GSP
Quick Navigator
Search Site

Unix VPS
A - Starter
B - Basic
C - Preferred
D - Commercial
MPS - Dedicated
Previous VPSs
* Sign Up! *

Support
Contact Us
Online Help
Handbooks
Domain Status
Man Pages

FAQ
Virtual Servers
Pricing
Billing
Technical

Network
Facilities
Connectivity
Topology Map

Miscellaneous
Server Agreement
Year 2038
Credits
 

USA Flag

 

 

Man Pages
Math::GSL::BLAS(3) User Contributed Perl Documentation Math::GSL::BLAS(3)

Math::GSL::BLAS - Basic Linear Algebra Subprograms 

    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";

The functions of this module are divised into 3 levels:

"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 $y. The function returns two values, the first is 0 if the operation suceeded, 1 otherwise and the second value is the result of the computation.
"gsl_blas_cdotu"
"gsl_blas_cdotc"
"gsl_blas_zdotu($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 $dotu. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_zdotc($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 $dotc. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_snrm2" =item "gsl_blas_sasum"
"gsl_blas_dnrm2($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 $y. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_dcopy($x, $y)"
This function copies the elements of the vector $x into the vector $y. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_daxpy($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"

"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 $y are vectors. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_dtrmv($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 $A are taken as unity and are not referenced. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_dtrsv($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 $A are taken as unity and are not referenced. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_cgemv "
"gsl_blas_ctrmv"
"gsl_blas_ctrsv"
"gsl_blas_zgemv "
"gsl_blas_ztrmv"
"gsl_blas_ztrsv"
"gsl_blas_ssymv"
"gsl_blas_sger "
"gsl_blas_ssyr"
"gsl_blas_ssyr2"
"gsl_blas_dsymv"
"gsl_blas_dger($alpha, $x, $y, $A)" - This function computes the rank-1 update A = alpha x y^T + A of the matrix $A. $x and $y are vectors. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_dsyr($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 $A are used. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_dsyr2($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 $y are complex vectors. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_zgerc"
"gsl_blas_zher($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 suceeded, 1 otherwise.
"gsl_blas_zher2 "

"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 $TransB. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_dsymm($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 $A are used. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_dsyrk($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 $C are used. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_dsyr2k($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 $C are used. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_dtrmm($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 $A are taken as unity and are not referenced. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_dtrsm($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 $A are taken as unity and are not referenced. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_cgemm"
"gsl_blas_csymm"
"gsl_blas_csyrk"
"gsl_blas_csyr2k "
"gsl_blas_ctrmm"
"gsl_blas_ctrsm"
"gsl_blas_zgemm($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 suceeded, 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 $C are complex matrices. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_zsyrk($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 $C are used. The function returns 0 if the operation suceeded, 1 otherwise.
"gsl_blas_zsyr2k($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 suceeded, 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 suceeded, 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 suceeded, 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 suceeded, 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 suceeded, 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 informations on the functions, we refer you to the GSL official documentation: <http://www.gnu.org/software/gsl/manual/html_node/>

Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>

Copyright (C) 2008-2021 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.

2022-04-08 perl v5.32.1
Search for    or go to Top of page |  Section 3 |  Main Index

Powered by GSP Visit the GSP FreeBSD Man Page Interface.
Output converted with ManDoc.