From: <andreyk1_at_post.tau.ac.il>

Date: Tue, 29 Aug 2006 11:58:24 +0300

This message was sent using IMP, the Internet Messaging Program. Received on Tue Aug 29 2006 - 10:58:56 MEST

Date: Tue, 29 Aug 2006 11:58:24 +0300

Hi Lorenzo,

Your method is very clever (change variables), but it (IntegralMultiple) behaves very strange. I wanted to check whether the integration is stable, so I changed the number of iteration (max_p) from 1e+4 to 1e+7. After max_p = 1e+6 the answer start appearing as "inf"......very unexpected...

Andrew.

Quoting Lorenzo Moneta <Lorenzo.Moneta_at_cern.ch>:

*> Hi Andrew,*

*>*

*> your integral, as you have written the attached pdf page, it should*

*> converge.*

*> When you use IntegralMultiple, have you tried changing the*

*> integration variable from (0,inf) to (0,1) transforming x -> t with*

*> x = (1-t)/t ?*

*>*

*> Otherwise an alternative for you could be to use Monte Carlo*

*> integration.*

*> In ROOT you can do using FOAM to sample randomly your function,*

*>*

*> Best Regards,*

*>*

*> Lorenzo*

*> On Aug 26, 2006, at 1:11 PM, andreyk1_at_post.tau.ac.il wrote:*

*>*

*> > Hi Lorenzo and George,*

*> >*

*> > Well, in order to avoid all misunderstandings, I attached here the*

*> > exact function I need to calculate. Everything inside the PDF file.*

*> > I will be glad for every solution you can suggest.*

*> >*

*> > Sincerely,*

*> > Andrew.*

*> >*

*> >> Quoting George Japaridze <george.japaridze_at_gmail.com>:*

*> >*

*> >> Hi,*

*> >>*

*> >> Lorenzo's right, the integral*

*> >>*

*> >> \int^{infinity}_{0} dx \int^{\infinity}_{0} dy J_{0}(x*y)*

*> >>*

*> >> is equal to one dimensional integral*

*> >>*

*> >> 2* \int^{\pi}_{0} dx/sin(x)*

*> >>*

*> >> which does not exists as an ordinary function - can be redefined as a*

*> >> generalized function (distribution).*

*> >> Depends on a specifics of the problem and are you or are you not*

*> >> allowed to use regularization.*

*> >>*

*> >> Cheers,*

*> >>*

*> >> George*

*> >> On Aug 25, 2006, at 9:50 AM, Lorenzo Moneta wrote:*

*> >>*

*> >>> Hi Andrew,*

*> >>>*

*> >>> actually I noticed now you want the integral between 0 and inf.*

*> >>> This is undefined, it is like getting the value of sin(x) for*

*> >>> x=inf.*

*> >>>*

*> >>> Best Regards,*

*> >>> Lorenzo*

*> >>>*

*> >>>*

*> >>> On Aug 25, 2006, at 12:49 PM, andreyk1_at_post.tau.ac.il wrote:*

*> >>>*

*> >>>> Dear Lorenzo,*

*> >>>>*

*> >>>> Thanks for solution, but this is not my case. The integral is too*

*> >>>> complicated to*

*> >>>> be done analitically. The only way is numerical calculation.*

*> >>>> Actually I can*

*> >>>> integrate between BesselJ zeroes and sum up these intervals, but*

*> >>>> it is not*

*> >>>> efficient.*

*> >>>>*

*> >>>> Andrew.*

*> >>>>*

*> >>>> Quoting Lorenzo Moneta <Lorenzo.Moneta_at_cern.ch>:*

*> >>>>*

*> >>>>> Hi Andrew,*

*> >>>>>*

*> >>>>> I don't know of a method for 2d with oscillatory function.*

*> >>>>> Hower, you should be able for a Bessel of order 0 to solve the*

*> >>>>> integral analytically,*

*> >>>>> using the Bessel J0 definition*

*> >>>>>*

*> >>>>> see http://en.wikipedia.org/wiki/Bessel_function*

*> >>>>>*

*> >>>>> Cheers,*

*> >>>>>*

*> >>>>> Lorenzo*

*> >>>>> On 24 Aug 2006, at 12:14, andreyk1_at_post.tau.ac.il wrote:*

*> >>>>>*

*> >>>>>>*

*> >>>>>>*

*> >>>>>> Dear rooters,*

*> >>>>>>*

*> >>>>>> I need to integrate over two dimensionl oscillating function*

*> >>>>>> (TMath::BesselJ(0,x*y), 0<x<inf, 0<y<inf). I use TF1 with*

*> >>>>>> IntegralMultiple, but*

*> >>>>>> the answer is not stable, a change in max_points leads to a*

*> >>>>>> different result. I*

*> >>>>>> tried to increas the number of max_points to 1e+6 but the*

*> >>>>>> result is*

*> >>>>>> still*

*> >>>>>> unstable. Is there some method of integrating over oscillating*

*> >>>>>> function with*

*> >>>>>> arbitry dimensions? (in my case it is dim = 2).*

*> >>>>>>*

*> >>>>>>*

*> >>>>>> Thanks a lot!*

*> >>>>>>*

*> >>>>>>*

*> >>>>>> Andrew*

*> >>>>>>*

*> >>>>>> ----------------------------------------------------------------*

*> >>>>>> This message was sent using IMP, the Internet Messaging Program.*

*> >>>>>>*

*> >>>>>>*

*> >>>>>*

*> >>>>>*

*> >>>>> +++++++++++++++++++++++++++++++++++++++++++*

*> >>>>> This Mail Was Scanned By Mail-seCure System*

*> >>>>> at the Tel-Aviv University CC.*

*> >>>>>*

*> >>>>*

*> >>>>*

*> >>>>*

*> >>>>*

*> >>>> ----------------------------------------------------------------*

*> >>>> This message was sent using IMP, the Internet Messaging Program.*

*> >>>>*

*> >>>*

*> >>*

*> >>*

*> >>*

*> >>*

*> >>*

*> >>*

*> >>*

*> >>*

*> >>*

*> >>*

*> >>*

*> >>*

*> >> **********************************************************************

*> >> ****

*> >> ********************

*> >> Dr. George Japaridze CTSPS, Clark*

*> >> Atlanta University*

*> >>*

*> >> japar_at_ctsps.cau.edu 404 880 6420*

*> >> Office*

*> >> http://www.robotics.cau.edu/people/japar404 226 3847 Cell*

*> >>*

*> >>*

*> >>*

*> >>*

*> >>*

*> >>*

*> >*

*> >*

*> >*

*> >*

*> > ----------------------------------------------------------------*

*> > This message was sent using IMP, the Internet Messaging Program.*

*> > <diff7.pdf>*

*>*

*>*

*> +++++++++++++++++++++++++++++++++++++++++++*

*> This Mail Was Scanned By Mail-seCure System*

*> at the Tel-Aviv University CC.*

*>*

This message was sent using IMP, the Internet Messaging Program. Received on Tue Aug 29 2006 - 10:58:56 MEST

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