#!/usr/local/bin/perl

# ----------------------------------------------------------------
# John Kerl
# kerl.john.r@gmail.com
# 2005-01-11
#
# This is an example of numerical integration in two variables:
# x^2 y^2 for x = -2 to 2 and y = -3 to 3.  Analytically one computes
# 96.00 for the integral; this program prints 96.002400.
# ----------------------------------------------------------------

$xlo = -2.0;
$xhi =  2.0;
$ylo = -3.0;
$yhi =  3.0;

$nx  = 400;
$ny  = 400;

if (@ARGV) {
	$nx = $ny = $ARGV[0];
}
$dx  = ($xhi - $xlo) / $nx;
$dy  = ($yhi - $ylo) / $ny;

# Alternatively:
#$dx  = 0.001;
#$dy  = 0.001;

$sum = 0.0;
for ($x = $xlo; $x < $xhi; $x += $dx) {
	for ($y = $ylo; $y < $yhi; $y += $dy) {
		$z = f($x, $y);
		$sum += $z * $dx * $dy;
	}
}
printf "%11.6f\n", $sum;

# ----------------------------------------------------------------
sub f {
	my ($x, $y) = @_;
	return $x*$x * $y*$y;
}