## Exercise for the course Python for MATLAB users, by Olivier Verdier¶

In [1]:
%pylab
%matplotlib inline

Using matplotlib backend: MacOSX
Populating the interactive namespace from numpy and matplotlib


A continuous functions $f$ which changes its sign in an interval $[a,b]$, i.e. $f(a)f(b)< 0$, has at least one root in this interval. Such a root can be found by the bisection method.

This method starts from the given interval. Then it investigates the sign changes in the subintervals $[a,\frac{a+b}{2}]$ and $[\frac{a+b}{2},b]$. If the sign changes in the first subinterval $b$ is redefined to be $b:=\frac{a+b}{2}$ otherwise $a$ is redefined in the same manner to $a:=\frac{a+b}{2}$, and the process is repeated until the $b-a$ is less than a given tolerance.

In [ ]:
def bisect(f, a, b):
return 0
# implement this!


Implement the function bisect above until the following does not complain:

In [ ]:
assert allclose(bisect(sin, 3., 4.), pi)