Best practice when working with sparse matrices

Question

This question is based on a discussion in this question. I have been working with sparse matrices earlier and my belief is that the way I\'ve been working with these is effi

Answer 1

MATLAB stores sparse matrices in compressed column format. This means that when you perform an operations like A(2,2) (to get the element in at row 2, column 2) MATLAB first access the second column and then finds the element in row 2 (row indices in each column are stored in ascending order). You can think of it as:

 A2 = A(:,2);
 A2(2)

If you are only accessing a single element of sparse matrix doing var = S(r,c) is fine. But if you are looping over the elements of a sparse matrix, you probably want to access one column at a time, and then loop over the nonzero row indices via [i,~,x]=find(S(:,c)). Or use something like spfun.

You should avoid constructing a dense matrix A and then doing S = sparse(A), as this operations just squeezes out zeros. Instead, as you note, it's much more efficient to build a sparse matrix from scratch using triplet-form and a call to sparse(i,j,x,m,n). MATLAB has a nice page which describes how to efficiently construct sparse matrices.

The original paper describing the implementation of sparse matrices in MATLAB is quite a good read. It provides some more info on how the sparse matrix algorithms were originally implemented.