Re: Quite Upset with NIntegrate
- To: mathgroup at smc.vnet.net
- Subject: [mg54275] Re: Quite Upset with NIntegrate
- From: Ismail Turan <ituran at bohr.concordia.ca>
- Date: Wed, 16 Feb 2005 14:35:55 -0500 (EST)
- References: <42120FED.60501@wolfram.com>
- Sender: owner-wri-mathgroup at wolfram.com
Dear Anton, Thank you for your interest. I am attaching the sample file that has only the integrand and the limits even though everything was carried out with Mathematica. Below I would like to respond to your questions/remarks separately. [contact the author to get the attachment - moderator] On Tue, 15 Feb 2005, Anton Antonov wrote: > Dear Ismail Turan, > > As some of the guys in the forum mentioned, it is difficult to answer your question > without more detailed information. > > Some questions/remarks: > > 1. From what field this integral comes from? It is from high energy physics. I am calculating the branching ratio of a particle decaying into three particles two of which are off-shell so that it doubles my phase space from 2 to 4-dimension. > 2. How you have entered the integrand in Mathematica? Have you imported it > from, say, a FORTRAN file? I did everything with Mathematica regardless of the warnings of my colleagues about the questionable capability of Mathematica in numerical integrations(for higher dimensions especially). > 3. Have you tested are your integrand and boundaries of integration correctly implemented? The integrand is checked especially in 2-dimension as a limit of 4-dimensional case and there is a full agreement with the literature results. The modification coming to the integrand in 4-dimension is to multipy it by two density functions which reduce to Dirac-Delta functions in 2-dimensional limit. In addition to that, the limits in 4-dim are modified quite simply as far as physics is concerned. > 4. Using MaxPoints invokes the MonteCarlo method. > You might try QuasiMonteCarlo method -- it is as fast as MonteCarlo, > and has more deterministic nature. I tried what you have suggested here and I got the same data points when I set MaxPoints to somevalue but leave the "Method" option "Automatic". > 5. The default option settings in NIntegrate invoke the MultiDimensional integration method. > You might try using a Cartesian rule method with Method->GaussKronrod. This made the process very slow. I haven't been able to get one data point so far (within aproximately five hours). Thank you very much again. I really appreciate all the help. Best Regards,