## F06 – Linear Algebra Support Routines

 RoutineName Mark ofIntroduction Purpose F06AAF (SROTG/DROTG) 12 Generate real plane rotation F06BAF 12 Generate real plane rotation, storing tangent F06BCF 12 Recover cosine and sine from given real tangent F06BEF 12 Generate real Jacobi plane rotation F06BHF 12 Apply real similarity rotation to 2 by 2 symmetric matrix F06BLF Example Text 12 Compute quotient of two real scalars, with overflow flag F06BMF 12 Compute Euclidean norm from scaled form F06BNF 12 Compute square root of (a2 + b2), real a and b F06BPF 12 Compute eigenvalue of 2 by 2 real symmetric matrix F06CAF 12 Generate complex plane rotation, storing tangent, real cosine F06CBF 12 Generate complex plane rotation, storing tangent, real sine F06CCF 12 Recover cosine and sine from given complex tangent, real cosine F06CDF 12 Recover cosine and sine from given complex tangent, real sine F06CHF 12 Apply complex similarity rotation to 2 by 2 Hermitian matrix F06CLF Example Text 12 Compute quotient of two complex scalars, with overflow flag F06DBF 12 Broadcast scalar into integer vector F06DFF 12 Copy integer vector F06EAF (SDOT/DDOT) Example Text 12 Dot product of two real vectors F06ECF (SAXPY/DAXPY) Example Text 12 Add scalar times real vector to real vector F06EDF (SSCAL/DSCAL) 12 Multiply real vector by scalar F06EFF (SCOPY/DCOPY) 12 Copy real vector F06EGF (SSWAP/DSWAP) 12 Swap two real vectors F06EJF (SNRM2/DNRM2) 12 Compute Euclidean norm of real vector F06EKF (SASUM/DASUM) 12 Sum absolute values of real vector elements F06EPF (SROT/DROT) 12 Apply real plane rotation F06ERF (SDOTI/DDOTI) Example Text Example Data 14 Dot product of two real sparse vectors F06ETF (SAXPYI/DAXPYI) Example Text Example Data 14 Add scalar times real sparse vector to real sparse vector F06EUF (SGTHR/DGTHR) 14 Gather real sparse vector F06EVF (SGTHRZ/DGTHRZ) 14 Gather and set to zero real sparse vector F06EWF (SSCTR/DSCTR) 14 Scatter real sparse vector F06EXF (SROTI/DROTI) 14 Apply plane rotation to two real sparse vectors F06FAF Example Text 12 Compute cosine of angle between two real vectors F06FBF 12 Broadcast scalar into real vector F06FCF 12 Multiply real vector by diagonal matrix F06FDF 12 Multiply real vector by scalar, preserving input vector F06FGF 12 Negate real vector F06FJF 12 Update Euclidean norm of real vector in scaled form F06FKF 12 Compute weighted Euclidean norm of real vector F06FLF 12 Elements of real vector with largest and smallest absolute value F06FPF 12 Apply real symmetric plane rotation to two vectors F06FQF 12 Generate sequence of real plane rotations F06FRF 12 Generate real elementary reflection, NAG style F06FSF 12 Generate real elementary reflection, LINPACK style F06FTF 12 Apply real elementary reflection, NAG style F06FUF 12 Apply real elementary reflection, LINPACK style F06GAF (CDOTU/ZDOTU) Example Text 12 Dot product of two complex vectors, unconjugated F06GBF (CDOTC/ZDOTC) Example Text 12 Dot product of two complex vectors, conjugated F06GCF (CAXPY/ZAXPY) 12 Add scalar times complex vector to complex vector F06GDF (CSCAL/ZSCAL) 12 Multiply complex vector by complex scalar F06GFF (CCOPY/ZCOPY) 12 Copy complex vector F06GGF (CSWAP/ZSWAP) 12 Swap two complex vectors F06GRF (CDOTUI/ZDOTUI) Example Text Example Data 14 Dot product of two complex sparse vector, unconjugated F06GSF (CDOTCI/ZDOTCI) 14 Dot product of two complex sparse vector, conjugated F06GTF (CAXPYI/ZAXPYI) Example Text Example Data 14 Add scalar times complex sparse vector to complex sparse vector F06GUF (CGTHR/ZGTHR) 14 Gather complex sparse vector F06GVF (CGTHRZ/ZGTHRZ) 14 Gather and set to zero complex sparse vector F06GWF (CSCTR/ZSCTR) 14 Scatter complex sparse vector F06HBF Example Text 12 Broadcast scalar into complex vector F06HCF 12 Multiply complex vector by complex diagonal matrix F06HDF 12 Multiply complex vector by complex scalar, preserving input vector F06HGF 12 Negate complex vector F06HPF 12 Apply complex plane rotation F06HQF 12 Generate sequence of complex plane rotations F06HRF 12 Generate complex elementary reflection F06HTF 12 Apply complex elementary reflection F06JDF (CSSCAL/ZDSCAL) 12 Multiply complex vector by real scalar F06JJF (SCNRM2/DZNRM2) 12 Compute Euclidean norm of complex vector F06JKF (SCASUM/DZASUM) 12 Sum absolute values of complex vector elements F06JLF (ISAMAX/IDAMAX) 12 Index, real vector element with largest absolute value F06JMF (ICAMAX/IZAMAX) 12 Index, complex vector element with largest absolute value F06KCF 12 Multiply complex vector by real diagonal matrix F06KDF 12 Multiply complex vector by real scalar, preserving input vector F06KFF 12 Copy real vector to complex vector F06KJF 12 Update Euclidean norm of complex vector in scaled form F06KLF 12 Last non-negligible element of real vector F06KPF 12 Apply real plane rotation to two complex vectors F06PAF (SGEMV/DGEMV) Example Text Example Data 12 Matrix-vector product, real rectangular matrix F06PBF (SGBMV/DGBMV) Example Text Example Data 12 Matrix-vector product, real rectangular band matrix F06PCF (SSYMV/DSYMV) 12 Matrix-vector product, real symmetric matrix F06PDF (SSBMV/DSBMV) 12 Matrix-vector product, real symmetric band matrix F06PEF (SSPMV/DSPMV) 12 Matrix-vector product, real symmetric packed matrix F06PFF (STRMV/DTRMV) 12 Matrix-vector product, real triangular matrix F06PGF (STBMV/DTBMV) 12 Matrix-vector product, real triangular band matrix F06PHF (STPMV/DTPMV) 12 Matrix-vector product, real triangular packed matrix F06PJF (STRSV/DTRSV) 12 System of equations, real triangular matrix F06PKF (STBSV/DTBSV) 12 System of equations, real triangular band matrix F06PLF (STPSV/DTPSV) 12 System of equations, real triangular packed matrix F06PMF (SGER/DGER) 12 Rank-1 update, real rectangular matrix F06PPF (SSYR/DSYR) 12 Rank-1 update, real symmetric matrix F06PQF (SSPR/DSPR) 12 Rank-1 update, real symmetric packed matrix F06PRF (SSYR2/DSYR2) 12 Rank-2 update, real symmetric matrix F06PSF (SSPR2/DSPR2) 12 Rank-2 update, real symmetric packed matrix F06QFF 13 Matrix copy, real rectangular or trapezoidal matrix F06QHF Example Text 13 Matrix initialisation, real rectangular matrix F06QJF Example Text 13 Permute rows or columns, real rectangular matrix, permutations represented by an integer array F06QKF 13 Permute rows or columns, real rectangular matrix, permutations represented by a real array F06QMF Example Text 13 Orthogonal similarity transformation of real symmetric matrix as a sequence of plane rotations F06QPF Example Text 13 QR factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix F06QQF Example Text 13 QR factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row F06QRF Example Text 13 QR or RQ factorization by sequence of plane rotations, real upper Hessenberg matrix F06QSF Example Text 13 QR or RQ factorization by sequence of plane rotations, real upper spiked matrix F06QTF Example Text 13 QR factorization of UZ or RQ factorization of ZU, U real upper triangular, Z a sequence of plane rotations F06QVF 13 Compute upper Hessenberg matrix by sequence of plane rotations, real upper triangular matrix F06QWF 13 Compute upper spiked matrix by sequence of plane rotations, real upper triangular matrix F06QXF 13 Apply sequence of plane rotations, real rectangular matrix F06RAF Example Text 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, real general matrix F06RBF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, real band matrix F06RCF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, real symmetric matrix F06RDF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage F06REF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, real symmetric band matrix F06RJF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix F06RKF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage F06RLF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, real triangular band matrix F06RMF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, real Hessenberg matrix F06SAF (CGEMV/ZGEMV) Example Text Example Data 12 Matrix-vector product, complex rectangular matrix F06SBF (CGBMV/ZGBMV) Example Text Example Data 12 Matrix-vector product, complex rectangular band matrix F06SCF (CHEMV/ZHEMV) 12 Matrix-vector product, complex Hermitian matrix F06SDF (CHBMV/ZHBMV) 12 Matrix-vector product, complex Hermitian band matrix F06SEF (CHPMV/ZHPMV) 12 Matrix-vector product, complex Hermitian packed matrix F06SFF (CTRMV/ZTRMV) 12 Matrix-vector product, complex triangular matrix F06SGF (CTBMV/ZTBMV) 12 Matrix-vector product, complex triangular band matrix F06SHF (CTPMV/ZTPMV) 12 Matrix-vector product, complex triangular packed matrix F06SJF (CTRSV/ZTRSV) 12 System of equations, complex triangular matrix F06SKF (CTBSV/ZTBSV) 12 System of equations, complex triangular band matrix F06SLF (CTPSV/ZTPSV) 12 System of equations, complex triangular packed matrix F06SMF (CGERU/ZGERU) 12 Rank-1 update, complex rectangular matrix, unconjugated vector F06SNF (CGERC/ZGERC) 12 Rank-1 update, complex rectangular matrix, conjugated vector F06SPF (CHER/ZHER) 12 Rank-1 update, complex Hermitian matrix F06SQF (CHPR/ZHPR) 12 Rank-1 update, complex Hermitian packed matrix F06SRF (CHER2/ZHER2) 12 Rank-2 update, complex Hermitian matrix F06SSF (CHPR2/ZHPR2) 12 Rank-2 update, complex Hermitian packed matrix F06TFF 13 Matrix copy, complex rectangular or trapezoidal matrix F06THF Example Text 13 Matrix initialisation, complex rectangular matrix F06TMF Example Text 13 Unitary similarity transformation of Hermitian matrix as a sequence of plane rotations F06TPF Example Text 13 QR factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix F06TQF Example Text 13 QR × k factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row F06TRF Example Text 13 QR or RQ factorization by sequence of plane rotations, complex upper Hessenberg matrix F06TSF Example Text 13 QR or RQ factorization by sequence of plane rotations, complex upper spiked matrix F06TTF Example Text 13 QR factorization of UZ or RQ factorization of ZU, U complex upper triangular, Z a sequence of plane rotations F06TVF 13 Compute upper Hessenberg matrix by sequence of plane rotations, complex upper triangular matrix F06TWF 13 Compute upper spiked matrix by sequence of plane rotations, complex upper triangular matrix F06TXF 13 Apply sequence of plane rotations, complex rectangular matrix, real cosine and complex sine F06TYF Example Text 13 Apply sequence of plane rotations, complex rectangular matrix, complex cosine and real sine F06UAF Example Text 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex general matrix F06UBF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex band matrix F06UCF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex Hermitian matrix F06UDF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage F06UEF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex Hermitian band matrix F06UFF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex symmetric matrix F06UGF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage F06UHF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex symmetric band matrix F06UJF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix F06UKF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage F06ULF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex triangular band matrix F06UMF 15 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex Hessenberg matrix F06VJF Example Text 13 Permute rows or columns, complex rectangular matrix, permutations represented by an integer array F06VKF 13 Permute rows or columns, complex rectangular matrix, permutations represented by a real array F06VXF Example Text 13 Apply sequence of plane rotations, complex rectangular matrix, real cosine and sine F06YAF (SGEMM/DGEMM) Example Text Example Data 14 Matrix-matrix product, two real rectangular matrices F06YCF (SSYMM/DSYMM) Example Text Example Data 14 Matrix-matrix product, one real symmetric matrix, one real rectangular matrix F06YFF (STRMM/DTRMM) 14 Matrix-matrix product, one real triangular matrix, one real rectangular matrix F06YJF (STRSM/DTRSM) 14 Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix F06YPF (SSYRK/DSYRK) 14 Rank-k update of a real symmetric matrix F06YRF (SSYR2K/DSYR2K) 14 Rank-2k update of a real symmetric matrix F06ZAF (CGEMM/ZGEMM) Example Text Example Data 14 Matrix-matrix product, two complex rectangular matrices F06ZCF (CHEMM/ZHEMM) Example Text Example Data 14 Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix F06ZFF (CTRMM/ZTRMM) 14 Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix F06ZJF (CTRSM/ZTRSM) 14 Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix F06ZPF (CHERK/ZHERK) 14 Rank-k update of a complex Hermitian matrix F06ZRF (CHER2K/ZHER2K) 14 Rank-2k update of a complex Hermitian matrix F06ZTF (CSYMM/ZSYMM) 14 Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix F06ZUF (CSYRK/ZSYRK) 14 Rank-k update of a complex symmetric matrix F06ZWF (CSYR2K/ZHER2K) 14 Rank-2k update of a complex symmetric matrix