The mechanics speedup idea is really just a narrow version of the profiling and benchmarking idea (focuses on just a couple of packages). Maybe a proposal that focuses on figuring out the main bottlenecks for sympy, creating benchmarks for them, and then improving performance is a good proposal idea that will ultimately help all the packages. I'm happy to support and mentor on that idea if someone wants to submit.
Jason moorepants.info +01 530-601-9791 On Thu, Mar 14, 2019 at 2:19 PM Aaron Meurer <[email protected]> wrote: > I agree. The biggest challenge with symbolic matrices is expression > blow up. In some cases it is unavoidable, for instance, symbolic > eigenvalues/eigenvectors use the symbolic solutions to polynomials, > which are complicated in the general case for n > 2. > > One thing I meant by "overhead" is that if the type of a matrix's > entries is known to all be rational numbers, for instance, we can > operate directly on those numbers, ideally using fast number types > like gmpy.mpq. If they are all rational functions, we can use > polynomial algorithms that operate on rational functions. These always > keep rational functions in canonical form, and the zero equivalence > testing becomes literally "expr == 0" (no simplification required). > These can be more efficient than general symbolic manipulation. > > This is how the polys module is structured. See > https://docs.sympy.org/latest/modules/polys/internals.html. It would > be nice to have a similar structure in the matrices, where a matrix > can have a ground domain (or type) associated with its underlying > data. > > Aaron Meurer > > On Thu, Mar 14, 2019 at 2:52 PM Oscar Benjamin > <[email protected]> wrote: > > > > (Replying on-list) > > > > On Thu, 14 Mar 2019 at 20:37, Alan Bromborsky <[email protected]> > wrote: > > > > > > Since most pc these days have multiple cores and threads what not use > > > parallel algorithyms. For honesty I must state I have a vested > interest > > > since I have a pc with a threadripper cpu with 16 cores and 32 threads. > > > > Parallel algorithms can offer improvement. Your 16 cores might amount > > to a 10x speed up if used well for this kind of thing. The > > double-threading probably can't be exploited in CPython. > > > > However I think that many of the things that SymPy is slow for have > > *really* bad asymptotic performance: think O(N!) rather than O(N^2). > > Many orders of magnitude improvements can be made by spotting these > > where more efficient methods are possible. It's not hard in a CAS to > > accidentally generate enormous expressions and end up simplifying them > > down again. This leads to many situations where it would be vastly > > more efficient to somehow take a more direct route. > > > > -- > > 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 https://groups.google.com/group/sympy. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAHVvXxTeAGZUv1kdtKCvBRodMZPyX5jHh76G0M49VshwMziJZA%40mail.gmail.com > . > > For more options, visit https://groups.google.com/d/optout. > > -- > 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 https://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAKgW%3D6JGfKjgHP3EaoX%3DXW_SMfnbGOZgi9LLJoUT3Ty7%3Dutd%2BA%40mail.gmail.com > . > For more options, visit https://groups.google.com/d/optout. > -- 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 https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAP7f1AiMm_i%2BJBLBnv3_xzG_8Czag10DWvAUfiAhe-QUzUANiw%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
