Hmmm, it appears I picked a bad example there (correct me if I'm wrong, I've never taken a CS class). Cholesky decomp is twice as fast as LU, which isn't an order of magnitude difference. For large n, this can be important though. A better example may be using `together` on factorable polynomials. We could print out code for the expanded form of (x + a1)*(x + a2)*...*(x + an), or we could factor it, and reduce the number of operations significantly.
On Thu, Sep 18, 2014 at 6:03 PM, James Crist <crist...@umn.edu> wrote: > Oh hey, that's kinda neat. > > On one of the slides you mention that by generating equations symbolically >> you can change change algorithmic complexity. Can you give an example of >> this? > > > That hasn't happened yet, but is planned. Mostly, it has to do with the > idea that in SymPy we have knowledge about the properties of the > computations. We know if a variable is always positive, or real, or (most > importantly) the properties of a matrix (upper triangular, symmetric, > positive definite, etc...). For selecting matrix solving routines, this is > important. Based on Matthew's talk at SciPy a few years back. This is a > long way off, but should be achievable. > > In the immediate future we can start applying transformations to the > expressions to improve computation speed (not an order of complexity > change, but still speed improvements). Horner's method is already part of > sympy, and could be applied to polynomials by default to reduce the number > of flops needed to compute. We can also apply CSE at a much higher level > than gcc will, which is necessary for some of the large expressions that > are computed in mechanics. > > -Jim > > On Thursday, September 18, 2014 1:33:48 PM UTC-5, Aaron Meurer wrote: >> >> They are good slides. Good job Jim. >> >> On one of the slides you mention that by generating equations >> symbolically you can change change algorithmic complexity. Can you give an >> example of this? >> >> Aaron Meurer >> >> On Thu, Sep 18, 2014 at 1:29 PM, Jason Moore <moore...@gmail.com> wrote: >> >>> Jim's slides on SymPy code gen got into the Python weekly. >>> >>> Jason >>> moorepants.info >>> +01 530-601-9791 >>> >>> ---------- Forwarded message ---------- >>> From: Python Weekly <ra...@pythonweekly.com> >>> Date: Thu, Sep 18, 2014 at 11:06 AM >>> Subject: Python Weekly - Issue 157 >>> To: moore...@gmail.com >>> >>> >>> Email not displaying correctly? View it in your browser. >>> <http://us2.campaign-archive1.com/?u=e2e180baf855ac797ef407fc7&id=ce99590cba&e=c9acab854b> >>> Welcome to issue 157 of Python Weekly. Another packed issue this >>> week. 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