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package Math::GSL::Eigen::Test;
use base q{Test::Class};
use Test::More tests => 59;
use Math::GSL qw/:all/;
use Math::GSL::Test qw/:all/;
use Math::GSL::Eigen qw/:all/;
use Math::GSL::Errno qw/:all/;
use Math::GSL::Matrix qw/:all/;
use Math::GSL::Vector qw/:all/;
use Math::GSL::Complex qw/:all/;
use Math::GSL::Machine qw/:all/;
use Math::GSL::MatrixComplex qw/:all/;
use Math::GSL::VectorComplex qw/:all/;
use Data::Dumper;
use strict;
BEGIN { gsl_set_error_handler_off() }
sub make_fixture : Test(setup) {
my $self = shift;
$self->{eigen} = gsl_eigen_symm_alloc(2);
}
sub teardown : Test(teardown) {
}
sub GSL_EIGEN_SYMM_ALLOC : Tests {
my $self = shift;
isa_ok($self->{eigen}, 'Math::GSL::Eigen');
}
sub GSL_EIGEN_SYMMV_ALLOC : Tests {
my $eigen = gsl_eigen_symmv_alloc(5);
isa_ok($eigen, 'Math::GSL::Eigen');
}
sub GSL_EIGEN_HERM_ALLOC : Tests {
my $eigen = gsl_eigen_herm_alloc(5);
isa_ok($eigen, 'Math::GSL::Eigen');
}
sub GSL_EIGEN_HERMV_ALLOC : Tests {
my $eigen = gsl_eigen_hermv_alloc(5);
isa_ok($eigen, 'Math::GSL::Eigen');
}
sub GSL_EIGEN_NONSYMM_ALLOC : Tests {
my $eigen = gsl_eigen_nonsymm_alloc(5);
isa_ok($eigen, 'Math::GSL::Eigen');
}
sub GSL_EIGEN_NONSYMMV_ALLOC : Tests {
my $eigen = gsl_eigen_nonsymmv_alloc(5);
isa_ok($eigen, 'Math::GSL::Eigen');
}
sub GSL_EIGEN_GENSYMM_ALLOC : Tests {
my $eigen = gsl_eigen_gensymm_alloc(5);
isa_ok($eigen, 'Math::GSL::Eigen');
}
sub GSL_EIGEN_GENSYMMV_ALLOC : Tests {
my $eigen = gsl_eigen_gensymmv_alloc(5);
isa_ok($eigen, 'Math::GSL::Eigen');
}
sub GSL_EIGEN_GENHERM_ALLOC : Tests {
my $eigen = gsl_eigen_genherm_alloc(5);
isa_ok($eigen, 'Math::GSL::Eigen');
}
sub GSL_EIGEN_GENHERMV_ALLOC : Tests {
my $eigen = gsl_eigen_genhermv_alloc(5);
isa_ok($eigen, 'Math::GSL::Eigen');
}
sub GSL_EIGEN_GEN_ALLOC : Tests {
my $eigen = gsl_eigen_gen_alloc(5);
isa_ok($eigen, 'Math::GSL::Eigen');
}
sub GSL_EIGEN_GENV_ALLOC : Tests {
my $eigen = gsl_eigen_genv_alloc(5);
isa_ok($eigen, 'Math::GSL::Eigen');
}
sub GSL_EIGEN_SYMM : Tests {
my $self = shift;
my $m = gsl_matrix_alloc(2,2);
my $v = Math::GSL::Vector->new(2);
gsl_matrix_set_identity($m);
ok_status(gsl_eigen_symm($m, $v->raw, $self->{eigen}));
ok_similar( [ sort $v->as_list ], [ 1, 1 ] );
}
sub GSL_EIGEN_SYMMV : Tests {
my $w = gsl_eigen_symmv_alloc(2);
my $m = gsl_matrix_alloc(2,2);
gsl_matrix_set($m, 0, 0, 2);
gsl_matrix_set($m, 0, 1, 1);
gsl_matrix_set($m, 1, 0, 1);
gsl_matrix_set($m, 1, 1, 2);
my $eval = gsl_vector_alloc(2);
my $evec = gsl_matrix_alloc(2,2);
ok_status(gsl_eigen_symmv($m, $eval, $evec, $w));
ok_similar(gsl_vector_get($eval, 0), 3);
ok_similar(gsl_vector_get($eval, 1), 1);
my $x = gsl_matrix_get($evec, 0, 0);
#this is the eigenvector for the eigenvalue 1, which is the second
#eigenvalue in the $eval vector, but the GSL documentation says the first
#eigenvector should correspond to the first eigenvalue... where'e the error?
ok_similar(gsl_matrix_get($evec, 0, 1), -$x);
ok_similar (sqrt($x**2+$x**2), 1);
$x = gsl_matrix_get($evec, 1, 0);
ok_similar(gsl_matrix_get($evec, 1, 1), $x);
ok_similar(sqrt($x**2+$x**2), 1);
my $v1 = gsl_vector_alloc(2);
my $v2 = gsl_vector_alloc(2);
gsl_matrix_get_col($v1, $evec, 0);
gsl_matrix_get_col($v2, $evec, 1);
gsl_vector_mul($v1, $v2);
ok_similar(gsl_vector_get($v1, 0) + gsl_vector_get($v1, 1) , 0);
}
sub GSL_EIGEN_SYMMV_SORT : Tests {
my $w = gsl_eigen_symmv_alloc(2);
my $m = gsl_matrix_alloc(2,2);
gsl_matrix_set($m, 0, 0, 2);
gsl_matrix_set($m, 0, 1, 1);
gsl_matrix_set($m, 1, 0, 1);
gsl_matrix_set($m, 1, 1, 2);
my $eval = gsl_vector_alloc(2);
my $evec = gsl_matrix_alloc(2,2);
ok_status(gsl_eigen_symmv($m, $eval, $evec, $w));
ok_status(gsl_eigen_symmv_sort ($eval, $evec, $GSL_EIGEN_SORT_VAL_ASC));
ok_similar(gsl_vector_get($eval, 0), 1);
ok_similar(gsl_vector_get($eval, 1), 3);
my $x = gsl_matrix_get($evec, 0, 0);
ok_similar(gsl_matrix_get($evec, 0, 1), -$x);
ok_similar(sqrt($x**2+$x**2), 1);
$x = gsl_matrix_get($evec, 1, 0);
ok_similar(gsl_matrix_get($evec, 1, 1), $x);
ok_similar(sqrt($x**2+$x**2), 1);
my $v1 = gsl_vector_alloc(2);
my $v2 = gsl_vector_alloc(2);
gsl_matrix_get_col($v1, $evec, 0);
gsl_matrix_get_col($v2, $evec, 1);
gsl_vector_mul($v1, $v2);
ok_similar(gsl_vector_get($v1, 0) + gsl_vector_get($v1, 1) , 0);
}
sub GSL_EIGEN_HERM : Tests {
my $matrix = gsl_matrix_complex_alloc (2, 2);
my $complex = gsl_complex_rect(3,0);
gsl_matrix_complex_set($matrix, 0, 0, $complex);
$complex = gsl_complex_rect(2,1);
gsl_matrix_complex_set($matrix, 0, 1, $complex);
$complex = gsl_complex_rect(2,-1);
gsl_matrix_complex_set($matrix, 1, 0, $complex);
$complex = gsl_complex_rect(1,0);
gsl_matrix_complex_set($matrix, 1, 1, $complex);
my $eigen = gsl_eigen_herm_alloc(2);
my $vector = gsl_vector_alloc(2);
ok_status(gsl_eigen_herm($matrix, $vector, $eigen));
ok_similar(gsl_vector_get($vector, 0), 2+sqrt(6));
ok_similar(gsl_vector_get($vector, 1), 2-sqrt(6));
}
sub GSL_EIGEN_HERMV : Tests {
my $matrix = gsl_matrix_complex_alloc (2, 2);
my $complex = gsl_complex_rect(3,0);
gsl_matrix_complex_set($matrix, 0, 0, $complex);
$complex = gsl_complex_rect(2,1);
gsl_matrix_complex_set($matrix, 0, 1, $complex);
$complex = gsl_complex_rect(2,-1);
gsl_matrix_complex_set($matrix, 1, 0, $complex);
$complex = gsl_complex_rect(1,0);
gsl_matrix_complex_set($matrix, 1, 1, $complex);
my $eigen = gsl_eigen_hermv_alloc(2);
my $vector = gsl_vector_alloc(2);
my $evec = gsl_matrix_complex_alloc(2,2);
ok_status(gsl_eigen_hermv($matrix, $vector, $evec, $eigen));
ok_similar(gsl_vector_get($vector, 0), 2+sqrt(6));
ok_similar(gsl_vector_get($vector, 1), 2-sqrt(6));
# my $x = gsl_matrix_complex_get($evec, 1, 1);
# ok_similar( [ gsl_parts($x) ], [-0.750532688285823, 0 ], "last row");
# ok_similar( [ gsl_parts($x) ], [ 2/(-1+sqrt(6)), 1/(-1+sqrt(6)) ], "first value");
}
sub GSL_EIGEN_NONSYMM : Tests {
my $matrix = gsl_matrix_alloc (2, 2);
gsl_matrix_set($matrix, 0, 0, -12);
gsl_matrix_set($matrix, 1, 0, 7);
gsl_matrix_set($matrix, 0, 1, 65);
gsl_matrix_set($matrix, 1, 1, 59);
my $eigen = gsl_eigen_nonsymm_alloc(2);
my $vector = gsl_vector_complex_alloc(2);
ok_status(gsl_eigen_nonsymm($matrix, $vector, $eigen));
my $x = gsl_vector_complex_real($vector);
my $y = gsl_vector_complex_imag($vector);
# this interface seems hokey
ok_similar( gsl_vector_get($x->{vector}, 1), (47/2)+(0.5*sqrt(6861)) );
ok_similar( gsl_vector_get($y->{vector}, 1), 0 );
}
sub GSL_EIGEN_NONSYMM_Z : Tests {
my $matrix = gsl_matrix_alloc (2, 2);
gsl_matrix_set($matrix, 0, 0, -12);
gsl_matrix_set($matrix, 1, 0, 7);
gsl_matrix_set($matrix, 0, 1, 65);
gsl_matrix_set($matrix, 1, 1, 59);
my $eigen = gsl_eigen_nonsymm_alloc(2);
my $vector = gsl_vector_complex_alloc(2);
my $Z = gsl_matrix_alloc(2,2);
ok_status(gsl_eigen_nonsymm($matrix, $vector, $eigen));
ok_status(gsl_eigen_nonsymm_Z($matrix,$vector, $Z, $eigen));
ok_similar(gsl_matrix_get($Z, 0, 0), 0.9958842418254068860784291, "Z matrix", 0.005);
ok_similar(gsl_matrix_get($Z, 0, 1), 0.09063430301952179629793610, "Z matrix", 0.1);
ok_similar(gsl_matrix_get($Z, 1, 1), 0.9958842418254068860784291, "Z matrix", 0.005);
ok_similar(gsl_matrix_get($Z, 1, 0), 0.09063430301952179629793610, "Z matrix", 0.1);
my $x = gsl_vector_complex_real($vector);
my $y = gsl_vector_complex_imag($vector);
# this interface seems hokey
ok_similar( gsl_vector_get($x->{vector}, 1), (47/2)+(0.5*sqrt(6861)) );
ok_similar( gsl_vector_get($y->{vector}, 1), 0 );
}
sub GSL_EIGEN_NONSYMMV : Tests {
my $matrix = gsl_matrix_alloc (2, 2);
gsl_matrix_set($matrix, 0, 0, -12);
gsl_matrix_set($matrix, 1, 0, 7);
gsl_matrix_set($matrix, 0, 1, 65);
gsl_matrix_set($matrix, 1, 1, 59);
my $evec = gsl_matrix_complex_alloc(2,2);
my $eigen = gsl_eigen_nonsymmv_alloc(2);
my $vector = gsl_vector_complex_alloc(2);
ok_status(gsl_eigen_nonsymmv($matrix,$vector, $evec, $eigen));
my $x = gsl_vector_complex_real($vector);
my $y = gsl_vector_complex_imag($vector);
# this interface seems hokey
ok_similar( gsl_vector_get($x->{vector}, 1), (47/2)+(0.5*sqrt(6861)) );
ok_similar( gsl_vector_get($y->{vector}, 1), 0 );
$x = gsl_matrix_complex_get($evec, 1, 0);
ok_similar(gsl_imag($x), 0, "evec matrix");
ok_similar(gsl_real($x), 7/((71/2)+(.5*sqrt(6861))), "evec matrix", 0.01);
$x = gsl_matrix_complex_get($evec, 0, 0);
ok_similar(gsl_imag($x), 0, "evec matrix");
ok_similar(gsl_real($x), 7/((71/2)-(.5*sqrt(6861))), "evec matrix", 0.19);
$x = gsl_matrix_complex_get($evec, 0, 1);
$y = gsl_matrix_complex_get($evec, 1, 1);
ok_similar(gsl_imag($x), 0, "evec matrix");
ok_similar(gsl_imag($y), 0, "evec matrix");
local $TODO = "matlab differences";
ok_similar(gsl_real($x), 1); # this is the value I get with maple
ok_similar(gsl_real($y), 1); # this is the value I get with maple
}
Test::Class->runtests;
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