Integration.i

   1 %module "Math::GSL::Integration"
   2 %include "typemaps.i"
   3 %include "gsl_typemaps.i"
   4
   5 %{
   6     #include "gsl/gsl_integration.h"
   7 %}
   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     use Math::GSL::Integration qw /:all/;
  60
  61     my $function = sub { $_[0]**2 } ;
  62     my ($lower, $upper ) = (0,1);
  63     my ($relerr,$abserr) = (0,1e-7);
  64
  65     my ($status, $result, $abserr, $num_evals) = gsl_integration_qng ( $function,
  66                                                     $lower, $upper, $relerr, $abserr
  67                                                  );
  68
  69 =head1 DESCRIPTION
  70
  71 Here is a list of all the functions in this module :
  72
  73 =over
  74
  75 =item * C<gsl_integration_workspace_alloc($n)>
  76
  77 This function allocates a workspace sufficient to hold $n double precision
  78 intervals, their integration results and error estimates.
  79
  80 =item * C<gsl_integration_workspace_free($w)>
  81
  82  This function frees the memory associated with the workspace $w.
  83
  84 =item * C<gsl_integration_qaws_table_alloc($alpha, $beta, $mu, $nu)>
  85
  86  This function allocates space for a gsl_integration_qaws_table struct
  87  describing a singular weight function W(x) with the parameters ($alpha, $beta,
  88  $mu, $nu), W(x) = (x-a)^alpha (b-x)^beta log^mu (x-a) log^nu (b-x) where
  89  $alpha > -1, $beta > -1, and $mu = 0, 1, $nu = 0, 1. The weight function can
  90  take four different forms depending on the values of $mu and $nu,
  91
  92               W(x) = (x-a)^alpha (b-x)^beta                   (mu = 0, nu = 0)
  93               W(x) = (x-a)^alpha (b-x)^beta log(x-a)          (mu = 1, nu = 0)
  94               W(x) = (x-a)^alpha (b-x)^beta log(b-x)          (mu = 0, nu = 1)
  95               W(x) = (x-a)^alpha (b-x)^beta log(x-a) log(b-x) (mu = 1, nu = 1)
  96
  97 The singular points (a,b) do not have to be specified until the integral is
  98 computed, where they are the endpoints of the integration range.  The function
  99 returns a pointer to the newly allocated table gsl_integration_qaws_table if no
 100 errors were detected, and 0 in the case of error.
 101
 102 =item * C<gsl_integration_qaws_table_set($t, $alpha, $beta, $mu, $nu)>
 103
 104  This function modifies the parameters ($alpha, $beta, $mu, $nu) of an existing
 105  gsl_integration_qaws_table struct $t.
 106
 107 =item * C<gsl_integration_qaws_table_free($t)>
 108
 109  This function frees all the memory associated with the
 110  gsl_integration_qaws_table struct $t.
 111
 112 =item * C<gsl_integration_qawo_table_alloc($omega, $L, $sine, $n)>
 113
 114 =item * C<gsl_integration_qawo_table_set($t, $omega, $L, $sine, $n)>
 115
 116  This function changes the parameters omega, L and sine of the existing
 117  workspace $t.
 118
 119 =item * C<gsl_integration_qawo_table_set_length($t, $L)>
 120
 121  This function allows the length parameter $L of the workspace $t to be
 122  changed.
 123
 124 =item * C<gsl_integration_qawo_table_free($t)>
 125
 126  This function frees all the memory associated with the workspace $t.
 127
 128 =item * C<gsl_integration_qk15 >
 129
 130 =item * C<gsl_integration_qk21 >
 131
 132 =item * C<gsl_integration_qk31 >
 133
 134 =item * C<gsl_integration_qk41 >
 135
 136 =item * C<gsl_integration_qk51 >
 137
 138 =item * C<gsl_integration_qk61 >
 139
 140 =item * C<gsl_integration_qcheb >
 141
 142 =item * C<gsl_integration_qk >
 143
 144 =item * C<gsl_integration_qng >
 145
 146 =item * C<gsl_integration_qag >
 147
 148 =item * C<gsl_integration_qagi >
 149
 150 =item * C<gsl_integration_qagiu >
 151
 152 =item * C<gsl_integration_qagil >
 153
 154 =item * C<gsl_integration_qags($func,$a,$b,$epsabs,$epsrel,$limit,$workspace)>
 155
 156     ($status, $result, $abserr) = gsl_integration_qags (
 157                             sub { 1/$_[0]} ,
 158                             1, 10, 0, 1e-7, 1000,
 159                             $workspace,
 160                         );
 161
 162  This function applies the Gauss-Kronrod 21-point integration rule
 163  adaptively until an estimate of the integral of $func over ($a,$b) is
 164  achieved within the desired absolute and relative error limits,
 165  $epsabs and $epsrel.
 166
 167
 168 =item * C<gsl_integration_qagp >
 169
 170 =item * C<gsl_integration_qawc >
 171
 172 =item * C<gsl_integration_qaws >
 173
 174 =item * C<gsl_integration_qawo >
 175
 176 =item * C<gsl_integration_qawf >
 177
 178 =back
 179
 180 This module also includes the following constants :
 181
 182 =over
 183
 184 =item * $GSL_INTEG_COSINE
 185
 186 =item * $GSL_INTEG_SINE
 187
 188 =item * $GSL_INTEG_GAUSS15
 189
 190 =item * $GSL_INTEG_GAUSS21
 191
 192 =item * $GSL_INTEG_GAUSS31
 193
 194 =item * $GSL_INTEG_GAUSS41
 195
 196 =item * $GSL_INTEG_GAUSS51
 197
 198 =item * $GSL_INTEG_GAUSS61
 199
 200 =back
 201
 202 The following error constants are part of the Math::GSL::Errno module and can
 203 be returned by the gsl_integration_* functions :
 204
 205 =over
 206
 207 =item * $GSL_EMAXITER
 208
 209 Maximum number of subdivisions was exceeded.
 210
 211 =item * $GSL_EROUND
 212
 213 Cannot reach tolerance because of roundoff error, or roundoff error was detected in the extrapolation table.
 214
 215 =item * GSL_ESING
 216
 217 A non-integrable singularity or other bad integrand behavior was found in the integration interval.
 218
 219 =item * GSL_EDIVERGE
 220
 221 The integral is divergent, or too slowly convergent to be integrated numerically.
 222
 223 =back
 224
 225 =head1 MORE INFO
 226
 227 For more informations on the functions, we refer you to the GSL offcial
 228 documentation: L<http://www.gnu.org/software/gsl/manual/html_node/>
 229
 230 =head1 AUTHORS
 231
 232 Jonathan Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
 233
 234 =head1 COPYRIGHT AND LICENSE
 235
 236 Copyright (C) 2008 Jonathan Leto and Thierry Moisan
 237
 238 This program is free software; you can redistribute it and/or modify it
 239 under the same terms as Perl itself.
 240
 241 =cut
 242
 243 %}