kronecker

Kronecker tensor product

Description

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

• Acknowledgements: This submission has inspired the following:; Kronecker product
• MATLAB release: MATLAB 7.4 (R2007a)

[Mayowa]

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));
  

[Matt Fig]

Mayowa,

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

[Matt Fig]

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.

[Bruno Luong]

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);

[Matt Fig]

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.

[Mayowa]

 

[Minchul Shin]