F06 Chapter Contents : NAG Library Manual, Mark 27

Routine	Mark of Introduction	Purpose
f06aaf	12	drotg nagf_blas_drotg Generate real plane rotation
f06baf	12	nagf_blas_drotgc Generate real plane rotation, storing tangent
f06bcf	12	nagf_blas_dcsg Recover cosine and sine from given real tangent
f06bef	12	nagf_blas_drotj Generate real Jacobi plane rotation
f06bhf	12	nagf_blas_drot2 Apply real similarity rotation to $2$ by $2$ symmetric matrix
f06blf	12	nagf_blas_ddiv Compute quotient of two real scalars, with overflow flag
f06bmf	12	nagf_blas_dnorm Compute Euclidean norm from scaled form
f06bnf	12	nagf_blas_dpyth Compute square root of $(a^{2} + b^{2})$ , real $a$ and $b$
f06bpf	12	nagf_blas_deig2 Compute eigenvalue of $2$ by $2$ real symmetric matrix
f06caf	12	nagf_blas_zrotgc Generate complex plane rotation, storing tangent, real cosine
f06cbf	12	nagf_blas_zrotgs Generate complex plane rotation, storing tangent, real sine
f06ccf	12	nagf_blas_zcsg Recover cosine and sine from given complex tangent, real cosine
f06cdf	12	nagf_blas_zcsgs Recover cosine and sine from given complex tangent, real sine
f06chf	12	nagf_blas_zrot2 Apply complex similarity rotation to $2$ by $2$ Hermitian matrix
f06clf	12	nagf_blas_zdiv Compute quotient of two complex scalars, with overflow flag
f06dbf	12	nagf_blas_iload Broadcast scalar into integer vector
f06dff	12	nagf_blas_icopy Copy integer vector
f06eaf	12	ddot nagf_blas_ddot Dot product of two real vectors
f06ecf	12	daxpy nagf_blas_daxpy Add scalar times real vector to real vector
f06edf	12	dscal nagf_blas_dscal Multiply real vector by scalar
f06eff	12	dcopy nagf_blas_dcopy Copy real vector
f06egf	12	dswap nagf_blas_dswap Swap two real vectors
f06ejf	12	dnrm2 nagf_blas_dnrm2 Compute Euclidean norm of real vector
f06ekf	12	dasum nagf_blas_dasum Sum absolute values of real vector elements
f06epf	12	drot nagf_blas_drot Apply real plane rotation
f06erf	14	ddoti nagf_blas_ddoti Dot product of a real sparse and a full vector
f06etf	14	daxpyi nagf_blas_daxpyi Add scalar times real sparse vector to a full vector
f06euf	14	dgthr nagf_blas_dgthr Gather real sparse vector
f06evf	14	dgthrz nagf_blas_dgthrz Gather and set to zero real sparse vector
f06ewf	14	dsctr nagf_blas_dsctr Scatter real sparse vector
f06exf	14	droti nagf_blas_droti Apply plane rotation to a real sparse and a full vector
f06faf	12	nagf_blas_dvcos Compute cosine of angle between two real vectors
f06fbf	12	nagf_blas_dload Broadcast scalar into real vector
f06fcf	12	nagf_blas_ddscl Multiply real vector by diagonal matrix
f06fdf	12	nagf_blas_axpzy Multiply real vector by scalar, preserving input vector
f06fef	21	nagf_blas_drscl Multiply real vector by reciprocal of scalar
f06fgf	12	nagf_blas_dnegv Negate real vector
f06fjf	12	nagf_blas_dssq Update Euclidean norm of real vector in scaled form
f06fkf	12	nagf_blas_dnrm2w Compute weighted Euclidean norm of real vector
f06flf	12	nagf_blas_darang Elements of real vector with largest and smallest absolute value
f06fpf	12	nagf_blas_drots Apply real symmetric plane rotation to two vectors
f06fqf	12	nagf_blas_dsrotg Generate sequence of real plane rotations
f06frf	12	nagf_blas_dnhousg Generate real elementary reflection, NAG style
f06fsf	12	nagf_blas_dlhousg Generate real elementary reflection, LINPACK style
f06ftf	12	nagf_blas_dnhous Apply real elementary reflection, NAG style
f06fuf	12	nagf_blas_dlhous Apply real elementary reflection, LINPACK style
f06gaf	12	zdotu nagf_blas_zdotu Dot product of two complex vectors, unconjugated
f06gbf	12	zdotc nagf_blas_zdotc Dot product of two complex vectors, conjugated
f06gcf	12	zaxpy nagf_blas_zaxpy Add scalar times complex vector to complex vector
f06gdf	12	zscal nagf_blas_zscal Multiply complex vector by complex scalar
f06gff	12	zcopy nagf_blas_zcopy Copy complex vector
f06ggf	12	zswap nagf_blas_zswap Swap two complex vectors
f06grf	14	zdotui nagf_blas_zdotui Dot product of a complex sparse and a full vector, unconjugated
f06gsf	14	zdotci nagf_blas_zdotci Dot product of a complex sparse and a full vector, conjugated
f06gtf	14	zaxpyi nagf_blas_zaxpyi Add scalar times complex sparse vector to a full vector
f06guf	14	zgthr nagf_blas_zgthr Gather complex sparse vector
f06gvf	14	zgthrz nagf_blas_zgthrz Gather and set to zero complex sparse vector
f06gwf	14	zsctr nagf_blas_zsctr Scatter complex sparse vector
f06hbf	12	nagf_blas_zload Broadcast scalar into complex vector
f06hcf	12	nagf_blas_zdscl Multiply complex vector by complex diagonal matrix
f06hdf	12	nagf_blas_zaxpzy Multiply complex vector by complex scalar, preserving input vector
f06hgf	12	nagf_blas_znegv Negate complex vector
f06hmf	21	zrot nagf_blas_zrot Apply plane rotation with real cosine and complex sine
f06hpf	12	nagf_blas_zcrot Apply complex plane rotation
f06hqf	12	nagf_blas_zsrotg Generate sequence of complex plane rotations
f06hrf	12	nagf_blas_zhousg Generate complex elementary reflection
f06htf	12	nagf_blas_zhous Apply complex elementary reflection
f06jdf	12	zdscal nagf_blas_zdscal Multiply complex vector by real scalar
f06jjf	12	dznrm2 nagf_blas_dznrm2 Compute Euclidean norm of complex vector
f06jkf	12	dzasum nagf_blas_dzasum Sum absolute values of complex vector elements
f06jlf	12	idamax nagf_blas_idamax Index, real vector element with largest absolute value
f06jmf	12	izamax nagf_blas_izamax Index, complex vector element with largest absolute value
f06kcf	12	nagf_blas_zddscl Multiply complex vector by real diagonal matrix
f06kdf	12	nagf_blas_zdaxpzy Multiply complex vector by real scalar, preserving input vector
f06kef	21	nagf_blas_zdrscl Multiply complex vector by reciprocal of real scalar
f06kff	12	nagf_blas_zdcopy Copy real vector to complex vector
f06kjf	12	nagf_blas_dzssq Update Euclidean norm of complex vector in scaled form
f06klf	12	nagf_blas_idrank Last non-negligible element of real vector
f06kpf	12	zdrot nagf_blas_zdrot Apply real plane rotation to two complex vectors
f06paf	12	dgemv nagf_blas_dgemv Matrix-vector product, real rectangular matrix
f06pbf	12	dgbmv nagf_blas_dgbmv Matrix-vector product, real rectangular band matrix
f06pcf	12	dsymv nagf_blas_dsymv Matrix-vector product, real symmetric matrix
f06pdf	12	dsbmv nagf_blas_dsbmv Matrix-vector product, real symmetric band matrix
f06pef	12	dspmv nagf_blas_dspmv Matrix-vector product, real symmetric packed matrix
f06pff	12	dtrmv nagf_blas_dtrmv Matrix-vector product, real triangular matrix
f06pgf	12	dtbmv nagf_blas_dtbmv Matrix-vector product, real triangular band matrix
f06phf	12	dtpmv nagf_blas_dtpmv Matrix-vector product, real triangular packed matrix
f06pjf	12	dtrsv nagf_blas_dtrsv System of equations, real triangular matrix
f06pkf	12	dtbsv nagf_blas_dtbsv System of equations, real triangular band matrix
f06plf	12	dtpsv nagf_blas_dtpsv System of equations, real triangular packed matrix
f06pmf	12	dger nagf_blas_dger Rank-1 update, real rectangular matrix
f06ppf	12	dsyr nagf_blas_dsyr Rank-1 update, real symmetric matrix
f06pqf	12	dspr nagf_blas_dspr Rank-1 update, real symmetric packed matrix
f06prf	12	dsyr2 nagf_blas_dsyr2 Rank-2 update, real symmetric matrix
f06psf	12	dspr2 nagf_blas_dspr2 Rank-2 update, real symmetric packed matrix
f06qff	13	nagf_blas_dmcopy Matrix copy, real rectangular or trapezoidal matrix
f06qhf	13	nagf_blas_dmload Matrix initialization, real rectangular matrix
f06qjf	13	nagf_blas_dgeap Permute rows or columns, real rectangular matrix, permutations represented by an integer array
f06qkf	13	nagf_blas_dgeapr Permute rows or columns, real rectangular matrix, permutations represented by a real array
f06qmf	13	nagf_blas_dsysrc Orthogonal similarity transformation of real symmetric matrix as a sequence of plane rotations
f06qpf	13	nagf_blas_dutr1 $Q R$ factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix
f06qqf	13	nagf_blas_dutupd $Q R$ factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row
f06qrf	13	nagf_blas_duhqr $Q R$ or $R Q$ factorization by sequence of plane rotations, real upper Hessenberg matrix
f06qsf	13	nagf_blas_dusqr $Q R$ or $R Q$ factorization by sequence of plane rotations, real upper spiked matrix
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
f06qvf	13	nagf_blas_dutsrh Compute upper Hessenberg matrix by sequence of plane rotations, real upper triangular matrix
f06qwf	13	nagf_blas_dutsrs Compute upper spiked matrix by sequence of plane rotations, real upper triangular matrix
f06qxf	13	nagf_blas_dgesrc Apply sequence of plane rotations, real rectangular matrix
f06raf	15	nagf_blas_dlange $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, real general matrix
f06rbf	15	nagf_blas_dlangb $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, real band matrix
f06rcf	15	nagf_blas_dlansy $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, real symmetric matrix
f06rdf	15	nagf_blas_dlansp $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage
f06ref	15	nagf_blas_dlansb $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, real symmetric band matrix
f06rjf	15	nagf_blas_dlantr $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix
f06rkf	15	nagf_blas_dlantp $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage
f06rlf	15	nagf_blas_dlantb $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, real triangular band matrix
f06rmf	15	nagf_blas_dlanhs $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, real upper Hessenberg matrix
f06rnf	21	nagf_blas_dlangt $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, real tridiagonal matrix
f06rpf	21	nagf_blas_dlanst $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix
f06saf	12	zgemv nagf_blas_zgemv Matrix-vector product, complex rectangular matrix
f06sbf	12	zgbmv nagf_blas_zgbmv Matrix-vector product, complex rectangular band matrix
f06scf	12	zhemv nagf_blas_zhemv Matrix-vector product, complex Hermitian matrix
f06sdf	12	zhbmv nagf_blas_zhbmv Matrix-vector product, complex Hermitian band matrix
f06sef	12	zhpmv nagf_blas_zhpmv Matrix-vector product, complex Hermitian packed matrix
f06sff	12	ztrmv nagf_blas_ztrmv Matrix-vector product, complex triangular matrix
f06sgf	12	ztbmv nagf_blas_ztbmv Matrix-vector product, complex triangular band matrix
f06shf	12	ztpmv nagf_blas_ztpmv Matrix-vector product, complex triangular packed matrix
f06sjf	12	ztrsv nagf_blas_ztrsv System of equations, complex triangular matrix
f06skf	12	ztbsv nagf_blas_ztbsv System of equations, complex triangular band matrix
f06slf	12	ztpsv nagf_blas_ztpsv System of equations, complex triangular packed matrix
f06smf	12	zgeru nagf_blas_zgeru Rank-1 update, complex rectangular matrix, unconjugated vector
f06snf	12	zgerc nagf_blas_zgerc Rank-1 update, complex rectangular matrix, conjugated vector
f06spf	12	zher nagf_blas_zher Rank-1 update, complex Hermitian matrix
f06sqf	12	zhpr nagf_blas_zhpr Rank-1 update, complex Hermitian packed matrix
f06srf	12	zher2 nagf_blas_zher2 Rank-2 update, complex Hermitian matrix
f06ssf	12	zhpr2 nagf_blas_zhpr2 Rank-2 update, complex Hermitian packed matrix
f06taf	21	nagf_blas_zsymv Matrix-vector product, complex symmetric matrix
f06tbf	21	nagf_blas_zsyr Rank-1 update, complex symmetric matrix
f06tcf	21	nagf_blas_zspmv Matrix-vector product, complex symmetric packed matrix
f06tdf	21	nagf_blas_zspr Rank-1 update, complex symmetric packed matrix
f06tff	13	nagf_blas_zmcopy Matrix copy, complex rectangular or trapezoidal matrix
f06thf	13	nagf_blas_zmload Matrix initialization, complex rectangular matrix
f06tmf	13	nagf_blas_zhesrc Unitary similarity transformation of Hermitian matrix as a sequence of plane rotations
f06tpf	13	nagf_blas_zutr1 $Q R$ factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix
f06tqf	13	nagf_blas_zutupd $Q R$ factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row
f06trf	13	nagf_blas_zuhqr $Q R$ or $R Q$ factorization by sequence of plane rotations, complex upper Hessenberg matrix
f06tsf	13	nagf_blas_zusqr $Q R$ or $R Q$ factorization by sequence of plane rotations, complex upper spiked matrix
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
f06tvf	13	nagf_blas_zutsrh Compute upper Hessenberg matrix by sequence of plane rotations, complex upper triangular matrix
f06twf	13	nagf_blas_zutsrs Compute upper spiked matrix by sequence of plane rotations, complex upper triangular matrix
f06txf	13	nagf_blas_zgesrc Apply sequence of plane rotations, complex rectangular matrix, real cosine and complex sine
f06tyf	13	nagf_blas_zgesrs Apply sequence of plane rotations, complex rectangular matrix, complex cosine and real sine
f06uaf	15	nagf_blas_zlange $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, complex general matrix
f06ubf	15	nagf_blas_zlangb $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, complex band matrix
f06ucf	15	nagf_blas_zlanhe $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, complex Hermitian matrix
f06udf	15	nagf_blas_zlanhp $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage
f06uef	15	nagf_blas_zlanhb $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, complex Hermitian band matrix
f06uff	15	nagf_blas_zlansy $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, complex symmetric matrix
f06ugf	15	nagf_blas_zlansp $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage
f06uhf	15	nagf_blas_zlansb $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, complex symmetric band matrix
f06ujf	15	nagf_blas_zlantr $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix
f06ukf	15	nagf_blas_zlantp $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage
f06ulf	15	nagf_blas_zlantb $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, complex triangular band matrix
f06umf	15	nagf_blas_zlanhs $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, complex Hessenberg matrix
f06unf	21	nagf_blas_zlangt $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, complex tridiagonal matrix
f06upf	21	nagf_blas_zlanht $1$ -norm, $\infty$ -norm, Frobenius norm, largest absolute element, complex Hermitian tridiagonal matrix
f06vjf	13	nagf_blas_zgeap Permute rows or columns, complex rectangular matrix, permutations represented by an integer array
f06vkf	13	nagf_blas_zgeapr Permute rows or columns, complex rectangular matrix, permutations represented by a real array
f06vxf	13	nagf_blas_zsgesr Apply sequence of plane rotations, complex rectangular matrix, real cosine and sine
f06waf Example Text Example Data	23	dlansf nagf_blas_dlansf 1-norm, $\infty$ -norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format
f06wbf Example Text Example Data	23	dtfsm nagf_blas_dtfsm Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix, Rectangular Full Packed format
f06wcf Example Text Example Data	23	dsfrk nagf_blas_dsfrk Rank- $k$ update of a real symmetric matrix, Rectangular Full Packed format
f06wnf Example Text Example Data	23	zlanhf nagf_blas_zlanhf 1-norm, $\infty$ -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format
f06wpf Example Text Example Data	23	ztfsm nagf_blas_ztfsm Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix, Rectangular Full Packed format
f06wqf Example Text Example Data	23	zhfrk nagf_blas_zhfrk Rank- $k$ update of a complex Hermitian matrix, Rectangular Full Packed format
f06yaf	14	dgemm nagf_blas_dgemm Matrix-matrix product, two real rectangular matrices
f06ycf	14	dsymm nagf_blas_dsymm Matrix-matrix product, one real symmetric matrix, one real rectangular matrix
f06yff	14	dtrmm nagf_blas_dtrmm Matrix-matrix product, one real triangular matrix, one real rectangular matrix
f06yjf	14	dtrsm nagf_blas_dtrsm Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix
f06ypf	14	dsyrk nagf_blas_dsyrk Rank- $k$ update of a real symmetric matrix
f06yrf	14	dsyr2k nagf_blas_dsyr2k Rank- $2 k$ update of a real symmetric matrix
f06zaf	14	zgemm nagf_blas_zgemm Matrix-matrix product, two complex rectangular matrices
f06zcf	14	zhemm nagf_blas_zhemm Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix
f06zff	14	ztrmm nagf_blas_ztrmm Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix
f06zjf	14	ztrsm nagf_blas_ztrsm Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix
f06zpf	14	zherk nagf_blas_zherk Rank- $k$ update of a complex Hermitian matrix
f06zrf	14	zher2k nagf_blas_zher2k Rank- $2 k$ update of a complex Hermitian matrix
f06ztf	14	zsymm nagf_blas_zsymm Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix
f06zuf	14	zsyrk nagf_blas_zsyrk Rank- $k$ update of a complex symmetric matrix
f06zwf	14	zsyr2k nagf_blas_zsyr2k Rank- $2 k$ update of a complex symmetric matrix

NAG FL InterfaceF06 (Blas)Linear Algebra Support Routines

NAG FL Interface
F06 (Blas)
Linear Algebra Support Routines