# Re: Oscillating method of integration

From: Lorenzo Moneta <Lorenzo.Moneta_at_cern.ch>
Date: Mon, 28 Aug 2006 11:45:34 +0200

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
>>>>>>
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>>>>>>
>>>>>>
>>>>>
>>>>>
>>>>> +++++++++++++++++++++++++++++++++++++++++++
>>>>> This Mail Was Scanned By Mail-seCure System
>>>>> at the Tel-Aviv University CC.
>>>>>
>>>>
>>>>
>>>>
>>>>
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>>>>
>>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> *********************************************************************
>> ***
>> *******************
>> 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
>>
>>
>>
>>
>>
>>
>
>
>
>
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> <diff7.pdf>
Received on Mon Aug 28 2006 - 11:48:07 MEST

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