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#!/usr/bin/perl
# interfc
# v0.2 Keith Lofstrom 2008 Sept 18
# with tweaks by Jonathan Leto
#
# Compare the results of numerical integration of
# (2.0/sqrt(PI)*integral[x,inf](e^(-x^2) ) with the
# erfc() function.
#
# The results are pretty good, within 1e-14 or better
# for the examples tried
use Math::GSL::SF qw/:all/;
use Math::GSL::Integration qw/:all/;
use Math::GSL::Const qw/:all/;
use strict;
my $workspace = gsl_integration_workspace_alloc(101);
my $maxdiff = 0;
printf " arg erfc int() difference\n";
for( my $i=-5.2 ; $i<=5.201 ; $i += 0.1 ) {
my $e = gsl_sf_erfc($i);
my ($status, $result, $abserr ) = gsl_integration_qagiu(
sub { exp( -($_[0]**2) ) },
$i, 0, 1e-9, 100, $workspace );
my $yy = $M_2_SQRTPI * $result ;
my $diff=$yy-$e ;
$maxdiff = abs($diff) > $maxdiff ? abs($diff) : $maxdiff;
printf "%4.1f%18.12f%18.12f %.18g\n", $i, $e, $yy, $diff ;
}
printf "Maximum local error: %.12g\n", $maxdiff;
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