# Python Course homework 5

### Exercise 1

Previously we discussed the concept of recursive function calls

Write a recursive implementation of the bisection function described above, which we repeat here for convenience

def bisect(f, a, b, tol=10e-5):
"""
Implements the bisection root finding algorithm, assuming that f is a
real-valued function on [a, b] satisfying f(a) < 0 < f(b).
"""
lower, upper = a, b

while upper - lower > tol:
middle = 0.5 * (upper + lower)
# === if root is between lower and middle === #
if f(middle) > 0:
lower, upper = lower, middle
# === if root is between middle and upper  === #
else:
lower, upper = middle, upper

return 0.5 * (upper + lower)

Test it on the function f = lambda x: np.sin(4 * (x - 0.25)) + x + x**20 - 1 discussed above

import numpy as np

def bisect(f, a, b, tol=10e-5):
"""
Implements the bisection root finding algorithm, assuming that f is a
real-valued function on [a, b] satisfying f(a) < 0 < f(b).
"""
lower, upper = a, b

while upper - lower > tol:
middle = 0.5 * (upper + lower)
# === if root is between lower and middle === #
if f(middle) > 0:
lower, upper = lower, middle
# === if root is between middle and upper  === #
else:
lower, upper = middle, upper

return 0.5 * (upper + lower)
f = lambda x: np.sin(4 * (x - 0.25)) + x + x**20 - 1
a,b = 1,20
result = bisect(f,a,b,tol=10e-5)
print(result)

Result

1.0000362396240234