Integration Exercise 3

Imports


In [1]:
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
from scipy import integrate

2d polar integration

The 2d polar integral of a scalar function $f(r, \theta)$ is defined as:

$$ I(r_{max}) = \int_0^{r_{max}} \int_0^{2\pi} f(r, \theta) r d\theta $$

Write a function integrate_polar(f, rmax) that performs this integral numerically using scipy.integrate.dblquad.


In [33]:
def integrate_polar(f, rmax):
    """Integrate the function f(r, theta) over r=[0,rmax], theta=[0,2*np.pi]"""
    func = lambda r,t:f(r,t)*r
    I, e = integrate.dblquad(func, 0, 2*np.pi, lambda r:0, lambda r:rmax)
    print(I)
    return I

In [35]:
assert np.allclose(integrate_polar(lambda r,t: 1, 1.0), np.pi)
assert np.allclose(integrate_polar(lambda r, t: np.exp(-r)*(np.cos(t)**2), np.inf), np.pi)


3.141592653589793
3.141592653589792

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