adding simple covariance code

doc/Programs/DimRed/covariance.py

@@ -0,0 +1,34 @@
+#The covariance matrix and its eigenvalues the hard way
+from random import random, seed
+import numpy as np
+
+def covariance(x, y, n):
+    sum = 0.0
+    mean_x = np.mean(x)
+    mean_y = np.mean(y)
+    for i in range(0, n):
+        sum += (x[(i)]-mean_x)*(y[i]-mean_y)
+    return  sum/n
+
+n = 10
+
+x = np.random.normal(size=n)
+y = x*np.random.normal(size=n)
+z = x*x+y*np.random.normal(size=n)
+covxx = covariance(x,x,n)
+covxy = covariance(x,y,n)
+covxz = covariance(x,z,n)
+covyy = covariance(y,y,n)
+covyz = covariance(y,z,n)
+covzz = covariance(z,z,n)
+
+SigmaCov = np.array([ [covxx, covxy, covxz], [covxy, covyy, covyz], [covxz, covyz, covzz]])
+print(SigmaCov)
+
+EigValues, EigVectors = np.linalg.eig(SigmaCov)
+# sort eigenvectors and eigenvalues
+permute = EigValues.argsort()
+EigValues = EigValues[permute]
+EigVectors = EigVectors[:,permute]
+print(EigValues)
+print(EigVectors)