Diagonal Gaussian Density

Problem

Return the density of a multivariate Gaussian with independent coordinates at the point x, given the mean vector mean and per-coordinate standard deviations sigmas. The density is exp(-0.5 * sum(((x[i] - mean[i]) / sigmas[i])^2)) divided by the product of sigmas[i] * sqrt(2 * pi). Return 0.0 when lengths differ or any standard deviation is nonpositive.

Hint

The diagonal covariance makes the multivariate density a product of univariate ones.

Test cases

case 1

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

expected: 0.3989422804014327

case 2

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

expected: 0.15915494309189537

case 3

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

expected: 0.013064233284684923

case 4

in: [[2],[2],[3]]

expected: 0.1329807601338109

case 5

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

expected: 0

Starter codePython

import math


def diagonal_gaussian_density(x, mean, sigmas):
    # Your code here
    pass

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