Linear programming (LP), |
dense, |
active-set method/primal simplex, |
alternative 1 | e04mff |
alternative 2 | e04ncf |
sparse, |
active-set method/primal simplex, |
recommended (see Section 3.3 in the E04 Chapter Introduction) | e04nqf |
alternative | e04nkf |
Airy function, |
, real argument, |
scalar | s17agf |
or , complex argument, optionally scaled | s17dgf |
, real argument, |
scalar | s17ajf |
, real argument, |
scalar | s17ahf |
or , complex argument, optionally scaled | s17dhf |
, real argument, |
scalar | s17akf |
Arccos, |
inverse circular cosine | s09abf |
Arccosh, |
inverse hyperbolic cosine | s11acf |
Arcsin, |
inverse circular sine | s09aaf |
Arcsinh, |
inverse hyperbolic sine | s11abf |
Arctanh, |
inverse hyperbolic tangent | s11aaf |
ARMA modelling, |
ACF | g13abf |
diagnostic checking | g13asf |
differencing | g13aaf |
estimation (easy-to-use) | g13aff |
forecasting from fully specified model | g13ajf |
forecasting from state set | g13ahf |
mean/range | g13auf |
PACF | g13acf |
preliminary estimation | g13adf |
update state set | g13agf |
Quadratic programming (QP), |
dense, |
active-set method for (possibly nonconvex) QP problem | e04nff |
active-set method for convex QP problem | e04ncf |
sparse, |
active-set method sparse convex QP problem, |
recommended (see Section 3.3 in the E04 Chapter Introduction) | e04nqf |
alternative | e04nkf |
Bessel function, |
, real argument, |
scalar | s18aef |
, real argument, |
scalar | s18aff |
, real argument, |
scalar | s17aef |
, real argument, |
scalar | s17aff |
, real argument, |
scalar | s18acf |
, real argument, |
scalar | s18adf |
, real argument, |
scalar | s17acf |
, real argument, |
scalar | s17adf |
Complement of the Cumulative Normal distribution, |
scalar | s15acf |
vectorized | s15aqf |
Complement of the Error function, |
real argument, |
scalar | s15adf |
vectorized | s15arf |
real argument, scaled, |
scalar | s15agf |
vectorized | s15auf |
Compute error estimates, |
real triangular matrix | f07thf |
Correlation-like coefficients, |
all variables, |
casewise treatment of missing values | g02bef |
no missing values | g02bdf |
pairwise treatment of missing values | g02bff |
subset of variables, |
casewise treatment of missing values | g02blf |
no missing values | g02bkf |
pairwise treatment of missing values | g02bmf |
Cosine, |
hyperbolic | s10acf |
Cosine Integral | s13acf |
Cumulative Normal distribution function, |
scalar | s15abf |
vectorized | s15apf |
Nonlinear programming (NLP), |
dense, |
active-set sequential quadratic programming (SQP), |
direct communication, |
recommended (see Section 3.3 in the E04 Chapter Introduction) | e04ucf |
alternative | e04wdf |
reverse communication | e04uff |
sparse, |
active-set sequential quadratic programming (SQP), |
alternative | e04vhf |
alternative | e04ugf |
Dawson's Integral, |
scalar | s15aff |
vectorized | s15atf |
Derivative, |
of interpolant, |
from e01bef | e01bgf |
Descriptive statistics / Exploratory analysis, |
summaries, |
frequency / contingency table, |
one variable | g01aef |
two variables, with and Fisher's exact test | g01aff |
mean, variance, skewness, kurtosis (one variable), |
from frequency table | g01adf |
median, hinges / quartiles, minimum, maximum | g01alf |
quantiles, |
unordered vector |
unweighted | g01amf |
Digamma function, scaled | s14adf |
Discrete Fourier Transform, |
one-dimensional, |
multiple transforms, |
Hermitian sequence, |
real storage by rows | c06fqf |
real sequence, |
real storage by rows | c06fpf |
Distributions, |
Beta, |
central, |
deviates, |
scalar | g01fef |
probabilities and probability density function, |
scalar | g01eef |
non-central, |
probabilities | g01gef |
binomial, |
distribution function, |
scalar | g01bjf |
Durbin–Watson statistic, |
probabilities | g01epf |
energy loss distributions, |
Landau, |
density | g01mtf |
derivative of density | g01rtf |
distribution | g01etf |
first moment | g01ptf |
inverse distribution | g01ftf |
second moment | g01qtf |
Vavilov, |
density | g01muf |
distribution | g01euf |
initialization | g01zuf |
: |
central, |
deviates, |
scalar | g01fdf |
probabilities, |
scalar | g01edf |
non-central, |
probabilities | g01gdf |
gamma, |
deviates, |
scalar | g01fff |
probabilities, |
scalar | g01eff |
Hypergeometric, |
distribution function, |
scalar | g01blf |
Kolomogorov–Smirnov, |
probabilities, |
one-sample | g01eyf |
two-sample | g01ezf |
Normal, |
bivariate, |
probabilities | g01haf |
multivariate, |
probabilities | g01hbf |
quadratic forms, |
cumulants and moments | g01naf |
moments of ratios | g01nbf |
univariate, |
deviates, |
scalar | g01faf |
probabilities, |
scalar | g01eaf |
reciprocal of Mill's Ratio | g01mbf |
Shapiro and Wilk's test for Normality | g01ddf |
Poisson, |
distribution function, |
scalar | g01bkf |
Student's : |
central, |
univariate, |
deviates, |
scalar | g01fbf |
probabilities, |
scalar | g01ebf |
non-central, |
probabilities | g01gbf |
Studentized range statistic, |
deviates | g01fmf |
probabilities | g01emf |
von Mises, |
probabilities | g01erf |
: |
central, |
deviates | g01fcf |
probabilities | g01ecf |
probability of linear combination | g01jdf |
non-central, |
probabilities | g01gcf |
probability of linear combination | g01jcf |
Nonlinear programming (NLP) – derivative-free optimization (DFO), |
model-based method for bound-constrained optimization | e04jcf |
model-based method for bound-constrained optimization, |
reverse communication | e04jef |
direct communication | e04jdf |
Nelder–Mead simplex method for unconstrained optimization | e04cbf |
Eigenvalue problems for condensed forms of matrices, |
complex Hermitian matrix, |
eigenvalues and eigenvectors, |
general matrix, |
all/selected eigenvalues and eigenvectors by root-free algorithm | f08fpf |
all eigenvalues and eigenvectors by a divide-and-conquer algorithm | f08fqf |
eigenvalues only, |
general matrix, |
all/selected eigenvalues by the Pal–Walker–Kahan variant of the or algorithm | f08fpf |
real symmetric matrix, |
eigenvalues and eigenvectors, |
general matrix, |
all/selected eigenvalues and eigenvectors by root-free algorithm | f08fbf |
all eigenvalues and eigenvectors by a divide-and-conquer algorithm | f08fcf |
all eigenvalues and eigenvectors by root-free algorithm | f08faf |
eigenvalues only, |
general matrix, |
all/selected eigenvalues by the Pal–Walker–Kahan variant of the or algorithm | f08fbf |
all eigenvalues by the Pal–Walker–Kahan variant of the or algorithm | f08faf |
Eigenvalue problems for nonsymmetric matrices, |
complex matrix, |
all eigenvalues and left/right eigenvectors, plus balancing transformation and reciprocal condition numbers | f08npf |
real matrix, |
all eigenvalues and left/right eigenvectors, plus balancing transformation and reciprocal condition numbers | f08nbf |
Elliptic functions, Jacobian, sn, cn, dn, |
complex argument | s21cbf |
real argument | s21caf |
Elliptic integral, |
Legendre form, |
complete of 1st kind, | s21bhf |
complete of 2nd kind, | s21bjf |
of 1st kind, | s21bef |
of 2nd kind, | s21bff |
of 3rd kind, | s21bgf |
symmetrised, |
degenerate of 1st kind, | s21baf |
of 1st kind, | s21bbf |
of 2nd kind, | s21bcf |
of 3rd kind, | s21bdf |
Erf, |
real argument, |
scalar | s15aef |
vectorized | s15asf |
Erfc, |
real argument, |
scalar | s15adf |
vectorized | s15arf |
erfcx, |
real argument, |
scalar | s15agf |
vectorized | s15auf |
Evaluation, |
at a point, |
of cubic splines | e02bbf |
of cubic splines and derivatives | e02bcf |
at vector of points, |
of bicubic splines at vector of points | e02def |
of interpolant, |
from e01bef | e01bff |
from triangulation from e01eaf | e01ebf |
on mesh, |
of bicubic splines | e02dff |
Exponential Integral | s13aaf |
Exponential smoothing | g13amf |
Extrapolation, |
one variable, |
piecewise cubic | e01bef |
polynomial, |
general data | e01aaf |
Nonlinear programming (NLP) – special cases, |
unidimensional optimization (one-dimensional) with bound constraints, |
method based on quadratic interpolation, no derivatives | e04abf |
method based on cubic interpolation | e04bbf |
unconstrained, |
preconditioned conjugate gradient method | e04dgf |
bound-constrained, |
quasi-Newton algorithm, no derivatives | e04jyf |
quasi-Newton algorithm, first derivatives | e04kyf |
modified Newton algorithm, first derivatives | e04kdf |
modified Newton algorithm, first derivatives, easy-to-use | e04kzf |
modified Newton algorithm, first and second derivatives | e04lbf |
modified Newton algorithm, first and second derivatives, easy-to-use | e04lyf |
Fresnel integral, |
, |
scalar | s20adf |
, |
scalar | s20acf |
Nonlinear programming (NLP) – global optimization, |
bound constrained, |
branching algorithm, multi-level coordinate search | e05kbf |
branching algorithm, multi-level coordinate search (D) | e05jbf |
generic, including nonlinearly constrained, |
multi-start | e05ucf |
Gamma function, |
incomplete, |
scalar | s14baf |
vectorized | s14bnf |
scalar | s14aaf |
vectorized | s14anf |
GARCH, |
EGARCH, |
fitting | g13fgf |
forecasting | g13fhf |
GJR GARCH, |
fitting | g13fef |
forecasting | g13fff |
symmetric or type I AGARCH, |
fitting | g13faf |
forecasting | g13fbf |
type II AGARCH, |
fitting | g13fcf |
forecasting | g13fdf |
Generalized eigenvalue problems for nonsymmetric matrix pairs, |
complex nonsymmetric matrix pairs, |
all eigenvalues and left/right eigenvectors, plus the balancing transformation and reciprocal condition numbers | f08wpf |
real nonsymmetric matrix pairs, |
all eigenvalues and left/right eigenvectors, plus the balancing transformation and reciprocal condition numbers | f08wbf |
Generalized factorial function, |
scalar | s14aaf |
vectorized | s14anf |
Generalized linear models, |
binomial errors | g02gbf |
computes estimable function | g02gnf |
gamma errors | g02gdf |
Normal errors | g02gaf |
Poisson errors | g02gcf |
prediction | g02gpf |
transform model parameters | g02gkf |
Generating samples, matrices and tables, |
random correlation matrix | g05pyf |
random orthogonal matrix | g05pxf |
random permutation of an integer vector | g05ncf |
random sample from an integer vector, |
unequal weights, without replacement | g05nef |
unweighted, without replacement | g05ndf |
random table | g05pzf |
resample from an integer vector, |
unequal weights | g05nff |
Generation of time series, |
asymmetric GARCH Type II | g05pef |
asymmetric GJR GARCH | g05pff |
EGARCH | g05pgf |
exponential smoothing | g05pmf |
type I AGARCH | g05pdf |
univariate ARMA | g05phf |
vector ARMA | g05pjf |
Linear least squares, linear regression, data fitting, |
constrained, |
bound-constrained least squares problem | e04pcf |
linearly-constrained active-set method | e04ncf |
Data fitting, |
general loss functions (for sum of squares, see nonlinear least squares) | e04gnf |
Nonlinear least squares, data fitting, |
unconstrained, |
combined Gauss–Newton and modified Newton algorithm, |
no derivatives | e04fcf |
no derivatives, easy-to-use | e04fyf |
first derivatives | e04gdf |
first derivatives, easy-to-use | e04gzf |
first and second derivatives | e04hef |
first and second derivatives, easy-to-use | e04hyf |
combined Gauss–Newton and quasi-Newton algorithm, |
first derivatives | e04gbf |
first derivatives, easy-to-use | e04gyf |
bound constrained, |
model-based derivative-free algorithm, |
direct communication | e04fff |
reverse communication | e04fgf |
trust region algorithm, |
first derivatives, optionally second derivatives | e04ggf |
generic, including nonlinearly constrained, |
nonlinear constraints active-set sequential quadratic programming (SQP) | e04usf |
Nonlinear least squares, data fitting – global optimization, |
generic, including nonlinearly constrained, |
multi-start | e05usf |
Mixed integer linear programming (MILP), |
dense, |
branch and bound method | h02bbf |
sparse, |
branch and bound method | h02cef |
Mixed integer quadratic programming (MIQP), |
dense, |
branch and bound method | h02cbf |
sparse, |
branch and bound method | h02cef |
Integration (definite) of interpolant from e01bef | e01bhf |
Interpolated values, |
one variable, |
from interpolant from e01bef | e01bff |
from interpolant from e01bef (including derivative) | e01bgf |
from polynomial, |
general data | e01aaf |
two variables, |
barycentric, from triangulation from e01eaf | e01ebf |
Interpolating function, |
one variable, |
cubic spline | e01baf |
other piecewise polynomial | e01bef |
two variables, |
bicubic spline | e01daf |
NAG optimization modelling suite, |
solvers, |
constrained nonlinear data fitting (NLDF) | e04gnf |
derivative-free optimisation (DFO) for nonlinear least squares problems, |
direct communication | e04fff |
reverse communication | e04fgf |
trust region optimisation for nonlinear least squares problems (BXNL) | e04ggf |
model-based method for bound-constrained optimization, |
direct communication | e04jdf |
reverse communication | e04jef |
Jacobian theta functions , |
real argument | s21ccf |
Service routines, |
derivative check and approximation, |
check user's routine for calculating first derivatives of function | e04hcf |
check user's routine for calculating second derivatives of function | e04hdf |
check user's routine for calculating Jacobian of first derivatives | e04yaf |
check user's routine for calculating Hessian of a sum of squares | e04ybf |
estimate (using numerical differentiation) gradient and/or Hessian of a function | e04xaf |
determine the pattern of nonzeros in the Jacobian matrix for e04vhf | e04vjf |
Kelvin function, |
, |
scalar | s19abf |
, |
scalar | s19aaf |
, |
scalar | s19adf |
, |
scalar | s19acf |
Korobov optimal coefficients for use in d01gcf and d01gdf: |
when number of points is a product of primes | d01gzf |
when number of points is prime | d01gyf |
least squares problems, |
real matrices, |
minimum norm solution using a complete orthogonal factorization | f08baf |
minimum norm solution using the singular value decomposition (divide-and-conquer) | f08kcf |
Least squares surface fit, |
with bicubic splines | e02daf |
Legendre functions of 1st kind , | s22aaf |
Level 0 (Scalar) operations, |
real numbers, |
compute | f06bnf |
Level 1 (Vector) operations, |
complex vector(s), |
Euclidean norm of a vector | f06jjf |
integer vector(s), |
broadcast a scalar into a vector | f06dbf |
real vector(s), |
copy a vector | f06eff |
dot product of two vectors | f06eaf |
Euclidean norm of a vector | f06ejf |
multiply vector by a scalar, preserving input vector | f06fdf |
Level 2 (Matrix-vector and matrix) operations, |
real matrix and vector(s), |
compute a norm or the element of largest absolute value, |
matrix initialization | f06qhf |
matrix-vector product, |
rectangular matrix | f06paf |
rank-2 update, |
matrix copy, rectangular or trapezoidal | f06qff |
solution of a system of equations, |
triangular matrix | f06pjf |
Level 3 (Matrix-matrix) operations, |
real matrices, |
matrix-matrix product, |
rectangular matrices | f06yaf |
solution of triangular systems of equations | f06yjf |
Linear mixed effects regression, |
via maximum likelihood (ML) | g02jbf |
via restricted maximum likelihood (REML) | g02jaf |
or factorization, |
real symmetric positive definite band matrix | f07hdf |
real symmetric positive definite matrix | f07fdf |
Logarithm of | s01baf |
Logarithm of gamma function, |
real, |
scalar | s14abf |
vectorized | s14apf |
factorization, |
complex matrix | f07arf |
real matrix | f07adf |
real tridiagonal matrix | f07cdf |
Matrix Arithmetic and Manipulation, |
matrix storage conversion, |
full to packed triangular storage, |
complex matrices | f01vbf |
real matrices | f01vaf |
full to Rectangular Full Packed storage, |
complex matrix | f01vff |
real matrix | f01vef |
packed triangular to full storage, |
complex matrices | f01vdf |
real matrices | f01vcf |
packed triangular to Rectangular Full Packed storage, |
complex matrices | f01vkf |
real matrices | f01vjf |
Rectangular Full Packed to full storage, |
complex matrices | f01vhf |
real matrices | f01vgf |
Rectangular Full Packed to packed triangular storage, |
complex matrices | f01vmf |
real matrices | f01vlf |
Matrix function, |
complex Hermitian matrix, |
matrix exponential | f01fdf |
matrix function | f01fff |
complex matrix, |
matrix exponential | f01fcf |
real symmetric matrix, |
matrix exponential | f01edf |
matrix function | f01eff |
Matrix inversion, |
after factorizing the matrix of coefficients, |
real matrix | f07ajf |
real symmetric positive definite matrix | f07fjf |
real triangular matrix | f07tjf |
Multidimensional quadrature, |
over a finite two-dimensional region | d01daf |
over a general product region, |
variant of d01gcf especially efficient on vector machines | d01gdf |
over a hyper-rectangle, |
adaptive method | d01fcf |
Gaussian quadrature rule-evaluation | d01fbf |
over an -simplex | d01paf |
over an -sphere , |
allowing for badly behaved integrands | d01jaf |
Multiple linear regression, |
from correlation coefficients | g02cgf |
from correlation-like coefficients | g02chf |
Multiple linear regression/General linear model, |
add/delete observation from model | g02dcf |
add independent variable to model | g02def |
computes estimable function | g02dnf |
delete independent variable from model | g02dff |
general linear regression model | g02daf |
regression for new dependent variable | g02dgf |
regression parameters from updated model | g02ddf |
transform model parameters | g02dkf |
Nearest correlation matrix, |
-factor structure | g02aef |
method of Qi and Sun, |
unweighted, unbounded | g02aaf |
weighted norm | g02abf |
Non-parametric rank correlation (Kendall and/or Spearman): |
missing values, |
casewise treatment of missing values, |
overwriting input data | g02bpf |
preserving input data | g02brf |
pairwise treatment of missing values | g02bsf |
no missing values, |
overwriting input data | g02bnf |
preserving input data | g02bqf |
Old routine for calculating weights and abscissae for Gaussian quadrature rules, |
replaced by d01tcf | d01bcf |
One-dimensional quadrature, |
adaptive integration of a function over a finite interval, |
strategy due to Gonnet, |
suitable for badly behaved integrals, |
vectorized interface | d01rgf |
strategy due to Patterson, |
suitable for well-behaved integrands, except possibly at end-points | d01ahf |
strategy due to Piessens and de Doncker, |
allowing for singularities at user-specified break-points | d01rlf |
allowing for singularities at user-specified break-points (Old) | d01alf |
suitable for badly behaved integrands | d01rjf |
suitable for badly behaved integrands, |
single abscissa interface | d01ajf |
suitable for highly oscillatory integrals | d01rkf |
suitable for highly oscillatory integrals, |
single abscissa interface | d01akf |
vectorized interface | d01auf |
weight function Cauchy principal value (Hilbert transform) | d01aqf |
weight function or | d01anf |
weight function with end-point singularities of algebraico-logarithmic type | d01apf |
adaptive integration of a function over an infinite interval or semi-infinite interval, |
no weight function (Old) | d01amf |
weight function or | d01asf |
integration of a function defined by data values only, |
Gill–Miller method | d01gaf |
non-adaptive integration over a finite interval | d01bdf |
non-adaptive integration over a finite interval, |
with provision for indefinite integrals also | d01arf |
Operations on eigenvectors of a real symmetric or complex Hermitian matrix, or singular vectors of a general matrix, |
estimate condition numbers | f08flf |
Option Pricing, |
American option, Bjerksund and Stensland option price | s30qcf |
Asian option, geometric continuous average rate price | s30saf |
Asian option, geometric continuous average rate price with Greeks | s30sbf |
binary asset-or-nothing option price | s30ccf |
binary asset-or-nothing option price with Greeks | s30cdf |
binary cash-or-nothing option price | s30caf |
binary cash-or-nothing option price with Greeks | s30cbf |
Black–Scholes implied volatility | s30acf |
Black–Scholes–Merton option price | s30aaf |
Black–Scholes–Merton option price with Greeks | s30abf |
European option, option prices, using Merton jump-diffusion model | s30jaf |
European option, option price with Greeks, using Merton jump-diffusion model | s30jbf |
floating-strike lookback option price | s30baf |
floating-strike lookback option price with Greeks | s30bbf |
Heston's model option price | s30naf |
Heston's model option price with Greeks | s30nbf |
Heston's model option price with Greeks, sensitivities of model parameters and negative rates | s30ndf |
Heston's model with term structure | s30ncf |
standard barrier option price | s30faf |
Outlier detection, |
Peirce, |
raw data or single variance supplied | g07gaf |
two variances supplied | g07gbf |
Overdetermined and underdetermined linear systems, |
complex matrices, |
solves an overdetermined or undetermined complex linear system | f08anf |
real matrices, |
solves an overdetermined or undetermined real linear system | f08aaf |
Partial least squares, |
calculates predictions given an estimated PLS model | g02ldf |
fits a PLS model for a given number of factors | g02lcf |
orthogonal scores using SVD | g02laf |
orthogonal scores using Wold's method | g02lbf |
Polygamma function, |
, real | s14aef |
Principal component analysis | g03aaf |
Product-moment correlation, |
correlation coefficients, all variables, |
casewise treatment of missing values | g02bbf |
no missing values | g02baf |
pairwise treatment of missing values | g02bcf |
correlation coefficients, subset of variables, |
casewise treatment of missing values | g02bhf |
no missing values | g02bgf |
pairwise treatment of missing values | g02bjf |
correlation matrix, |
compute correlation and covariance matrices | g02bxf |
compute from sum of squares matrix | g02bwf |
compute partial correlation and covariance matrices | g02byf |
sum of squares matrix, |
compute | g02buf |
update | g02btf |
Pseudorandom numbers, |
array of variates from multivariate distributions, |
Dirichlet distribution | g05sef |
multinomial distribution | g05tgf |
Normal distribution | g05rzf |
Student's distribution | g05ryf |
copulas, |
Gaussian copula | g05rdf |
Student's copula | g05rcf |
initialize generator, |
multiple streams, |
leap-frog | g05khf |
skip-ahead | g05kjf |
skip-ahead (power of 2) | g05kkf |
vector of variates from discrete univariate distributions, |
binomial distribution | g05taf |
geometric distribution | g05tcf |
hypergeometric distribution | g05tef |
logarithmic distribution | g05tff |
logical value .TRUE. or .FALSE. | g05tbf |
negative binomial distribution | g05thf |
Poisson distribution | g05tjf |
uniform distribution | g05tlf |
user-supplied distribution | g05tdf |
variate array from discrete distributions with array of parameters, |
Poisson distribution with varying mean | g05tkf |
vectors of variates from continuous univariate distributions, |
beta distribution | g05sbf |
Cauchy distribution | g05scf |
exponential mix distribution | g05sgf |
-distribution | g05shf |
gamma distribution | g05sjf |
logistic distribution | g05slf |
log-normal distribution | g05smf |
negative exponential distribution | g05sff |
Normal distribution | g05skf |
real number from the continuous uniform distribution | g05saf |
Student's -distribution | g05snf |
triangular distribution | g05spf |
uniform distribution | g05sqf |
von Mises distribution | g05srf |
Weibull distribution | g05ssf |
square distribution | g05sdf |
psi function | s14acf |
psi function derivatives, scaled | s14adf |
factorization and related operations, |
real matrices, |
general matrices, |
apply orthogonal matrix | f08agf |
factorization, |
with column pivoting, using BLAS-3 | f08bff |
factorization, orthogonal matrix | f08aef |
factorization, with column pivoting, deprecated | f08bef |
Quantile regression, |
linear, |
comprehensive | g02qgf |
simple | g02qff |
Quasi-random numbers, |
array of variates from univariate distributions, |
uniform distribution | g05ymf |
initialize generator, |
scrambled Sobol or Niederreiter | g05ynf |
Sobol, Niederreiter or Faure | g05ylf |
Residuals, |
Durbin–Watson test | g02fcf |
standardized residuals and influence statistics | g02faf |
Ridge regression, |
ridge parameter(s) supplied | g02kbf |
ridge parameter optimized | g02kaf |
Robust correlation, |
Huber's method | g02hkf |
user-supplied weight function only | g02hmf |
user-supplied weight function plus derivatives | g02hlf |
Robust regression, |
compute weights for use with g02hdf | g02hbf |
standard -estimates | g02haf |
user-supplied weight functions | g02hdf |
variance-covariance matrix following g02hdf | g02hff |
Scaled modified Bessel function(s), |
, real argument, |
scalar | s18cef |
, real argument, |
scalar | s18cff |
, real argument, |
scalar | s18ccf |
, real argument, |
scalar | s18cdf |
Scores, |
Normal scores, |
accurate | g01daf |
approximate | g01dbf |
variance-covariance matrix | g01dcf |
Normal scores, ranks or exponential (Savage) scores | g01dhf |
Service routines, |
for multiple linear regression, |
reorder elements from vectors and matrices | g02cff |
select elements from vectors and matrices | g02cef |
Simple linear regression, |
no intercept | g02cbf |
no intercept with missing values | g02cdf |
with intercept | g02caf |
with intercept and with missing values | g02ccf |
Sine, |
hyperbolic | s10abf |
Sine Integral | s13adf |
Singular value decomposition, |
complex matrix, |
using bidiagonal iteration | f08kpf |
real matrix, |
using a divide-and-conquer algorithm | f08kdf |
using bidiagonal iteration | f08kbf |
Solution of simultaneous linear equations, |
after factorizing the matrix of coefficients, |
complex matrix | f07asf |
real symmetric positive definite band matrix | f07hef |
real symmetric positive definite matrix | f07fef |
real tridiagonal matrix | f07cef |
expert drivers (with condition and error estimation): |
complex Hermitian positive definite matrix | f07fpf |
complex matrix | f07apf |
real matrix | f07abf |
real symmetric positive definite matrix | f07fbf |
simple drivers, |
real matrix | f07aaf |
real symmetric positive definite matrix | f07faf |
real triangular matrix | f07tef |
real tridiagonal matrix | f07caf |
Spectral analysis |
Bivariate, |
Bartlett, Tukey, Parzen windows | g13ccf |
cross amplitude spectrum | g13cef |
direct smoothing | g13cdf |
gain and phase | g13cff |
noise spectrum | g13cgf |
Univariate, |
Bartlett, Tukey, Parzen windows | g13caf |
direct smoothing | g13cbf |
Stepwise linear regression, |
Clarke's sweep algorithm | g02eff |
Tangent, |
circular | s07aaf |
hyperbolic | s10aaf |
Transfer function modelling, |
cross-correlations | g13bcf |
filtering | g13bbf |
fitting | g13bef |
forecasting from fully specified model | g13bjf |
preliminary estimation | g13bdf |
pre-whitening | g13baf |
update state set | g13bgf |
Trigamma function, scaled | s14adf |
Vector ARMA, |
differencing | g13dlf |
fitting | g13ddf |
forecasting | g13djf |
update forecast | g13dkf |
zeros of ARIMA operator | g13dxf |
Weights and abscissae for Gaussian quadrature rules, |
more general choice of rule, |
calculating the weights and abscissae | d01tcf |
Zeros of Bessel functions , , , , |
scalar | s17alf |
Zeros of functions of one variable, |
direct communication, |
binary search followed by Brent algorithm | c05auf |
Brent algorithm | c05ayf |
continuation method | c05awf |
reverse communication, |
binary search | c05avf |
Brent algorithm | c05azf |
continuation method | c05axf |
Zeros of functions of several variables, |
checking routine, |
checks user-supplied Jacobian | c05zdf |
direct communication, |
easy-to-use, |
derivatives required | c05rbf |
no derivatives required | c05qbf |
sophisticated, |
derivatives required | c05rcf |
no derivatives required | c05qcf |
reverse communication, |
sophisticated, |
derivatives required | c05rdf |
no derivatives required | c05qdf |