Sparse vs Normal Array Matlab

Question

In Matlab, at what point is having a sparse array better than a normal array if I still have a lot of calculations to do on it, and about 25% of the array are non-zeros?

Answer 1

Personally, I'd rarely bother with sparse for an array that is only 25% non-zeros. If you don't believe me, try it yourself.

A = sprand(2000,2000,0.25);
tic,B = A*A;toc
Elapsed time is 1.771668 seconds.

Af = full(A);
tic,B = Af*Af;toc
Elapsed time is 0.499045 seconds.

The extra work involved with this as a sparse matrix costs too much to be worth the bother. Now try it with a really sparse matrix.

A = sprand(2000,2000,0.005);
Af = full(A);

tic,B = A*A;toc
Elapsed time is 0.037763 seconds.

tic,B = Af*Af;toc
Elapsed time is 0.446680 seconds.

Of course, your own problem will be different, but it will not be that different. Sparse matrices are a true boon for the person who uses truly sparse matrices, but 25% non-zeros is simply not "sparse" enough for any gain in most cases.