Update of mlab.pca - updated docstring, added saving the eigenvalues.

blackw1ng · blackw1ng · commit 38c60350a9d4 · 2013-07-22T00:18:48.000-07:00
The old version of pca class did not save the Eigenvalues - just the "fractions" that are just percentage values.

Also added info which row of Wt one can find the Eigenvectors.
diff --git a/lib/matplotlib/mlab.py b/lib/matplotlib/mlab.py
@@ -827,19 +827,23 @@ def __init__(self, a):
 
           *numrows*, *numcols*: the dimensions of a
 
-          *mu* : a numdims array of means of a
+          *mu* : a numdims array of means of a. This is the vector that points to the 
+          origin of PCA space. 
 
-          *sigma* : a numdims array of atandard deviation of a
+          *sigma* : a numdims array of standard deviation of a
 
           *fracs* : the proportion of variance of each of the principal components
+        
+          *s* : the actual eigenvalues of the decomposition
 
           *Wt* : the weight vector for projecting a numdims point or array into PCA space
 
           *Y* : a projected into PCA space
 
 
         The factor loadings are in the Wt factor, ie the factor
-        loadings for the 1st principal component are given by Wt[0]
+        loadings for the 1st principal component are given by Wt[0].
+        This row is also the 1st eigenvector.
 
         """
         n, m = a.shape
@@ -856,15 +860,27 @@ def __init__(self, a):
 
         U, s, Vh = np.linalg.svd(a, full_matrices=False)
 
-
-        Y = np.dot(Vh, a.T).T
-
-        vars = s**2/float(len(s))
-        self.fracs = vars/vars.sum()
-
-
+        # Note: .H indicates the conjugate transposed / Hermitian.
+        
+        # The SVD is commonly written as a = U s V.H.
+        # If U is a unitary matrix, it means that it satisfies U.H = inv(U).
+        
+        # The rows of Vh are the eigenvectors of a.H a.
+        # The columns of U are the eigenvectors of a a.H. 
+        # For row i in Vh and column i in U, the corresponding eigenvalue is s[i]**2.
+         
         self.Wt = Vh
+        
+        # save the transposed coordinates
+        Y = np.dot(Vh, a.T).T
         self.Y = Y
+        
+        # save the eigenvalues
+        self.s = s**2
+        
+        # and now the contribution of the individual components
+        vars = self.s/float(len(s))
+        self.fracs = vars/vars.sum()
 
 
     def project(self, x, minfrac=0.):
