multivariate gaussian

rasbt · rasbt · commit 2a3d9aa32511 · 2014-04-16T01:58:02.000-04:00
diff --git a/useful_scripts/multivariate_gaussian_pdf.py b/useful_scripts/multivariate_gaussian_pdf.py
@@ -0,0 +1,33 @@
+# 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():
+    x = np.array([[0],[0]])
+    mu  = np.array([[0],[0]])
+    cov = np.eye(2) 
+
+    print(pdf_multivariate_gauss(x, mu, cov))
+
+	# prints 0.15915494309189535
+
+if __name__ == '__main__':
+    test_gauss_pdf()
