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

[Vasu Jaganath]

HI Martin, Yes one of my Q is very discontinuous with respect to my
integration variable Z.

I have attached the plots for you to see

On Sun, Dec 31, 2017 at 9:20 PM, Vasu Jaganath <address@hidden>
wrote:

> Yes, I will show you the plots soon, Q is actually 2 variable function but
> for my calculations I am treating one of the variables as a parameter,
> which is a physically valid assumption. Yes I do encounter alpha and beta
> values less than 1.
>
> On Sun, Dec 31, 2017, 9:13 PM Martin Jansche <address@hidden> wrote:
>
>> 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
>> > >>>
>> > >>
>> >
>> >
>> >
>>
>

discontinuity.zip
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