Re: [Help-gsl] fixed point or adaptive integration for calculating moments using beta PDF?

[Martin Jansche]

So you want to find E[f] = \int_0^1 f(x) dbeta(x | a, b) dx. Can you plot
your typical f? And what are typical values of the parameters a and b? Do
you encounter a<=1 or b<=1? If so, how does f(x) behave as x approaches 0
or 1?

On Mon, Jan 1, 2018 at 3:37 AM, Patrick Alken <address@hidden> wrote:

> The question is whether your Q contains any singularities, or is highly
> oscillatory? Is such cases fixed point quadrature generally doesn't do
> well. If Q varies fairly smoothly over your interval, you should give
> fixed point quadrature a try and report back if it works well enough for
> your problem. The routines you want are documented here:
>
> http://www.gnu.org/software/gsl/doc/html/integration.html#
> fixed-point-quadratures
>
> Also, if QAGS isn't working well for you, try also the CQUAD routines.
> I've found CQUAD is more robust than QAGS in some cases
>
> On 12/31/2017 05:28 PM, Vasu Jaganath wrote:
> > I have attached my entire betaIntegrand function. It is a bit complicated
> > and very boiler-plate, It's OpenFOAM code (where scalar = double etc.) I
> > hope you can get the jist from it.
> > I can integrate the Q using monte-carlo sampling integration.
> >
> > Q is nothing but tabulated values of p,rho, mu etc. I lookup Q using the
> > object "solver" in the snippet.
> >
> > I have verified evaluating <Q> when I am not using those <Q> values back
> in
> > the solution, It works OK.
> >
> > Please ask me anything if it seems unclear.
> >
> >
> >
> >
> >
> >
> > On Sun, Dec 31, 2017 at 3:55 PM, Martin Jansche <address@hidden>
> wrote:
> >
> >> Can you give a concrete example of a typical function Q?
> >>
> >> On Sat, Dec 30, 2017 at 3:42 AM, Vasu Jaganath <
> address@hidden>
> >> wrote:
> >>
> >>> Hi forum,
> >>>
> >>> I am trying to integrate moments, basically first order moments <Q>,
> i.e.
> >>> averages of some flow fields like temperature, density and mu. I am
> >>> assuming they distributed according to beta-PDF which is parameterized
> on
> >>> variable Z, whose mean and variance i am calculating separately and
> using
> >>> it to define the shape of the beta-PDF, I have a cut off of not using
> the
> >>> beta-PDF when my mean Z value, i.e <Z> is less than a threshold.
> >>>
> >>> I am using qags, the adaptive integration routine to calculate the
> moment
> >>> integral, however I am restricted to threshold of <Z> = 1e-2.
> >>>
> >>> It complains that the integral is too slowly convergent. However
> >>> physically
> >>> my threshold should be around 5e-5 atleast.
> >>>
> >>> I can integrate these moments with threshold upto 5e-6, using
> Monte-Carlo
> >>> integration, by generating random numbers which are beta-distributed.
> >>>
> >>> Should I look into fixed point integration routines? What routines
> would
> >>> you suggest?
> >>>
> >>> Here is the (very simplified) code snippet where, I calculate alpha and
> >>> beta parameter of the PDF
> >>>
> >>>                     zvar   = min(zvar,0.9999*zvar_lim);
> >>>                     alpha = zmean*((zmean*(1 - zmean)/zvar) - 1);
> >>>                     beta = (1 - zmean)*alpha/zmean;
> >>>
> >>>                     // inside the fucntion to be integrated
> >>>                     // lots of boilerplate for Q(x)
> >>>                     f = Q(x) * gsl_ran_beta_pdf(x, alpha, beta);
> >>>
> >>>                    // my integration call
> >>>
> >>>                    helper::gsl_integration_qags (&F, 0, 1, 0, 1e-2,
> 1000,
> >>>                                                   w, &result, &error);
> >>>
> >>> And also, I had to give relative error pretty large, 1e-2. However
> some of
> >>> Qs are pretty big order of 1e6.
> >>>
> >>> Thanks,
> >>> Vasu
> >>>
> >>
>
>
>