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Sparse Matrix - More Efficient Assignment Operation

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I have a large sparse matrix for which I am attempting to assign certain segments (simplified example as per below snippet) to some identity matrices. The assignment method below is extremely inefficient, taking up a large amount of memory and too much time (10sec for example below on my server, but my real dataset is much bigger). Looking at the screenshot from taskmanager, we can see clearly a large spike in memory usage while the operation is being carried out.
For somebody used to dealing with large sparse matrices, there should be a more efficient way of carrying out such an assignment operation. Probably a pretty simple solution but I have little experience with sparse-matrix syntax.
A = sparse(20000,60000);
A(10001:end,20001:50000) = ([speye(10000,10000),-speye(10000,10000),speye(10000,10000)]);

Accepted Answer

the cyclist
the cyclist on 2 Apr 2013
Edited: the cyclist on 2 Apr 2013
That operation took less than 3 milliseconds on my machine.
The resulting array is 960,008 bytes.
  4 Comments
Sean de Wolski
Sean de Wolski on 3 Apr 2013
Hi Mark,
I can run the timings for you on any and all releases when I return to Natick on Friday.

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More Answers (2)

Cedric Wannaz
Cedric Wannaz on 2 Apr 2013
Edited: Cedric Wannaz on 2 Apr 2013
The structure of sparse matrices in memory makes this kind of indexing operations slower than building the sparse matrix directly using vectors of row/col IDs and values.
I = [10001:20000, 10001:20000, 10001:20000] ;
J = [20001:50000] ;
V = [ones(1, 1e4), -ones(1, 1e4), ones(1, 1e4)] ;
S = sparse(I, J, V, 2e4, 6e4) ;
spy(S) ; % Check structure.
You can easily make it more flexible/concise. I can't test it now though.
  6 Comments
Cedric Wannaz
Cedric Wannaz on 3 Apr 2013
It would be interesting to test with a smaller size matrix that would fit in memory as a dense matrix. There might be some conversion to dense in particular cases of indexing that could be spotted this way. I've been using quite intensely sparse matrices in MATLAB since ~2006 I guess, and I already had troubles with unsuspected conversions to dense a few times (but not while CAT-ing sparse matrices, as it is not an operation that I am doing frequently).

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Teja Muppirala
Teja Muppirala on 3 Apr 2013
The performance of sparse matrix indexing was enhanced in R2011a.
If you can't upgrade, as somewhat of a workaround, you should be able to get away with something like this:
A = sparse(20000,60000);
A = spreplace(A,10001:20000,20001:50000,[speye(10000,10000),-speye(10000,10000),speye(10000,10000)]);
Where SPREPLACE is the following general purpose function:
function A = spreplace(A,I,J,B)
% Equivalent to
% >> A(I,J) = B
% But does not support "end" indexing in I and J
I = I(:);
J = J(:);
[iA,jA,sA] = find(A);
[iB,jB,sB] = find(B);
trimA = ~(ismember(iA,I) & ismember(jA,J));
A = sparse([iA(trimA); I(iB)],...
[jA(trimA); J(jB)],...
[sA(trimA); sB],...
size(A,1),size(A,2));
When I try this in R2007a, Your original code takes 15 seconds, The workaround above gets it done in about 5 milliseconds.

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