Today we talked about finding the zeros (roots) of a function.

We used this function as an example.

def f(x):
    return np.sin(10*x) - x**3 + 1

In class we came up with a function like this:

def trapZero(f, x0, x1):
    if f(x0) > 0:
        x0,x1 = x1,x0 # swap so f(x0) is the negative one
    while abs(x0 - x1) > 1e-6:
        xm = (x0 + x1) / 2.0 # compute the midpoint
        fm = f(xm) # evaluate the function at the midpoint
        if np.sign(fm) == -1: # close in on the root from the negative side
            x0 = xm
        elif np.sign(fm) == 1: # close in on the root from the positive side
            x1 = xm
        elif np.sign(fm) == 0: # we happened to hit it (very rare)
            return xm
    return (x0 + x1) / 2.0 # why didn't I return xm?