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

# NAG Library Chapter ContentsF06 – Linear Algebra Support Routines

### F06 Chapter Introduction

 RoutineName Mark ofIntroduction 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 $\left({a}^{2}+{b}^{2}\right)$, 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_zdrot Apply plane rotation with real cosine and complex sine F06HPF 12 nagf_blas_zrot 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 nagf_blas_zrots 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 $QR$ 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 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, $\infty$-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-$2k$ 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

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