[SciPy-User] iterative matrix methods seem slow

[eat]

Hi,

On Fri, Jun 24, 2011 at 11:34 AM, Richard Sharp <richsharp at stanford.edu>wrote:

> Hello,
>
> I'm attempting to solve a largish sparse, banded diagonal, linear
> system resulting from a finite difference approximation of a
> diffusion-like equation.
>
> I can use `spsolve` on smaller matrices, but get an odd memory error
> when they get to around (640k)^2:
>
> ...Can't expand MemType 1
>
> I've also looked into using some of the iterative solvers, but they
> are all painfully slow.  For example, on a (40k)^2 system `spsolve`
> runs in 0.8s while gmres takes 4.5s  Bumping up to (90k)^2 takes 2.4s
> with `spsolve` and 15.4s on `gmres`.  The other methods don't work, or
> run so long I don't wait for them to converge.
>
> I've tried using a Jacobi preconditioner and making good
> approximations to the solution for `gmres`, but I only end up with
> slower times.  I think I'm doing something wrong, because It's my
> impression that the iterative methods should run pretty quickly
> especially compared against a direct solver.
>
> My code looks something like this:
>
>    #A holds diagonals
>    matrix = spdiags(A,[-m,-1,0,1,m],n*m,n*m,"csr")
>    if direct:
>        result = spsolve(matrix,b)
>    else:
>        print ' system too large trying iteration'
>        result = scipy.sparse.linalg.gmres(matrix,b)[0]
>
> I'd appreciate any help with anything I could be doing wrong with
> setting up the system, making the calls, or a fundamental
> misunderstanding of the methods.
>
I played a little with your files. I can reproduce the error on Vista 64 bit
and Scipy 0.9.0.

However giving to spsolve parameter permc_spec value ='MMD_AT_PLUS_A' it
will pass (algtough takes some 25 sec.). Also with slightly higher cell size
h = 0.01075 and  permc_spec= None it will pass.


My 2 cents
eat

>
> Thanks for any help,
> Rich
>
> --
> Richard P. Sharp Jr.
> Lead Software Developer
> Natural Capital Project
> Stanford University, U Minnesota, TNC, WWF
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> Stanford, CA 94305
> http://www.stanford.edu/~rpsharp/
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