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 <[email protected]> wrote: > >> Can you give a concrete example of a typical function Q? >> >> On Sat, Dec 30, 2017 at 3:42 AM, Vasu Jaganath <[email protected]> >> 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 >>> >>
