On Sun, Mar 27, 2011 at 11:51 PM, Aaron S. Meurer <[email protected]> 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.
Nope. > > 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). Algorithms can be unstable no matter what representation of the numbers that are used, numerical algorithms are just particularly susceptible to stability problems because their numbers are inexact. Its not stability that makes numerical algorithms terrible for symbolics but rather the in place iterations that tend to expand symbolics. -- Andy > > Aaron Meurer > > On Mar 27, 2011, at 2:42 PM, Andy Ray Terrel wrote: > >> Aaron, >> >> I don't understand your comment. The storage of a sparse matrix has >> nothing to do with the types being stored. Everything is still exact >> and has nothing at all to do with numerical stability. Algorithms are >> about stability (even in symbolics), storage is about space and >> access. >> >> -- Andy >> >> On Sun, Mar 27, 2011 at 10:54 PM, Aaron S. Meurer <[email protected]> wrote: >>> Remember that SymPy's matrices store symbolic expressions, or at least >>> exact numerical expressions (rational numbers). Therefore, some of the >>> sparse schemes won't work in SymPy, and the goals can be different too (for >>> example, we are more concerned about symbolic expression explosion than >>> with numerical stability). >>> >>> Aaron Meurer >>> >>> On Mar 27, 2011, at 12:39 AM, Andy Ray Terrel wrote: >>> >>>> Hello Frank, >>>> >>>> We would be happy to get your application! There are about as many >>>> Sparse Matrix storage algorithms as there are stars in the sky. I >>>> think a good place to look at the common storage types is at scipy's >>>> sparse matrix reference [0]. It would be good to have a similar >>>> structure where there are several storage schemes, mostly because >>>> different algorithms with different storage formats. Hope that helps >>>> a bit. >>>> >>>> -- Andy >>>> >>>> [0] http://docs.scipy.org/doc/scipy/reference/sparse.html >>>> >>>> On Sun, Mar 27, 2011 at 5:42 AM, Frank K. <[email protected]> wrote: >>>>> Hello all! My name is Frank Kreimendahl and I'm just finishing up my >>>>> first year as a computer science graduate student at the University of >>>>> New Hampshire. My undergraduate degree was in mathematics, but >>>>> somewhere along the line I decided I like staring at a terminal >>>>> slightly more than at a piece of paper. >>>>> >>>>> Last fall, I saw a member of Matlab's matrix team talk about sparse >>>>> matrix optimizations, which got me quite excited about the subject. I >>>>> read some discussions then on implementations and improvements to >>>>> allow for small memory footprints without impacting runtime speeds. I >>>>> am happy to see that the same subject appeared on the project list! I >>>>> will certainly be reading more to put together a proposal for Google's >>>>> Summer of Code. If anyone has any previous experience or >>>>> recommendations for sparse matrix information, please let me know. >>>>> >>>>> >>>>> I will be hanging out in the chat room (as ylfchild) so feel free to >>>>> smother me with advice there. I'll probably be asking all sorts of >>>>> questions about git, since I've only had a cursory introduction to it >>>>> so far. >>>>> >>>>> -- >>>>> 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. >>>>> >>>>> >>>> >>>> -- >>>> 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. >>>> >>> >>> -- >>> 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. >>> >>> > > -- 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.
