[SciPy-User] iterative matrix methods seem slow

[Richard Sharp]

Thanks Pauli,

> I don't see you passing in a preconditioner here -- it goes in via
> the M= parameter of gmres.

Right, I had one in there to begin with, but removed it later since it
seemed to slow down the convergence.

> On preconditioners: If you want "automatic" preconditioners, you can
> try the following:
>
> http://docs.scipy.org/doc/scipy/reference/sparse.linalg.html#scipy.sparse.linalg.spilu

Thanks for this.  Using the incomplete as follows LU I was able to cut
the iterative runtimes from 1700s to 30s

        P = scipy.sparse.linalg.spilu(matrix, drop_tol=1e-5)
        M_x = lambda x: P.solve(x)
        M = scipy.sparse.linalg.LinearOperator((n * m, n * m), M_x)
        result = scipy.sparse.linalg.lgmres(matrix, b, tol=1e-4, M=M)[0]

But the spilu factors in about 3s, solves in 0.1s and seems to give a
result that's very close to my continuous solution, so I'm using that
now with no memory or runtime problems:

        P = scipy.sparse.linalg.spilu(matrix, drop_tol=1e-5)
        result = P.solve(b)

Thanks for the guidance and help!
Rich