How to find indices of non zero elements in large sparse matrix?

Question

i have two sq matrix (a, b) of size in order of 100000 X 100000. I have to take difference of these two matrix (c = a-b). Resultant matrix 'c' is a sparse matrix. I want to find the indices of all non-zero elements. I have to do this operation many times (>100).

Simplest way is to use two for loops. But that's computationally intensive. Can you tell me any algorithm or package/library preferably in R/python/c to do this as quickly as possible?

Answer 1

Since you have two dense matrices then the double for loop is the only option you have. You don't need a sparse matrix class at all since you only want to know the list of indices (i,j) for which a[i,j] != b[i,j].

In languages like R and Python the double for loop will perform poorly. I'd probably write this in native code for a double for loop and add the indices to a list object. But no doubt the wizards of interpreted code (i.e. R, Python etc.) know efficient ways to do it without resorting to native coding.