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 >
