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Re: [Bug-apl] tensor product

From: Elias Mårtenson
Subject: Re: [Bug-apl] tensor product
Date: Wed, 20 May 2015 21:57:16 +0800

Wouldn't that be because ∘.× is not the tensor product operation? The result of the ∘.OP function with arguments of rank n and m will always yield a matrix of rank n×m.

I'd rather refer to the ∘. operator as the cartesian operator since it applies its function on all possible permutations of the inputs.


On 20 May 2015 at 21:31, Fausto Saporito <address@hidden> wrote:
Hello all,

I don't understand why the tensor product in APL (∘.×) between two
matrices, gives a multidimensional array as result.

>From linear algebra, tensor product (or kronecker product) gives a
matrix as result,

for example

if I2 is identity matrix

1 0
0 1

I2 (tensor product) I2 gives

1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

instead if I use the APL operator I have :

1 0
0 1

0 0
0 0

0 0
0 0

1 0
0 1

the result is correct but why the shape is different ?

Is there a way to have a behaviour similar to linear algebra result ?

I wrote a generic tensor product function, but I'm not happy because
it uses loops and I don't like APL with loops :) but I didn't figure
out a loopless solution.


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