Question

Assume the following function:

f(x) = x * cos(x-4)

With x = [-2.5, 2.5] this function crosses 0 at f(0) = 0 and f(-0.71238898) = 0.

This was determined with the following code:

import math
from scipy.optimize import fsolve
def func(x):
    return x*math.cos(x-4)
x0 = fsolve(func, 0.0)
# returns [0.]
x0 = fsolve(func, -0.75)
# returns [-0.71238898]

What is the proper way to use fzero (or any other Python root finder) to find both roots in one call? Is there a different scipy function that does this?

fzero reference

Answer 1

Define your function so that it can take either a scalar or a numpy array as an argument:

>>> import numpy as np
>>> f = lambda x : x * np.cos(x-4)

Then pass a vector of arguments to fsolve.

>>> x = np.array([0.0, -0.75])
>>> fsolve(f,x)
array([ 0.        , -0.71238898])