def test_inverse_iteration(self):
M = random_symmetric(3)
expected_eigval, expected_eigvec = self.np_eig(M, largest=False)
actual_eigval, actual_eigvec = single.inverse_iteration(M)
self.assertTrue(self.absallclose(actual_eigvec, expected_eigvec))
self.assertTrue(self.absallclose(actual_eigval, expected_eigval))
def test_factorization_equals_initial_symmetric(self):
A = utils.random_symmetric(3)
U, S, V = SVD(A).decompose()
actual = U @ S @ V.T
expected = A
self.assertTrue(np.allclose(actual, expected))
def test_power_iteration(self):
M = random_symmetric(3)
expected_eigval, expected_eigvec = self.np_eig(M)
actual_eigval, actual_eigvec = single.power_iteration(M)
self.assertTrue(self.absallclose(actual_eigval, expected_eigval))
self.assertTrue(self.absallclose(actual_eigvec, expected_eigvec))
def test_rayleigh_smallest(self):
M = random_symmetric(3)
expected_eigval, expected_eigvec = self.np_eig(M, largest=False)
initial_eigval = single.inverse_iteration(M)[0]
actual_eigval, actual_eigvec = single.rayleigh_quotient_iteration(
M, initial_eigval)
self.assertTrue(self.absallclose(actual_eigvec, expected_eigvec))
self.assertTrue(self.absallclose(actual_eigval, expected_eigval))
def test_projected_iteration(self):
M = random_symmetric(3)
eigvals, eigvecs = LA.eig(M)
idx = np.abs(eigvals).argsort()[::-1]
expected_eigvecs = eigvecs[:, idx]
expected_eigvals = eigvals[idx]
actual_eigvals, actual_eigvecs = multi.projected_iteration(M, 3)
self.assertTrue(self.absallclose(actual_eigvecs, expected_eigvecs))
self.assertTrue(self.absallclose(actual_eigvals, expected_eigvals))
def test_qr_algorithm_with_hessenberg(self):
M = random_symmetric(4)
eigvals, eigvecs = LA.eig(M)
idx = np.abs(eigvals).argsort()[::-1]
expected_eigvecs = eigvecs[:, idx]
expected_eigvals = eigvals[idx]
actual_eigvals, actual_eigvecs = multi.qr_algorithm(M)
self.assertTrue(self.absallclose(actual_eigvecs, expected_eigvecs))
self.assertTrue(self.absallclose(actual_eigvals, expected_eigvals))
def test_hessenberg_symmetric_stays_symmetric(self):
M = random_symmetric(4)
hess = multi.hessenberg(M)
self.assertTrue(is_symmetric(hess))