"""
Ex. A.10 from "A primer on..."
Implement the secant method. 
"""

import numpy as np
import matplotlib.pyplot as plt

def secant(f, x0, x1, tol=1e-6):
    n = 0
    while abs(f(x1)) > tol:
        x2 = x1 - f(x1) * (x1 - x0) / (f(x1) - f(x0))
        x0 = x1   #x_{n-1} => x_{n-2}
        x1 = x2   #x_n => x_{n-1}
        n += 1
    return x2, n

#solve x**5 - sin(x) = 0:
def g(x):
    return x**5 - np.sin(x)

x = secant(g, 1.5, 1.4)
print(x)