Re: Integration

[Mike Marchywka]

On Thu, Mar 05, 2020 at 04:01:16PM +0100, Patrick Dupre wrote:
> 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

I'm not that familiar with gsl but curious about the integral. Just to 
clarify, you have an integrand of the form

h(x)/(1+a*h(x))*exp(-x^2) 

where h happens to be a sum over n Lorentzians that differ only in their
location and h is bounded between 0 and n/g (x=x_0 all the same )  with g>0  ? 

> > 
> > 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
> > > > ===========================================================================
> > > >
> > > >
> > > 
> > > 
> > >
> > 
> >
> 

-- 

mike marchywka
306 charles cox
canton GA 30115
USA, Earth 
address@hidden
404-788-1216
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