Finding the root of a mathematical function

In this short recipe, we will see how to use SciPy to find the root of a simple mathematical function of a single real variable.

How to do it…

1. Let's import NumPy, SciPy, scipy.optimize, and matplotlib:

   In [1]: import numpy as np
           import scipy as sp
           import scipy.optimize as opt
           import matplotlib.pyplot as plt
           %matplotlib inline

2. We define the mathematical function f(x)=cos(x)-x in Python. We will try to find a root of this function numerically. Here, a root corresponds to a fixed point of the cosine function:

   In [2]: f = lambda x: np.cos(x) - x

3. Let's plot this function on the interval [-5, 5] (using 1000 samples):

   In [3]: x = np.linspace(-5, 5, 1000)
           y = f(x)
           plt.plot(x, y)
           plt.axhline(0, color='k')
           plt.xlim(-5,5)

   

4. We see that this function has a unique root on this interval (this is because the function's sign changes on this interval). The scipy.optimize module contains a few root-finding functions...