Based on the tests you posted it seems like Gauss-Hermite fills the capability CM was missing of doing one class of improper integrals.
However, the infinite class would have allowed integration from [-Inf, C!=0]. Can you manage that with Gauss Hermite? So, given this development, I'm not particularly motivated to develop AQ further. I'll get back if I hit a "high frequency" function to bother with it. However, if you chose to adapt the code I provided note that it: 1) avoids using recursive function calls, so you stack size is not a constraint as implementations typically do. 2) it uses Simpson's rule, but you should be able to swap in other quadrature rules. Cheers, Ajo On Sun, Jul 21, 2013 at 5:16 PM, Gilles <gil...@harfang.homelinux.org>wrote: > On Sun, 21 Jul 2013 08:04:05 -0700, Ajo Fod wrote: > >> [...] >> >> >> Here is some numerical analysis on the issue: >> >> Laguerre is defined only in [0,+ve Inf] >> Hermite is defined in [-Inf,+Inf] >> >> I have two issues with the above: >> 1: Cant imagine how someone would use AQ. Which means as Gilles noticed, >> you can't focus on the hard to converge sections of the integral. >> 2: If you use the integration without AQ. Any function that has a high >> frequency region somewhere off the region where the polynomial focuses, >> the >> integral probably won't converge. For Hermite with its weighting in >> e^(-x^2) ... good luck with convergence with say computing CDF of N(0,100) >> or for that matter N(100,1). >> > > I'm afraid that these are counter-examples to your suppositions. > Please have a look at > > https://issues.apache.org/**jira/browse/MATH-997<https://issues.apache.org/jira/browse/MATH-997> > > > > For an idea look at : >> https://en.wikipedia.org/wiki/**Gauss%E2%80%93Hermite_**quadrature<https://en.wikipedia.org/wiki/Gauss%E2%80%93Hermite_quadrature> >> >> > Look at what, precisely? > > > > Regards, > Gilles > > > ------------------------------**------------------------------**--------- > To unsubscribe, e-mail: > dev-unsubscribe@commons.**apache.org<dev-unsubscr...@commons.apache.org> > For additional commands, e-mail: dev-h...@commons.apache.org > >
