Method for performing numpy vectorized integration of a function over a discrete range, at several points.

gistfile1.py

import numpy as np

def cellAverageIntegrator1D(f, x0, dx, N=10):
    """
    This function calculates the integral of a given (numpy vectorized)
    function f over the interval [x0-dx/2., x0+dx/2.]. The number of discrete
    points may be set using N.

    The argument x0 may be a numpy array of discrete points (e.g. cell-centers)
    to evaluate the integral. Because everything is vectorized this function
    executes very fast.
    """
    x = x0 + np.outer(np.linspace(-dx/2., +dx/2., N), np.ones((len(x0),)))

    return np.sum(f(x), axis=0)/N


if __name__ == "__main__":
    # 1D test
    f = np.sin
    dx = 0.1
    x0 = np.array([0.3, 0.4, 0.5])

    F = lambda x: (np.cos(x-dx/2.) - np.cos(x+dx/2.))/dx

    for N in [2**n for n in range(20)]:
        F_int = cellAverageIntegrator1D(f=f, x0=x0, dx=dx, N=N)
        print N, F_int - F(x0), f(x0) - F(x0)