--- name: "Math::GSL::BLAS" section: "3pm" platform: "linux" package: "libmath-gsl-perl" version: "0.45-2+b1" release: "Debian 13 (Trixie)" platforms: ["linux"] url: "https://new.carta.tech/Math::GSL::BLAS" --- # Math::GSL::BLAS(3pm) Basic Linear Algebra Subprograms ## NAME Math::GSL::BLAS - Basic Linear Algebra Subprograms ## SYNOPSIS ``` use Math::GSL::BLAS qw/:all/; use Math::GSL::Matrix qw/:all/; # matrix-matrix product of double numbers my $A = Math::GSL::Matrix->new(2,2); $A->set_row(0, [1, 4]); ->set_row(1, [3, 2]); my $B = Math::GSL::Matrix->new(2,2); $B->set_row(0, [2, 1]); ->set_row(1, [5,3]); my $C = Math::GSL::Matrix->new(2,2); gsl_matrix_set_zero($C->raw); gsl_blas_dgemm($CblasNoTrans, $CblasNoTrans, 1, $A->raw, $B->raw, 1, $C->raw); my @got = $C->row(0)->as_list; print "The resulting matrix is: \n["; print "$got[0] $got[1]\n"; @got = $C->row(1)->as_list; print "$got[0] $got[1] ]\n"; # compute the scalar product of two vectors : use Math::GSL::Vector qw/:all/; use Math::GSL::CBLAS qw/:all/; my $vec1 = Math::GSL::Vector->new([1,2,3,4,5]); my $vec2 = Math::GSL::Vector->new([5,4,3,2,1]); my ($status, $result) = gsl_blas_ddot($vec1->raw, $vec2->raw); if($status == 0) { print "The function has succeeded. \n"; } print "The result of the vector multiplication is $result.\n"; ``` ## DESCRIPTION The functions of this module are divised into 3 levels: ### Level 1 - Vector operations - "gsl\_blas\_sdsdot" - "gsl\_blas\_dsdot" - "gsl\_blas\_sdot" - "gsl\_blas\_ddot($x, $y)" This function computes the scalar product x^T y for the vectors `$x` and `$y`. The function returns two values, the first is 0 if the operation succeeded, 1 otherwise and the second value is the result of the computation. - "gsl\_blas\_cdotu" - "gsl\_blas\_cdotc" - "gsl\_blas\_zdotu($x, $y, $dotu)" This function computes the complex scalar product x^T y for the complex vectors `$x` and `$y`, returning the result in the complex number `$dotu`. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_zdotc($x, $y, $dotc)" This function computes the complex conjugate scalar product x^H y for the complex vectors `$x` and `$y`, returning the result in the complex number `$dotc`. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_snrm2" =item "gsl\_blas\_sasum" - gsl\_blas\_dnrm2($x) This function computes the Euclidean norm ``` ||x||_2 = \sqrt {\sum x_i^2} ``` of the vector `$x`. - gsl\_blas\_dasum($x) This function computes the absolute sum \\sum \|x\_i\| of the elements of the vector `$x`. - "gsl\_blas\_scnrm2" - "gsl\_blas\_scasum" - gsl\_blas\_dznrm2($x) This function computes the Euclidean norm of the complex vector `$x`, \|\|x\|\|\_2 = \\sqrt {\\sum (\\Re(x\_i)^2 + \\Im(x\_i)^2)}. - gsl\_blas\_dzasum($x) This function computes the sum of the magnitudes of the real and imaginary parts of the complex vector `$x`, \\sum \|\\Re(x\_i)\| + \|\\Im(x\_i)\|. - "gsl\_blas\_isamax" - "gsl\_blas\_idamax" - "gsl\_blas\_icamax" - "gsl\_blas\_izamax " - "gsl\_blas\_sswap" - "gsl\_blas\_scopy" - "gsl\_blas\_saxpy" - "gsl\_blas\_dswap($x, $y)" This function exchanges the elements of the vectors `$x` and `$y`. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_dcopy($x, $y)" This function copies the elements of the vector `$x` into the vector `$y`. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_daxpy($alpha, $x, $y)" These functions compute the sum `$y` = `$alpha` \* `$x` + `$y` for the vectors `$x` and `$y`. - "gsl\_blas\_cswap" - "gsl\_blas\_ccopy " - "gsl\_blas\_caxpy" - "gsl\_blas\_zswap" - "gsl\_blas\_zcopy" - "gsl\_blas\_zaxpy " - "gsl\_blas\_srotg" - "gsl\_blas\_srotmg" - "gsl\_blas\_srot" - "gsl\_blas\_srotm " - "gsl\_blas\_drotg" - "gsl\_blas\_drotmg" - "gsl\_blas\_drot($x, $y, $c, $s)" This function applies a Givens rotation (x', y') = (c x + s y, -s x + c y) to the vectors `$x`, `$y`. - "gsl\_blas\_drotm " - "gsl\_blas\_sscal" - "gsl\_blas\_dscal($alpha, $x)" This function rescales the vector `$x` by the multiplicative factor `$alpha`. - "gsl\_blas\_cscal" - "gsl\_blas\_zscal " - "gsl\_blas\_csscal" - "gsl\_blas\_zdscal" ### Level 2 - Matrix-vector operations - "gsl\_blas\_sgemv" - "gsl\_blas\_strmv " - "gsl\_blas\_strsv" - "gsl\_blas\_dgemv($TransA, $alpha, $A, $x, $beta, $y)" - This function computes the matrix-vector product and sum y = \\alpha op(A) x + \\beta y, where op(A) = A, A^T, A^H for $TransA = $CblasNoTrans, $CblasTrans, $CblasConjTrans (constant values coming from the CBLAS module). $A is a matrix and $x and $y are vectors. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_dtrmv($Uplo, $TransA, $Diag, $A, $x)" - This function computes the matrix-vector product x = op(A) x for the triangular matrix $A, where op(A) = A, A^T, A^H for $TransA = $CblasNoTrans, $CblasTrans, $CblasConjTrans (constant values coming from the CBLAS module). When $Uplo is $CblasUpper then the upper triangle of $A is used, and when $Uplo is $CblasLower then the lower triangle of $A is used. If $Diag is $CblasNonUnit then the diagonal of the matrix is used, but if $Diag is $CblasUnit then the diagonal elements of the matrix $A are taken as unity and are not referenced. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_dtrsv($Uplo, $TransA, $Diag, $A, $x)" - This function computes inv(op(A)) x for the vector $x, where op(A) = A, A^T, A^H for $TransA = $CblasNoTrans, $CblasTrans, $CblasConjTrans (constant values coming from the CBLAS module). When $Uplo is $CblasUpper then the upper triangle of $A is used, and when $Uplo is $CblasLower then the lower triangle of $A is used. If $Diag is $CblasNonUnit then the diagonal of the matrix is used, but if $Diag is $CblasUnit then the diagonal elements of the matrix $A are taken as unity and are not referenced. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_cgemv " - "gsl\_blas\_ctrmv" - "gsl\_blas\_ctrsv" - "gsl\_blas\_zgemv " - "gsl\_blas\_ztrmv" - "gsl\_blas\_ztrsv" - "gsl\_blas\_ssymv" - "gsl\_blas\_sger " - "gsl\_blas\_ssyr" - "gsl\_blas\_ssyr2" - "gsl\_blas\_dsymv" - "gsl\_blas\_dger($alpha, $x, $y, $A)" - This function computes the rank-1 update A = alpha x y^T + A of the matrix $A. $x and $y are vectors. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_dsyr($Uplo, $alpha, $x, $A)" - This function computes the symmetric rank-1 update A = \\alpha x x^T + A of the symmetric matrix $A and the vector $x. Since the matrix $A is symmetric only its upper half or lower half need to be stored. When $Uplo is $CblasUpper then the upper triangle and diagonal of $A are used, and when $Uplo is $CblasLower then the lower triangle and diagonal of $A are used. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_dsyr2($Uplo, $alpha, $x, $y, $A)" - This function computes the symmetric rank-2 update A = \\alpha x y^T + \\alpha y x^T + A of the symmetric matrix $A, the vector $x and vector $y. Since the matrix $A is symmetric only its upper half or lower half need to be stored. When $Uplo is $CblasUpper then the upper triangle and diagonal of $A are used, and when $Uplo is $CblasLower then the lower triangle and diagonal of $A are used. - "gsl\_blas\_chemv" - "gsl\_blas\_cgeru " - "gsl\_blas\_cgerc" - "gsl\_blas\_cher" - "gsl\_blas\_cher2" - "gsl\_blas\_zhemv " - "gsl\_blas\_zgeru($alpha, $x, $y, $A)" - This function computes the rank-1 update A = alpha x y^T + A of the complex matrix $A. $alpha is a complex number and $x and $y are complex vectors. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_zgerc" - "gsl\_blas\_zher($Uplo, $alpha, $x, $A)" - This function computes the hermitian rank-1 update A = \\alpha x x^H + A of the hermitian matrix $A and of the complex vector $x. Since the matrix $A is hermitian only its upper half or lower half need to be stored. When $Uplo is $CblasUpper then the upper triangle and diagonal of $A are used, and when $Uplo is $CblasLower then the lower triangle and diagonal of $A are used. The imaginary elements of the diagonal are automatically set to zero. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_zher2 " ### Level 3 - Matrix-matrix operations - "gsl\_blas\_sgemm" - "gsl\_blas\_ssymm" - "gsl\_blas\_ssyrk" - "gsl\_blas\_ssyr2k " - "gsl\_blas\_strmm" - "gsl\_blas\_strsm" - "gsl\_blas\_dgemm($TransA, $TransB, $alpha, $A, $B, $beta, $C)" - This function computes the matrix-matrix product and sum C = \\alpha op(A) op(B) + \\beta C where op(A) = A, A^T, A^H for $TransA = $CblasNoTrans, $CblasTrans, $CblasConjTrans and similarly for the parameter $TransB. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_dsymm($Side, $Uplo, $alpha, $A, $B, $beta, $C)" - This function computes the matrix-matrix product and sum C = \\alpha A B + \\beta C for $Side is $CblasLeft and C = \\alpha B A + \\beta C for $Side is $CblasRight, where the matrix $A is symmetric. When $Uplo is $CblasUpper then the upper triangle and diagonal of $A are used, and when $Uplo is $CblasLower then the lower triangle and diagonal of $A are used. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_dsyrk($Uplo, $Trans, $alpha, $A, $beta, $C)" - This function computes a rank-k update of the symmetric matrix $C, C = \\alpha A A^T + \\beta C when $Trans is $CblasNoTrans and C = \\alpha A^T A + \\beta C when $Trans is $CblasTrans. Since the matrix $C is symmetric only its upper half or lower half need to be stored. When $Uplo is $CblasUpper then the upper triangle and diagonal of $C are used, and when $Uplo is $CblasLower then the lower triangle and diagonal of $C are used. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_dsyr2k($Uplo, $Trans, $alpha, $A, $B, $beta, $C)" - This function computes a rank-2k update of the symmetric matrix $C, C = \\alpha A B^T + \\alpha B A^T + \\beta C when $Trans is $CblasNoTrans and C = \\alpha A^T B + \\alpha B^T A + \\beta C when $Trans is $CblasTrans. Since the matrix $C is symmetric only its upper half or lower half need to be stored. When $Uplo is $CblasUpper then the upper triangle and diagonal of $C are used, and when $Uplo is $CblasLower then the lower triangle and diagonal of $C are used. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_dtrmm($Side, $Uplo, $TransA, $Diag, $alpha, $A, $B)" - This function computes the matrix-matrix product B = \\alpha op(A) B for $Side is $CblasLeft and B = \\alpha B op(A) for $Side is $CblasRight. The matrix $A is triangular and op(A) = A, A^T, A^H for $TransA = $CblasNoTrans, $CblasTrans, $CblasConjTrans. When $Uplo is $CblasUpper then the upper triangle of $A is used, and when $Uplo is $CblasLower then the lower triangle of $A is used. If $Diag is $CblasNonUnit then the diagonal of $A is used, but if $Diag is $CblasUnit then the diagonal elements of the matrix $A are taken as unity and are not referenced. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_dtrsm($Side, $Uplo, $TransA, $Diag, $alpha, $A, $B)" - This function computes the inverse-matrix matrix product B = \\alpha op(inv(A))B for $Side is $CblasLeft and B = \\alpha B op(inv(A)) for $Side is $CblasRight. The matrix $A is triangular and op(A) = A, A^T, A^H for $TransA = $CblasNoTrans, $CblasTrans, $CblasConjTrans. When $Uplo is $CblasUpper then the upper triangle of $A is used, and when $Uplo is $CblasLower then the lower triangle of $A is used. If $Diag is $CblasNonUnit then the diagonal of $A is used, but if $Diag is $CblasUnit then the diagonal elements of the matrix $A are taken as unity and are not referenced. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_cgemm" - "gsl\_blas\_csymm" - "gsl\_blas\_csyrk" - "gsl\_blas\_csyr2k " - "gsl\_blas\_ctrmm" - "gsl\_blas\_ctrsm" - "gsl\_blas\_zgemm($TransA, $TransB, $alpha, $A, $B, $beta, $C)" - This function computes the matrix-matrix product and sum C = \\alpha op(A) op(B) + \\beta C where op(A) = A, A^T, A^H for $TransA = $CblasNoTrans, $CblasTrans, $CblasConjTrans and similarly for the parameter $TransB. The function returns 0 if the operation succeeded, 1 otherwise. $A, $B and $C are complex matrices - "gsl\_blas\_zsymm($Side, $Uplo, $alpha, $A, $B, $beta, $C)" - This function computes the matrix-matrix product and sum C = \\alpha A B + \\beta C for $Side is $CblasLeft and C = \\alpha B A + \\beta C for $Side is $CblasRight, where the matrix $A is symmetric. When $Uplo is $CblasUpper then the upper triangle and diagonal of $A are used, and when $Uplo is $CblasLower then the lower triangle and diagonal of $A are used. $A, $B and $C are complex matrices. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_zsyrk($Uplo, $Trans, $alpha, $A, $beta, $C)" - This function computes a rank-k update of the symmetric complex matrix $C, C = \\alpha A A^T + \\beta C when $Trans is $CblasNoTrans and C = \\alpha A^T A + \\beta C when $Trans is $CblasTrans. Since the matrix $C is symmetric only its upper half or lower half need to be stored. When $Uplo is $CblasUpper then the upper triangle and diagonal of $C are used, and when $Uplo is $CblasLower then the lower triangle and diagonal of $C are used. The function returns 0 if the operation succeeded, 1 otherwise. - "gsl\_blas\_zsyr2k($Uplo, $Trans, $alpha, $A, $B, $beta, $C)" - This function computes a rank-2k update of the symmetric matrix $C, C = \\alpha A B^T + \\alpha B A^T + \\beta C when $Trans is $CblasNoTrans and C = \\alpha A^T B + \\alpha B^T A + \\beta C when $Trans is $CblasTrans. Since the matrix $C is symmetric only its upper half or lower half need to be stored. When $Uplo is $CblasUpper then the upper triangle and diagonal of $C are used, and when $Uplo is $CblasLower then the lower triangle and diagonal of $C are used. The function returns 0 if the operation succeeded, 1 otherwise. $A, $B and $C are complex matrices and $beta is a complex number. - "gsl\_blas\_ztrmm($Side, $Uplo, $TransA, $Diag, $alpha, $A, $B)" - This function computes the matrix-matrix product B = \\alpha op(A) B for $Side is $CblasLeft and B = \\alpha B op(A) for $Side is $CblasRight. The matrix $A is triangular and op(A) = A, A^T, A^H for $TransA = $CblasNoTrans, $CblasTrans, $CblasConjTrans. When $Uplo is $CblasUpper then the upper triangle of $A is used, and when $Uplo is $CblasLower then the lower triangle of $A is used. If $Diag is $CblasNonUnit then the diagonal of $A is used, but if $Diag is $CblasUnit then the diagonal elements of the matrix $A are taken as unity and are not referenced. The function returns 0 if the operation succeeded, 1 otherwise. $A and $B are complex matrices and $alpha is a complex number. - "gsl\_blas\_ztrsm($Side, $Uplo, $TransA, $Diag, $alpha, $A, $B)" - This function computes the inverse-matrix matrix product B = \\alpha op(inv(A))B for $Side is $CblasLeft and B = \\alpha B op(inv(A)) for $Side is $CblasRight. The matrix $A is triangular and op(A) = A, A^T, A^H for $TransA = $CblasNoTrans, $CblasTrans, $CblasConjTrans. When $Uplo is $CblasUpper then the upper triangle of $A is used, and when $Uplo is $CblasLower then the lower triangle of $A is used. If $Diag is $CblasNonUnit then the diagonal of $A is used, but if $Diag is $CblasUnit then the diagonal elements of the matrix $A are taken as unity and are not referenced. The function returns 0 if the operation succeeded, 1 otherwise. $A and $B are complex matrices and $alpha is a complex number. - "gsl\_blas\_chemm" - "gsl\_blas\_cherk" - "gsl\_blas\_cher2k" - "gsl\_blas\_zhemm($Side, $Uplo, $alpha, $A, $B, $beta, $C)" - This function computes the matrix-matrix product and sum C = \\alpha A B + \\beta C for $Side is $CblasLeft and C = \\alpha B A + \\beta C for $Side is $CblasRight, where the matrix $A is hermitian. When Uplo is CblasUpper then the upper triangle and diagonal of A are used, and when Uplo is CblasLower then the lower triangle and diagonal of A are used. The imaginary elements of the diagonal are automatically set to zero. - "gsl\_blas\_zherk($Uplo, $Trans, $alpha, $A, $beta, $C)" - This function computes a rank-k update of the hermitian matrix $C, C = \\alpha A A^H + \\beta C when $Trans is $CblasNoTrans and C = \\alpha A^H A + \\beta C when $Trans is $CblasTrans. Since the matrix $C is hermitian only its upper half or lower half need to be stored. When $Uplo is $CblasUpper then the upper triangle and diagonal of $C are used, and when $Uplo is $CblasLower then the lower triangle and diagonal of $C are used. The imaginary elements of the diagonal are automatically set to zero. The function returns 0 if the operation succeeded, 1 otherwise. $A, $B and $C are complex matrices and $alpha and $beta are complex numbers. - "gsl\_blas\_zher2k($Uplo, $Trans, $alpha, $A, $B, $beta, $C)" - This function computes a rank-2k update of the hermitian matrix $C, C = \\alpha A B^H + \\alpha^\* B A^H + \\beta C when $Trans is $CblasNoTrans and C = \\alpha A^H B + \\alpha^\* B^H A + \\beta C when $Trans is $CblasConjTrans. Since the matrix $C is hermitian only its upper half or lower half need to be stored. When $Uplo is $CblasUpper then the upper triangle and diagonal of $C are used, and when $Uplo is $CblasLower then the lower triangle and diagonal of $C are used. The imaginary elements of the diagonal are automatically set to zero. The function returns 0 if the operation succeeded, 1 otherwise. You have to add the functions you want to use inside the qw /put\_function\_here /. You can also write use Math::GSL::BLAS qw/:all/ to use all available functions of the module. Other tags are also available, here is a complete list of all tags for this module : - "level1" - "level2" - "level3" For more information on the functions, we refer you to the GSL official documentation: \ ## AUTHORS Jonathan "Duke" Leto \ and Thierry Moisan \ ## COPYRIGHT AND LICENSE Copyright (C) 2008-2024 Jonathan "Duke" Leto and Thierry Moisan This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.