Quickly finding the first point at which a function equals 0 using scipy.optimize

Question

Basically, given a function that produces outputs like this for different parameters:

I want to quickly find the first x at which the function equals 0. So with parameters that produce the blue curve over x, I want to find x=134. For the green curve, I want to find x=56, etc.

I think the function will always be monotonically decreasing until it hits zero, but I'm not totally sure.

The function is not necessarily monotonically decreasing.

I am sure that it will only hit 0 once, and then remain zero.

Currently I'm brute-forcing it by iterating through x values until I hit zero, but I want something that will be better at making educated guesses (based on slope?) and iterating.

Ideally I want to use something already-baked (since 90% of programmers can't even write a binary search correctly), like something from scipy.optimize, but it seems like those all want to find either a global minimum or a zero-crossing.

(This function is sort of a distance_to_the_wall of the RGB cube for a given chroma in Lch color space (so basically building a "sanely clip to RGB" function), but since the mapping between IRGB and LCh can vary by library and with parameters like illuminant etc. I think it's best to just try a few values until the right one is found rather than trying to reverse-calculate the value directly?)

Answer 1

Here is some code to flesh out @ExP's bisection/binary search answer:

def find_first_zero(func, min, max, tol=1e-3):
    min, max = float(min), float(max)
    assert (max + tol) > max
    while (max - min) > tol:
        mid = (min + max) / 2
        if func(mid) == 0:
            max = mid
        else:
            min = mid
    return max