montecarlo

The MWE below shows two ways of integrating the same 2D kernel density estimate, obtained for this data using the stats.gaussian_kde() function. The integration is performed for all (x, y) below the threshold point (x1, y1) , which defines the upper integration limits (lower integration limits are -infinity ; see MWE). The int1 function uses simple a Monte Carlo approach. The int2 function uses the scipy.integrate.nquad function. The issue is that int1 (ie: the Monte Carlo method) gives systematically larger values for the integral than int2 . I don't know why this happens. Here's an example

So i'm implementing a heuristic algorithm, and i've come across this function. I have an array of 1 to n (0 to n-1 on C, w/e). I want to choose a number of elements i'll copy to another array. Given a parameter y, (0 < y <= 1), i want to have a distribution of numbers whose average is (y * n). That means that whenever i call this function, it gives me a number, between 0 and n, and the average of these numbers is y*n. According to the author, "l" is a random number: 0 < l < n . On my test code its currently generating 0 <= l <= n. And i had the right code, but i'm messing with this for hours

For a program, I need an algorithm to very quickly compute the volume of a solid. This shape is specified by a function that, given a point P(x,y,z), returns 1 if P is a point of the solid and 0 if P is not a point of the solid. I have tried using numpy using the following test: import numpy from scipy.integrate import * def integrand(x,y,z): if x**2. + y**2. + z**2. <=1.: return 1. else: return 0. g=lambda x: -2. f=lambda x: 2. q=lambda x,y: -2. r=lambda x,y: 2. I=tplquad(integrand,-2.,2.,g,f,q,r) print I but it fails giving me the following errors: Warning (from warnings module): File "C: