Lagrange Interpolation Value

Problem

Evaluate the Lagrange interpolating polynomial through the given points at x.

points is a list of [x_i, y_i] pairs and the result is sum over i of y_i times the product over j != i of (x - x_j) / (x_i - x_j). A single point returns its y value everywhere.

Hint

Each basis polynomial equals 1 at its own node and 0 at every other node.

Test cases

case 1

in: [[[0,1],[1,3]],2]

expected: 5

case 2

in: [[[0,0],[1,1],[2,4]],3]

expected: 9

case 3

in: [[[0,0],[1,1],[2,4]],0.5]

expected: 0.25

case 4

in: [[[-1,1],[1,1]],0]

expected: 1

case 5

in: [[[2,5]],7]

expected: 5

Starter codePython

def lagrange_interpolate(points, x):
    # Your code here
    pass

5 test cases · run your code against them in the editor