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Re: Integration


From: Patrick Dupre
Subject: Re: Integration
Date: Thu, 5 Mar 2020 15:48:07 +0100

Hello,

Thank for the suggestions.

However, here is the problem.
The "singularities" at x=x0 I guess.
If I use QAGP and I provide the singular points, then I get:
Error during integration: 7168.4707442 (420) integral or series is divergent

If I use gsl_integration_cquad
there is not error, but I get a wrong value at one of the "singularities"

Then I do not see any solution.

For the interval, I can calculate the limits. It is not an issue for now.
The behavior is the same, what ever is the values are.

===========================================================================
 Patrick DUPRÉ                                 | | email: address@hidden
 Laboratoire interdisciplinaire Carnot de Bourgogne
 9 Avenue Alain Savary, BP 47870, 21078 DIJON Cedex FRANCE
 Tel: +33 (0)380395988
===========================================================================


> Sent: Thursday, March 05, 2020 at 2:49 PM
> From: "Patrick Alken" <address@hidden>
> To: address@hidden
> Subject: Re: Integration
>
> Hello, did you try transforming the integral to have finite limits (i.e.
> https://www.youtube.com/watch?v=fkxAlCfZ67E). Once you have it in this
> form, I would suggest trying the CQUAD algorithm:
> 
> https://www.gnu.org/software/gsl/doc/html/integration.html#cquad-doubly-adaptive-integration
> 
> Patrick
> 
> On 3/5/20 2:02 AM, Patrick Dupre wrote:
> > Hello,
> >
> >
> > Can I collect your suggestions:
> >
> > I need to make the following integration:
> >
> > int_a^b g(x) f(x) dx
> >
> > where a can be 0 of -infinity, and b +infinity
> > g(x) is a Gaussian function
> > f(x) = sum (1/((x-x0)^2 + g)) / (1 + S* sum (1 / ((x-x0)^2 + g)))
> >
> > Typically, f(x) is a fraction whose numerator is a sum of Lorentzians
> > and the denominator is 1 + the same sum of Lorentzians weighted by a factor.
> >
> > Thank for your suggestions
> >
> > ===========================================================================
> >  Patrick DUPRÉ                                 | | email: address@hidden
> >  Laboratoire interdisciplinaire Carnot de Bourgogne
> >  9 Avenue Alain Savary, BP 47870, 21078 DIJON Cedex FRANCE
> >  Tel: +33 (0)380395988
> > ===========================================================================
> >
> >
> 
> 
>



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