Gather and set to zero complex sparse vector
Related keywords: BLASblas, complex matriceselementary arithmeticlinear algebra support routines
ZGTRFS F07CVF   22  nagf_lapacklin_zgtrfs
Refined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, tridiagonal matrixforward errorLAPACKlinear equations L U decompositionmatrix, band
ZGTSV F07CNF   21  nagf_lapacklin_zgtsv
Computes the solution to a complex tridiagonal system of linear equations
Related keywords: complex, tridiagonal matrixLAPACKlinear equations L U decompositionmatrix, band
ZGTSVX F07CPF   21  nagf_lapacklin_zgtsvx
Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations
Related keywords: backward errorcomplex, tridiagonal matrixforward errorLAPACKlinear equations L U decompositionmatrix, band
ZGTTRF F07CRF   22  nagf_lapacklin_zgttrf
L U factorization of complex tridiagonal matrix
Related keywords: complex, tridiagonal matrixLAPACKlinear equations L U decompositionmatrix, band
ZGTTRS F07CSF   22  nagf_lapacklin_zgttrs
Solves a complex tridiagonal system of linear equations using the L U factorization computed by F07CDF
Related keywords: complex, tridiagonal matrixLAPACKlinear equations L U decompositionmatrix, band
ZHBEV F08HNF   21  nagf_lapackeig_zhbev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
Related keywords: complex, band, Hermitian matrixeigenproblemLAPACKLAPACKleast squaresmatrix, band QR algorithmunitary transformations
ZHBEVD F08HQF   19  nagf_lapackeig_zhbevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
Related keywords: complex, band, Hermitian matrixdivide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandPal–Walker–Kahan ( QL or QR ) algorithm
ZHBEVX F08HPF   21  nagf_lapackeig_zhbevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
Related keywords: complex, band, Hermitian matrixeigenproblemLAPACKLAPACKleast squaresmatrix, bandunitary transformations
ZHBGST F08USF   19  nagf_lapackeig_zhbgst
Performs a reduction of complex Hermitian-definite banded generalized eigenproblem A x = λ B x to standard form C y = λ y , such that C has the same bandwidth as A
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, band
ZHBGV F08UNF   21  nagf_lapackeig_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, band
ZHBGVD F08UQF   21  nagf_lapackeig_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: complex, band, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, band
ZHBGVX F08UPF   21  nagf_lapackeig_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, band
zhbmv F06SDF   12  nagf_blas_zhbmv
Matrix-vector product, complex Hermitian band matrix
Related keywords: BLASblas, complex matricescomplex, band, Hermitian matrixlinear algebra support routinesmatrix, bandmultiply, matrix
ZHBTRD F08HSF   16  nagf_lapackeig_zhbtrd
Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
Related keywords: complex, band, Hermitian matrixeigenproblemLAPACKLAPACKleast squaresmatrix, bandunitary transformations
ZHECON F07MUF   15  nagf_lapacklin_zhecon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07MRF
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixcondition number, matrixdiagonal pivoting methodLAPACKlinear equations
ZHEEV F08FNF   21  nagf_lapackeig_zheev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares
ZHEEVD F08FQF   19  nagf_lapackeig_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
Related keywords: complex, Hermitian, indefinite matrixdivide-and-conquer methodeigenproblemeigenvalueseigenvectorsfinanceLAPACKLAPACKleast squares
ZHEEVR F08FRF   21  nagf_lapackeig_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresrelatively robust representationsunitary transformations
ZHEEVX F08FPF   21  nagf_lapackeig_zheevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvalueseigenvectorsfinanceLAPACKLAPACKleast squares
ZHEGST F08SSF   16  nagf_lapackeig_zhegst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , B factorized by F07FRF
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squares
ZHEGV F08SNF   21  nagf_lapackeig_zhegv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
ZHEGVD F08SQF   21  nagf_lapackeig_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
Related keywords: complex, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
ZHEGVX F08SPF   21  nagf_lapackeig_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
zhemv F06SCF   12  nagf_blas_zhemv
Matrix-vector product, complex Hermitian matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian matrixlinear algebra support routinesmultiply, matrix
zher F06SPF   12  nagf_blas_zher
Rank-1 update, complex Hermitian matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian matrixlinear algebra support routinesrank k matrix updates
zher2 F06SRF   12  nagf_blas_zher2
Rank-2 update, complex Hermitian matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian matrixlinear algebra support routinesrank k matrix updates
zher2k F06ZRF   14  nagf_blas_zher2k
Rank- 2 k update of a complex Hermitian matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian, indefinite matrixlinear algebra support routinesrank k matrix updates
F06ZUF   14  nagf_blas_zsyrk
Rank- k update of a complex symmetric matrix
Related keywords: BLASblas, complex matricescomplex, symmetric matrixlinear algebra support routinesrank k matrix updates
ZHERFS F07MVF   15  nagf_lapacklin_zherfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
Related keywords: backward errorBunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equations
zherk F06WQF   23  nagf_blas_zhfrk
Rank- k update of a complex Hermitian matrix, Rectangular Full Packed format
Related keywords: BLASblas, complex matricescomplex, Hermitian, indefinite matrixlinear algebra support routinesrank k matrix updates
F06ZPF   14  nagf_blas_zherk
Rank- k update of a complex Hermitian matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian, indefinite matrixlinear algebra support routinesrank k matrix updates
ZHESV F07MNF   21  nagf_lapacklin_zhesv
Computes the solution to a complex Hermitian system of linear equations
Related keywords: complex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACK LDL H decompositionlinear equations UDU H decomposition
ZHESVX F07MPF   21  nagf_lapacklin_zhesvx
Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations
Related keywords: backward errorcomplex, Hermitian, indefinite matrixdiagonal pivoting methodforward errorLAPACK LDL H decompositionlinear equations UDU H decomposition
ZHETRD F08FSF   16  nagf_lapackeig_zhetrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
Related keywords: complex, Hermitian, indefinite matrixeigenproblemLAPACKLAPACKleast squaresunitary transformations
ZHETRF F07MRF   15  nagf_lapacklin_zhetrf
Bunch–Kaufman factorization of complex Hermitian indefinite matrix
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACKlinear equations
ZHETRI F07MWF   15  nagf_lapacklin_zhetri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07MRF
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methodinverse, matrixLAPACKlinear equations
ZHETRS F07MSF   15  nagf_lapacklin_zhetrs
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MRF
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACKlinear equations
ZHGEQZ F08XSF   20  nagf_lapackeig_zhgeqz
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenproblem, generalizedeigenvaluesgeneralized eigenproblemgeneralized Schur formLAPACKLAPACKleast squaresQZ algorithm
ZHPCON F07PUF   15  nagf_lapacklin_zhpcon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07PRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixcondition number, matrixdiagonal pivoting methodLAPACKlinear equations
ZHPEV F08GNF   21  nagf_lapackeig_zhpev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares
ZHPEVD F08GQF   19  nagf_lapackeig_zhpevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer or Pal–Walker–Kahan variant of the Q L or Q R algorithm)
Related keywords: complex, Hermitian, indefinite matrixdivide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresPal–Walker–Kahan ( QL or QR ) algorithm
ZHPEVX F08GPF   21  nagf_lapackeig_zhpevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
Related keywords: complex, Hermitian, indefinite matrixeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares
ZHPGV F08TNF   21  nagf_lapackeig_zhpgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
ZHPGVD F08TQF   21  nagf_lapackeig_zhpgvd
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
Related keywords: complex, Hermitian, positive-definite matrixdivide-and-conquer methodeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
F08TSF   16  nagf_lapackeig_zhpgst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , packed storage, B factorized by F07GRF
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squares
ZHPGVX F08TPF   21  nagf_lapackeig_zhpgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
Related keywords: complex, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedeigenvalueseigenvectorsgeneralized eigenproblemLAPACKLAPACKleast squares
zhpmv F06SEF   12  nagf_blas_zhpmv
Matrix-vector product, complex Hermitian packed matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian matrixlinear algebra support routinesmultiply, matrix
zhpr F06SQF   12  nagf_blas_zhpr
Rank-1 update, complex Hermitian packed matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian matrixlinear algebra support routinesrank k matrix updates
zhpr2 F06SSF   12  nagf_blas_zhpr2
Rank-2 update, complex Hermitian packed matrix
Related keywords: BLASblas, complex matricescomplex, Hermitian matrixlinear algebra support routinesrank k matrix updates
ZHPRFS F07PVF   15  nagf_lapacklin_zhprfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorBunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equations
ZHPSV F07PNF   21  nagf_lapacklin_zhpsv
Computes the solution to a complex Hermitian system of linear equations, packed storage
Related keywords: complex, Hermitian, indefinite matrixdiagonal pivoting methodinverse, matrixLAPACK LDL H decompositionlinear equations UDU H decomposition
ZHPSVX F07PPF   21  nagf_lapacklin_zhpsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, Hermitian, system of linear equations, error bounds and condition estimates. Packed storage
Related keywords: backward errorcomplex, Hermitian, indefinite matrixdiagonal pivoting methodforward errorinverse, matrixLAPACK LDL H decompositionlinear equations UDU H decomposition
ZHPTRD F08GSF   16  nagf_lapackeig_zhptrd
Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
Related keywords: complex, Hermitian, indefinite matrixeigenproblemLAPACKLAPACKleast squaresunitary transformations
ZHPTRF F07PRF   15  nagf_lapacklin_zhptrf
Bunch–Kaufman factorization of complex Hermitian indefinite matrix, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACKlinear equations
ZHPTRI F07PWF   15  nagf_lapacklin_zhptri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07PRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methodinverse, matrixLAPACKlinear equations
ZHPTRS F07PSF   15  nagf_lapacklin_zhptrs
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, Hermitian, indefinite matrixdiagonal pivoting methodLAPACKlinear equations
ZHSEIN F08PXF   16  nagf_lapackeig_zhsein
Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
Related keywords: complex, Hessenberg matrixeigenproblemeigenvectorsinverse iterationLAPACKLAPACKleast squares
ZHSEQR F08PSF   16  nagf_lapackeig_zhseqr
Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
Related keywords: complex, Hessenberg matrixeigenproblemeigenvaluesLAPACKLAPACKleast squaresSchur form
zlanhf F06WNF   23  nagf_blas_zlanhf
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format
Related keywords: 1-normBLASBLASblas, complex matricescomplex, Hermitian matrixFrobenius norminfinity-normlinear algebra support routineslinear algebra support routines;
ZPBCON F07HUF   15  nagf_lapacklin_zpbcon
Estimate condition number of complex Hermitian positive definite band matrix, matrix already factorized by F07HRF
Related keywords: complex, band, Hermitian, positive-definite matrixcondition number, matrixLAPACKlinear equationsmatrix, band
ZPBEQU F07HTF   22  nagf_lapacklin_zpbequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite banded matrix and reduce its condition number
Related keywords: complex, band, Hermitian, positive-definite matrixequilibrationLAPACKlinear equationsmatrix, bandscaling
ZPBRFS F07HVF   15  nagf_lapacklin_zpbrfs
Refined solution with error bounds of complex Hermitian positive definite band system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositioncomplex, band, Hermitian, positive-definite matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, band
ZPBSTF F08UTF   19  nagf_lapackeig_zpbstf
Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
Related keywords: complex, band, Hermitian, positive-definite matrixeigenproblemeigenproblem, generalizedgeneralized eigenproblemLAPACKLAPACKleast squaresmatrix, bandSplit Cholesky factorization
ZPBSV F07HNF   21  nagf_lapacklin_zpbsv
Computes the solution to a complex Hermitian positive definite banded system of linear equations
Related keywords: Cholesky decompositioncomplex, band, Hermitian, positive-definite matrixLAPACKlinear equationsmatrix, band
ZPBSVX F07HPF   21  nagf_lapacklin_zpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite banded system of linear equations
Related keywords: backward errorCholesky decompositioncomplex, band, Hermitian, positive-definite matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, band
ZPBTRF F07HRF   15  nagf_lapacklin_zpbtrf
Cholesky factorization of complex Hermitian positive definite band matrix
Related keywords: Cholesky decompositioncomplex, band, Hermitian, positive-definite matrixLAPACKlinear equationsmatrix, band
ZPBTRS F07HSF   15  nagf_lapacklin_zpbtrs
Solution of complex Hermitian positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HRF
Related keywords: Cholesky decompositioncomplex, band, Hermitian, positive-definite matrixLAPACKlinear equationsmatrix, band
ZPETRI F07WWF   23  nagf_lapacklin_zpftri
Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07WRF, Rectangular Full Packed format
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixLAPACKlinear equations
ZPFTRF F07WRF   23  nagf_lapacklin_zpftrf
Cholesky factorization of complex Hermitian positive definite matrix, Rectangular Full Packed format
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixLAPACKlinear equations
ZPFTRS F07WSF   23  nagf_lapacklin_zpftrs
Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by F07WRF, Rectangular Full Packed format
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixLAPACKlinear equations
ZPOCON F07FUF   15  nagf_lapacklin_zpocon
Estimate condition number of complex Hermitian positive definite matrix, matrix already factorized by F07FRF
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixcondition number, matrixLAPACKlinear equations
ZPOEQU F07FTF   22  nagf_lapacklin_zpoequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number
Related keywords: complex, Hermitian, positive-definite matrixequilibrationLAPACKlinear equationsscaling
ZPORFS F07FVF   15  nagf_lapacklin_zporfs
Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite matrixerror bound, matrixforward errorLAPACKlinear equations
ZPOSV F07FNF   21  nagf_lapacklin_zposv
Computes the solution to a complex Hermitian positive definite system of linear equations
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixLAPACKlinear equations
ZPOSVX F07FPF   21  nagf_lapacklin_zposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite matrixcondition number, matrixerror bound, matrixfinanceforward errorLAPACKlinear equations
ZPOTRF F07FRF   15  nagf_lapacklin_zpotrf
Cholesky factorization of complex Hermitian positive definite matrix
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixLAPACKlinear equations
ZPOTRI F07FWF   15  nagf_lapacklin_zpotri
Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07FRF
Related keywords: complex, Hermitian, positive-definite matrixinverse, matrixLAPACKlinear equations
ZPOTRS F07FSF   15  nagf_lapacklin_zpotrs
Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FRF
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixLAPACKlinear equations
ZPPCON F07GUF   15  nagf_lapacklin_zppcon
Estimate condition number of complex Hermitian positive definite matrix, matrix already factorized by F07GRF, packed storage
Related keywords: complex, Hermitian, positive-definite matrixcondition number, matrixLAPACKlinear equations
ZPPEQU F07GTF   22  nagf_lapacklin_zppequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number, packed storage
Related keywords: complex, Hermitian, positive-definite matrixequilibrationLAPACKlinear equationsscaling
ZPPRFS F07GVF   15  nagf_lapacklin_zpprfs
Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite matrixerror bound, matrixforward errorLAPACKlinear equations
ZPPSV F07GNF   21  nagf_lapacklin_zppsv
Computes the solution to a complex Hermitian positive definite system of linear equations, packed storage
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixLAPACKlinear equations
ZPPSVX F07GPF   21  nagf_lapacklin_zppsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations, packed storage
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equations
ZPPTRF F07GRF   15  nagf_lapacklin_zpptrf
Cholesky factorization of complex Hermitian positive definite matrix, packed storage
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixLAPACKlinear equations
F07JRF   22  nagf_lapacklin_zpttrf
Computes the LDL H factorization of a complex Hermitian positive definite tridiagonal matrix
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixLAPACKlinear equationsmatrix, band
ZPPTRI F07GWF   15  nagf_lapacklin_zpptri
Inverse of complex Hermitian positive definite matrix, matrix already factorized by F07GRF, packed storage
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixinverse, matrixLAPACKlinear equations
ZPPTRS F07GSF   15  nagf_lapacklin_zpptrs
Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GRF, packed storage
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite matrixLAPACKlinear equations
F07JSF   22  nagf_lapacklin_zpttrs
Solves a complex Hermitian positive definite tridiagonal system using the LDL H factorization computed by F07JRF
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixLAPACKlinear equationsmatrix, band
ZPSTRF F07KRF   23  nagf_lapacklin_zpstrf
Cholesky factorization of complex Hermitian positive semidefinite matrix
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-semidefinite matrixLAPACKlinear equations
ZPTCON F07JUF   22  nagf_lapacklin_zptcon
Computes the reciprocal of the condition number of a complex Hermitian positive definite tridiagonal system using the LDL H factorization computed by F07JRF
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixcondition number, matrixLAPACKlinear equationsmatrix, band
ZPTEQR F08JUF   16  nagf_lapackeig_zpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACK LDL H decompositionleast squaresreal, symmetric, tridiagonal matrix
ZPTRFS F07JVF   22  nagf_lapacklin_zptrfs
Refined solution with error bounds of complex Hermitian positive definite tridiagonal system of linear equations, multiple right-hand sides
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixforward errorLAPACKlinear equationsmatrix, band
ZPTSV F07JNF   21  nagf_lapacklin_zptsv
Computes the solution to a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: Cholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixLAPACKlinear equationsmatrix, band
ZPTSVX F07JPF   21  nagf_lapacklin_zptsvx
Uses the LDL T factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite tridiagonal system of linear equations
Related keywords: backward errorCholesky decompositioncomplex, Hermitian, positive-definite, tridiagonal matrixcondition number, matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, band
zrot F06HMF   21  nagf_blas_zrot
Apply plane rotation with real cosine and complex sine
Related keywords: BLASblas, complex matriceslinear algebra support routinesrotation, elementary
zscal F06GDF   12  nagf_blas_zscal
Multiply complex vector by complex scalar
Related keywords: BLASblas, complex matriceselementary arithmeticlinear algebra support routines
z-scores G03ZAF   15  nagf_mv_z_scores
Produces standardized values ( z -scores) for a data matrix
Related keywords: multivariate methodsstandardized values
zsctr F06GWF   14  nagf_blas_zsctr
Scatter complex sparse vector
Related keywords: BLASblas, complex matriceselementary arithmeticlinear algebra support routines
ZSPCON F07QUF   15  nagf_lapacklin_zspcon
Estimate condition number of complex symmetric matrix, matrix already factorized by F07QRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixcondition number, matrixdiagonal pivoting methodLAPACKlinear equations
ZSPRFS F07QVF   15  nagf_lapacklin_zsprfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorBunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equations
ZSPSV F07QNF   21  nagf_lapacklin_zspsv
Computes the solution to a complex symmetric system of linear equations, packed storage
Related keywords: complex, symmetric matrixdiagonal pivoting methodLAPACK LDL T decompositionlinear equations UDU T decomposition
ZSPSVX F07QPF   21  nagf_lapacklin_zspsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, symmetric, system of linear equations, error bounds and condition estimates. Packed storage
Related keywords: backward errorcomplex, symmetric matrixdiagonal pivoting methodforward errorLAPACK LDL T decompositionlinear equations UDU T decomposition
ZSPTRF F07QRF   15  nagf_lapacklin_zsptrf
Bunch–Kaufman factorization of complex symmetric matrix, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methodLAPACKlinear equations
ZSPTRI F07QWF   15  nagf_lapacklin_zsptri
Inverse of complex symmetric matrix, matrix already factorized by F07QRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methodinverse, matrixLAPACKlinear equations
ZSPTRS F07QSF   15  nagf_lapacklin_zsptrs
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07QRF, packed storage
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methodLAPACKlinear equations
ZSTEDC F08JVF   22  nagf_lapackeig_zstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
Related keywords: divide-and-conquer methodeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares QL algorithm QR algorithmreal, symmetric, tridiagonal matrix
ZSTEGR F08JYF   22  nagf_lapackeig_zstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
Related keywords: dqds algorithmeigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrixrelatively robust representations
ZSTEIN F08JXF   16  nagf_lapackeig_zstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
Related keywords: eigenproblemeigenvectorsinverse iterationLAPACKLAPACKleast squaresmatrix, bandreal, symmetric, tridiagonal matrix
ZSTEQR F08JSF   16  nagf_lapackeig_zsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit Q L or Q R algorithm
Related keywords: eigenproblemeigenvalueseigenvectorsLAPACKLAPACKleast squares QR algorithmreal, symmetric, tridiagonal matrix
zswap F06GGF   12  nagf_blas_zswap
Swap two complex vectors
Related keywords: BLASblas, complex matriceselementary arithmeticlinear algebra support routines
ZSYCON F07NUF   15  nagf_lapacklin_zsycon
Estimate condition number of complex symmetric matrix, matrix already factorized by F07NRF
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixcondition number, matrixdiagonal pivoting methodLAPACKlinear equations
zsymm F06ZTF   14  nagf_blas_zsymm
Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix
Related keywords: BLASblas, complex matricescomplex, m by n matrixcomplex, symmetric matrixlinear algebra support routinesmultiply, matrix
zsyr2k F06ZWF   14  nagf_blas_zsyr2k
Rank- 2 k update of a complex symmetric matrix
Related keywords: BLASblas, complex matricescomplex, symmetric matrixlinear algebra support routinesrank k matrix updates
ZSYRFS F07NVF   15  nagf_lapacklin_zsyrfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
Related keywords: backward errorBunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methoderror bound, matrixforward errorLAPACKlinear equations
ZSYSV F07NNF   21  nagf_lapacklin_zsysv
Computes the solution to a complex symmetric system of linear equations
Related keywords: complex, symmetric matrixdiagonal pivoting methodLAPACK LDL H decompositionlinear equations UDU H decomposition
ZSYSVX F07NPF   21  nagf_lapacklin_zsysvx
Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations
Related keywords: backward errorcomplex, symmetric matrixdiagonal pivoting methodforward errorLAPACK LDL H decompositionlinear equations UDU H decomposition
ZSYTRF F07NRF   15  nagf_lapacklin_zsytrf
Bunch–Kaufman factorization of complex symmetric matrix
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methodLAPACKlinear equations
ZSYTRI F07NWF   15  nagf_lapacklin_zsytri
Inverse of complex symmetric matrix, matrix already factorized by F07NRF
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methodinverse, matrixLAPACKlinear equations
ZSYTRS F07NSF   15  nagf_lapacklin_zsytrs
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07NRF
Related keywords: Bunch–Kaufman factorizationcomplex, symmetric matrixdiagonal pivoting methodLAPACKlinear equations
ZTBCON F07VUF   15  nagf_lapacklin_ztbcon
Estimate condition number of complex band triangular matrix
Related keywords: complex, band, triangular matrixcondition number, matrixLAPACKlinear equationsmatrix, band
ztbmv F06SGF   12  nagf_blas_ztbmv
Matrix-vector product, complex triangular band matrix
Related keywords: BLASblas, complex matricescomplex, band, triangular matrixlinear algebra support routinesmatrix, bandmultiply, matrix
ZTBRFS F07VVF   15  nagf_lapacklin_ztbrfs
Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, band, triangular matrixerror bound, matrixforward errorLAPACKlinear equationsmatrix, band
ztbsv F06SKF   12  nagf_blas_ztbsv
System of equations, complex triangular band matrix
Related keywords: BLASblas, complex matricescomplex, band, triangular matrixlinear algebra support routineslinear equationsmatrix, band
F06SLF   12  nagf_blas_ztpsv
System of equations, complex triangular packed matrix
Related keywords: BLASblas, complex matricescomplex, triangular matrixlinear algebra support routineslinear equations
ZTBTRS F07VSF   15  nagf_lapacklin_ztbtrs
Solution of complex band triangular system of linear equations, multiple right-hand sides
Related keywords: complex, band, triangular matrixLAPACKlinear equationsmatrix, band
ztfsm F06WPF   23  nagf_blas_ztfsm
Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix, Rectangular Full Packed format
Related keywords: BLASBLASblas, complex matricescomplex, triangular matrixlinear algebra support routineslinear algebra support routines;linear equations
ZTFTRI F07WXF   23  nagf_lapacklin_ztftri
Inverse of complex triangular matrix, Rectangular Full Packed format
Related keywords: complex, triangular matrixinverse, matrixLAPACKlinear equations
ZTFTTP F01VMF   23  nagf_matop_ztfttp
Copies a complex triangular matrix from Rectangular Full Packed format to packed format
Related keywords: complex, triangular matrixfinanceinversionLAPACKmatrix operations
ZTFTTR F01VHF   23  nagf_matop_ztfttr
Copies a complex triangular matrix from Rectangular Full Packed format to full format
Related keywords: complex, triangular matrixfinanceinversionLAPACKmatrix operations
ZTGEVC F08YXF   20  nagf_lapackeig_ztgevc
Computes left and right eigenvectors of a pair of complex upper triangular matrices
Related keywords: complex, triangular matrixeigenproblemeigenvectorsgeneralized Schur formLAPACKLAPACKleast squares
ZTGEXC F08YTF   22  nagf_lapackeig_ztgexc
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
Related keywords: complex, nonsymmetric matrixeigenproblemgeneralized Schur formLAPACKLAPACKleast squaresunitary transformations
F08YUF   22  nagf_lapackeig_ztgsen
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemeigenvaluesgeneralized Schur formLAPACKLAPACKleast squaresunitary transformations
ZTGSJA F08YSF   22  nagf_lapackeig_ztgsja
Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
Related keywords: complex, trapezoidal matrixcomplex, triangular matrixeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squares
ZTGSNA F08YYF   22  nagf_lapackeig_ztgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
Related keywords: complex, nonsymmetric matrixcondition number, matrixeigenproblemgeneralized Schur formLAPACKLAPACKleast squares
ZTGSYL F08YVF   22  nagf_lapackeig_ztgsyl
Solves the complex generalized Sylvester equation
Related keywords: complex, triangular matrixeigenproblemLAPACKLAPACKleast squaresSylvester equation
ZTPCON F07UUF   15  nagf_lapacklin_ztpcon
Estimate condition number of complex triangular matrix, packed storage
Related keywords: complex, triangular matrixcondition number, matrixLAPACKlinear equations
ZTPMQRT F08BQF   25  nagf_lapackeig_ztpmqrt
Applies the unitary transformation determined by F08BPF
Related keywords: eigenproblemexplicit blockingLAPACKleast squaresQR factorizationrecursive QRunitary transformations
ztpmv F06SHF   12  nagf_blas_ztpmv
Matrix-vector product, complex triangular packed matrix
Related keywords: BLASblas, complex matricescomplex, triangular matrixlinear algebra support routinesmultiply, matrix
ZTPQRT F08BPF   25  nagf_lapackeig_ztpqrt
Q R factorization of complex triangular-pentagonal matrix
Related keywords: complex, triangular-pentagonal matrixeigenproblemexplicit blockingLAPACKleast squaresQR factorizationrecursive QR
ZTPRFS F07UVF   15  nagf_lapacklin_ztprfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
Related keywords: backward errorcomplex, triangular matrixerror bound, matrixforward errorLAPACKlinear equations
ZTPTRI F07UWF   15  nagf_lapacklin_ztptri
Inverse of complex triangular matrix, packed storage
Related keywords: complex, triangular matrixinverse, matrixLAPACKlinear equations
ZTPTRS F07USF   15  nagf_lapacklin_ztptrs
Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
Related keywords: complex, triangular matrixLAPACKlinear equations
ZTPTTF F01VKF   23  nagf_matop_ztpttf
Copies a complex triangular matrix from packed format to Rectangular Full Packed format
Related keywords: complex, triangular matrixfinanceinversionLAPACKmatrix operations
ZTPTTR F01VDF   23  nagf_matop_ztpttr
Copies a complex triangular matrix from packed format to full format
Related keywords: complex, triangular matrixfinanceinversionLAPACKmatrix operations
ZTRCON F07TUF   15  nagf_lapacklin_ztrcon
Estimate condition number of complex triangular matrix
Related keywords: complex, triangular matrixcondition number, matrixLAPACKlinear equations
ZTREVC F08QXF   16  nagf_lapackeig_ztrevc
Computes left and right eigenvectors of complex upper triangular matrix
Related keywords: complex, triangular matrixeigenproblemeigenvectorsLAPACKLAPACKleast squares
ZTREXC F08QTF   16  nagf_lapackeig_ztrexc
Reorders a Schur factorization of complex matrix using unitary similarity transformation
Related keywords: eigenproblemLAPACKLAPACKleast squaresSchur formunitary transformations
ztrmm F06ZFF   14  nagf_blas_ztrmm
Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix
Related keywords: BLASblas, complex matricescomplex, m by n matrixcomplex, triangular matrixlinear algebra support routinesmultiply, matrix
ztrmv F06SFF   12  nagf_blas_ztrmv
Matrix-vector product, complex triangular matrix
Related keywords: BLASblas, complex matricescomplex, triangular matrixlinear algebra support routinesmultiply, matrix
ZTRRFS F07TVF   15  nagf_lapacklin_ztrrfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides
Related keywords: backward errorcomplex, triangular matrixerror bound, matrixforward errorLAPACKlinear equations
ZTRSEN F08QUF   16  nagf_lapackeig_ztrsen
Reorders a Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
Related keywords: condition number, matrixeigenproblemLAPACKLAPACKleast squaresSchur form
ztrsm F06ZJF   14  nagf_blas_ztrsm
Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix
Related keywords: BLASblas, complex matricescomplex, triangular matrixlinear algebra support routineslinear least squares
ztrsv F06SJF   12  nagf_blas_ztrsv
System of equations, complex triangular matrix
Related keywords: BLASblas, complex matricescomplex, triangular matrixlinear algebra support routineslinear equations
ZTRSYL F08QVF   16  nagf_lapackeig_ztrsyl
Solves the complex Sylvester matrix equation A X + X B = C , A and B are upper triangular or conjugate-transposes
Related keywords: complex, triangular matrixeigenproblemLAPACKLAPACKleast squaresSylvester equation
ZTRTRI F07TWF   15  nagf_lapacklin_ztrtri
Inverse of complex triangular matrix
Related keywords: complex, triangular matrixinverse, matrixLAPACKlinear equations
ZTRTRS F07TSF   15  nagf_lapacklin_ztrtrs
Solution of complex triangular system of linear equations, multiple right-hand sides
Related keywords: complex, triangular matrixLAPACKlinear equations
ZTRTTF F01VFF   23  nagf_matop_ztrttf
Copies a complex triangular matrix from full format to Rectangular Full Packed format
Related keywords: complex, triangular matrixfinanceinversionLAPACKmatrix operations
ZTRTTP F01VBF   23  nagf_matop_ztrttp
Copies a complex triangular matrix from full format to packed format
Related keywords: complex, triangular matrixfinanceinversionLAPACKmatrix operations
ZTZRZF F08BVF   22  nagf_lapackeig_ztzrzf
Reduces a complex upper trapezoidal matrix to upper triangular form
Related keywords: complex, trapezoidal matrixeigenproblemLAPACKLAPACKleast squaresmatrix, upper trapezoidalmatrix, upper triangular
ZUNCSD F08RNF   25  nagf_lapackeig_zuncsd
Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices
Related keywords: complete CS decompositioncomplex, unitary matrixeigenproblemGSVD, generalized singular value decompositionLAPACKLAPACKleast squares
ZUNGBR F08KTF   16  nagf_lapackeig_zungbr
Generates unitary transformation matrices from the reduction to bidiagonal form determined by F08KSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary matrix, generationunitary transformations
ZUNGHR F08NTF   16  nagf_lapackeig_zunghr
Generates a unitary transformation matrix from reduction to Hessenberg form determined by F08NSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary matrix, generationunitary matrix, generation
ZUNGLQ F08AWF   16  nagf_lapackeig_zunglq
Forms all or part of unitary Q from L Q factorization determined by F08AVF
Related keywords: eigenproblemLAPACKLAPACKleast squares LQ factorizationunitary matrix, generationunitary transformations
ZUNGQL F08CTF   22  nagf_lapackeig_zungql
Form all or part of unitary Q from Q L factorization determined by F08CSF
Related keywords: eigenproblemLAPACKLAPACKleast squares QL factorizationunitary matrix, generationunitary transformations
ZUNGQR F08ATF   16  nagf_lapackeig_zungqr
Forms all or part of unitary Q from Q R factorization determined by F08ASF F08BSF F08BTF
Related keywords: eigenproblemLAPACKLAPACKleast squares QR factorizationunitary matrix, generationunitary transformations
ZUNGRQ F08CWF   22  nagf_lapackeig_zungrq
Form all or part of unitary Q from R Q factorization determined by F08CVF
Related keywords: eigenproblemLAPACKLAPACKleast squaresRQ factorizationsunitary matrix, generationunitary transformations
ZUNGTR F08FTF   16  nagf_lapackeig_zungtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary matrix, generationunitary transformations
ZUNMBR F08KUF   16  nagf_lapackeig_zunmbr
Applies the unitary transformations from reduction to bidiagonal form determined by F08KSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformations
ZUNMHR F08NUF   16  nagf_lapackeig_zunmhr
Applies the unitary transformation matrix from reduction to Hessenberg form determined by F08NSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformations
ZUNMLQ F08AXF   16  nagf_lapackeig_zunmlq
Applies the unitary transformation determined by F08AVF
Related keywords: eigenproblemLAPACKLAPACKleast squares LQ factorizationunitary transformations
ZUNMQL F08CUF   22  nagf_lapackeig_zunmql
Applies the unitary transformation determined by F08CSF
Related keywords: eigenproblemLAPACKLAPACKleast squares QL factorizationunitary transformations
ZUNMQR F08AUF   16  nagf_lapackeig_zunmqr
Applies a unitary transformation determined by F08ASF F08BSF F08BTF
Related keywords: eigenproblemLAPACKLAPACKleast squares QR factorizationunitary transformations
ZUNMRQ F08CXF   22  nagf_lapackeig_zunmrq
Applies the unitary transformation determined by F08CVF
Related keywords: eigenproblemLAPACKLAPACKleast squaresRQ factorizationsunitary transformations
ZUNMRZ F08BXF   22  nagf_lapackeig_zunmrz
Applies the unitary transformation determined by F08BVF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformations
ZUNMTR F08FUF   16  nagf_lapackeig_zunmtr
Applies the unitary transformation matrix determined by F08FSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformations
ZUPGTR F08GTF   16  nagf_lapackeig_zupgtr
Generates a unitary transformation matrix from reduction to tridiagonal form determined by F08GSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary matrix, generationunitary transformations
F08GUF   16  nagf_lapackeig_zupmtr
Applies the unitary transformation matrix determined by F08GSF
Related keywords: eigenproblemLAPACKLAPACKleast squaresunitary transformations

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