def test_get_eigenvectors_left():
# just some random counts
N = 100
counts = np.random.randint(1, 10, size=(N,N))
transmat, pi = build_msm(scipy.sparse.csr_matrix(counts), 'MLE')[1:3]
values0, vectors0 = get_eigenvectors(transmat, 10)
values1, vectors1 = get_reversible_eigenvectors(transmat, 10)
values2, vectors2 = get_reversible_eigenvectors(transmat, 10, populations=pi)
# check that the eigenvalues are the same using the two methods
np.testing.assert_array_almost_equal(values0, values1)
# check that the eigenvectors returned by both methods are _actually_
# left eigenvectors of the transmat
def test_eigenpairs(values, vectors):
for value, vector in zip(values, vectors.T):
np.testing.assert_array_almost_equal(
(transmat.T.dot(vector) / vector).flatten(), np.ones(N)*value)
np.testing.assert_array_almost_equal(pi, vectors0[:, 0])
np.testing.assert_array_almost_equal(pi, vectors1[:, 0])
np.testing.assert_array_almost_equal(pi, vectors2[:, 0])
test_eigenpairs(values0, vectors0)
test_eigenpairs(values1, vectors1)
test_eigenpairs(values2, vectors2)
def test_eigenvector_norm():
N = 100
counts = np.random.randint(1, 10, size=(N,N))
transmat, pi = build_msm(scipy.sparse.csr_matrix(counts), 'MLE')[1:3]
left_values0, left_vectors0 = get_eigenvectors(transmat, 10, right=False, normalized=True)
right_values0, right_vectors0 = get_eigenvectors(transmat, 10, right=True, normalized=True)
left_values1, left_vectors1 = get_reversible_eigenvectors(transmat, 10, right=False, normalized=True)
right_values1, right_vectors1 = get_reversible_eigenvectors(transmat, 10, right=True, normalized=True)
np.testing.assert_array_almost_equal(left_values0, right_values0)
np.testing.assert_array_almost_equal(left_values1, right_values1)
test_left_vectors1 = left_vectors1 * np.sign(left_vectors0[0].reshape((1,-1))) * np.sign(left_vectors1[0].reshape((1,-1)))
test_right_vectors1 = right_vectors1 * np.sign(right_vectors0[0].reshape((1,-1))) * np.sign(right_vectors1[0].reshape((1,-1)))
np.testing.assert_array_almost_equal(left_vectors0, test_left_vectors1)
np.testing.assert_array_almost_equal(right_vectors0, test_right_vectors1)
Id = np.eye(10)
np.testing.assert_array_almost_equal(np.abs(left_vectors0.T.dot(right_vectors0)), Id)
np.testing.assert_array_almost_equal(np.abs(left_vectors1.T.dot(right_vectors1)), Id)