Normalizing a sparse matrix so that rows sum to 1

I have the following sparse matrix, which relates to a markov process. The parts of the matrix have been assembled sequentially, adding new entries to row, column, and probability one at a time, and only then creating

S = sparse(row,column,probability)

Because the sequential process involves aggregating probabilities from some states that are equaivalent

full(S)

results in a matrix, whose rows sum to more than one. What I wish to achieve is a normalization of each row in S, such that all rows sum to one. How can that be done by operating on S without needing to create the full matrix?

Answer 1

[John D'Errico]

WTP?

M = sprand(10000,10000,.00001);
mean(sum(M,2))
ans =
   (1,1)        0.050375

So M is large, sparse, and its rows sum to whatever they want to sum to.

M = M./sum(M,2);
[min(sum(M,2)),max(sum(M,2))]
ans =
   (1,1)               1
   (1,2)               1

So now normalized. The above will work properly in R2016b or later. I could have done the normalization by multiplying by a sparse diagonal matrix too, probably created using spdiags.