AoC day 2, Perl (matrix)

#!/usr/bin/perl

use strict;
use warnings;

use List::AllUtils  qw(pairwise sum);

#
# The calculation of a step is pos = pos + (vec * matrix).
# With the center of the matrix set to aim for next.
#
# pos is (x, y, a), matrix is [ 1 0 0 ]
#                             [ 0 a 0 ]
#                             [ 0 0 1 ]
#
# vec is (m, m, 0) for forward, (0, 0, +/-m) for down/up
#
my @matrix = ([1, 0, 0],
              [0, 0, 0],
              [0, 0, 1]);

my @pos = (0, 0, 0);

while (<>) {
    my ($cmd, $mag) = m#^(\w)\w+ (\d+)#;

    # scalar * vector using map
    my @vec  = map { $mag * $_ } ('f' eq $cmd, 'f' eq $cmd, 'f' cmp $cmd);

    # vector * matrix with map-sum-pairwise
    my @prod = map { sum pairwise { $a * $b } @vec, @$_ } @matrix;

    # vector + vector with pairwise
    @pos = pairwise { $a + $b } @pos, @prod;

    # set center value of matrix to aim
    $matrix[1][1] = $pos[2];
}

print "Part 1: ", $pos[0] * $pos[2], "\n";
print "Part 2: ", $pos[0] * $pos[1], "\n";