#!/usr/bin/perl
use warnings;
use strict;
use Math::MatrixReal;

my ($a1, $b1, $c1, $d1, $e1,
$a2, $b2, $c2, $d2, $e2,
$a3, $b3, $c3, $d3, $e3,
$a4, $b4, $c4, $d4, $e4) =
(1,  -2,   3,   4,  17,
 4,  -5,   6,   7,  18,
 7,   8,  -9,  10,  19,
 8,   9,  -9, -11,  20);


my $A = Math::MatrixReal->new_from_string(<<EOF);
[ $a1 $b1 $c1 $d1 ]
[ $a2 $b2 $c2 $d2 ]
[ $a3 $b3 $c3 $d3 ]
[ $a4 $b4 $c4 $d4 ]
EOF

my $b = Math::MatrixReal->new_from_string(<<EOF);
[ $e1 ]
[ $e2 ]
[ $e3 ]
[ $e4 ]
EOF

print "det-> ",$A->det(),"\n";

my $LR = $A->decompose_LR();

my ($dim, $solution, $B) = $LR->solve_LR($b);

#print "dim->$dim\n\nsolution->\n$solution\n\nbase->\n$B\n\n";
print "dim->$dim\n\nsolution->\n\n$solution\n\n";

my $out = $A * $solution;
print $out,"\n";