F06 Chapter Contents (PDF version)
F06 Chapter Introduction
NAG Library Manual

NAG Library Chapter Contents

F06 – Linear Algebra Support Routines


F06 Chapter Introduction – a description of the Chapter and an overview of the algorithms available

Routine
Name
Mark of
Introduction

Purpose
F06AAF (DROTG) 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 a2+b2, 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 (DDOT) 12 DDOT
nagf_blas_ddot
Dot product of two real vectors
F06ECF (DAXPY) 12 DAXPY
nagf_blas_daxpy
Add scalar times real vector to real vector
F06EDF (DSCAL) 12 DSCAL
nagf_blas_dscal
Multiply real vector by scalar
F06EFF (DCOPY) 12 DCOPY
nagf_blas_dcopy
Copy real vector
F06EGF (DSWAP) 12 DSWAP
nagf_blas_dswap
Swap two real vectors
F06EJF (DNRM2) 12 DNRM2
nagf_blas_dnrm2
Compute Euclidean norm of real vector
F06EKF (DASUM) 12 DASUM
nagf_blas_dasum
Sum absolute values of real vector elements
F06EPF (DROT) 12 DROT
nagf_blas_drot
Apply real plane rotation
F06ERF (DDOTI) 14 DDOTI
nagf_blas_ddoti
Dot product of a real sparse and a full vector
F06ETF (DAXPYI) 14 DAXPYI
nagf_blas_daxpyi
Add scalar times real sparse vector to a full vector
F06EUF (DGTHR) 14 DGTHR
nagf_blas_dgthr
Gather real sparse vector
F06EVF (DGTHRZ) 14 DGTHRZ
nagf_blas_dgthrz
Gather and set to zero real sparse vector
F06EWF (DSCTR) 14 DSCTR
nagf_blas_dsctr
Scatter real sparse vector
F06EXF (DROTI) 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 (ZDOTU) 12 ZDOTU
nagf_blas_zdotu
Dot product of two complex vectors, unconjugated
F06GBF (ZDOTC) 12 ZDOTC
nagf_blas_zdotc
Dot product of two complex vectors, conjugated
F06GCF (ZAXPY) 12 ZAXPY
nagf_blas_zaxpy
Add scalar times complex vector to complex vector
F06GDF (ZSCAL) 12 ZSCAL
nagf_blas_zscal
Multiply complex vector by complex scalar
F06GFF (ZCOPY) 12 ZCOPY
nagf_blas_zcopy
Copy complex vector
F06GGF (ZSWAP) 12 ZSWAP
nagf_blas_zswap
Swap two complex vectors
F06GRF (ZDOTUI) 14 ZDOTUI
nagf_blas_zdotui
Dot product of a complex sparse and a full vector, unconjugated
F06GSF (ZDOTCI) 14 ZDOTCI
nagf_blas_zdotci
Dot product of a complex sparse and a full vector, conjugated
F06GTF (ZAXPYI) 14 ZAXPYI
nagf_blas_zaxpyi
Add scalar times complex sparse vector to a full vector
F06GUF (ZGTHR) 14 ZGTHR
nagf_blas_zgthr
Gather complex sparse vector
F06GVF (ZGTHRZ) 14 ZGTHRZ
nagf_blas_zgthrz
Gather and set to zero complex sparse vector
F06GWF (ZSCTR) 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 (ZROT) 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 (ZDSCAL) 12 ZDSCAL
nagf_blas_zdscal
Multiply complex vector by real scalar
F06JJF (DZNRM2) 12 DZNRM2
nagf_blas_dznrm2
Compute Euclidean norm of complex vector
F06JKF (DZASUM) 12 DZASUM
nagf_blas_dzasum
Sum absolute values of complex vector elements
F06JLF (IDAMAX) 12 IDAMAX
nagf_blas_idamax
Index, real vector element with largest absolute value
F06JMF (IZAMAX) 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 (ZDROT) 12 ZDROT
nagf_blas_zdrot
Apply real plane rotation to two complex vectors
F06PAF (DGEMV) 12 DGEMV
nagf_blas_dgemv
Matrix-vector product, real rectangular matrix
F06PBF (DGBMV) 12 DGBMV
nagf_blas_dgbmv
Matrix-vector product, real rectangular band matrix
F06PCF (DSYMV) 12 DSYMV
nagf_blas_dsymv
Matrix-vector product, real symmetric matrix
F06PDF (DSBMV) 12 DSBMV
nagf_blas_dsbmv
Matrix-vector product, real symmetric band matrix
F06PEF (DSPMV) 12 DSPMV
nagf_blas_dspmv
Matrix-vector product, real symmetric packed matrix
F06PFF (DTRMV) 12 DTRMV
nagf_blas_dtrmv
Matrix-vector product, real triangular matrix
F06PGF (DTBMV) 12 DTBMV
nagf_blas_dtbmv
Matrix-vector product, real triangular band matrix
F06PHF (DTPMV) 12 DTPMV
nagf_blas_dtpmv
Matrix-vector product, real triangular packed matrix
F06PJF (DTRSV) 12 DTRSV
nagf_blas_dtrsv
System of equations, real triangular matrix
F06PKF (DTBSV) 12 DTBSV
nagf_blas_dtbsv
System of equations, real triangular band matrix
F06PLF (DTPSV) 12 DTPSV
nagf_blas_dtpsv
System of equations, real triangular packed matrix
F06PMF (DGER) 12 DGER
nagf_blas_dger
Rank-1 update, real rectangular matrix
F06PPF (DSYR) 12 DSYR
nagf_blas_dsyr
Rank-1 update, real symmetric matrix
F06PQF (DSPR) 12 DSPR
nagf_blas_dspr
Rank-1 update, real symmetric packed matrix
F06PRF (DSYR2) 12 DSYR2
nagf_blas_dsyr2
Rank-2 update, real symmetric matrix
F06PSF (DSPR2) 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
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, -norm, Frobenius norm, largest absolute element, real general matrix
F06RBF 15 nagf_blas_dlangb
1-norm, -norm, Frobenius norm, largest absolute element, real band matrix
F06RCF 15 nagf_blas_dlansy
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix
F06RDF 15 nagf_blas_dlansp
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage
F06REF 15 nagf_blas_dlansb
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric band matrix
F06RJF 15 nagf_blas_dlantr
1-norm, -norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix
F06RKF 15 nagf_blas_dlantp
1-norm, -norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage
F06RLF 15 nagf_blas_dlantb
1-norm, -norm, Frobenius norm, largest absolute element, real triangular band matrix
F06RMF 15 nagf_blas_dlanhs
1-norm, -norm, Frobenius norm, largest absolute element, real upper Hessenberg matrix
F06RNF 21 nagf_blas_dlangt
1-norm, -norm, Frobenius norm, largest absolute element, real tridiagonal matrix
F06RPF 21 nagf_blas_dlanst
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix
F06SAF (ZGEMV) 12 ZGEMV
nagf_blas_zgemv
Matrix-vector product, complex rectangular matrix
F06SBF (ZGBMV) 12 ZGBMV
nagf_blas_zgbmv
Matrix-vector product, complex rectangular band matrix
F06SCF (ZHEMV) 12 ZHEMV
nagf_blas_zhemv
Matrix-vector product, complex Hermitian matrix
F06SDF (ZHBMV) 12 ZHBMV
nagf_blas_zhbmv
Matrix-vector product, complex Hermitian band matrix
F06SEF (ZHPMV) 12 ZHPMV
nagf_blas_zhpmv
Matrix-vector product, complex Hermitian packed matrix
F06SFF (ZTRMV) 12 ZTRMV
nagf_blas_ztrmv
Matrix-vector product, complex triangular matrix
F06SGF (ZTBMV) 12 ZTBMV
nagf_blas_ztbmv
Matrix-vector product, complex triangular band matrix
F06SHF (ZTPMV) 12 ZTPMV
nagf_blas_ztpmv
Matrix-vector product, complex triangular packed matrix
F06SJF (ZTRSV) 12 ZTRSV
nagf_blas_ztrsv
System of equations, complex triangular matrix
F06SKF (ZTBSV) 12 ZTBSV
nagf_blas_ztbsv
System of equations, complex triangular band matrix
F06SLF (ZTPSV) 12 ZTPSV
nagf_blas_ztpsv
System of equations, complex triangular packed matrix
F06SMF (ZGERU) 12 ZGERU
nagf_blas_zgeru
Rank-1 update, complex rectangular matrix, unconjugated vector
F06SNF (ZGERC) 12 ZGERC
nagf_blas_zgerc
Rank-1 update, complex rectangular matrix, conjugated vector
F06SPF (ZHER) 12 ZHER
nagf_blas_zher
Rank-1 update, complex Hermitian matrix
F06SQF (ZHPR) 12 ZHPR
nagf_blas_zhpr
Rank-1 update, complex Hermitian packed matrix
F06SRF (ZHER2) 12 ZHER2
nagf_blas_zher2
Rank-2 update, complex Hermitian matrix
F06SSF (ZHPR2) 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
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, -norm, Frobenius norm, largest absolute element, complex general matrix
F06UBF 15 nagf_blas_zlangb
1-norm, -norm, Frobenius norm, largest absolute element, complex band matrix
F06UCF 15 nagf_blas_zlanhe
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix
F06UDF 15 nagf_blas_zlanhp
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage
F06UEF 15 nagf_blas_zlanhb
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian band matrix
F06UFF 15 nagf_blas_zlansy
1-norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix
F06UGF 15 nagf_blas_zlansp
1-norm, -norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage
F06UHF 15 nagf_blas_zlansb
1-norm, -norm, Frobenius norm, largest absolute element, complex symmetric band matrix
F06UJF 15 nagf_blas_zlantr
1-norm, -norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix
F06UKF 15 nagf_blas_zlantp
1-norm, -norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage
F06ULF 15 nagf_blas_zlantb
1-norm, -norm, Frobenius norm, largest absolute element, complex triangular band matrix
F06UMF 15 nagf_blas_zlanhs
1-norm, -norm, Frobenius norm, largest absolute element, complex Hessenberg matrix
F06UNF 21 nagf_blas_zlangt
1-norm, -norm, Frobenius norm, largest absolute element, complex tridiagonal matrix
F06UPF 21 nagf_blas_zlanht
1-norm, -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 (DLANSF)
Example Text
Example Data
23 DLANSF
nagf_blas_dlansf
1-norm, -norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format
F06WBF (DTFSM)
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 (DSFRK)
Example Text
Example Data
23 DSFRK
nagf_blas_dsfrk
Rank-k update of a real symmetric matrix, Rectangular Full Packed format
F06WNF (ZLANHF)
Example Text
Example Data
23 ZLANHF
nagf_blas_zlanhf
1-norm, -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, Rectangular Full Packed format
F06WPF (ZTFSM)
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 (ZHFRK)
Example Text
Example Data
23 ZHFRK
nagf_blas_zhfrk
Rank-k update of a complex Hermitian matrix, Rectangular Full Packed format
F06YAF (DGEMM) 14 DGEMM
nagf_blas_dgemm
Matrix-matrix product, two real rectangular matrices
F06YCF (DSYMM) 14 DSYMM
nagf_blas_dsymm
Matrix-matrix product, one real symmetric matrix, one real rectangular matrix
F06YFF (DTRMM) 14 DTRMM
nagf_blas_dtrmm
Matrix-matrix product, one real triangular matrix, one real rectangular matrix
F06YJF (DTRSM) 14 DTRSM
nagf_blas_dtrsm
Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix
F06YPF (DSYRK) 14 DSYRK
nagf_blas_dsyrk
Rank-k update of a real symmetric matrix
F06YRF (DSYR2K) 14 DSYR2K
nagf_blas_dsyr2k
Rank-2k update of a real symmetric matrix
F06ZAF (ZGEMM) 14 ZGEMM
nagf_blas_zgemm
Matrix-matrix product, two complex rectangular matrices
F06ZCF (ZHEMM) 14 ZHEMM
nagf_blas_zhemm
Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix
F06ZFF (ZTRMM) 14 ZTRMM
nagf_blas_ztrmm
Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix
F06ZJF (ZTRSM) 14 ZTRSM
nagf_blas_ztrsm
Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix
F06ZPF (ZHERK) 14 ZHERK
nagf_blas_zherk
Rank-k update of a complex Hermitian matrix
F06ZRF (ZHER2K) 14 ZHER2K
nagf_blas_zher2k
Rank-2k update of a complex Hermitian matrix
F06ZTF (ZSYMM) 14 ZSYMM
nagf_blas_zsymm
Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix
F06ZUF (ZSYRK) 14 ZSYRK
nagf_blas_zsyrk
Rank-k update of a complex symmetric matrix
F06ZWF (ZSYR2K) 14 ZSYR2K
nagf_blas_zsyr2k
Rank-2k update of a complex symmetric matrix

F06 Chapter Contents (PDF version)
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2016