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#!/usr/bin/perl
#
# Task 2: Kronecker Product
#
# You are given 2 matrices.
#
# Write a script to implement Kronecker Product on the given 2 matrices.
#
# For more information, please refer to the wikipedia page
# https://en.wikipedia.org/wiki/Kronecker_product
#
# For example,
#
# A = [ 1 2 ]
# [ 3 4 ]
#
# B = [ 5 6 ]
# [ 7 8 ]
#
# A x B = [ 1 x [ 5 6 ] 2 x [ 5 6 ] ]
# [ [ 7 8 ] [ 7 8 ] ]
# [ 3 x [ 5 6 ] 4 x [ 5 6 ] ]
# [ [ 7 8 ] [ 7 8 ] ]
#
# = [ 1x5 1x6 2x5 2x6 ]
# [ 1x7 1x8 2x7 2x8 ]
# [ 3x5 3x6 4x5 4x6 ]
# [ 3x7 3x8 4x7 4x8 ]
#
# = [ 5 6 10 12 ]
# [ 7 8 14 16 ]
# [ 15 18 20 24 ]
# [ 21 24 28 32 ]
#
# MY NOTES: Ok, at least it has nothing to do with prime numbers:-)
# I note in the Wikipedia page the useful formula:
# (A x B)ij = Ai/p,j/q * Bi%p,j%q [where B is of size p x q]
#
use strict;
use warnings;
use feature 'say';
use Getopt::Long;
use Function::Parameters;
use Data::Dumper;
my $debug=0;
die "Usage: kronecker-product [--debug]\n"
unless GetOptions( "debug"=>\$debug ) && @ARGV==0;
#
# mat_show( $m );
# Show matrix $m
#
fun mat_show( $m )
{
my $rows = @$m;
my $cols = @{$m->[0]};
#die "rows=$rows, cols=$cols, m=".Dumper($m);
# first, calculate the max cell width
my $width = 1;
foreach my $i (0..$rows-1)
{
my $row = $m->[$i];
foreach my $j (0..$cols-1)
{
my $len = length($row->[$j]);
$width = $len if $len > $width;
}
}
#die "width=$width\n";
foreach my $i (0..$rows-1)
{
my $row = $m->[$i];
print "[ ";
foreach my $j (0..$cols-1)
{
printf( "%${width}d ", $row->[$j] );
}
print "]\n";
}
}
#
# my $c = kronecker_product( $a, $b );
# Form the Kronecker product of two matrices $a and $b.
# using the formula (A x B)i,j = Ai/p,j/q * Bi%p,j%q
# [where B is of size p x q]
#
fun kronecker_product( $a, $b )
{
my $m = @$a;
my $n = @{$a->[0]};
my $p = @$b;
my $q = @{$b->[0]};
my $rows = $m * $p;
my $cols = $n * $q;
my $c = [ map { [] } 1..$rows ];
#die "rows=$rows, cols=$cols, c=".Dumper($c);
foreach my $i (0..$rows-1)
{
my $arow = int( $i / $p );
my $brow = int( $i % $p );
foreach my $j (0..$cols-1)
{
my $acol = int( $j / $q );
my $bcol = int( $j % $q );
$c->[$i][$j] = $a->[$arow][$acol] * $b->[$brow][$bcol];
}
}
#die "rows=$rows, cols=$cols, c=".Dumper($c);
return $c;
}
my $a = [
[1, 2],
[3, 4],
];
my $b = [
[5, 6],
[7, 8],
];
say "[ 1, 2 ] [5, 6]";
say "[ 3, 4 ] k* [7, 8]";
say "is:";
my $c = kronecker_product( $a, $b );
mat_show( $c );
say "";
$a = [
[1, -4, 7],
[-2, 3, 3],
];
$b = [
[8, -9, -6, 5],
[1, -3, -4, 7],
[2, 8, -8, -3],
[1, 2, -5, -1],
];
$c = kronecker_product( $a, $b );
say "[ 1, -4, 7 ] [8, -9, -6, 5]";
say "[ -2, 3, 3 ] [1, -3, -4, 7]";
say " k* [2, 8, -8, -3]";
say " [1, 2, -5, -1]";
say "is:";
mat_show( $c );
|
