%perlcode %{

@EXPORT_OK_level1 = qw/
                        gsl_blas_sdsdot gsl_blas_dsdot gsl_blas_sdot gsl_blas_ddot
                        gsl_blas_cdotu gsl_blas_cdotc gsl_blas_zdotu gsl_blas_zdotc
                        gsl_blas_snrm2 gsl_blas_sasum gsl_blas_dnrm2 gsl_blas_dasum
                        gsl_blas_scnrm2 gsl_blas_scasum gsl_blas_dznrm2 gsl_blas_dzasum
                        gsl_blas_isamax gsl_blas_idamax gsl_blas_icamax gsl_blas_izamax
                        gsl_blas_sswap gsl_blas_scopy gsl_blas_saxpy gsl_blas_dswap
                        gsl_blas_dcopy gsl_blas_daxpy 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 gsl_blas_drotm
                        gsl_blas_sscal gsl_blas_dscal gsl_blas_cscal gsl_blas_zscal
                        gsl_blas_csscal gsl_blas_zdscal
                    /;
@EXPORT_OK_level2 = qw/
                        gsl_blas_sgemv gsl_blas_strmv
                        gsl_blas_strsv gsl_blas_dgemv gsl_blas_dtrmv gsl_blas_dtrsv
                        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
                        gsl_blas_dsyr gsl_blas_dsyr2 gsl_blas_chemv gsl_blas_cgeru
                        gsl_blas_cgerc gsl_blas_cher gsl_blas_cher2 gsl_blas_zhemv
                        gsl_blas_zgeru gsl_blas_zgerc gsl_blas_zher gsl_blas_zher2
                    /;

@EXPORT_OK_level3 = qw/
                        gsl_blas_sgemm gsl_blas_ssymm gsl_blas_ssyrk gsl_blas_ssyr2k
                        gsl_blas_strmm gsl_blas_strsm gsl_blas_dgemm gsl_blas_dsymm
                        gsl_blas_dsyrk gsl_blas_dsyr2k gsl_blas_dtrmm gsl_blas_dtrsm
                        gsl_blas_cgemm gsl_blas_csymm gsl_blas_csyrk gsl_blas_csyr2k
                        gsl_blas_ctrmm gsl_blas_ctrsm gsl_blas_zgemm gsl_blas_zsymm
                        gsl_blas_zsyrk gsl_blas_zsyr2k gsl_blas_ztrmm gsl_blas_ztrsm
                        gsl_blas_chemm gsl_blas_cherk gsl_blas_cher2k gsl_blas_zhemm
                        gsl_blas_zherk gsl_blas_zher2k
                    /;
@EXPORT_OK = (@EXPORT_OK_level1, @EXPORT_OK_level2, @EXPORT_OK_level3);
%EXPORT_TAGS = (
                all    => [ @EXPORT_OK ],
                level1 => [ @EXPORT_OK_level1 ],
                level2 => [ @EXPORT_OK_level2 ],
                level3 => [ @EXPORT_OK_level3 ],
               );

__END__

=encoding utf8

=head1 NAME

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

=head1 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";

=head1 DESCRIPTION

The functions of this module are divised into 3 levels:

=head2 Level 1 - Vector operations

=over 3

=item C<gsl_blas_sdsdot>

=item C<gsl_blas_dsdot>

=item C<gsl_blas_sdot>

=item C<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.

=item C<gsl_blas_cdotu>

=item C<gsl_blas_cdotc>

=item C<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.

=item C<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.

=item C<gsl_blas_snrm2>
=item C<gsl_blas_sasum>

=item C<gsl_blas_dnrm2($x)>

This function computes the Euclidean norm

    ||x||_2 = \sqrt {\sum x_i^2}

of the vector $x.

=item C<gsl_blas_dasum($x)>

This function computes the absolute sum \sum |x_i| of the elements of the vector $x.

=item C<gsl_blas_scnrm2>

=item C<gsl_blas_scasum>

=item C<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)}.

=item C<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)|.

=item C<gsl_blas_isamax>

=item C<gsl_blas_idamax>

=item C<gsl_blas_icamax>

=item C<gsl_blas_izamax >

=item C<gsl_blas_sswap>

=item C<gsl_blas_scopy>

=item C<gsl_blas_saxpy>

=item C<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.

=item C<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.

=item C<gsl_blas_daxpy($alpha, $x, $y)>

These functions compute the sum $y = $alpha * $x + $y for the vectors $x and $y.

=item C<gsl_blas_cswap>

=item C<gsl_blas_ccopy >

=item C<gsl_blas_caxpy>

=item C<gsl_blas_zswap>

=item C<gsl_blas_zcopy>

=item C<gsl_blas_zaxpy >

=item C<gsl_blas_srotg>

=item C<gsl_blas_srotmg>

=item C<gsl_blas_srot>

=item C<gsl_blas_srotm >

=item C<gsl_blas_drotg>

=item C<gsl_blas_drotmg>

=item C<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.

=item C<gsl_blas_drotm >

=item C<gsl_blas_sscal>

=item C<gsl_blas_dscal($alpha, $x)>

This function rescales the vector $x by the multiplicative factor $alpha.

=item C<gsl_blas_cscal>

=item C<gsl_blas_zscal >

=item C<gsl_blas_csscal>

=item C<gsl_blas_zdscal>

=back

=head2 Level 2 - Matrix-vector operations

=over 3

=item C<gsl_blas_sgemv>

=item C<gsl_blas_strmv >

=item C<gsl_blas_strsv>

=item C<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.

=item C<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.

=item C<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.

=item C<gsl_blas_cgemv >

=item C<gsl_blas_ctrmv>

=item C<gsl_blas_ctrsv>

=item C<gsl_blas_zgemv >

=item C<gsl_blas_ztrmv>

=item C<gsl_blas_ztrsv>

=item C<gsl_blas_ssymv>

=item C<gsl_blas_sger >

=item C<gsl_blas_ssyr>

=item C<gsl_blas_ssyr2>

=item C<gsl_blas_dsymv>

=item C<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.

=item C<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.

=item C<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.

=item C<gsl_blas_chemv>

=item C<gsl_blas_cgeru >

=item C<gsl_blas_cgerc>

=item C<gsl_blas_cher>

=item C<gsl_blas_cher2>

=item C<gsl_blas_zhemv >

=item C<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.

=item C<gsl_blas_zgerc>

=item C<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.


=item C<gsl_blas_zher2 >

=back

=head2 Level 3 - Matrix-matrix operations

=over 3

=item C<gsl_blas_sgemm>

=item C<gsl_blas_ssymm>

=item C<gsl_blas_ssyrk>

=item C<gsl_blas_ssyr2k >

=item C<gsl_blas_strmm>

=item C<gsl_blas_strsm>

=item C<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.

=item C<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.

=item C<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.

=item C<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.

=item C<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.

=item C<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.

=item C<gsl_blas_cgemm>

=item C<gsl_blas_csymm>

=item C<gsl_blas_csyrk>

=item C<gsl_blas_csyr2k >

=item C<gsl_blas_ctrmm>

=item C<gsl_blas_ctrsm>

=item C<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

=item C<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.

=item C<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.

=item C<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.

=item C<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.

=item C<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.

=item C<gsl_blas_chemm>

=item C<gsl_blas_cherk>

=item C<gsl_blas_cher2k>

=item C<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.

=item C<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.

=item C<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.

=back

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 :

=over 3

=item C<level1>

=item C<level2>

=item C<level3>

=back

For more information on the functions, we refer you to the GSL official documentation: L<http://www.gnu.org/software/gsl/manual/html_node/>

=head1 AUTHORS

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

=head1 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.

=cut

%}