MATLAB: Backslash with triangular matrices

backslashmultithreadingspeedtriangular matrices

I'm using a LU decomposition on a matrix A (square, sparse, complex, symmetric (not Hermitian)):
[M1,M2,P,Q,R] = lu(A);
I then apply the backslash operator to these resulting matrices to build a Schur complement:
T = Q*(M2\(M1\(P*(R\B))));
If B were a vector, this second line executes sufficiently fast. But when B is a square matrix, which it is in my case, this operation is very slow since Matlab internally loops through the columns of B (which is my conclusion after having done some tic/tocs). The second line of code runs on a single thread using Matlab 2013b on Win7 64bit which makes this even slower.
What is a good way of speeding this up? A parfor loop working on the columns of B didn't work for me in Matlab 2013b due to reasons discussed in http://www.mathworks.com.au/matlabcentral/answers/59250-error-with-parfor-and-big-matrices (despite Edric Ellis saying it had been fixed in 2013a). Anything else I can try?
Thanks!

Best Answer

Your operation looks equivalent to
 T=A\B
I would expect that to be the fastest. Note that backslash already does its own lu decomposition internally, but with optimized multi-threading. You seem to be just repeating the decomposition work. Moreover, you've turned one backslash operation into three, possibly triggering three times as many internal lu decompositions.
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