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34 lines
1.1 KiB
Python
34 lines
1.1 KiB
Python
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# Sebastian Raschka 04/2014
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import numpy as np
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def pdf_multivariate_gauss(x, mu, cov):
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'''
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Caculate the multivariate normal density (pdf)
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Keyword arguments:
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x = numpy array of a "d x 1" sample vector
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mu = numpy array of a "d x 1" mean vector
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cov = "numpy array of a d x d" covariance matrix
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'''
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assert(mu.shape[0] > mu.shape[1]), 'mu must be a row vector'
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assert(x.shape[0] > x.shape[1]), 'x must be a row vector'
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assert(cov.shape[0] == cov.shape[1]), 'covariance matrix must be square'
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assert(mu.shape[0] == cov.shape[0]), 'cov_mat and mu_vec must have the same dimensions'
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assert(mu.shape[0] == x.shape[0]), 'mu and x must have the same dimensions'
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part1 = 1 / ( ((2* np.pi)**(len(mu)/2)) * (np.linalg.det(cov)**(1/2)) )
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part2 = (-1/2) * ((x-mu).T.dot(np.linalg.inv(cov))).dot((x-mu))
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return float(part1 * np.exp(part2))
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def test_gauss_pdf():
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x = np.array([[0],[0]])
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mu = np.array([[0],[0]])
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cov = np.eye(2)
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print(pdf_multivariate_gauss(x, mu, cov))
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# prints 0.15915494309189535
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if __name__ == '__main__':
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test_gauss_pdf()
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