How to implement linear interpolation?

Question

Say I am given data as follows:

x = [1, 2.5, 3.4, 5.8, 6]
y = [2, 4, 5.8, 4.3, 4]

I want to design a function that will interpolate linearl

Answer 1

Building on Lauritz` answer, here's a version with the following changes

• Updated to python3 (the map was causing problems for me and is unnecessary)
• Fixed behavior at edge values
• Raise exception when x is out of bounds
• Use __call__ instead of __getitem__

from bisect import bisect_right

class Interpolate:
    def __init__(self, x_list, y_list):
        if any(y - x <= 0 for x, y in zip(x_list, x_list[1:])):
            raise ValueError("x_list must be in strictly ascending order!")
        self.x_list = x_list
        self.y_list = y_list
        intervals = zip(x_list, x_list[1:], y_list, y_list[1:])
        self.slopes = [(y2 - y1) / (x2 - x1) for x1, x2, y1, y2 in intervals]

    def __call__(self, x):
        if not (self.x_list[0] <= x <= self.x_list[-1]):
            raise ValueError("x out of bounds!")
        if x == self.x_list[-1]:
            return self.y_list[-1]
        i = bisect_right(self.x_list, x) - 1
        return self.y_list[i] + self.slopes[i] * (x - self.x_list[i])

Example usage:

>>> interp = Interpolate([1, 2.5, 3.4, 5.8, 6], [2, 4, 5.8, 4.3, 4])
>>> interp(4)
5.425