def test_singular_values():
# Check that the TruncatedSVD output has the correct singular values
rng = np.random.RandomState(0)
n_samples = 100
n_features = 80
X = rng.randn(n_samples, n_features)
dX = da.from_array(X, chunks=(n_samples // 2, n_features))
apca = dd.TruncatedSVD(n_components=2, algorithm="tsqr", random_state=rng).fit(dX)
rpca = sd.TruncatedSVD(n_components=2, algorithm="arpack", random_state=rng).fit(X)
assert_array_almost_equal(apca.singular_values_, rpca.singular_values_, 12)
# Compare to the Frobenius norm
X_apca = apca.transform(X)
X_rpca = rpca.transform(X)
assert_array_almost_equal(
np.sum(apca.singular_values_ ** 2.0), np.linalg.norm(X_apca, "fro") ** 2.0, 12
)
assert_array_almost_equal(
np.sum(rpca.singular_values_ ** 2.0), np.linalg.norm(X_rpca, "fro") ** 2.0, 12
)
# Compare to the 2-norms of the score vectors
assert_array_almost_equal(
apca.singular_values_, np.sqrt(np.sum(X_apca ** 2.0, axis=0)), 12
)
assert_array_almost_equal(
rpca.singular_values_, np.sqrt(np.sum(X_rpca ** 2.0, axis=0)), 12
)
# Set the singular values and see what we get back
rng = np.random.RandomState(0)
n_samples = 100
n_features = 110
X = rng.randn(n_samples, n_features)
dX = da.from_array(X, chunks=(50, n_features))
apca = dd.TruncatedSVD(n_components=3, algorithm="randomized", random_state=0)
rpca = sd.TruncatedSVD(n_components=3, algorithm="randomized", random_state=0)
X_apca = apca.fit_transform(dX).compute()
X_rpca = rpca.fit_transform(X)
X_apca /= np.sqrt(np.sum(X_apca ** 2.0, axis=0))
X_rpca /= np.sqrt(np.sum(X_rpca ** 2.0, axis=0))
X_apca[:, 0] *= 3.142
X_apca[:, 1] *= 2.718
X_rpca[:, 0] *= 3.142
X_rpca[:, 1] *= 2.718
X_hat_apca = np.dot(X_apca, apca.components_)
X_hat_rpca = np.dot(X_rpca, rpca.components_)
apca.fit(da.from_array(X_hat_apca, chunks=(50, n_features)))
rpca.fit(X_hat_rpca)
assert_array_almost_equal(apca.singular_values_, [3.142, 2.718, 1.0], 14)
assert_array_almost_equal(rpca.singular_values_, [3.142, 2.718, 1.0], 14)
def test_compute(algorithm, compute):
est = dd.TruncatedSVD(random_state=0, algorithm=algorithm, compute=compute)
est.fit(dXdense)
array_class = np.ndarray if compute else da.Array
assert isinstance(est.components_, array_class)
assert isinstance(est.explained_variance_, array_class)
assert isinstance(est.explained_variance_ratio_, array_class)
assert isinstance(est.singular_values_, array_class)
def test_inverse_transform():
# We need a lot of components for the reconstruction to be "almost
# equal" in all positions. XXX Test means or sums instead?
a = dd.TruncatedSVD(n_components=52, random_state=42, n_iter=5)
b = sd.TruncatedSVD(n_components=52, random_state=42)
b.fit(Xdense)
Xt = a.fit_transform(dXdense)
Xinv = a.inverse_transform(Xt)
assert_array_almost_equal(Xinv.compute(), Xdense, decimal=1)
def test_algorithms():
svd_a = sd.TruncatedSVD(30, algorithm="arpack")
svd_r = dd.TruncatedSVD(30, algorithm="tsqr", random_state=42)
Xa = svd_a.fit_transform(Xdense)[:, :6]
Xr = svd_r.fit_transform(dXdense)[:, :6]
assert_array_almost_equal(Xa, Xr, decimal=5)
comp_a = np.abs(svd_a.components_)
comp_r = np.abs(svd_r.components_)
# All elements are equal, but some elements are more equal than others.
assert_array_almost_equal(comp_a[:9], comp_r[:9])
assert_array_almost_equal(comp_a[9:], comp_r[9:], decimal=2)
def test_basic(algorithm):
a = dd.TruncatedSVD(random_state=0, algorithm=algorithm)
b = sd.TruncatedSVD(random_state=0)
b.fit(Xdense)
a.fit(dXdense)
np.testing.assert_allclose(a.components_, b.components_, atol=1e-3)
assert_estimator_equal(a,
b,
exclude=["components_", "explained_variance_"],
atol=1e-3)
assert a.explained_variance_.shape == b.explained_variance_.shape
np.testing.assert_allclose(a.explained_variance_,
b.explained_variance_,
rtol=0.01)
def test_integers():
Xint = dXdense.astype(np.int64)
tsvd = dd.TruncatedSVD(n_components=6)
Xtrans = tsvd.fit_transform(Xint)
Xtrans.shape == (n_samples, tsvd.n_components)
def test_too_many_components():
for n_components in (n_features, n_features + 1):
tsvd = dd.TruncatedSVD(n_components=n_components)
with pytest.raises(ValueError):
tsvd.fit(dXdense)
def test_attributes():
for n_components in (10, 25, 41):
tsvd = dd.TruncatedSVD(n_components).fit(dXdense)
assert tsvd.n_components == n_components
assert tsvd.components_.shape == (n_components, n_features)
