Hello all

-----Original Message----- From: numpy-discussion-bounces@lists.sourceforge.net [mailto:numpy- discussion-bounces@lists.sourceforge.net] On Behalf Of David Grant Sent: 16 August 2006 17:11 To: Discussion of Numerical Python Subject: Re: [Numpy-discussion] some work on arpack

On 8/16/06, Keith Goodman <kwgoodman@gmail.com> wrote:

On 8/15/06, David Grant <davidgrant@gmail.com> wrote:

My idea is (if I have time) to write an eigs-like function in python that will only perform a subset of what Matlab's eigs does for. It will, for example, compute a certain number of eigenvalues and eigenvectors for a real, sparse, symmetric matrix (the case I'm interested in)

Will it also work for a real, dense, symmetric matrix? That's the case I'm interested in. But even if it doesn't, your work is great news for numpy.

Real, dense, symmetric, well doesn't scipy already have something for this? I'm honestly not sure on the arpack side of things, I thought arpack was only useful (over other tools) for sparse matrices, I could be wrong.

Maybe SciPy can also do this, but what makes ARPACK useful is that it can get you a few eigenvalues and eigenvectors of a massive matrix without having to have the whole thing in memory. Instead, you provide ARPACK with a function that does A*x on your matrix. ARPACK passes a few x's to your function and a few eigenvalues and eigenvectors fall out. I recently used MATLAB's eigs to do exactly this. I had a dense matrix A with dimensions m x n, where m >> n. I wanted the eigenvalues of A'A (which has dimensions m x m, which is too large to keep in memory). But I could keep A and A' in memory I could quickly calculate A'A*x, which is what ARPACK needs. Cheers, Albert