quant-econ Solutions: SciPy

Solutions for http://quant-econ.net/scipy.html

Exercise 1

Here's a reasonable solution:



In [6]:

    
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
    if upper - lower < tol:
        return 0.5 * (upper + lower)
    else:
        middle = 0.5 * (upper + lower)
        print('Current mid point = {}'.format(middle))
        if f(middle) > 0:   # Implies root is between lower and middle
            bisect(f, lower, middle)
        else:               # Implies root is between middle and upper
            bisect(f, middle, upper)

We can test it as follows



In [8]:

    
import numpy as np
f = lambda x: np.sin(4 * (x - 0.25)) + x + x**20 - 1

bisect(f, 0, 1)









    



Current mid point = 0.5
Current mid point = 0.25
Current mid point = 0.375
Current mid point = 0.4375
Current mid point = 0.40625
Current mid point = 0.421875
Current mid point = 0.4140625
Current mid point = 0.41015625
Current mid point = 0.408203125
Current mid point = 0.4091796875
Current mid point = 0.40869140625
Current mid point = 0.408447265625
Current mid point = 0.408325195312
Current mid point = 0.408264160156



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