Is it faster to operate a sparse matrix than a dense one when they have the same size?

Hi all,

Imagine I have 2 same size matrices, both takes only the upper triangular part and sparse, their sparsity is like this:

a:

b:

I'm being a bit exaggerate here, in reality a would be more dense. Of course a takes much less memory than b.

If I do some operations on a and b, for example, a.*c and b.*c, where matrix c has same size, but dense, will a.*c faster than b.*c?

Answer 1

[Star Strider]

The best way to find out is to experiment! This is especially true if you have a specific example, such as you illustrated in your Question.

Use the timeit (link) function with two functions, one with a sparse matrix and one with a dense matrix. Compute the results you want to test with various sparse matrix and dense matrix functions and see how they compare.

EDIT —

For an extended discussion of sparse matrix computations, see the documentation on Sparse Matrix Operations (link).

Answer 2

[Matt J]

a.*c should be faster. Since a is sparser than b, there are fewer multiplication operations that need executing. The question is, how much faster. That depends on how MATLAB parallelizes the operation and could be hard to predict. If you are working on the GPU, I suspect that the performance difference may be a lot less than on the CPU.

[Xh Du]

If the sparse matrix is large but very sparse, like this 1501 by 1501 matrix "exam_a":

and I have some operations like

exam = exam_a .* mtx_b

obviously in 'exam', wherever is zero in 'exam_a' will also be zero in 'exam'. But does MATLAB know this such that it only multiplies the non-zero part, or MATLAB doesn't know and multiplies everything?

If MATLAB does not know and multiplies everything, maybe I should extract these non-zero part and operate on them only.

[Matt J]

Yes, MATLAB knows. If you do the extraction you describe, you will be duplicating what MATLAB already does.