Kronecker product

An efficient implementation of the Kronecker product for dense, sparse and logical matrices.

Description

This file serves as a replacement for Matlab's kron.m. It contains a more efficient implementation of the Kronecker product for dense, sparse and logical matrices.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
kronecker

• MATLAB release: MATLAB 7.11 (2010b)

[Christophe]

As promised, the program does the job faster than the original implementation.
Very good!

[Matt J]

Very good, but like the original kron, this version cannot handle logical inputs, e.g.

kron(sparse(true(3)),sparse(true(6)));
??? Error using ==> mtimes
Logical inputs must be scalar.

Error in ==> kron at 25
     X = sparse(ix,jx,sb*sa.',I*K,J*L);

Consider making the following modification

    if islogical(sb) && islogical(sa)
     X = sparse(ix,jx,bsxfun(@and,sb,sa.'),I*K,J*L);
     return;
    elseif islogical(sb)
     sb=double(sb);
    elseif islogical(sa)
     sa=double(sa);
    end
     X = sparse(ix,jx,sb*sa.',I*K,J*L);

[Laurent S]

@Matt J: The updated version supports logical matrices (adding only one line of code), thanks for your comment!

[Matt J]

Nice 1-line trick, but it prevents you from having full class support when you're already so close!

Notice that mixed sparse/single ops still don't work

>> kron(sparse(rand(6)),rand(6,'single'));
??? Undefined function or method 'sparse' for input arguments of type 'single'.

This is my revised recommendation

    if islogical(sb) && islogical(sa)
     X = sparse(ix,jx,bsxfun(@and,sb,sa.'),I*K,J*L);
     return;
    end
    
    if ~(isdouble(sa)||islogical(sa)); sa=double(sa); end
    if ~(isdouble(sb)||islogical(sb)); sb=double(sb); end
    
    X = sparse(ix,jx,sb*sa.',I*K,J*L);

[Laurent S]

@Matt J: I updated the code again to include support for other class types, thanks for catching that.

[Matt J]

 

[Matt J]

I'm going to stop bothering you, but my recommended solution also handled integer types, whereas, your current one does not.

kron(sparse(rand(6)),uint16(rand(5)*5));
??? Error using ==> mtimes
Integers can only be combined with integers of the same class, or scalar doubles.

Is there a reason you're trying so hard to economize on if-statements and lines of code?

[Laurent S]

@Matt J: I was under the impression converting sa and sb to doubles would be slower than converting their outer product to double, unfortunately Matlab isn't too good about handling operations between different types of data. I updated the code again.

[Paulo]

kron(1:3, speye(3)) does not work (Matlab 2010b 64bit Linux).

Here's the error message:

??? Error using ==> mtimes
Inner matrix dimensions must agree.

Error in ==> kron at 24
        X = sparse(ix,jx,double(sb)*double(sa.'),I*K,J*L);
 

[Matt J]

These two modified lines of code are needed:

 [ia,ja,sa] = find(A); ia=ia(:); ja=ja(:); sa=sa(:);
    [ib,jb,sb] = find(B); ib=ib(:); jb=jb(:); sb=sb(:);

[Laurent S]

@Paulo,Matt J: Thanks for letting me know, I submitted an updated version.

[Paulo]

Works great now! Thanks a lot for the fix and the update.