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#!/usr/bin/perl
use warnings;
use strict;
use PDL;
use PDL::NiceSlice;
sub kronecker_product {
my ($x, $y) = @_;
my ($x0, $x1) = $x->dims;
my ($y0, $y1) = $y->dims;
return (
$y * $x->dummy(0, $y0)->dummy(1, $y1)
)->xchg(1, 2)->reshape($x0 * $y0, $x1 * $y1)
}
sub kron_rosetta {
my $A = shift;
my $B = shift;
my ($r0, $c0) = $A->dims;
my ($r1, $c1) = $B->dims;
my $kron = zeroes($r0 * $r1, $c0 * $c1);
for(my $i = 0; $i < $r0; ++$i){
for(my $j = 0; $j < $c0; ++$j){
$kron(
($i * $r1) : (($i + 1) * $r1 - 1),
($j * $c1) : (($j + 1) * $c1 - 1)
) .= $A($i,$j) * $B;
}
}
return $kron;
}
use Test::More tests => 4;
my $A = pdl([1, 2], [3, 4]);
my $B = pdl([5, 6], [7, 8]);
my $AB = pdl([ 5, 6, 10, 12],
[ 7, 8, 14, 16],
[15, 18, 20, 24],
[21, 24, 28, 32]);
is_deeply kronecker_product($A, $B), $AB;
is_deeply kron_rosetta($A, $B), $AB;
my $X = pdl([1, -4, 7], [-2, 3, 3]);
my $Y = pdl([8, -9, -6, 5],
[1, -3, -4, 7],
[2, 8, -8, -3],
[1, 2, -5, -1]);
my $XY =pdl([8, -9, -6, 5, -32, 36, 24, -20, 56, -63, -42, 35],
[1, -3, -4, 7, -4, 12, 16, -28, 7, -21, -28, 49],
[2, 8, -8, -3, -8, -32, 32, 12, 14, 56, -56, -21],
[1, 2, -5, -1, -4, -8, 20, 4, 7, 14, -35, -7],
[-16, 18, 12, -10, 24, -27, -18, 15, 24, -27, -18, 15],
[-2, 6, 8, -14, 3, -9, -12, 21, 3, -9, -12, 21],
[-4, -16, 16, 6, 6, 24, -24, -9, 6, 24, -24, -9],
[-2, -4, 10, 2, 3, 6, -15, -3, 3, 6, -15, -3]);
is_deeply kronecker_product($X, $Y), $XY;
is_deeply kron_rosetta($X, $Y), $XY;
use Benchmark qw{ cmpthese };
cmpthese(-3, {
choroba => sub { kronecker_product($X, $Y) },
rosetta => sub { kron_rosetta($X, $Y) }
});
__END__
Rate rosetta choroba
rosetta 9509/s -- -63%
choroba 25377/s 167% --
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