Perl power of the adjacency matrix - perl

Question

Does anyone know how they would find the n-th power of the adjacency matrix?
Here is the matrix I am trying to write the code for
0 0 1 0
0 0 1 0
1 1 0 1
0 0 1 0
and the 2nd power adjacency matrix is:
1 1 0 1
1 1 0 1
0 0 3 0
1 1 0 1
I am not sure how I can calculate it with a perl code
I only have a code for reading in my file
sub matrix_read_file {
my ($filename) = #_;
my #matrix;
open (my $F, '<', $filename) or die "Could not open $filename: $!";
while (my $line =<$F> ) {
chomp $line;
next if $line =~ /^\s*$/; # skip blank lines
my #row = split /\s+/, $line;
push #matrix, \#row;
}
close $F;
print "$matrix[2][1]\n"; #test to see if individual elements print
print "$matrix[1][2]\n";
return \#matrix;
}

Answer 1

Here is an example:
use v5.22.0; # signatures requires perl >= 5.22
use feature qw(say);
use strict;
use warnings;
use experimental qw(signatures);
use Data::Dumper;
{
my $m = [[0,0,1,0],[0,0,1,0],[1,1,0,1],[0,0,1,0]];
my $m2 = matmul( $m, $m );
print Dumper($m2);
}
# Assume $m1 has size [pxq] and $m2 has size [qxr] :
# p = number of rows in $m1
# q = number of columns in $m1 == number of rows in $m2
# r = number of columns in $m2
# result = [pxq] * [qxr] => [p x r]
sub matmul( $m1, $m2 ) {
my $p = $#$m1;
my $q = $#{$m1->[0]};
my $r = $#{$m2->[0]};
my #res;
for my $i (0..$p) {
for my $j (0..$r) {
my $sum = 0;
for my $k (0..$q) {
$sum += $m1->[$i][$k] * $m2->[$k][$j];
}
$res[$i][$j] = $sum;
}
}
return \#res;
}
Or alternatively, using the PDL module:
use feature qw(say);
use strict;
use warnings;
use PDL;
my $m = pdl [[0,0,1,0],[0,0,1,0],[1,1,0,1],[0,0,1,0]];
my $m2 = $m x $m;
print $m2;