MATLAB: Max / Min of sparse matrices

maxminsparse

I previously asked this question:
http://www.mathworks.com/matlabcentral/answers/35224-max-min-of-nonzero-rows-cols
It was answered perfectly, except now I realize that I need to deal with a sparse matrix. If I set the zero elements to be NaN, I run out of memory. So the question is, how to find the row and column max and min of a sparse matrix, excluding the zero elements. Creating a full matrix is not an option. Any help would be appreciated.

Best Answer

EDIT There was a mistake in the markers line and the s= line, fixed now.
OK, here's an accelerated version. What made my previous answer slower was the S(I == i) line, this is pretty wasteful. Vectorisation sometimes hurts you rather than helping, this is one of those cases.
So, here goes. Again, I'll just focus on the rows and assume that it is possible for a row to be all zeros.
First, define a test matrix
A = sprand(50000, 60000, 1/20000);
Preallocate the rowMin and rowMax vectors
[m,n] = size(A);
rowMin = nan(m, 1);
rowMax = nan(m, 1);
Find all the NZ entries ;) and sort them by row index
[I,J,S] = find(A);
[I,K] = sort(I);
S = S(K);
Now we need to find where the index changes, diff is great for this. Just got to be careful with how you pad the left hand end. I also add in an extra entry to mark the final entry (saves unnecessary calls to end).
markers = [find([1; diff(I)]); numel(I)+1];
Pull out the identified rows, (end-1) makes sure that we don't get the final row twice.
iRows = I(markers(1:end-1));
The loop ought to be faster now:
for i = 1:numel(iRows)
  s = S(markers(i):(markers(i+1)-1));
  rowMin(iRows(i)) = min(s);
  rowMax(iRows(i)) = max(s);
end
This completes in 0.2 seconds on my laptop ...
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