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From: Matt J on 5 Aug 2010 16:52
But mightn't one be better off not summing the Kronecker products? What if instead, you evaluate y=A*x by first applying all the Kronecker products to x and then sum the result?

I created the following FEX tools to allow this kind of thing to be done in an object-oriented way.

http://www.mathworks.com/matlabcentral/fileexchange/25969-efficient-object-oriented-kronecker-product-manipulation

http://www.mathworks.com/matlabcentral/fileexchange/26611-on-the-fly-definition-of-custom-matrix-objects

which I use in the following short test, with L=2. As shown, the memory saving is considerable. I also get considerable speed-up, although that could depend generally on L and how many operations y=A*x you're going to perform...


%data
n=50;
K1=rand(n); K2=rand(n);
x=rand(n^2,1);



%Numeric representation of A
tic;
A=kron(conj(K1),K1) + kron(conj(K2),K2);

y1=A*x;

toc %Elapsed time is 0.388593 seconds.




tic;

%Object-oriented representation of A (as Aobj);
Kobj1=KronProd({conj(K1),K1},[1,2]);
Kobj2=KronProd({conj(K2),K2},[1,2]);
Aobj=MatrixObj;
Aobj.Ops.mtimes=@(A,x) Kobj1*x + Kobj2*x;

y2=Aobj*x;

toc%Elapsed time is 0.147291 seconds.



Error=max(abs(y1-y2))./max(abs(y1)) %3.7477e-015


whos A Aobj

%{
Name Size Bytes Class Attributes

A 2500x2500 50000000 double
Aobj 1x1 8458 MatrixObj

%}
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