Perl integral equation

gistfile1.pl

#!/usr/bin/env perl

use strict;
use warnings;

use PerlGSL ':all';

# General concept:
# For a given d solve for c
#   _               
#  /  1             
#  |    f(x,c) dx  =  d
# _/  0             
#

# in this case use f as a gaussian
sub f {
  my ($x, $c) = @_;
  return exp( - ($x/$c)**2 )
}

# pick some value of d
my $d = 0.5;

my $found_c = findroot_1d(
  sub {
    my $c = shift;
    my $integrand = sub {
      my $x = shift;
      return f( $x, $c );
    };
    return int_1d( $integrand, 0, 1) - $d;
  },
  # range over which to search for c
  1e-12, 5
);

print "Found c = $found_c\n";