Re: Integration

[Patrick Dupre]

I also can get roundoff error
with QAGP

===========================================================================
 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 3:48 PM
> From: "Patrick Dupre" <address@hidden>
> To: "Patrick Alken" <address@hidden>
> Cc: address@hidden
> Subject: Re: Integration
>
> 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
> > > ===========================================================================
> > >
> > >
> > 
> > 
> >
> 
>