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## kronecker

version 1.2 (1.86 KB) by

Kronecker tensor product

Updated

This function does exactly what Matlab KRON does, but for large full matrices, the engine uses BSXFUN to accelerate the calculation.
Another advantage is no intermediate large matrices are generated (four temporary arrays in case of KRON).

Here is the benchmark code and result:

clear,
gain=[];
mem = memory;
maxn = (mem.MaxPossibleArrayBytes/32)^0.25;
n = 10:10:maxn;
for sz=n
A=rand(sz); B=rand(sz);
t1=Inf;
for ntry=1:10
tic; K = kron(A,B); t1=min(t1,toc);
end
clear K
t2=Inf;
for ntry=1:10
tic; K = kronecker(A,B); t2=min(t2,toc);
end
clear K
gain(end+1) = t1/t2;
end

fprintf('Size A/B Speed gain\n');
fprintf(' %02d %1.2f \n', [n; gain]);

Size A/B Speed gain
10 1.17
20 3.48
30 3.78
40 3.73
50 3.68
60 4.22
70 3.81

Yair Altman

### Yair Altman (view profile)

Congratulating in having your efficient code incorporated in the stock KRON function in R2013b - well done, Bruno!

Minchul Shin

### Minchul Shin (view profile)

Mayowa Aregbesola

### Mayowa Aregbesola (view profile)

Fast, slick, well done.
Thanks for answering my question. I was waiting on that in order to give a rating, now I know it is my old (!, 2007b) version of MATLAB which is out of alignment.

Bruno Luong

### Bruno Luong (view profile)

To Matt's comment #2: 2D error checking is introduced in KRON in recent Matlab version. KORNECKER is designed to replicate the same behavior (desirable?).

A workaround (beside delete the error checing line) is:

A = reshape(A,size(A,1),[]);
B = reshape(B,size(B,1),[]);
C = kronecker(A,B);

My only question is why the function errors out for non- 2D inputs? The stock MATLAB function does not error, and if I take the offending lines of code out of kronecker, the results match.

Mayowa,

Indeed that is faster for smaller A,B. However, for larger A and B, kronecker is several times faster.

Mayowa Aregbesola

### Mayowa Aregbesola (view profile)

Hi,

I found a faster implementaion here
http://ftp.icm.edu.pl/packages/octave/MAILING-LISTS/octave-sources/1999/77. I have translated it into matlab below

function c = kron2(a,b)
[ra, ca]=size(a);
[rb, cb]=size(b);
c = a(ones(rb,1)*(1:ra), ones(cb,1)*(1:ca)).* b((1:rb)'*ones(1,ra), (1:cb)'*ones(1,ca));