# F06 - Linear Algebra Support Routines

 Chapter Introduction F06AAF (SROTG/DROTG) Generate real plane rotation F06BAF Generate real plane rotation, storing tangent F06BCF Recover cosine and sine from given real tangent F06BEF Generate real Jacobi plane rotation F06BHF Apply real similarity rotation to 2 by 2 symmetric matrix F06BLF Compute quotient of two real scalars, with overflow flag F06BMF Compute Euclidean norm from scaled form F06BNF Compute square root of ( a2 + b2), real a and b F06BPF Compute eigenvalue of 2 by 2 real symmetric matrix F06CAF Generate complex plane rotation, storing tangent, real cosine F06CBF Generate complex plane rotation, storing tangent, real sine F06CCF Recover cosine and sine from given complex tangent, real cosine F06CDF Recover cosine and sine from given complex tangent, real sine F06CHF Apply complex similarity rotation to 2 by 2 Hermitian matrix F06CLF Compute quotient of two complex scalars, with overflow flag F06DBF Broadcast scalar into integer vector F06DFF Copy integer vector F06EAF (SDOT/DDOT) Dot product of two real vectors F06ECF (SAXPY/DAXPY) Add scalar times real vector to real vector F06EDF (SSCAL/DSCAL) Multiply real vector by scalar F06EFF (SCOPY/DCOPY) Copy real vector F06EGF (SSWAP/DSWAP) Swap two real vectors F06EJF (SNRM2/DNRM2) Compute Euclidean norm of real vector F06EKF (SASUM/DASUM) Sum absolute values of real vector elements F06EPF (SROT/DROT) Apply real plane rotation F06ERF (SDOTI/DDOTI) Dot product of two real sparse vectors F06ETF (SAXPYI/DAXPYI) Add scalar times real sparse vector to real sparse vector F06EUF (SGTHR/DGTHR) Gather real sparse vector F06EVF (SGTHRZ/DGTHRZ) Gather and set to zero real sparse vector F06EWF (SSCTR/DSCTR) Scatter real sparse vector F06EXF (SROTI/DROTI) Apply plane rotation to two real sparse vectors F06FAF Compute cosine of angle between two real vectors F06FBF Broadcast scalar into real vector F06FCF Multiply real vector by diagonal matrix F06FDF Multiply real vector by scalar, preserving input vector F06FGF Negate real vector F06FJF Update Euclidean norm of real vector in scaled form F06FKF Compute weighted Euclidean norm of real vector F06FLF Elements of real vector with largest and smallest absolute value F06FPF Apply real symmetric plane rotation to two vectors F06FQF Generate sequence of real plane rotations F06FRF Generate real elementary reflection, NAG style F06FSF Generate real elementary reflection, LINPACK style F06FTF Apply real elementary reflection, NAG style F06FUF Apply real elementary reflection, LINPACK style F06GAF (CDOTU/ZDOTU) Dot product of two complex vectors, unconjugated F06GBF (CDOTC/ZDOTC) Dot product of two complex vectors, conjugated F06GCF (CAXPY/ZAXPY) Add scalar times complex vector to complex vector F06GDF (CSCAL/ZSCAL) Multiply complex vector by complex scalar F06GFF (CCOPY/ZCOPY) Copy complex vector F06GGF (CSWAP/ZSWAP) Swap two complex vectors F06GRF (CDOTUI/ZDOTUI) Dot product of two complex sparse vector, unconjugated F06GSF (CDOTCI/ZDOTCI) Dot product of two complex sparse vector, conjugated F06GTF (CAXPYI/ZAXPYI) Add scalar times complex sparse vector to complex sparse vector F06GUF (CGTHR/ZGTHR) Gather complex sparse vector F06GVF (CGTHRZ/ZGTHRZ) Gather and set to zero complex sparse vector F06GWF (CSCTR/ZSCTR) Scatter complex sparse vector F06HBF Broadcast scalar into complex vector F06HCF Multiply complex vector by complex diagonal matrix F06HDF Multiply complex vector by complex scalar, preserving input vector F06HGF Negate complex vector F06HPF Apply complex plane rotation F06HQF Generate sequence of complex plane rotations F06HRF Generate complex elementary reflection F06HTF Apply complex elementary reflection F06JDF (CSSCAL/ZDSCAL) Multiply complex vector by real scalar F06JJF (SCNRM2/DZNRM2) Compute Euclidean norm of complex vector F06JKF (SCASUM/DZASUM) Sum absolute values of complex vector elements F06JLF (ISAMAX/IDAMAX) Index, real vector element with largest absolute value F06JMF (ICAMAX/IZAMAX) Index, complex vector element with largest absolute value F06KCF Multiply complex vector by real diagonal matrix F06KDF Multiply complex vector by real scalar, preserving input vector F06KFF Copy real vector to complex vector F06KJF Update Euclidean norm of complex vector in scaled form F06KLF Last non-negligible element of real vector F06KPF Apply real plane rotation to two complex vectors F06PAF (SGEMV/DGEMV) Matrix-vector product, real rectangular matrix F06PBF (SGBMV/DGBMV) Matrix-vector product, real rectangular band matrix F06PCF (SSYMV/DSYMV) Matrix-vector product, real symmetric matrix F06PDF (SSBMV/DSBMV) Matrix-vector product, real symmetric band matrix F06PEF (SSPMV/DSPMV) Matrix-vector product, real symmetric packed matrix F06PFF (STRMV/DTRMV) Matrix-vector product, real triangular matrix F06PGF (STBMV/DTBMV) Matrix-vector product, real triangular band matrix F06PHF (STPMV/DTPMV) Matrix-vector product, real triangular packed matrix F06PJF (STRSV/DTRSV) System of equations, real triangular matrix F06PKF (STBSV/DTBSV) System of equations, real triangular band matrix F06PLF (STPSV/DTPSV) System of equations, real triangular packed matrix F06PMF (SGER/DGER) Rank-1 update, real rectangular matrix F06PPF (SSYR/DSYR) Rank-1 update, real symmetric matrix F06PQF (SSPR/DSPR) Rank-1 update, real symmetric packed matrix F06PRF (SSYR2/DSYR2) Rank-2 update, real symmetric matrix F06PSF (SSPR2/DSPR2) Rank-2 update, real symmetric packed matrix F06QFF Matrix copy, real rectangular or trapezoidal matrix F06QHF Matrix initialisation, real rectangular matrix F06QJF Permute rows or columns, real rectangular matrix, permutations represented by an integer array F06QKF Permute rows or columns, real rectangular matrix, permutations represented by a real array F06QMF Orthogonal similarity transformation of real symmetric matrix as a sequence of plane rotations F06QPF QR factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix F06QQF QR factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row F06QRF QR or RQ factorization by sequence of plane rotations, real upper Hessenberg matrix F06QSF QR or RQ factorization by sequence of plane rotations, real upper spiked matrix F06QTF QR factorization of UZ or RQ factorization of ZU, U real upper triangular, Z a sequence of plane rotations F06QVF Compute upper Hessenberg matrix by sequence of plane rotations, real upper triangular matrix F06QWF Compute upper spiked matrix by sequence of plane rotations, real upper triangular matrix F06QXF Apply sequence of plane rotations, real rectangular matrix F06RAF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real general matrix F06RBF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real band matrix F06RCF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real symmetric matrix F06RDF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage F06REF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real symmetric band matrix F06RJF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix F06RKF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage F06RLF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real triangular band matrix F06RMF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real Hessenberg matrix F06SAF (CGEMV/ZGEMV) Matrix-vector product, complex rectangular matrix F06SBF (CGBMV/ZGBMV) Matrix-vector product, complex rectangular band matrix F06SCF (CHEMV/ZHEMV) Matrix-vector product, complex Hermitian matrix F06SDF (CHBMV/ZHBMV) Matrix-vector product, complex Hermitian band matrix F06SEF (CHPMV/ZHPMV) Matrix-vector product, complex Hermitian packed matrix F06SFF (CTRMV/ZTRMV) Matrix-vector product, complex triangular matrix F06SGF (CTBMV/ZTBMV) Matrix-vector product, complex triangular band matrix F06SHF (CTPMV/ZTPMV) Matrix-vector product, complex triangular packed matrix F06SJF (CTRSV/ZTRSV) System of equations, complex triangular matrix F06SKF (CTBSV/ZTBSV) System of equations, complex triangular band matrix F06SLF (CTPSV/ZTPSV) System of equations, complex triangular packed matrix F06SMF (CGERU/ZGERU) Rank-1 update, complex rectangular matrix, unconjugated vector F06SNF (CGERC/ZGERC) Rank-1 update, complex rectangular matrix, conjugated vector F06SPF (CHER/ZHER) Rank-1 update, complex Hermitian matrix F06SQF (CHPR/ZHPR) Rank-1 update, complex Hermitian packed matrix F06SRF (CHER2/ZHER2) Rank-2 update, complex Hermitian matrix F06SSF (CHPR2/ZHPR2) Rank-2 update, complex Hermitian packed matrix F06TFF Matrix copy, complex rectangular or trapezoidal matrix F06THF Matrix initialisation, complex rectangular matrix F06TMF Unitary similarity transformation of Hermitian matrix as a sequence of plane rotations F06TPF QR factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix F06TQF QRxk factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row F06TRF QR or RQ factorization by sequence of plane rotations, complex upper Hessenberg matrix F06TSF QR or RQ factorization by sequence of plane rotations, complex upper spiked matrix F06TTF QR factorization of UZ or RQ factorization of ZU, U complex upper triangular, Z a sequence of plane rotations F06TVF Compute upper Hessenberg matrix by sequence of plane rotations, complex upper triangular matrix F06TWF Compute upper spiked matrix by sequence of plane rotations, complex upper triangular matrix F06TXF Apply sequence of plane rotations, complex rectangular matrix, real cosine and complex sine F06TYF Apply sequence of plane rotations, complex rectangular matrix, complex cosine and real sine F06UAF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex general matrix F06UBF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex band matrix F06UCF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex Hermitian matrix F06UDF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage F06UEF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex Hermitian band matrix F06UFF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex symmetric matrix F06UGF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage F06UHF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex symmetric band matrix F06UJF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix F06UKF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage F06ULF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex triangular band matrix F06UMF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex Hessenberg matrix F06VJF Permute rows or columns, complex rectangular matrix, permutations represented by an integer array F06VKF Permute rows or columns, complex rectangular matrix, permutations represented by a real array F06VXF Apply sequence of plane rotations, complex rectangular matrix, real cosine and sine F06YAF (SGEMM/DGEMM) Matrix-matrix product, two real rectangular matrices F06YCF (SSYMM/DSYMM) Matrix-matrix product, one real symmetric matrix, one real rectangular matrix F06YFF (STRMM/DTRMM) Matrix-matrix product, one real triangular matrix, one real rectangular matrix F06YJF (STRSM/DTRSM) Solves system of equations with multiple right-hand sides, real triangular coefficient matrix F06YPF (SSYRK/DSYRK) Rank-k update of real symmetric matrix F06YRF (SSYR2K/DSYR2K) Rank-2k update of real symmetric matrix F06ZAF (CGEMM/ZGEMM) Matrix-matrix product, two complex rectangular matrices F06ZCF (CHEMM/ZHEMM) Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix F06ZFF (CTRMM/ZTRMM) Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix F06ZJF (CTRSM/ZTRSM) Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix F06ZPF (CHERK/ZHERK) Rank-k update of complex Hermitian matrix F06ZRF (CHER2K/ZHER2K) Rank-2k update of complex Hermitian matrix F06ZTF (CSYMM/ZSYMM) Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix F06ZUF (CSYRK/ZSYRK) Rank-k update of complex symmetric matrix F06ZWF (CSYR2K/ZHER2K) Rank-2k update of complex symmetric matrix

© The Numerical Algorithms Group Ltd, Oxford UK. 1999