On 03-27-2011, at 4:51 PM, Aaron S. Meurer wrote: > Well, I was under the impression that some numerical sparse data structures > used some kind of compression scheme that cannot be extended to symbolic > matrices. This is just from what I have heard, though. >
I know quite a bit about numerical methods for sparse linear algebra. The different storage methods (data structures) are just different ways of storing and therefore accessing the non-zero entries in the sparse matrix. > The algorithms have to do with numerical stability. An algorithm that is > best for numerical stability with floating point numbers might not be the > best algorithm to prevent expression explosion with symbolic matrices. The > algorithms are important, because they will have to be implemented along with > the sparse matrices (or else the implementation will be useless), and also > the algorithm chosen might depend on the data structure chosen (this is all > very abstract, but it's just some things to keep in mind). > Very true. Methods that eliminate entries in a numerical situation might cause the symbolic case to just add new non-zero entries and add terms to existing entries (I've seen this happen). So, care has to be taken in algorithms for sparse symbolic matrices. That said, a good sparse matrix implementation is needed for good handling of larger symbolic matrices. Cheers, Tim. --- Tim Lahey PhD Candidate, Systems Design Engineering University of Waterloo http://about.me/tjlahey -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
