#!/usr/bin/perl -w

# ----------------------------------------------------------------
# John Kerl
# kerl.john.r@gmail.com
# 2005-06-30
# See http://math.arizona.edu/~kerl/doc/ssdda.pdf for information.
# ----------------------------------------------------------------

use PMATLIB;

while (@ARGV) {
	last unless $ARGV[0] =~ m/^-/;
	if (pmatlib_opt(\@ARGV)) {
		;
	}
	else {
		usage();
	}
}

if (@ARGV != 3) {
	usage();
}
$n = shift @ARGV;
$d = read_scalar(shift @ARGV);
$a = read_scalar(shift @ARGV);

for ($i = 0; $i < $n; $i++) {
	for ($j = 0; $j < $n; $j++) {
		$Q[$i][$j] = 1.0;
		for ($k = 0; $k < $n; $k++) {
			next if $j == $k;
			$Q[$i][$j] *= ($d + $a*$i - $k) / ($j - $k);
		}
	}
}
print_matrix(\@Q, $n, $n);

# ----------------------------------------------------------------
sub usage
{
	die
		"Usage: $0 [options] {n} {d} {a}\n" .
		"Options:\n" .
		pmatlib_options_string();
}