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## Re: [Help-gsl] fixed point or adaptive integration for calculating momen

 From: Martin Jansche Subject: Re: [Help-gsl] fixed point or adaptive integration for calculating moments using beta PDF? Date: Sun, 31 Dec 2017 22:55:10 +0000

```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
>

```

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