Mahalanobis Distance in 2D

Problem

Compute the Mahalanobis distance in 2D: sqrt(d^T * inv_cov * d), where d = x - mean and inv_cov is the 2x2 inverse covariance matrix.

Return 0.0 if the quadratic form is non-positive.

Hint

Expand d^T * inv_cov * d as a quadratic form in d0 and d1.

case 1

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

expected: 5

case 2

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

expected: 2

case 3

in: [[1,-1],[0,0],[[1,-0.5],[-0.5,1]]]

expected: 1.7320508075688772

case 4

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

expected: 0

Starter codePython

import math
def mahalanobis_distance_2d(x, mean, inv_cov):
    # Your code here
    pass

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