matrix determinants

[ysth]

Category:

Miscellaneous

Description:

A friend was reviewing precalculus (in preparation to return to school after a decade off and place into a real math class), and was working through some maxtrix determinant problems. I wrote this to help her catch arithmetic errors when calculating minors of a larger matrix. I only spent about 15 minutes, so its kind of rough, but I'm pretty satisfied, especially with how the input code handles errors.

#!/usr/bin/perl
use strict;
use warnings;

sub getmatrix {
    my $m = [];
    my $cols;
    rand()<.85 ? print "Enter matrix:\n" : print "tell me your matrix 
+and I'll tell you no lies:\n";
    while (!$cols || @$m != $cols) {
#    print "enter row:\n";
        my @row = split ' ', <>;
        if (@row < 2 || $cols && @row != $cols || grep /.\D|^[^\d-]/s,
+ @row) {
        print "try that row again:\n";
            @row = split ' ', <>;
            goto &getmatrix
                if @row < 2 || $cols && @row != $cols || grep /.\D|^[^
+\d-]/s, @row;
        }
        $cols ||= @row;
        push @$m, \@row;
    }
#    use Data::Dumper;
#    print Dumper $m;
    $m;
}

sub determine {
    my $m = shift;
    my $det = 0;
    if (@$m == 2) {
        $det = $m->[0][0] * $m->[1][1] - $m->[0][1] * $m->[1][0];
    } else {
        my @subm = map [@$_[1..$#$_]], @$m;
        for (0..$#$m) {
        if ($_ & 1) {
        $det -= $m->[$_][0] * determine([@subm[0..$_-1,$_+1..$#subm]])
+;
            } else {
                $det += $m->[$_][0] * determine([@subm[0..$_-1,$_+1..$
+#subm]]);
            }
        }
    }
    $det
}

while (1) {
    my $m = getmatrix();
    my $det = determine($m) || (rand()<.333 ? 0 : rand() < .5 ? 'zippo
+' : 'zilch');
    print "got: $det\n";
}

[Anonymous Monk]

A determinant operation is offered in Math::Matrix, and PDL's PDL::MatrixOps, and probably others.

[etj]

PDL::LinearAlgebra is probably the ideal module to check out for this.