def test_randomized_svd_execution(setup):
n_samples = 100
n_features = 500
rank = 5
k = 10
for dtype in (np.int64, np.float64):
# generate a matrix X of approximate effective rank `rank` and no noise
# component (very structured signal):
X = make_low_rank_matrix(n_samples=n_samples,
n_features=n_features,
effective_rank=rank,
tail_strength=0.0,
random_state=0).astype(dtype, copy=False)
assert X.shape == (n_samples, n_features)
dtype = np.dtype(dtype)
decimal = 5 if dtype == np.float32 else 7
# compute the singular values of X using the slow exact method
X_res = X.execute().fetch()
U, s, V = np.linalg.svd(X_res, full_matrices=False)
# Convert the singular values to the specific dtype
U = U.astype(dtype, copy=False)
s = s.astype(dtype, copy=False)
V = V.astype(dtype, copy=False)
for normalizer in ['auto', 'LU', 'QR']: # 'none' would not be stable
# compute the singular values of X using the fast approximate method
Ua, sa, Va = randomized_svd(X,
k,
n_iter=1,
power_iteration_normalizer=normalizer,
random_state=0)
# If the input dtype is float, then the output dtype is float of the
# same bit size (f32 is not upcast to f64)
# But if the input dtype is int, the output dtype is float64
if dtype.kind == 'f':
assert Ua.dtype == dtype
assert sa.dtype == dtype
assert Va.dtype == dtype
else:
assert Ua.dtype == np.float64
assert sa.dtype == np.float64
assert Va.dtype == np.float64
assert Ua.shape == (n_samples, k)
assert sa.shape == (k, )
assert Va.shape == (k, n_features)
# ensure that the singular values of both methods are equal up to the
# real rank of the matrix
sa_res = sa.execute().fetch()
np.testing.assert_almost_equal(s[:k], sa_res, decimal=decimal)
# check the singular vectors too (while not checking the sign)
dot_res = dot(Ua, Va).execute().fetch()
np.testing.assert_almost_equal(np.dot(U[:, :k], V[:k, :]),
dot_res,
decimal=decimal)
def testMakeLowRankMatrix(self):
X = make_low_rank_matrix(n_samples=50, n_features=25, effective_rank=5,
tail_strength=0.01, random_state=0)
self.assertEquals(X.shape, (50, 25), "X shape mismatch")
_, s, _ = svd(X)
self.assertLess((s.sum() - 5).execute(n_parallel=1), 0.1, "X rank is not approximately 5")
def test_make_low_rank_matrix(setup):
X = make_low_rank_matrix(n_samples=50,
n_features=25,
effective_rank=5,
tail_strength=0.01,
random_state=0)
assert X.shape == (50, 25)
_, s, _ = svd(X)
assert (s.sum() - 5).to_numpy() < 0.1
