Provided by: libmath-gsl-perl_0.43-4build1_amd64 
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:
<http://www.gnu.org/software/gsl/manual/html_node/>
AUTHORS
Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
COPYRIGHT AND LICENSE
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.