MATLAB: Normalizing a sparse matrix so that rows sum to 1

markovnormalizingsparse

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?

Best Answer

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.
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