def testMatrixPower(self):
A = numpy.random.rand(10, 10)
tol = 10**-6
A2 = A.dot(A)
lmbda, V = scipy.linalg.eig(A)
A12 = Util.matrixPower(A, 0.5)
self.assertTrue(numpy.linalg.norm(A12.dot(A12) - A) < tol)
self.assertTrue(numpy.linalg.norm(numpy.linalg.inv(A) - Util.matrixPower(A, -1)) < tol)
self.assertTrue(numpy.linalg.norm(A - Util.matrixPower(A, 1)) < tol)
self.assertTrue(numpy.linalg.norm(A2 - Util.matrixPower(A, 2)) < tol)
self.assertTrue(numpy.linalg.norm(numpy.linalg.inv(A).dot(numpy.linalg.inv(A)) - Util.matrixPower(A, -2)) < tol)
#Now lets test on a low rank matrix
lmbda[5:] = 0
A = V.dot(numpy.diag(lmbda)).dot(numpy.linalg.inv(V))
A2 = A.dot(A)
A12 = Util.matrixPower(A, 0.5)
Am12 = Util.matrixPower(A, -0.5)
self.assertTrue(numpy.linalg.norm(numpy.linalg.pinv(A) - Util.matrixPower(A, -1)) < tol)
self.assertTrue(numpy.linalg.norm(numpy.linalg.pinv(A) - Am12.dot(Am12)) < tol)
self.assertTrue(numpy.linalg.norm(A12.dot(A12) - A) < tol)
self.assertTrue(numpy.linalg.norm(A - Util.matrixPower(A, 1)) < tol)
self.assertTrue(numpy.linalg.norm(A2 - Util.matrixPower(A, 2)) < tol)
def testMatrixPower(self):
A = numpy.random.rand(10, 10)
tol = 10**-6
A2 = A.dot(A)
lmbda, V = scipy.linalg.eig(A)
A12 = Util.matrixPower(A, 0.5)
self.assertTrue(numpy.linalg.norm(A12.dot(A12) - A) < tol)
self.assertTrue(
numpy.linalg.norm(numpy.linalg.inv(A) -
Util.matrixPower(A, -1)) < tol)
self.assertTrue(numpy.linalg.norm(A - Util.matrixPower(A, 1)) < tol)
self.assertTrue(numpy.linalg.norm(A2 - Util.matrixPower(A, 2)) < tol)
self.assertTrue(
numpy.linalg.norm(
numpy.linalg.inv(A).dot(numpy.linalg.inv(A)) -
Util.matrixPower(A, -2)) < tol)
#Now lets test on a low rank matrix
lmbda[5:] = 0
A = V.dot(numpy.diag(lmbda)).dot(numpy.linalg.inv(V))
A2 = A.dot(A)
A12 = Util.matrixPower(A, 0.5)
Am12 = Util.matrixPower(A, -0.5)
self.assertTrue(
numpy.linalg.norm(numpy.linalg.pinv(A) -
Util.matrixPower(A, -1)) < tol)
self.assertTrue(
numpy.linalg.norm(numpy.linalg.pinv(A) - Am12.dot(Am12)) < tol)
self.assertTrue(numpy.linalg.norm(A12.dot(A12) - A) < tol)
self.assertTrue(numpy.linalg.norm(A - Util.matrixPower(A, 1)) < tol)
self.assertTrue(numpy.linalg.norm(A2 - Util.matrixPower(A, 2)) < tol)
