Mahalanobis Distance 2x2

Problem

The Mahalanobis distance between x and mean under the symmetric 2x2 covariance matrix [[a, b], [b, c]] is sqrt(d^T S^-1 d) with d = x - mean. Using det = a * c - b^2, d^T S^-1 d equals (c * d0^2 - 2 * b * d0 * d1 + a * d1^2) / det. Return 0.0 when the covariance is not positive definite or shapes are wrong.

Hint

Invert the 2x2 covariance with the determinant and compute the quadratic form.

Test cases

case 1

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

expected: 1

case 2

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

expected: 1

case 3

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

expected: 0.816496580927726

case 4

in: [[2,3],[1,1],[[1,0.5],[0.5,1]]]

expected: 2

case 5

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

expected: 1.4142135623730951

Starter codePython

import math


def mahalanobis_distance_2x2(x, mean, covariance):
    # Your code here
    pass

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