Math::GSL::BLAS - Basic Linear Algebra Subprograms
use Math::GSL::BLAS qw/:all/;
The functions of this module are divised into 3 levels:
gsl_blas_sdsdotgsl_blas_dsdotgsl_blas_sdotgsl_blas_ddot($x,
$y) - This function computes the scalar product x^T y for the vectors $x and $y.
The function returns two values,
the first is 0 if the operation suceeded,
1 otherwise and the second value is the result of the computation.gsl_blas_cdotugsl_blas_cdotcgsl_blas_zdotu($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 $dotc.
The function returns 0 if the operation suceeded,
1 otherwise.gsl_blas_snrm2 =item gsl_blas_sasumgsl_blas_dnrm2($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 $x.gsl_blas_scnrm2gsl_blas_scasumgsl_blas_dznrm2($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 $x,
\sum |\Re(x_i)| + |\Im(x_i)|.gsl_blas_isamaxgsl_blas_idamaxgsl_blas_icamaxgsl_blas_izamax gsl_blas_sswapgsl_blas_scopygsl_blas_saxpygsl_blas_dswap($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 $y.gsl_blas_cswapgsl_blas_ccopy gsl_blas_caxpygsl_blas_zswapgsl_blas_zcopygsl_blas_zaxpy gsl_blas_srotggsl_blas_srotmggsl_blas_srotgsl_blas_srotm gsl_blas_drotggsl_blas_drotmggsl_blas_drot($x,
$y,
$c,
$s) - This function applies a Givens rotation (x',
y') = (c x + s y,
-s x + c y) to the vectors $x,
$y.gsl_blas_drotm gsl_blas_sscalgsl_blas_dscal($alpha,
$x) - This function rescales the vector $x by the multiplicative factor $alpha.gsl_blas_cscalgsl_blas_zscal gsl_blas_csscalgsl_blas_zdscalgsl_blas_sgemvgsl_blas_strmv gsl_blas_strsvgsl_blas_dgemv($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 $A are taken as unity and are not referenced.
The function returns 0 if the operation suceeded,
1 otherwise.gsl_blas_cgemv gsl_blas_ctrmvgsl_blas_ctrsvgsl_blas_zgemv gsl_blas_ztrmvgsl_blas_ztrsvgsl_blas_ssymvgsl_blas_sger gsl_blas_ssyrgsl_blas_ssyr2gsl_blas_dsymvgsl_blas_dger($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 $A are used.gsl_blas_chemvgsl_blas_cgeru gsl_blas_cgercgsl_blas_chergsl_blas_cher2gsl_blas_zhemv gsl_blas_zgeru($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 $y are complex vectors.
The function returns 0 if the operation suceeded,
1 otherwise.gsl_blas_zgercgsl_blas_zher($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 $A are used.
The imaginary elements of the diagonal are automatically set to zero.
The function returns 0 if the operation suceeded,
1 otherwise.gsl_blas_zher2 gsl_blas_sgemmgsl_blas_ssymmgsl_blas_ssyrkgsl_blas_ssyr2k gsl_blas_strmmgsl_blas_strsmgsl_blas_dgemm($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 $A are taken as unity and are not referenced.
The function returns 0 if the operation suceeded,
1 otherwise.gsl_blas_cgemmgsl_blas_csymmgsl_blas_csyrkgsl_blas_csyr2k gsl_blas_ctrmmgsl_blas_ctrsmgsl_blas_zgemm($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 $C are complex matricesgsl_blas_zsymm($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 $alpha is a complex number.gsl_blas_chemmgsl_blas_cherkgsl_blas_cher2kgsl_blas_zhemm($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 :
For more informations on the functions, we refer you to the GSL offcial documentation: http://www.gnu.org/software/gsl/manual/html_node/
Tip : search on google: site:http://www.gnu.org/software/gsl/manual/html_node/ name_of_the_function_you_want
This example shows how to do a matrix-matrix product of double numbers :
use Math::GSL::Matrix qw/:all/;
use Math::GSL::BLAS qw/:all/;
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";
This example shows how to compute the scalar product of two vectors :
use Math::GSL::Vector qw/:all/;
use Math::GSL::CBLAS qw/:all/;
use Math::GSL::BLAS 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";
Jonathan Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
Copyright (C) 2008-2009 Jonathan Leto and Thierry Moisan
This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.
