F06 Chapter Introduction
NAG Library Manual

# NAG Library Chapter ContentsF06 – Linear Algebra Support Routines

### F06 Chapter Introduction

 RoutineName Mark ofIntroduction Purpose F06AAF 12 DROTG 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 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), reala 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 12 Compute quotient of two complex scalars, with overflow flag F06DBF 12 Broadcast scalar into integer vector F06DFF 12 Copy integer vector F06EAF 12 DDOT Dot product of two real vectors F06ECF 12 DAXPY Add scalar times real vector to real vector F06EDF 12 DSCAL Multiply real vector by scalar F06EFF 12 DCOPY Copy real vector F06EGF 12 DSWAP Swap two real vectors F06EJF 12 DNRM2 Compute Euclidean norm of real vector F06EKF 12 DASUM Sum absolute values of real vector elements F06EPF 12 DROT Apply real plane rotation F06ERF 14 DDOTI Dot product of two real sparse vectors F06ETF 14 DAXPYI Add scalar times real sparse vector to real sparse vector F06EUF 14 DGTHR Gather real sparse vector F06EVF 14 DGTHRZ Gather and set to zero real sparse vector F06EWF 14 DSCTR Scatter real sparse vector F06EXF 14 DROTI Apply plane rotation to two real sparse vectors F06FAF 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 F06FEF 21 Multiply real vector by reciprocal of scalar 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 12 ZDOTU Dot product of two complex vectors, unconjugated F06GBF 12 ZDOTC Dot product of two complex vectors, conjugated F06GCF 12 ZAXPY Add scalar times complex vector to complex vector F06GDF 12 ZSCAL Multiply complex vector by complex scalar F06GFF 12 ZCOPY Copy complex vector F06GGF 12 ZSWAP Swap two complex vectors F06GRF 14 ZDOTUI Dot product of two complex sparse vector, unconjugated F06GSF 14 ZDOTCI Dot product of two complex sparse vector, conjugated F06GTF 14 ZAXPYI Add scalar times complex sparse vector to complex sparse vector F06GUF 14 ZGTHR Gather complex sparse vector F06GVF 14 ZGTHRZ Gather and set to zero complex sparse vector F06GWF 14 ZSCTR Scatter complex sparse vector F06HBF 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 F06HMF 21 ZROT Apply plane rotation with real cosine and complex sine 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 12 ZDSCAL Multiply complex vector by real scalar F06JJF 12 DZNRM2 Compute Euclidean norm of complex vector F06JKF 12 DZASUM Sum absolute values of complex vector elements F06JLF 12 IDAMAX Index, real vector element with largest absolute value F06JMF 12 IZAMAX 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 F06KEF 21 Multiply complex vector by reciprocal of real scalar 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 12 DGEMV Matrix-vector product, real rectangular matrix F06PBF 12 DGBMV Matrix-vector product, real rectangular band matrix F06PCF 12 DSYMV Matrix-vector product, real symmetric matrix F06PDF 12 DSBMV Matrix-vector product, real symmetric band matrix F06PEF 12 DSPMV Matrix-vector product, real symmetric packed matrix F06PFF 12 DTRMV Matrix-vector product, real triangular matrix F06PGF 12 DTBMV Matrix-vector product, real triangular band matrix F06PHF 12 DTPMV Matrix-vector product, real triangular packed matrix F06PJF 12 DTRSV System of equations, real triangular matrix F06PKF 12 DTBSV System of equations, real triangular band matrix F06PLF 12 DTPSV System of equations, real triangular packed matrix F06PMF 12 DGER Rank-1 update, real rectangular matrix F06PPF 12 DSYR Rank-1 update, real symmetric matrix F06PQF 12 DSPR Rank-1 update, real symmetric packed matrix F06PRF 12 DSYR2 Rank-2 update, real symmetric matrix F06PSF 12 DSPR2 Rank-2 update, real symmetric packed matrix F06QFF 13 Matrix copy, real rectangular or trapezoidal matrix F06QHF 13 Matrix initialization, real rectangular matrix F06QJF 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 13 Orthogonal similarity transformation of real symmetric matrix as a sequence of plane rotations F06QPF 13 QR factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix F06QQF 13 QR factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row F06QRF 13 QR or RQ factorization by sequence of plane rotations, real upper Hessenberg matrix F06QSF 13 QR or RQ factorization by sequence of plane rotations, real upper spiked matrix F06QTF 13 QR factorization of UP or RQ factorization of PU, Ureal upper triangular, P 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 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 F06RNF 21 1-norm, ∞-norm, Frobenius norm, largest absolute element, real tridiagonal matrix F06RPF 21 1-norm, ∞-norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix F06SAF 12 ZGEMV Matrix-vector product, complex rectangular matrix F06SBF 12 ZGBMV Matrix-vector product, complex rectangular band matrix F06SCF 12 ZHEMV Matrix-vector product, complex Hermitian matrix F06SDF 12 ZHBMV Matrix-vector product, complex Hermitian band matrix F06SEF 12 ZHPMV Matrix-vector product, complex Hermitian packed matrix F06SFF 12 ZTRMV Matrix-vector product, complex triangular matrix F06SGF 12 ZTBMV Matrix-vector product, complex triangular band matrix F06SHF 12 ZTPMV Matrix-vector product, complex triangular packed matrix F06SJF 12 ZTRSV System of equations, complex triangular matrix F06SKF 12 ZTBSV System of equations, complex triangular band matrix F06SLF 12 ZTPSV System of equations, complex triangular packed matrix F06SMF 12 ZGERU Rank-1 update, complex rectangular matrix, unconjugated vector F06SNF 12 ZGERC Rank-1 update, complex rectangular matrix, conjugated vector F06SPF 12 ZHER Rank-1 update, complex Hermitian matrix F06SQF 12 ZHPR Rank-1 update, complex Hermitian packed matrix F06SRF 12 ZHER2 Rank-2 update, complex Hermitian matrix F06SSF 12 ZHPR2 Rank-2 update, complex Hermitian packed matrix F06TAF 21 Matrix-vector product, complex symmetric matrix F06TBF 21 Rank-1 update, complex symmetric matrix F06TCF 21 Matrix-vector product, complex symmetric packed matrix F06TDF 21 Rank-1 update, complex symmetric packed matrix F06TFF 13 Matrix copy, complex rectangular or trapezoidal matrix F06THF 13 Matrix initialization, complex rectangular matrix F06TMF 13 Unitary similarity transformation of Hermitian matrix as a sequence of plane rotations F06TPF 13 QR factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix F06TQF 13 QR × k factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row F06TRF 13 QR or RQ factorization by sequence of plane rotations, complex upper Hessenberg matrix F06TSF 13 QR or RQ factorization by sequence of plane rotations, complex upper spiked matrix F06TTF 13 QR factorization of UP or RQ factorization of PU, U complex upper triangular, P 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 13 Apply sequence of plane rotations, complex rectangular matrix, complex cosine and real sine F06UAF 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 F06UNF 21 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex tridiagonal matrix F06UPF 21 1-norm, ∞-norm, Frobenius norm, largest absolute element, complex Hermitian tridiagonal matrix F06VJF 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 13 Apply sequence of plane rotations, complex rectangular matrix, real cosine and sine F06YAF 14 DGEMM Matrix-matrix product, two real rectangular matrices F06YCF 14 DSYMM Matrix-matrix product, one real symmetric matrix, one real rectangular matrix F06YFF 14 DTRMM Matrix-matrix product, one real triangular matrix, one real rectangular matrix F06YJF 14 DTRSM Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix F06YPF 14 DSYRK Rank-k update of a real symmetric matrix F06YRF 14 DSYR2K Rank-2k update of a real symmetric matrix F06ZAF 14 ZGEMM Matrix-matrix product, two complex rectangular matrices F06ZCF 14 ZHEMM Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix F06ZFF 14 ZTRMM Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix F06ZJF 14 ZTRSM Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix F06ZPF 14 ZHERK Rank-k update of a complex Hermitian matrix F06ZRF 14 ZHER2K Rank-2k update of a complex Hermitian matrix F06ZTF 14 ZSYMM Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix F06ZUF 14 ZSYRK Rank-k update of a complex symmetric matrix F06ZWF 14 ZSYR2K Rank-2k update of a complex symmetric matrix