How to perform cartesian product in PDL

Question

I want to take an arbitrary 1D vector a = [k] and b = [m] and form the matrix of ordered pairs c = [2 x k x m] such that $c->(:,(i),(j)) = [ $a->(i), $b->(j) ]. I.e. the set of all ordered pairs of the elements in a and b a.k.a the cartesian product.

Of course I could use a loop and the [glue] function to accomplish this, but that isn't in the spirit of Perl/PDL. Is there a fancy method that involves slices, dummy dimensions, and glue that gets me there?

Also, using Math::Cartesian::Product (as answered here: In Perl, how can I get the Cartesian product of multiple sets? is cheating! :3 I want straight perl/PDL and hopefully learn something in the process.

Answer 1

I got something that meets my criteria:

my $a = pdl 1,2,3,4;
my $b = pdl 5,6,7;
print "a = $a\n";
print "b = $b\n";
print "dummy dimensioned:\n";
$a = $a->dummy(0,$b->dim(0));
print "a".$a->shape." = $a\n";

$b = $b->dummy(0, $a->dim(1))->transpose;
print "b".$b->shape." = $b\n";

print "Glued together:\n"
my $c = $a->dummy(0,1)->glue(0, $b->dummy(0,1));
print "c".$c->shape." = $c\n";

---

a = [1 2 3 4]  
b = [5 6 7]  
dummy dimensioned:  
a[3 4] = 
[
 [1 1 1]
 [2 2 2]
 [3 3 3]
 [4 4 4]
]

b[3 4] = 
[
 [5 6 7]
 [5 6 7]
 [5 6 7]
 [5 6 7]
]  
Glued together:  
c[2 3 4] = [[[1 5][1 6][1 7]][[2 5][2 6][2 7]][[3 5][3 6][3 7]][[4 5][4 6][4 7]]]