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# Sebastian Raschka 04/2014

import numpy as np

def pdf_multivariate_gauss(x, mu, cov):

'''

Caculate the multivariate normal density (pdf)

Keyword arguments:

x = numpy array of a "d x 1" sample vector

mu = numpy array of a "d x 1" mean vector

cov = "numpy array of a d x d" covariance matrix

'''

assert(mu.shape[0] > mu.shape[1]), 'mu must be a row vector'

assert(x.shape[0] > x.shape[1]), 'x must be a row vector'

assert(cov.shape[0] == cov.shape[1]), 'covariance matrix must be square'

assert(mu.shape[0] == cov.shape[0]), 'cov_mat and mu_vec must have the same dimensions'

assert(mu.shape[0] == x.shape[0]), 'mu and x must have the same dimensions'

part1 = 1 / ( ((2* np.pi)**(len(mu)/2)) * (np.linalg.det(cov)**(1/2)) )

part2 = (-1/2) * ((x-mu).T.dot(np.linalg.inv(cov))).dot((x-mu))

return float(part1 * np.exp(part2))

def test_gauss_pdf():

from matplotlib.mlab import bivariate_normal

x = np.array([[0],[0]])

mu = np.array([[0],[0]])

cov = np.eye(2)

mlab_gauss = bivariate_normal(x,x)

mlab_gauss = float(mlab_gauss[0]) # because mlab returns an np.array

impl_gauss = pdf_multivariate_gauss(x, mu, cov)

print('mlab_gauss:', mlab_gauss)

print('impl_gauss:', impl_gauss)

assert(mlab_gauss == impl_gauss), 'Implementations of the mult. Gaussian return different pdfs'

if __name__ == '__main__':

test_gauss_pdf()