- #1

wuliwong

- 9

- 0

One of the main areas that I am having trouble with is using the density function. The density function is p(x) = |f(x)|/int(|f(x)|dx).

This is how I THINK this is supposed to work.

1. Calculate int(|f(x)|dx) using regular Monte-Carlo.

2. Use this result to calculate p(x) = |f(x)|/int(|f(x)|dx).

3. Calculate int((f(x)/p(x))*p(x)dx).

3(a). This integral is represents the first problem for me. I know I am to use p(x) to create a new "mesh" to integrate over, let's call it xp. xp is some function of p(x) and x.

3(b). Another issue I have needs us to now assume I have figured out how to calculate xp. Is the integral in step 3 calculated like this:

int((f(x)/p(x))*p(x)dx) = (1/N)*sum((f_i/g_i)*dxp_i) ?

And finally, assuming that I have learned all of the above and can approximate the integral in 3, how do I extract the original integral I wanted to calculate?

Also, I'm open to other suggestions too. I'm not married to this VEGAS algorithm, not by a long shot.

Thanks in advance.