StatRed: added comments to q22.

statred/ass1/Makefile

+.PHONY: all clean
+
+all:
+
+clean:
+	rm -vf *.pyc q*.pdf

statred/ass1/q22_estimate.py

 from q21_multivariate import dataset
-from numpy import array, mean, tile, newaxis, dot
-from pylab import eigvals, axis, figure, clf, show, plot
+from pylab import array, mean, tile, newaxis, dot, eigvals, \
+        axis, figure, clf, show, plot
 
 def eigenvalues(n):
+    """Return eigenvalues of unbiased estimators for the covariance matrix
+    Sigma (based on a pseudo-random generated dataset)."""
+
     Y = array([mean(dataset(), 1) for i in range(n)]).T
+
+    # Sigma = 1 / (n - 1) * Sum for i=1 to n: (x_i - x_mean) T(x_i - x_mean),
+    # where T(x) is the transpose of `x'. Mu = x_mean and
+    # Yzm = Sum for i=1 to n: x_i - x_mean.
     mu = mean(Y, 1)
     Yzm = Y - tile(mu[:,newaxis], n)
     S = dot(Yzm, Yzm.T) / (n - 1)
@@ -11,14 +18,17 @@ def eigenvalues(n):
 
 figure(1)
 clf()
-samples = range(2, 10000, 500)
+
+max_range = 10000
+
+samples = range(2, max_range, 500)
 data = [[] for i in range(4)]
+
 for n in samples:
     e = eigenvalues(n)
     for i in range(4):
         data[i].append(e[i])
 for i in range(4):
-    #subplot(2, 2, i+1)
     plot(samples, data[i], 'x')
-axis([0, 10000, 0., 0.025])
+axis([0, max_range, 0., 0.025])
 show()