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use strict;
use warnings;
pp_addpm({At=>'Top'},<<'EOD');
use strict;
use warnings;
=head1 NAME
PDL::GSL::LINALG - PDL interface to linear algebra routines in GSL
=head1 SYNOPSIS
use PDL::LiteF;
use PDL::MatrixOps; # for 'x'
use PDL::GSL::LINALG;
my $A = pdl [
[0.18, 0.60, 0.57, 0.96],
[0.41, 0.24, 0.99, 0.58],
[0.14, 0.30, 0.97, 0.66],
[0.51, 0.13, 0.19, 0.85],
];
my $B = sequence(2,4); # column vectors
LU_decomp(my $lu=$A->copy, my $p=null, my $signum=null);
# transpose so first dim means is vector, higher dims broadcast
LU_solve($lu, $p, $B->transpose, my $x=null);
$x = $x->inplace->transpose; # now can be matrix-multiplied
=head1 DESCRIPTION
This is an interface to the linear algebra package present in the
GNU Scientific Library. Functions are named as in GSL, but with the
initial C<gsl_linalg_> removed. They are provided in both real and
complex double precision.
Currently only LU decomposition interfaces here. Pull requests welcome!
EOD
pp_addpm({At=>'Bot'},<<'EOD');
=head1 SEE ALSO
L<PDL>
The GSL documentation for linear algebra is online at
L<https://www.gnu.org/software/gsl/doc/html/linalg.html>
=cut
EOD
pp_addhdr('
#include <gsl/gsl_linalg.h>
#include "gslerr.h"
#define MATRIX_SETUP(m, rows, cols, lda, datap) \\
m.size1 = rows; \\
m.size2 = cols; \\
m.tda = lda; \\
m.data = (double *)datap; \\
m.owner = 0;
/* rely on optimiser for this to produce sensible code */
#define PERM_SETUP(p, psize, datap) \\
gsl_permutation *p ## _local = gsl_permutation_alloc(psize); \\
size_t *p ## _local_data = p ## _local->data; \\
size_t p ## _i_local = 0; \\
for (p ## _i_local = 0; p ## _i_local < (size_t)psize; p ## _i_local++) { \\
p ## _local_data[p ## _i_local] = datap[p ## _i_local]; \\
} \\
p.data = p ## _local_data; \\
p.size = psize;
#define PERM_RETURN(p, psize, datap) \\
for (p ## _i_local = 0; p ## _i_local < (size_t)psize; p ## _i_local++) { \\
datap[p ## _i_local] = p ## _local_data[p ## _i_local]; \\
} \\
gsl_permutation_free(p ## _local);
#define VECTOR_SETUP(v, vsize, datap) \\
v.size = vsize; \\
v.stride = 1; \\
v.data = (double *)datap; \\
v.owner = 0;
');
pp_def('LU_decomp',
HandleBad => 0,
Pars => '[io,phys]A(n,m); indx [o,phys]ipiv(p=CALC($PDL(A)->ndims > 1 ? PDLMIN($PDL(A)->dims[0], $PDL(A)->dims[1]) : 1)); int [o,phys]signum()',
GenericTypes => [qw(C D)],
Code => <<'EOF',
/* make sure the PDL data types match */
gsl_matrix$TDC(,_complex) m;
gsl_permutation p;
int s;
MATRIX_SETUP(m, $SIZE(m), $SIZE(n), $SIZE(n), $P(A))
PERM_SETUP(p, $SIZE(p), $P(ipiv))
GSLERR(gsl_linalg$TDC(,_complex)_LU_decomp, (&m, &p, &s))
PERM_RETURN(p, $SIZE(p), $P(ipiv))
$signum() = s;
EOF
Doc => <<'EOF',
=for ref
LU decomposition of the given (real or complex) matrix.
EOF
);
pp_def('LU_solve',
HandleBad => 0,
Pars => '[phys]LU(n,m); indx [phys]ipiv(p); [phys]B(n); [o,phys]x(n)',
GenericTypes => [qw(C D)],
Code => <<'EOF',
gsl_matrix$TDC(,_complex) m;
gsl_permutation p;
gsl_vector$TDC(,_complex) b, x;
int s;
MATRIX_SETUP(m, $SIZE(m), $SIZE(n), $SIZE(n), $P(LU))
PERM_SETUP(p, $SIZE(p), $P(ipiv))
VECTOR_SETUP(b, $SIZE(n), $P(B))
VECTOR_SETUP(x, $SIZE(n), $P(x))
GSLERR(gsl_linalg$TDC(,_complex)_LU_solve, (&m, &p, &b, &x))
PERM_RETURN(p, $SIZE(p), $P(ipiv))
EOF
Doc => <<'EOF',
=for ref
Solve C<A x = B> using the LU and permutation from L</LU_decomp>, real
or complex.
EOF
);
pp_def('LU_det',
HandleBad => 0,
Pars => '[phys]LU(n,m); int [phys]signum(); [o]det()',
GenericTypes => [qw(C D)],
Code => <<'EOF',
gsl_matrix$TDC(,_complex) m;
MATRIX_SETUP(m, $SIZE(m), $SIZE(n), $SIZE(n), $P(LU))
types (D) %{
$det() = gsl_linalg_LU_det(&m, $signum());
%}
types (C) %{
gsl_complex z = gsl_linalg_complex_LU_det(&m, $signum());
$det() = GSL_REAL(z) + I*GSL_IMAG(z);
%}
EOF
Doc => <<'EOF',
=for ref
Find the determinant from the LU decomp.
EOF
);
pp_def('solve_tridiag',
HandleBad => 0,
Pars => '[phys]diag(n); [phys]superdiag(n); [phys]subdiag(n); [phys]B(n); [o,phys]x(n)',
GenericTypes => [qw(D)],
Code => <<'EOF',
gsl_vector d, sup, sub, b, x;
VECTOR_SETUP(d, $SIZE(n), $P(diag))
VECTOR_SETUP(sup, $SIZE(n)-1, $P(superdiag))
VECTOR_SETUP(sub, $SIZE(n)-1, $P(subdiag))
VECTOR_SETUP(b, $SIZE(n), $P(B))
VECTOR_SETUP(x, $SIZE(n), $P(x))
#define CONST_VEC (const gsl_vector *)
GSLERR(gsl_linalg_solve_tridiag, (
CONST_VEC &d, CONST_VEC &sup, CONST_VEC &sub, CONST_VEC &b, &x
))
#undef CONST_VEC
EOF
Doc => <<'EOF',
=for ref
Solve C<A x = B> where A is a tridiagonal system. Real only, because
GSL does not have a complex function.
EOF
);
pp_add_boot('gsl_set_error_handler_off();
');
pp_done();
|
