Re: Quite Upset with NIntegrate

• To: mathgroup at smc.vnet.net
• Subject: [mg54286] Re: Quite Upset with NIntegrate
• From: Anton Antonov <antonov at wolfram.com>
• Date: Wed, 16 Feb 2005 14:36:04 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```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?
2. How you have entered the integrand in Mathematica? Have you imported it
from, say, a FORTRAN file?
3. Have you tested are your integrand and boundaries of integration correctly implemented?
4. Using MaxPoints invokes the MonteCarlo method.
You might try QuasiMonteCarlo method -- it is as fast as MonteCarlo,
and has more deterministic nature.
5. The default option settings in NIntegrate invoke the MultiDimensional integration method.
You might try using a Cartesian rule method with Method->GaussKronrod.

Also, you can send me your notebook, and I will look at it.

Best regards,
Anton Antonov
Wolfram Research, Inc.

> Dear Yehuda,
>
> [Attachments like the Sample.nb below are not permitted.  Contact
> the author to obtain it - moderator]
>
> It is kind of hard to show the details here but I am enclosing the
> Sample.nb file (hopefully you will get it) including a slightly simplified
> integrand (I have much more complicated integrands). When I integrate "in"
> with using default options of NIntegrate, I am getting the following data
> points :
>
>                  -12            -38
> 150    9.58287 10    + 1.4816 10    I
>                 -11             -58
> 152    8.1392 10    + 2.82326 10    I
>                  -11            -53
> 154    2.02365 10    + 1.1625 10    I
>                  -6             -58
> 156    1.05475 10   + 2.71146 10    I
>                  -12             -39
> 158    6.94259 10    + 1.63694 10    I
>                  -12             -53
> 160    5.42794 10    + 6.25923 10    I
>                  -11             -39
> 162    1.02786 10    + 1.63133 10    I
>                  -11             -39
> 164    4.53046 10    + 2.37653 10    I
>                  -12             -59
> 166    9.44247 10    + 4.01258 10    I
>                 -11             -40
> 168    4.8126 10    + 3.48983 10    I
>                  -10             -40
> 170    3.71222 10    + 3.94167 10    I
>
> Here the first column is the varying parameter (mt) and the full range of
> it is from 150 to 200 but I only include part of the data points.
>
> The behavior of the curve is certainly expected to increase smoothly as
> "mt" increases. Obviously, there is no such pattern here. Setting
> MaxPoints something like 500000 (I checked that at least I need to set it
> 10 times bigger to be sure that data points are accurate enough
> but this will increase process time enormously) makes the above values
> better looking but still far from being accaptable. So, What is wrong
> here?
>
> Thanks,
>
> ismail
>
>
>
> On Sat, 12 Feb 2005, yehuda ben-shimol wrote:
>
> > It is difficult to comment without seeing the details. Is there any
> > way we can see it?
> > yehuda
>
> > On Fri, 11 Feb 2005 03:34:40 -0500 (EST), I. Turan
> > <ituran at bohr.concordia.ca> wrote:
> > > Hi:
> > >
> > > I have been trying to evaluate a 4-dimensional integral by using
> > > NIntegrate with Mathematica 4 w2k.  The integrand and even the
> > > integration limits are quite complicated (depending on int.
> > > variables). The length of the integrand is around 2000 lines in the
> > > FortranForm.
> > >
> > > If I don't play with any options of NIntegrate, It takes one day to
> > > get one data point and gives very  unreasonably weird values. By
> > > setting, however, MaxPoints something like 100000 it is possible to
> > > get faster results but still it seems that Mathematica couldn't handle
> > > it. When I draw a figure from these data points, it appears very very
> > > spiky such that it is even not possible to fit the curve. However, it
> > > is supposed to be very smooth.
> > >
> > > Should I accept that Mathematica can not handle such a
> > > numerical integration or is there a way to make Nintegrate working
> > > better?
> > >
> > > Thanks a lot,
> > >
> > > Ismail
> > >
> > >
> >

```

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