MATLAB: Mldivide with sparse matrix

linear systemmldividesparsesparse and full matrix

Hi,
I need to solve large sparse system of linear equations A*x=b. A is a sparse matrix, but b is vector which has only few zero entries. The question is, regarding memory consumption, when I call
   mldivide(A,b)
when A is sparse matrix and b is full vector, will matlab internally transform A into full matrix and solve the system, or handle it like sparse.
Thanks! K

Best Answer

The following speed comparison is pretty good evidence that only the type of A (sparse or full) dictates how things will be handled,
    >> N=6000; A=speye(N); b=rand(N,1); bsp=sparse(b); Af=full(A);
    >> tic;A\b;toc
    Elapsed time is 0.000316 seconds.
    >> tic;A\bsp;toc
    Elapsed time is 0.000301 seconds.
    >> tic;Af\b;toc
    Elapsed time is 0.071560 seconds.
    >> tic;Af\bsp;toc
    Elapsed time is 0.030398 seconds.
In principle, though, it wouldn't matter. You could have still converted b to sparse type, no matter how dense it actually is, if that's what was needed to force a sparse algorithm to be used. The memory penalty is negligible if b is just a vector.
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