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|
%perlcode %{
@EXPORT_OK = qw/
gsl_integration_workspace_alloc
gsl_integration_workspace_free
gsl_integration_qaws_table_alloc
gsl_integration_qaws_table_set
gsl_integration_qaws_table_free
gsl_integration_qawo_table_alloc
gsl_integration_qawo_table_set
gsl_integration_qawo_table_set_length
gsl_integration_qawo_table_free
gsl_integration_qk15
gsl_integration_qk21
gsl_integration_qk31
gsl_integration_qk41
gsl_integration_qk51
gsl_integration_qk61
gsl_integration_qcheb
gsl_integration_qk
gsl_integration_qng
gsl_integration_qag
gsl_integration_qagi
gsl_integration_qagiu
gsl_integration_qagil
gsl_integration_qags
gsl_integration_qagp
gsl_integration_qawc
gsl_integration_qaws
gsl_integration_qawo
gsl_integration_qawf
$GSL_INTEG_COSINE
$GSL_INTEG_SINE
$GSL_INTEG_GAUSS15
$GSL_INTEG_GAUSS21
$GSL_INTEG_GAUSS31
$GSL_INTEG_GAUSS41
$GSL_INTEG_GAUSS51
$GSL_INTEG_GAUSS61
/;
%EXPORT_TAGS = ( all => [ @EXPORT_OK ] );
__END__
=encoding utf8
=head1 NAME
Math::GSL::Integration - Routines for performing numerical integration (quadrature) of a function in one dimension
=head1 SYNOPSIS
use Math::GSL::Integration qw /:all/;
my $function = sub { $_[0]**2 } ;
my ($lower, $upper ) = (0,1);
my ($relerr,$abserr) = (0,1e-7);
my ($status, $result, $abserr, $num_evals) = gsl_integration_qng ( $function,
$lower, $upper, $relerr, $abserr
);
=head1 DESCRIPTION
This module allows you to numerically integrate a Perl subroutine. Depending
on the properties of your function (singularities, smoothness) and the type
of integration range (finite, infinite, semi-infinite), you will need to
choose a quadrature routine that fits your needs.
=over
=item * C<gsl_integration_workspace_alloc($n)>
This function allocates a workspace sufficient to hold $n double precision
intervals, their integration results and error estimates.
=item * C<gsl_integration_workspace_free($w)>
This function frees the memory associated with the workspace $w.
=item * C<gsl_integration_qaws_table_alloc($alpha, $beta, $mu, $nu)>
This function allocates space for a gsl_integration_qaws_table struct
describing a singular weight function W(x) with the parameters ($alpha, $beta,
$mu, $nu), W(x) = (x-a)^alpha (b-x)^beta log^mu (x-a) log^nu (b-x) where
$alpha > -1, $beta > -1, and $mu = 0, 1, $nu = 0, 1. The weight function can
take four different forms depending on the values of $mu and $nu,
W(x) = (x-a)^alpha (b-x)^beta (mu = 0, nu = 0)
W(x) = (x-a)^alpha (b-x)^beta log(x-a) (mu = 1, nu = 0)
W(x) = (x-a)^alpha (b-x)^beta log(b-x) (mu = 0, nu = 1)
W(x) = (x-a)^alpha (b-x)^beta log(x-a) log(b-x) (mu = 1, nu = 1)
The singular points (a,b) do not have to be specified until the integral is
computed, where they are the endpoints of the integration range. The function
returns a pointer to the newly allocated table gsl_integration_qaws_table if no
errors were detected, and 0 in the case of error.
=item * C<gsl_integration_qaws_table_set($t, $alpha, $beta, $mu, $nu)>
This function modifies the parameters ($alpha, $beta, $mu, $nu) of an existing
gsl_integration_qaws_table struct $t.
=item * C<gsl_integration_qaws_table_free($t)>
This function frees all the memory associated with the
gsl_integration_qaws_table struct $t.
=item * C<gsl_integration_qawo_table_alloc($omega, $L, $sine, $n)>
=item * C<gsl_integration_qawo_table_set($t, $omega, $L, $sine, $n)>
This function changes the parameters omega, L and sine of the existing
workspace $t.
=item * C<gsl_integration_qawo_table_set_length($t, $L)>
This function allows the length parameter $L of the workspace $t to be
changed.
=item * C<gsl_integration_qawo_table_free($t)>
This function frees all the memory associated with the workspace $t.
=item * C<gsl_integration_qk15($function,$a,$b,$resabs,$resasc) >
=item * C<gsl_integration_qk21($function,$a,$b,$resabs,$resasc) >
=item * C<gsl_integration_qk31($function,$a,$b,$resabs,$resasc) >
=item * C<gsl_integration_qk41($function,$a,$b,$resabs,$resasc) >
=item * C<gsl_integration_qk51($function,$a,$b,$resabs,$resasc) >
=item * C<gsl_integration_qk61($function,$a,$b,$resabs,$resasc) >
=item * C<gsl_integration_qcheb($function, $a, $b, $cheb12, $cheb24) >
=item * C<gsl_integration_qk >
=item * C<gsl_integration_qng($function,$a,$b,$epsabs,$epsrel,$num_evals) >
This routine QNG (Quadrature Non-Adaptive Gaussian) is inexpensive is the sense
that it will evaluate the function much fewer times than the adaptive routines.
Because of this it does not need any workspaces, so it is also more memory
efficient. It should be perfectly fine for well-behaved functions (smooth and
nonsingular), but will not be able to get the required accuracy or may not
converge for more complicated functions.
=item * C<gsl_integration_qag($function,$a,$b,$epsabs,$epsrel,$limit,$key,$workspace) >
This routine QAG (Quadrature Adaptive Gaussian) ...
=item * C<gsl_integration_qagi($function,$epsabs,$epsrel,$limit,$workspace) >
=item * C<gsl_integration_qagiu($function,$a,$epsabs,$epsrel,$limit,$workspace) >
=item * C<gsl_integration_qagil($function,$b,$epsabs,$epsrel,$limit,$workspace) >
=item * C<gsl_integration_qags($func,$a,$b,$epsabs,$epsrel,$limit,$workspace)>
($status, $result, $abserr) = gsl_integration_qags (
sub { 1/$_[0]} ,
1, 10, 0, 1e-7, 1000,
$workspace,
);
This function applies the Gauss-Kronrod 21-point integration rule
adaptively until an estimate of the integral of $func over ($a,$b) is
achieved within the desired absolute and relative error limits,
$epsabs and $epsrel.
=item * C<gsl_integration_qagp($function, $pts, $npts, $epsbs, $epsrel, $limit, $workspace) >
=item * C<gsl_integration_qawc($function, $a, $b, $c, $epsabs, $epsrel, $limit, $workspace) >
=item * C<gsl_integration_qaws($function, $a, $b, $qaws_table, $epsabs, $epsrel, $limit, $workspace) >
=item * C<gsl_integration_qawo($function, $a, $epsabs, $epsrel, $limit, $workspace, $qawo_table) >
=item * C<gsl_integration_qawf($function, $a, $epsabs, $limit, $workspace, $cycle_workspace, $qawo_table) >
=back
This module also includes the following constants :
=over
=item * $GSL_INTEG_COSINE
=item * $GSL_INTEG_SINE
=item * $GSL_INTEG_GAUSS15
=item * $GSL_INTEG_GAUSS21
=item * $GSL_INTEG_GAUSS31
=item * $GSL_INTEG_GAUSS41
=item * $GSL_INTEG_GAUSS51
=item * $GSL_INTEG_GAUSS61
=back
The following error constants are part of the Math::GSL::Errno module and can
be returned by the gsl_integration_* functions :
=over
=item * $GSL_EMAXITER
Maximum number of subdivisions was exceeded.
=item * $GSL_EROUND
Cannot reach tolerance because of roundoff error, or roundoff error was detected in the extrapolation table.
=item * GSL_ESING
A non-integrable singularity or other bad integrand behavior was found in the integration interval.
=item * GSL_EDIVERGE
The integral is divergent, or too slowly convergent to be integrated numerically.
=back
=head1 MORE INFO
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
%}
|
