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matlabmatrixsparse-matrix

Relational operators between big sparse matrices in Matlab

I have two big sparse double matrices in Matlab:

  • P with dimension 1048576 x 524288

  • I with dimension 1048576 x 524288

I want to find the number of entrances i,j such that P(i,j)<=I(i,j)

Naively I tried to run 

 n=sum(sum(P<=I));

but it is extremely slow (I had to shut down Matlab because it was running since forever and I wasn't able to stop it).

Is there any other more efficient way to proceed or what I want to do is unfeasible?

Solution

  • From some simple tests,

    n = numel(P) - nnz(P>I);

    seems to be faster than sum(sum(P<=I)) or even nnz(P<=I). The reason is probably that the sparse matrix P<=I has many more nonzero entries than P>I, and thus requires more memory.

    Example:

    >> P = sprand(10485, 52420, 1e-3);
>> I = sprand(10485, 52420, 1e-3);
>> tic, disp(sum(sum(P<=I))); toc
   (1,1)      549074582
Elapsed time is 3.529121 seconds.
>> tic, disp(nnz(P<=I)); toc
   549074582
Elapsed time is 3.538129 seconds.
>> tic, disp(nnz(P<=I)); toc
   549074582
Elapsed time is 3.499927 seconds.
>> tic, disp(numel(P) - nnz(P>I)); toc
   549074582
Elapsed time is 0.010624 seconds.

    Of course this highly depends on the matrix sizes and density.