Perl Cookbook

Multiplying Matrices

Problem

You want to multiply a pair of two-dimensional arrays. Mathematicians and engineers often need this.

Solution

Use the PDL modules, available from CPAN. PDL is the Perl Data Language— modules that give fast access to compact matrix and mathematical functions:

use PDL;
# $a and $b are both pdl objects
$c = $a * $b;

Alternatively, apply the matrix multiplication algorithm to your two-dimensional array:

sub mmult {
    my ($m1,$m2) = @_;
    my ($m1rows,$m1cols) = matdim($m1);
    my ($m2rows,$m2cols) = matdim($m2);

    unless ($m1cols == $m2rows) {  # raise exception
        die "IndexError: matrices don't match: $m1cols != $m2rows";
    }

    my $result = [];
    my ($i, $j, $k);

    for $i (range($m1rows)) {
        for $j (range($m2cols)) {
            for $k (range($m1cols)) {
                $result->[$i][$j] += $m1->[$i][$k] * $m2->[$k][$j];
            }
        }
    }
    return $result;
}

sub range { 0 .. ($_[0] - 1) }

sub veclen {
    my $ary_ref = $_[0];
    my $type = ref $ary_ref;
    if ($type ne "ARRAY") { die "$type is bad array ref for $ary_ref" }
    return scalar(@$ary_ref);
}

sub matdim {
    my $matrix = $_[0];
    my $rows = veclen($matrix);
    my $cols = veclen($matrix->[0]);
    return ($rows, $cols);
}

Discussion

If you have the PDL library installed, you can make use of its lightning-fast manipulation of numbers. This requires far less memory and CPU than Perl’s array manipulation. When using PDL objects, many numeric operators (such as + and *) are overloaded and work on an element-by-element basis (e.g., * is the so-called scalar multiplication operator). To get ...