This is a template for working on Exercise 1 of Section 1.1, Root Finding by Interval Halving
Create a Python function bisection1 which implements the first algorithm for bisection, performing a fixed number iterations of iterations.
(The iteration count was called $N$ in the mathematical description, but in code it is encouraged to use descriptive names.)
The usage will be:
root = bisection1(f, a, b, iterations)
Test it with the example: $f(x) = x - \cos x = 0$, $[a, b] = [-1, 1]$
# We will often need resources from the modules numpy and pyplot:
import numpy as np
import matplotlib.pyplot as plt
# We can also import items from a module individually, so they can be used by "first name only".
# This will often be done for mathematical functions.
from numpy import cos
def bisection1(f, a, b, iterations):
"""
This is a "stub": it functions in that it is "syntactically correct",
but does not do the right thing.
Instead it gives the best available answer without having done any real work!
Inputs:
f: a continuous function from and to real values
a: to be continued ...
"""
root=(a+b)/2
return root
Aside: look what the function help does:
help(bisection1)
Help on function bisection1 in module __main__:
bisection1(f, a, b, iterations)
This is a "stub": it functions in that it is "syntactically correct",
but does not do the right thing.
Inputs:
f: a continuous function from and to real values
a: to be continued ...
Now test this, by first defining the needed inputs f, a, b and the iteration count iterations ...