[SciPy-user] Finding a point where a function becomes constant

[Alan G Isaac]

On Tue, 17 Jul 2007, Mathias Wagner apparently wrote:
> I have a numerical function defined f(x) that is zero for x < x_0 and f(x)>0 
> for x > x_0. I have to find x_0. 
> The problem with conventional root finding is that if the algorithm evaluates 
> the function for any x < x_0 it will return this as a solution. 
> Does anyone know whether there is some suitable algorithm for this problem or 
> do I have to modify an existing method like bisection for my needs? 

This one does not require any modification at all, I think.
(License: MIT.)

Cheers,
Alan Isaac


def bisect(f, x1, x2, eps=1e-8):
    f1, f2 = f(x1), f(x2)
    if f1*f2 > 0:
        raise ValueError
    #initialize xneg, xpos
    xneg, xpos = (x1,x2) if(f2>0) else (x2,x1)
    while xpos-xneg > eps:
        xmid = (xneg+xpos)/2
        if f(xmid) > 0:
            xpos = xmid
        else:
            xneg = xmid
    return (xneg+xpos)/2