Hi Peter, On Fri, Apr 25, 2014 at 11:35 AM, Peter Brady <[email protected]> wrote: > So I start with two sparse matrices, L, and R each with data on just a few > bands (ie 3 to 5) > > My goal is compute the largest and smallest eigenvalues of the matrix A > given by: > > A = -c*(L^-1*R)+d*(L^-1*R)**2 where c and d are constants > > In my code this is written as: > > L = SparseMatrix(...) > R = SparseMatrix(...) > > B = L.inv()*R > > A = np.array(-c*B+d*B**2).astype('double') > > I can then use scipy/ARPACK to get the values I want. If I convert L,R or B > to numpy arrays before computing A, I get crappy eigenvalues so this has to > be done symbolically. My problem is that while computing B is manageable > for the matrices I'm interested (from 20x20 to 160x160), computing A takes > about 5 minutes and eats up a 15-30% of my memory so I need to run this in > serial. In contrast, if I convert B to a numpy array, it takes < 1s to > compute A (although it is the wrong A, so it's essentially worthless).
Can you post code that does the above? You can use gist: https://gist.github.com/ or IPython notebook or whatever you prefer. Essentialy doing L.inv() means you can't use Lapack, because the condition number will be bad. But I wonder if there is a way to rewrite the problem without doing L.inv(), possibly using some generalized eigenvalue problem or something, so that you can still use Lapack. It's always good to do solid numerics, it's faster, you can use Fortran and so on. But a separate issue is how to do this symbolically, and SymPy should have the best algorithms. I need to play with your code to get better opinion how to speed this up. > Is there some way to speed this up and/or reduce the memory footprint? > Ideally, I would like to run hundreds (maybe thousands) of different cases. > I'm fine with installing the necessary libraries on my machine (linux). Perfect. This might be another great application for CSymPy. We are implementing the matrix support this summer as part of GSoC. Ondrej -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CADDwiVC%2B5J-qg%3DOQAwEFBzpajS8mRtio7tFGyxbWByDyc23hvg%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
