def test_initialize_A_condition(self):
dummy = hilbert(14)
dummy = dummy[:, :-1]
dummy[:, 0] = 1.0
with pytest.raises(ValueError, match="The condition number .*"):
_initialize_rot_matrix(dummy)
def _generate_ground_truth_rot_matrices(self):
# this function generates the data for "test_init_final_rotation_matrix"
P, sd = get_known_input(mu(0))
g_ks = GPCCA(csr_matrix(P), method="krylov").optimize(3)
g_kd = GPCCA(P, method="krylov").optimize(3)
for g in [g_ks, g_kd]:
g.schur_vectors
_initialize_rot_matrix(sd)
g.rotation_matrix
def test_initialize_A_first_is_not_constant(self):
X = np.zeros((4, 4))
X[0, 0] = 1.0
with pytest.raises(
ValueError,
match=
"First Schur vector is not constant 1. This indicates that the Schur vectors are incorrectly sorted. "
"Cannot search for a simplex structure in the data.",
):
_initialize_rot_matrix(X)
def test_initialize_A_shape_error_1(self):
X = np.zeros((3, 4))
X[:, 0] = 1.0
with pytest.raises(
ValueError,
match=
r"The Schur vector matrix of shape \(\d+, \d+\) has more columns than rows. "
r"You can't get a \d+-dimensional simplex from \d+ data vectors.",
):
_initialize_rot_matrix(X)
def test_initialize_A_second_and_rest_are_constant(self):
X = np.zeros((3, 3))
X[:, 0] = 1.0
X[:, 2] = 2
with pytest.raises(
ValueError,
match=
r"2 Schur vector\(s\) after the first one are constant. Probably the Schur vectors are incorrectly "
"sorted. Cannot search for a simplex structure in the data.",
):
_initialize_rot_matrix(X)
def test_initialize_A_condition_warning(self):
dummy = hilbert(6)
dummy = dummy[:, :-1]
dummy[:, 0] = 1.0
with pytest.warns(UserWarning):
_ = _initialize_rot_matrix(dummy)
def test_init_final_rot_matrix_krylov_dense(
self,
svecs_mu0_krylov_dense: np.ndarray,
A_mu0_krylov_dense_init: np.ndarray,
A_mu0_krylov_dense: np.ndarray,
):
init_rot = _initialize_rot_matrix(svecs_mu0_krylov_dense)
_, final_rot, _ = _gpcca_core(svecs_mu0_krylov_dense)
assert_allclose(init_rot, A_mu0_krylov_dense_init)
assert_allclose(final_rot, A_mu0_krylov_dense)
def test_initialize_A(self):
mu0 = mu(0)
P, sd = get_known_input(mu0)
X, _, _ = _do_schur(P, sd, m=4)
evs = X[:, :4]
A = _initialize_rot_matrix(evs)
index = _indexsearch(evs)
A_exp = pinv(X[index, :4])
assert_allclose(A, A_exp)
def test_init_final_rot_matrix_brandts(
self,
svecs_mu0: np.ndarray,
A_mu0_init: np.ndarray,
A_mu0: np.ndarray,
):
init_rot = _initialize_rot_matrix(svecs_mu0)
_, final_rot, _ = _gpcca_core(svecs_mu0)
assert_allclose(init_rot, A_mu0_init)
assert_allclose(final_rot, A_mu0)
def test_opt_soft_nelder_mead_more(self):
kmin, kmax = 2, 8
kopt = []
ks = np.arange(kmin, kmax)
for mu_ in [10, 50, 100, 200, 500, 1000]:
mu_ = mu(mu_)
P, sd = get_known_input(mu_)
X, _, _ = _do_schur(P, eta=sd, m=kmax)
crisp = [-np.inf] * (kmax - kmin)
for j, k in enumerate(range(kmin, kmax)):
svecs = X[:, :k]
A = _initialize_rot_matrix(svecs)
_, _, fopt = _opt_soft(svecs, A)
crisp[j] = (k - fopt) / k
kopt.append(ks[np.argmax(crisp)])
np.testing.assert_array_equal(kopt, [3, 3, 3, 2, 2, 7])