Integral Cauchy

ROOT
1

Hi all,
I’m trying to implement a code able to perform numerical integration and to provide the principal value of an integral of a function. Unfortunately, the integration doesn’t work.
In particular, I have this error:

 Error in <GSLError>: Error 21 in qawc.c at 209 : bad integrand behavior found in the integration interval

And the result doesn’t make any sense. Below, the piece of code which performs the integration:

   ROOT::Math::Functor1D F_tobeintegrated(&Function_tobeintegrated);
	  
   ROOT::Math::IntegratorOneDim ig (F_tobeintegrated, ROOT::Math::IntegrationOneDim::kADAPTIVE);
  	
   ig.SetFunction(F_tobeintegrated,false);

   double integral=ig.IntegralCauchy(x_low, x_high, E);;

Is there any error? The sad fact is that I can’t find any example of use of the Cauchy Integral method in root.

2

I think @moneta can help you…

3

Hi,

Did you define correctly the value E and the function f(x) ?

The IntegralCauchy(a, b,c) function computes

$$I = \int_a^b dx f(x) / (x - c) $$

It is true we don’t have an example, but I could make one if you need it

Cheers

Lorenzo

4

It would be great to have an example, if possible!
By the way, yes, I think I’ve correctly defined the value of the pole and the function to integrate but, maybe, with an example I can better understand if my code contains bug which I’m not finding or not.

Cheers,
Grazia

5

By the way the function to be integrated is the following:

f=(((cross_section/(x*(x-E)))-(cross_section/(x*(x+E)))))*sqrt((pow(x,2))-(pow(m_p,2)));

6

Looking at your function only the first part can be computed with IntegralCauchy. The rest you can use the normal Integral function

7

Yes, of course. The problem is that I have the same error even integrating a simple function, for example 1./(x-a), where a is the pole.

8

The integral of the function 1./(x-a) = log(x-a) so it is -infinite, if it contains the pole, so it cannot work.
Attached is a simple dummy example

Cheers

Lorenzo

IntegralCauchy.C (326 Bytes)

9

Yes,this is exactly what I need…to integrate a function within a range in which the pole is contained. So what you tell me is that there is no way to do this with the numerical integration implemented in root?