mirror of
https://github.com/rasbt/python_reference.git
synced 2024-10-06 04:59:28 +00:00
41 lines
1.4 KiB
Python
41 lines
1.4 KiB
Python
# 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()
|