PowerMethod in Python

python/PowerMethod.py

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+import numpy as np
+import math
+
+def PowerMethod(A, tol, max_iter):
+    # Function that returns the largest eigenvalue of the matrix and the characteristic vector
+    (n,n) = A.shape
+    # Randomly choose the vector y with the values in the interval (0,1)
+    y = np.random.rand (n , 1 )
+    val = np.inf
+    # Iterate to the maximum number of iterations
+
+    for step in range(1,max_iter):
+        z = np.matmul(A,y)
+        # update the eigenvector
+        y = z / np.linalg.norm(z)
+        # backup the last eigenvalue approximation
+        val_old = val
+        # update the val value
+        yt = np.transpose(y,axes=None)
+        val = np.matmul(np.matmul(yt,A),y)
+       # print val
+        # when the new values get close enough to the last values
+        # regarding the imposed tolerance "tol", we reached the solution
+        if np.all(np.absolute(val - val_old) / val < tol):
+            break
+    return val, y, step        
+
+
+#Example for a 2x2 matrix
+A = np.random.rand(2,2) * 10
+tol = 0.1
+max_iter = 10
+(val, y, step) =PowerMethod(A,tol,max_iter)
+print val
+print y
+print step