# 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 "$got$got\n";
@got = $C->row(1)->as_list; print "$got  $got ]\n"; # compute the scalar product of two vectors : use Math::GSL::Vector qw/:all/; use Math::GSL::CBLAS qw/:all/; my$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 $y. The function returns two values, the first is 0 if the operation suceeded, 1 otherwise and the second value is the result of the computation. gsl_blas_cdotu gsl_blas_cdotc gsl_blas_zdotu($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

## 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 $y are vectors. The function returns 0 if the operation suceeded, 1 otherwise. gsl_blas_dtrmv($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 $A are used. The imaginary elements of the diagonal are automatically set to zero. The function returns 0 if the operation suceeded, 1 otherwise. gsl_blas_zher2  ## Level 3 - Matrix-matrix operations gsl_blas_sgemm gsl_blas_ssymm gsl_blas_ssyrk gsl_blas_ssyr2k  gsl_blas_strmm gsl_blas_strsm gsl_blas_dgemm($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 $TransB. The function returns 0 if the operation suceeded, 1 otherwise. gsl_blas_dsymm($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_funtion_here /. You can also write use Math::GSL::BLAS qw/:all/ to use all avaible functions of the module. Other tags are also avaible, 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 offcial documentation: http://www.gnu.org/software/gsl/manual/html_node/

# AUTHORS

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