NAG Fortran Library

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