Integration.i

   1 %module "Math::GSL::Integration"
   2 %{
   3     #include "gsl/gsl_integration.h"
   4 %}
   5
   6 %include "typemaps.i"
   7 %include "gsl_typemaps.i"
   8 %include "gsl/gsl_integration.h"
   9
  10 %perlcode %{
  11 @EXPORT_OK = qw/
  12                gsl_integration_workspace_alloc
  13                gsl_integration_workspace_free
  14                gsl_integration_qaws_table_alloc
  15                gsl_integration_qaws_table_set
  16                gsl_integration_qaws_table_free
  17                gsl_integration_qawo_table_alloc
  18                gsl_integration_qawo_table_set
  19                gsl_integration_qawo_table_set_length
  20                gsl_integration_qawo_table_free
  21                gsl_integration_qk15
  22                gsl_integration_qk21
  23                gsl_integration_qk31
  24                gsl_integration_qk41
  25                gsl_integration_qk51
  26                gsl_integration_qk61
  27                gsl_integration_qcheb
  28                gsl_integration_qk
  29                gsl_integration_qng
  30                gsl_integration_qag
  31                gsl_integration_qagi
  32                gsl_integration_qagiu
  33                gsl_integration_qagil
  34                gsl_integration_qags
  35                gsl_integration_qagp
  36                gsl_integration_qawc
  37                gsl_integration_qaws
  38                gsl_integration_qawo
  39                gsl_integration_qawf
  40                $GSL_INTEG_COSINE
  41                $GSL_INTEG_SINE
  42                $GSL_INTEG_GAUSS15
  43                $GSL_INTEG_GAUSS21
  44                $GSL_INTEG_GAUSS31
  45                $GSL_INTEG_GAUSS41
  46                $GSL_INTEG_GAUSS51
  47                $GSL_INTEG_GAUSS61
  48              /;
  49 %EXPORT_TAGS = ( all => [ @EXPORT_OK ] );
  50
  51 __END__
  52
  53 =head1 NAME
  54
  55 Math::GSL::Integration - Routines for performing numerical integration (quadrature) of a function in one dimension
  56
  57 =head1 SYNOPSIS
  58
  59 This module is not yet implemented. Patches Welcome!
  60
  61     use Math::GSL::Integration qw /:all/;
  62
  63 =head1 DESCRIPTION
  64
  65 Here is a list of all the functions in this module :
  66
  67 =over
  68
  69 =item * C<gsl_integration_workspace_alloc($n)> - This function allocates a workspace sufficient to hold $n double precision intervals, their integration results and error estimates.
  70
  71 =item * C<gsl_integration_workspace_free($w)> - This function frees the memory associated with the workspace $w.
  72
  73 =item * C<gsl_integration_qaws_table_alloc($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 $nu,
  74
  75               W(x) = (x-a)^alpha (b-x)^beta                   (mu = 0, nu = 0)
  76               W(x) = (x-a)^alpha (b-x)^beta log(x-a)          (mu = 1, nu = 0)
  77               W(x) = (x-a)^alpha (b-x)^beta log(b-x)          (mu = 0, nu = 1)
  78               W(x) = (x-a)^alpha (b-x)^beta log(x-a) log(b-x) (mu = 1, nu = 1)
  79
  80 The singular points (a,b) do not have to be specified until the integral is computed, where they are the endpoints of the integration range.
  81 The function returns a pointer to the newly allocated table gsl_integration_qaws_table if no errors were detected, and 0 in the case of error.
  82
  83 =item * C<gsl_integration_qaws_table_set($t, $alpha, $beta, $mu, $nu)> - This function modifies the parameters ($alpha, $beta, $mu, $nu) of an existing gsl_integration_qaws_table struct $t.
  84
  85 =item * C<gsl_integration_qaws_table_free($t)> - This function frees all the memory associated with the gsl_integration_qaws_table struct $t.
  86
  87 =item * C<gsl_integration_qawo_table_alloc($omega, $L, $sine, $n)>
  88
  89 =item * C<gsl_integration_qawo_table_set($t, $omega, $L, $sine, $n)> - This function changes the parameters omega, L and sine of the existing workspace $t.
  90
  91 =item * C<gsl_integration_qawo_table_set_length($t, $L)> - This function allows the length parameter $L of the workspace $t to be changed.
  92
  93 =item * C<gsl_integration_qawo_table_free($t)> - This function frees all the memory associated with the workspace $t.
  94
  95 =item * C<gsl_integration_qk15 >
  96
  97 =item * C<gsl_integration_qk21 >
  98
  99 =item * C<gsl_integration_qk31 >
 100
 101 =item * C<gsl_integration_qk41 >
 102
 103 =item * C<gsl_integration_qk51 >
 104
 105 =item * C<gsl_integration_qk61 >
 106
 107 =item * C<gsl_integration_qcheb >
 108
 109 =item * C<gsl_integration_qk >
 110
 111 =item * C<gsl_integration_qng >
 112
 113 =item * C<gsl_integration_qag >
 114
 115 =item * C<gsl_integration_qagi >
 116
 117 =item * C<gsl_integration_qagiu >
 118
 119 =item * C<gsl_integration_qagil >
 120
 121 =item * C<gsl_integration_qags($func,$a,$b,$epsabs,$epsrel,$limit,$workspace)>
 122
 123     ($status, $result, $abserr) = gsl_integration_qags (
 124                             sub { 1/$_[0]} ,
 125                             1, 10, 0, 1e-7, 1000,
 126                             $workspace,
 127                         );
 128
 129  This function applies the Gauss-Kronrod 21-point integration rule
 130  adaptively until an estimate of the integral of $func over ($a,$b) is
 131  achieved within the desired absolute and relative error limits,
 132  $epsabs and $epsrel.
 133
 134
 135 =item * C<gsl_integration_qagp >
 136
 137 =item * C<gsl_integration_qawc >
 138
 139 =item * C<gsl_integration_qaws >
 140
 141 =item * C<gsl_integration_qawo >
 142
 143 =item * C<gsl_integration_qawf >
 144
 145 =back
 146
 147 This module also includes the following constants :
 148
 149 =over
 150
 151 =item * $GSL_INTEG_COSINE
 152
 153 =item * $GSL_INTEG_SINE
 154
 155 =item * $GSL_INTEG_GAUSS15
 156
 157 =item * $GSL_INTEG_GAUSS21
 158
 159 =item * $GSL_INTEG_GAUSS31
 160
 161 =item * $GSL_INTEG_GAUSS41
 162
 163 =item * $GSL_INTEG_GAUSS51
 164
 165 =item * $GSL_INTEG_GAUSS61
 166
 167 =back
 168
 169 The following errors constants are part of the Math::GSL::Errno module and can be returned by the gsl_integration functions :
 170
 171 =over
 172
 173 =item * $GSL_EMAXITER - the maximum number of subdivisions was exceeded.
 174
 175 =item * $GSL_EROUND - cannot reach tolerance because of roundoff error, or roundoff error was detected in the extrapolation table.
 176
 177 =item * GSL_ESING - a non-integrable singularity or other bad integrand behavior was found in the integration interval.
 178
 179 =item * GSL_EDIVERGE - the integral is divergent, or too slowly convergent to be integrated numerically.
 180
 181 =back
 182
 183 For more informations on the functions, we refer you to the GSL offcial
 184 documentation: L<http://www.gnu.org/software/gsl/manual/html_node/>
 185
 186 Tip : search on google: site:http://www.gnu.org/software/gsl/manual/html_node/ name_of_the_function_you_want
 187
 188
 189 =head1 AUTHORS
 190
 191 Jonathan Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
 192
 193 =head1 COPYRIGHT AND LICENSE
 194
 195 Copyright (C) 2008 Jonathan Leto and Thierry Moisan
 196
 197 This program is free software; you can redistribute it and/or modify it
 198 under the same terms as Perl itself.
 199
 200 =cut
 201
 202 %}