Using scipy.integrate.quad to perform 3D integral

Question

Motivation for the question

I\'m trying to integrate a function f(x,y,z) over all space.

I have tried using scipy.integrate.tplquad & scipy.integrate.nquad

Answer 1

Here is an example with nested call to quad performing the integration giving 1/8th of the sphere volume:

import numpy as np
from scipy.integrate import quad

def fz(x, y):
    return quad( lambda z:1, 0, np.sqrt(x**2+y**2) )[0]

def fy(x):
    return quad( fz, 0, np.sqrt(1-x**2), args=(x, ) )[0]

def fx():
    return quad( fy, 0, 1 )[0]

fx()
>>> 0.5235987755981053

4/3*np.pi/8
>>> 0.5235987755982988

Answer 2

I'm trying to integrate a function f(x,y,z) over all space.

First of all you'll have to ask yourself why the integral should converge at all. Does it have a factor exp(-r) or exp(-r^2)? In both of these cases, quadpy (a project of mine has something for you), e.g.,

import quadpy

scheme = quadpy.e3r2.stroud_secrest_10a()
val = scheme.integrate(lambda x: x[0]**2)
print(val)

2.784163998415853