Sum.i

   1 %module "Math::GSL::Sum"
   2 %include "gsl_typemaps.i"
   3
   4 %apply double *OUTPUT { double * sum_accel, double * abserr, double * abserr_trunc };
   5
   6 %{
   7     #include "gsl/gsl_sum.h"
   8 %}
   9
  10 %include "gsl/gsl_sum.h"
  11
  12 %perlcode %{
  13 @EXPORT_OK = qw/
  14                gsl_sum_levin_u_alloc
  15                gsl_sum_levin_u_free
  16                gsl_sum_levin_u_accel
  17                gsl_sum_levin_u_minmax
  18                gsl_sum_levin_u_step
  19                gsl_sum_levin_utrunc_alloc
  20                gsl_sum_levin_utrunc_free
  21                gsl_sum_levin_utrunc_accel
  22                gsl_sum_levin_utrunc_minmax
  23                gsl_sum_levin_utrunc_step
  24              /;
  25 %EXPORT_TAGS = ( all => \@EXPORT_OK );
  26
  27 __END__
  28
  29 =head1 NAME
  30
  31 Math::GSL::Sum - Functions to accelerate the convergence of a series using the Levin u-transform.
  32
  33 =head1 SYNOPSIS
  34
  35     use Math::GSL::Sum qw/:all/;
  36
  37     my $w = gsl_sum_levin_u_alloc(5);
  38     $values = [8,2,3,4,6];
  39     my ($status, $sum_accel, $abserr) = gsl_sum_levin_u_accel($values, 5, $w);
  40     gsl_sum_levin_u_free($w);
  41
  42     my $w2 = gsl_sum_levin_utrunc_alloc(5);
  43     my ($status2, $sum_accel2, $abserr_trunc) = gsl_sum_levin_utrunc_accel($values, 5, $w2);
  44     gsl_sum_levin_utrunc_free($w);
  45
  46 =head1 DESCRIPTION
  47
  48 Here is a list of all the functions included in this module :
  49
  50 =over
  51
  52 =item * gsl_sum_levin_u_alloc($n) - This function allocates a workspace for a Levin u-transform of $n terms.
  53
  54 =item * gsl_sum_levin_u_free($w) - This function frees the memory associated with the workspace $w.
  55
  56 =item * gsl_sum_levin_u_accel($array, $array_size, $w) - This function takes the terms of a series in the array reference $array of size $array_size and computes the extrapolated limit of the series using a Levin u-transform. Additional working space must be provided in $w. The function returns multiple values in this order : 0 if the operation succeeded, 1 otherwise, the extrapolated sum and an estimate of the absolute error. The actual term-by-term sum is returned in $w->{sum_plain}. The algorithm calculates the truncation error (the difference between two successive extrapolations) and round-off error (propagated from the individual terms) to choose an optimal number of terms for the extrapolation. All the terms of the series passed in through array should be non-zero.
  57
  58 =item * gsl_sum_levin_u_minmax
  59
  60 =item * gsl_sum_levin_u_step
  61
  62 =item * gsl_sum_levin_utrunc_alloc($n) - This function allocates a workspace for a Levin u-transform of $n terms, without error estimation.
  63
  64 =item * gsl_sum_levin_utrunc_free($w) - This function frees the memory associated with the workspace $w.
  65
  66 =item * gsl_sum_levin_utrunc_accel($array, $array_size, $w) - This function takes the terms of a series in the array reference $array of size $array_size and computes the extrapolated limit of the series using a Levin u-transform. Additional working space must be provided in $w. The function returns multiple values in this order : 0 if the operation succeeded, 1 otherwise, the extrapolated sum and an estimate of the error. The actual term-by-term sum is returned in $w->{sum_plain}. The algorithm terminates when the difference between two successive extrapolations reaches a minimum or is sufficiently small. To improve the reliability of the algorithm the extrapolated values are replaced by moving averages when calculating the truncation error, smoothing out any fluctuations.
  67
  68 =item * gsl_sum_levin_utrunc_minmax
  69
  70 =item * gsl_sum_levin_utrunc_step
  71
  72 =back
  73
  74 =head1 AUTHORS
  75
  76 Jonathan Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
  77
  78 =head1 COPYRIGHT AND LICENSE
  79
  80 Copyright (C) 2008 Jonathan Leto and Thierry Moisan
  81
  82 This program is free software; you can redistribute it and/or modify it
  83 under the same terms as Perl itself.
  84
  85 =cut
  86
  87 %}