Efficiently process all possible 2D array combinations in Perl - performance

Question

I have a 2D array containing numbers. I am attempting to work out the product of multiplying a single number from each sub-array with one from each of the other sub-arrays; I then need to do this for all possible combinations.
The aim is that I input a file of the frequency of individual events, and get an output of the probability of a particular series of these events happening, with one event from each set.
I have fudged together some code with the help of a previous question:
for my $aref ( getCartesian(#freq) ) {
my $p = 1;
foreach my $n (#$aref) {
$p = $p * $n;
}
print "$p\n";
}
sub getCartesian {
my #input = #_;
my #ret = map [$_], #{ shift #input };
for my $a2 (#input) {
#ret = map {
my $v = $_;
map [#$v, $_], #$a2;
}
#ret;
}
return #ret;
}
where #freq is an array of arrays, such as:
#freq = [0.1, 0.2, 0.3,]
[0.4, 0.5, 0.6,]
[0.7, 0.8, 0.9,]; `and ~ 20 more sub arrays`
This works fine for a small test file, but when I give it my required input of 24 sub-arrays with 3 items each, the generation of combinations is clearly far too intensive, with 3^24 possibilities.
I have run it on a machine with 22 GB RAM, and it maxed out after 4 minutes before any output.
My question is, how could I modify the code so that I can print out $p for each combination, without having to hold the whole set of combinations in memory, which kills it. I presume that time would be the only limiting factor for computation then, not resources.
Edit: a method in base Perl without packages would be great. I don't have admin on the HPC facility sadly,

Answer 1

Set::CrossProduct lets you iterate through the Cartesian product so you don't have to store everything in memory:
use List::Util qw(reduce);
use Set::CrossProduct;
my #array = (
[0.1, 0.2, 0.3],
[0.4, 0.5, 0.6],
[0.7, 0.8, 0.9]
);
my $iterator = Set::CrossProduct->new(\#array);
while (my $tuple = $iterator->get) {
say '(', join(', ', #$tuple), '): ', reduce { $a * $b } #$tuple;
}
Outputs:
(0.1, 0.4, 0.7): 0.028
(0.1, 0.4, 0.8): 0.032
(0.1, 0.4, 0.9): 0.036
(0.1, 0.5, 0.7): 0.035
(0.1, 0.5, 0.8): 0.04
(0.1, 0.5, 0.9): 0.045
(0.1, 0.6, 0.7): 0.042
(0.1, 0.6, 0.8): 0.048
(0.1, 0.6, 0.9): 0.054
(0.2, 0.4, 0.7): 0.056
(0.2, 0.4, 0.8): 0.064
(0.2, 0.4, 0.9): 0.072
(0.2, 0.5, 0.7): 0.07
(0.2, 0.5, 0.8): 0.08
(0.2, 0.5, 0.9): 0.09
(0.2, 0.6, 0.7): 0.084
(0.2, 0.6, 0.8): 0.096
(0.2, 0.6, 0.9): 0.108
(0.3, 0.4, 0.7): 0.084
(0.3, 0.4, 0.8): 0.096
(0.3, 0.4, 0.9): 0.108
(0.3, 0.5, 0.7): 0.105
(0.3, 0.5, 0.8): 0.12
(0.3, 0.5, 0.9): 0.135
(0.3, 0.6, 0.7): 0.126
(0.3, 0.6, 0.8): 0.144
(0.3, 0.6, 0.9): 0.162