def test_assess_dimension_bad_rank():
# Test error when tested rank not in [1, n_features - 1]
spectrum = np.array([1, 1e-30, 1e-30, 1e-30])
n_samples = 10
for rank in (0, 5):
with pytest.raises(ValueError, match=r"should be in \[1, n_features - 1\]"):
_assess_dimension(spectrum, rank, n_samples)
def test_assess_dimesion_rank_one():
# Make sure assess_dimension works properly on a matrix of rank 1
n_samples, n_features = 9, 6
X = np.ones((n_samples, n_features)) # rank 1 matrix
_, s, _ = np.linalg.svd(X, full_matrices=True)
assert sum(s[1:]) == 0 # except for rank 1, all eigenvalues are 0
assert np.isfinite(_assess_dimension(s, rank=1, n_samples=n_samples))
for rank in range(2, n_features):
assert _assess_dimension(s, rank, n_samples) == -np.inf
def test_assess_dimesion_rank_one():
# Make sure assess_dimension works properly on a matrix of rank 1
n_samples, n_features = 9, 6
X = np.ones((n_samples, n_features)) # rank 1 matrix
_, s, _ = np.linalg.svd(X, full_matrices=True)
# except for rank 1, all eigenvalues are 0 resp. close to 0 (FP)
assert_allclose(s[1:], np.zeros(n_features - 1), atol=1e-12)
assert np.isfinite(_assess_dimension(s, rank=1, n_samples=n_samples))
for rank in range(2, n_features):
assert _assess_dimension(s, rank, n_samples) == -np.inf
def test_small_eigenvalues_mle():
# Test rank associated with tiny eigenvalues are given a log-likelihood of
# -inf. The inferred rank will be 1
spectrum = np.array([1, 1e-30, 1e-30, 1e-30])
assert _assess_dimension(spectrum, rank=1, n_samples=10) > -np.inf
for rank in (2, 3):
assert _assess_dimension(spectrum, rank, 10) == -np.inf
assert _infer_dimension(spectrum, 10) == 1
def test_assess_dimension_error_rank_greater_than_features():
# Test error when tested rank is greater than the number of features
# for PR #16224
spectrum = np.array([1, 1e-30, 1e-30, 1e-30])
n_samples = 10
n_features = 4
rank = 5
with pytest.raises(ValueError,
match="The tested rank cannot exceed "
"the rank of the dataset"):
_assess_dimension(spectrum, rank, n_samples, n_features)
def test_assess_dimension_small_eigenvalues():
# Test tiny eigenvalues appropriately when using 'mle'
# for PR #16224
spectrum = np.array([1, 1e-30, 1e-30, 1e-30])
n_samples = 10
n_features = 5
rank = 3
ret = _assess_dimension(spectrum, rank, n_samples, n_features)
assert ret == -np.inf
def test_infer_dim_1():
# TODO: explain what this is testing
# Or at least use explicit variable names...
n, p = 1000, 5
rng = np.random.RandomState(0)
X = (rng.randn(n, p) * 0.1 + rng.randn(n, 1) * np.array([3, 4, 5, 1, 2]) +
np.array([1, 0, 7, 4, 6]))
pca = PCA(n_components=p, svd_solver="full")
pca.fit(X)
spect = pca.explained_variance_
ll = np.array([_assess_dimension(spect, k, n) for k in range(1, p)])
assert ll[1] > ll.max() - 0.01 * n
