# NAG FL InterfaceF06 (Blas)Linear Algebra Support Routines

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F06 (Blas) Chapter Introduction – A description of the Chapter and an overview of the algorithms available.

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 $2×2$ 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 $\left({a}^{2}+{b}^{2}\right)$, real $a$ and $b$
f06bpf 12 nagf_blas_deig2
Compute eigenvalue of $2×2$ 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 $2×2$ Hermitian matrix
f06clf 12 nagf_blas_zdiv
Compute quotient of two complex scalars, with overflow flag
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
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
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
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
$QR$ factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix
f06qqf 13 nagf_blas_dutupd
$QR$ factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row
f06qrf 13 nagf_blas_duhqr
$QR$ or $RQ$ factorization by sequence of plane rotations, real upper Hessenberg matrix
f06qsf 13 nagf_blas_dusqr
$QR$ or $RQ$ factorization by sequence of plane rotations, real upper spiked matrix
f06qtf 13 nagf_blas_dutsqr
$QR$ factorization of $UP$ or $RQ$ factorization of $PU$, $U$ 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
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
$QR$ factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix
f06tqf 13 nagf_blas_zutupd
$QR$ factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row
f06trf 13 nagf_blas_zuhqr
$QR$ or $RQ$ factorization by sequence of plane rotations, complex upper Hessenberg matrix
f06tsf 13 nagf_blas_zusqr
$QR$ or $RQ$ factorization by sequence of plane rotations, complex upper spiked matrix
f06ttf 13 nagf_blas_zutsqr
$QR$ factorization of $UP$ or $RQ$ factorization of $PU$, $U$ 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 23 dlansf
nagf_blas_dlansf
1-norm, $\infty$-norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format
f06wbf 23 dtfsm
nagf_blas_dtfsm
Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix, Rectangular Full Packed format
f06wcf 23 dsfrk
nagf_blas_dsfrk
Rank-$k$ update of a real symmetric matrix, Rectangular Full Packed format
f06wnf 23 zlanhf
nagf_blas_zlanhf
1-norm, $\infty$-norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format
f06wpf 23 ztfsm
nagf_blas_ztfsm
Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix, Rectangular Full Packed format
f06wqf 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-$2k$ 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-$2k$ 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-$2k$ update of a complex symmetric matrix