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:

   >>> 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 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:

   >>> def f(x):
           return np.cos(x) - x

3. Let's plot this function on the interval (using 1000 samples):

   >>> x = np.linspace(-5, 5, 1000)
       y = f(x)
       fig, ax = plt.subplots(1, 1, figsize=(5, 3))
       ax.axhline(0, color='k')
       ax.plot(x, y)
       ax.set_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...