Mailman 3 June 2007 - SciPy-User

odeint with digital data
by Ryan Krauss June 4, 2007

June 4, 2007

I have a vector of experimental data that I need to use as part of a system of ode's. I would like to solve this system using integrate.odeint. Can odeint be forced to solve only at the discrete points in time where the experimentally measured signal is available? Or do I need to set up some interpolation function to find the measured signal at any time? If that signal is the only thing that explictly depends on time and I set up a digital look-up table that returns the same constant value for the range from t to t+dt, would I effectively force odeint to do what I want? Am I making any sense? Is there a better way? Thanks, Ryan

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signal processing chapter for book
by Giorgio Luciano June 4, 2007

June 4, 2007

first of all sorry for cross posting As I wrote some time ago we are trying to write a book proposal about the use of python/scipy/numpy in chemometrics and analytical chemistry. Since now I've received positive answer from eight authors and the only "missing" chapter is one about the use of python in digital signal processing (I've contacted some possible authors but since now they are busy). The schedule will not too tight and the chapter doesnt' need to be too long. Hope to hear from you soon Giorgio

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Announcement: VFGEN
by Warren Weckesser June 4, 2007

June 4, 2007

Dear SciPy users: I would like to let the users of the SciPy ODE solvers know about a tool that I have developed called VFGEN. VFGEN is a program that takes a specification of a vector field (in other words, a system of differential equations) and generates source code for a wide variety of ODE solvers and other numerical tools. VFGEN includes a command for generating Python code to be used with the SciPy ODEINT function. You can find the program here: http://math.colgate.edu/~wweckesser/software/vfgen Comments, corrections, and requests for enhancements would all be appreciated. Best regards, Warren Weckesser

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hyp2f1 - bad performance for some values of the argument
by Anne Archibald June 3, 2007

June 3, 2007

On 30/05/07, Anne Archibald <peridot.faceted(a)gmail.com> wrote: > So this is not generally useful, but I have cured my problem through > an application of one of the "quadratic transformations" (equation > 15.3.32 in Abramowitz & Stegun - which is online!). It gives me > accuracies on the order of one part in 10^13, not as good as I was > hoping but better than the 1 in 10^8 I was getting from the averaging > shortcut. Good enough to get positive definite matrices out of it > anyway. Perhaps I spoke too soon. It appears that scipy evaluates hyp2f1 very slowly for certain values of the argument: In [92]: x=0.1; n=1000; m=100; timeit.Timer("hyp2f1(1/2.,1.,3.2,x)",setup="from scipy.special import hyp2f1; from numpy import ones; x=%f*ones(%d)"%(x,m)).timeit(n)/float(n*m) Out[92]: 2.2619605064392088e-06 In [93]: x=0.999; n=1000; m=100; timeit.Timer("hyp2f1(1/2.,1.,3.2,x)",setup="from scipy.special import hyp2f1; from numpy import ones; x=%f*ones(%d)"%(x,m)).timeit(n)/float(n*m) Out[93]: 0.00085240376949310298 (uh, no I don't write real code like this; those numbers are seconds for a single function evaluation. I use the vectorized version because for small x the function-call overhead swamps the evaluation time.) Presumably it works by transforming the function until |x|<1 and then using the series. But the series converges very slowly for |x| close to 1. It is possible to keep transforming the function until |x|<1/2, where the series converges at a respectable speed. Of course these transformations suffer from the same difficulties as the ones used to get |x|<1, namely, they are singular for certain values of the arguments; while there are special-case formulas in A&S for these situations, they do not handle points *near* the singularities (although conceivably a derivative formula could be used there...) Any suggestions on how to efficiently evaluate hyp2f1(0.5,1,a+2,x) for x near 1? It turns out to be the limiting factor for performance of my program (dwarfing the linear algebra on 300 by 300 matrices). Thanks, Anne M. Archibald

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