Re: Integration

[Patrick Dupre]

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

This is more correct to see it that way
h(x0-x)/(1+a*h(x0-x))*exp(-x^2) 

x0 is a constant
h(x0-x) is a Lorentzian profile (with different "locations")
we can have a sum of h(x) with different x0. This is not the problem
The issue seems to come for the value of g when it is too small
(g is always > 0)

The function is set to 0 when we are far way from the center of the Lorenztian.
The value of the function is always finite.


===========================================================================
 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 4:58 PM
> From: "Mike Marchywka" <address@hidden>
> To: address@hidden
> Subject: Re: Integration
>
> 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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> 
>