Date: Sep 9, 2012 4:00 AM
Author: kumar vishwajeet
Subject: Monte Carlo Integration
I am integrating the following function between L and U using dblquad. I get "NaN" and a warning of singularity.

F = real(constantForM.*((x-L).^(A(1)-1).*(y-L).^(A(2)-1).*(U-L-((x-L)+(y-L))).^(A(3)-1)).^2

where, constantForM = 3.378137617443966e-038.

L = 1e-7

U = 3.2e5

A = [3.75 0.25 0.02]

In order to check for singularity, I generated 1e6 points between L and U and evaluated F at each of the points. I get a sharp peak(singularity) at halfway. But the value at that point is still less than 1. In fact the maximum value of F along these points is 0.00116 and minimum is close to zero. Then why do I get NaN??

Another thing:

I used Monte Carlo Integration using the following method:

1. Evaluated F at all 1e6 points.

2. Found the average of all those values.

3. Multiplied by the volume i.e. (U-L)*(U-L).

4. I get 119 as the answer.

Which of these two methods is correct??

Thanks.