F06 – Linear Algebra Support Routines

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 (a^{2} + b^{2}), 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 |