NAG Fortran Library

F06 – Linear Algebra Support Routines

F06 Chapter Introduction

Routine
Name
Mark of
Introduction

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

Table of Contents
© The Numerical Algorithms Group Ltd, Oxford UK. 2002