def test_init_arpack_v0(seed):
# check that the initalization a sampling from an uniform distribution
# where we can fix the random state
size = 1000
v0 = _init_arpack_v0(size, seed)
rng = check_random_state(seed)
assert_allclose(v0, rng.uniform(-1, 1, size=size))
def _decompose_truncated(self, mat):
if not 1 <= self.n_components <= self.n_samples_:
raise ValueError("n_components=%r must be between 1 and "
"n_samples=%r with "
"svd_solver='%s'" % (
self.n_components,
self.n_samples_,
self.svd_solver,
))
elif not isinstance(self.n_components, numbers.Integral):
raise ValueError(
"n_components=%r must be of type int "
"when greater than or equal to 1, was of type=%r" %
(self.n_components, type(self.n_components)))
elif self.svd_solver == "arpack" and self.n_components == self.n_samples_:
raise ValueError("n_components=%r must be strictly less than "
"n_samples=%r with "
"svd_solver='%s'" % (
self.n_components,
self.n_samples_,
self.svd_solver,
))
random_state = check_random_state(self.random_state)
if self._fit_svd_solver == "arpack":
v0 = _init_arpack_v0(min(mat.shape), random_state)
U, S, Vt = svds(mat, k=self.n_components, tol=self.tol, v0=v0)
# svds doesn't abide by scipy.linalg.svd/randomized_svd
# conventions, so reverse its outputs.
S = S[::-1]
# flip eigenvectors' sign to enforce deterministic output
U, Vt = svd_flip(U[:, ::-1], Vt[::-1])
# We have already eliminated all other solvers, so this must be "randomized"
else:
# sign flipping is done inside
U, S, Vt = randomized_svd(
mat,
n_components=self.n_components,
n_iter=self.iterated_power,
flip_sign=True,
random_state=random_state,
)
U[:, S < self.tol] = 0.0
Vt[S < self.tol] = 0.0
S[S < self.tol] = 0.0
return U, S, Vt
def norm_diff(A, norm=2, msg=True, random_state=None):
"""
Compute the norm diff with the original matrix, when randomized
SVD is called with *params.
norm: 2 => spectral; 'fro' => Frobenius
"""
if msg:
print("... computing %s norm ..." % norm)
if norm == 2:
# s = sp.linalg.norm(A, ord=2) # slow
v0 = _init_arpack_v0(min(A.shape), random_state)
value = sp.sparse.linalg.svds(A, k=1, return_singular_vectors=False, v0=v0)
else:
if sp.sparse.issparse(A):
value = sp.sparse.linalg.norm(A, ord=norm)
else:
value = sp.linalg.norm(A, ord=norm)
return value
def test_randomized_eigsh_compared_to_others(k):
"""Check that `_randomized_eigsh` is similar to other `eigsh`
Tests that for a random PSD matrix, `_randomized_eigsh` provides results
comparable to LAPACK (scipy.linalg.eigh) and ARPACK
(scipy.sparse.linalg.eigsh).
Note: some versions of ARPACK do not support k=n_features.
"""
# make a random PSD matrix
n_features = 200
X = make_sparse_spd_matrix(n_features, random_state=0)
# compare two versions of randomized
# rough and fast
eigvals, eigvecs = _randomized_eigsh(
X, n_components=k, selection="module", n_iter=25, random_state=0
)
# more accurate but slow (TODO find realistic settings here)
eigvals_qr, eigvecs_qr = _randomized_eigsh(
X,
n_components=k,
n_iter=25,
n_oversamples=20,
random_state=0,
power_iteration_normalizer="QR",
selection="module",
)
# with LAPACK
eigvals_lapack, eigvecs_lapack = linalg.eigh(
X, eigvals=(n_features - k, n_features - 1)
)
indices = eigvals_lapack.argsort()[::-1]
eigvals_lapack = eigvals_lapack[indices]
eigvecs_lapack = eigvecs_lapack[:, indices]
# -- eigenvalues comparison
assert eigvals_lapack.shape == (k,)
# comparison precision
assert_array_almost_equal(eigvals, eigvals_lapack, decimal=6)
assert_array_almost_equal(eigvals_qr, eigvals_lapack, decimal=6)
# -- eigenvectors comparison
assert eigvecs_lapack.shape == (n_features, k)
# flip eigenvectors' sign to enforce deterministic output
dummy_vecs = np.zeros_like(eigvecs).T
eigvecs, _ = svd_flip(eigvecs, dummy_vecs)
eigvecs_qr, _ = svd_flip(eigvecs_qr, dummy_vecs)
eigvecs_lapack, _ = svd_flip(eigvecs_lapack, dummy_vecs)
assert_array_almost_equal(eigvecs, eigvecs_lapack, decimal=4)
assert_array_almost_equal(eigvecs_qr, eigvecs_lapack, decimal=6)
# comparison ARPACK ~ LAPACK (some ARPACK implems do not support k=n)
if k < n_features:
v0 = _init_arpack_v0(n_features, random_state=0)
# "LA" largest algebraic <=> selection="value" in randomized_eigsh
eigvals_arpack, eigvecs_arpack = eigsh(
X, k, which="LA", tol=0, maxiter=None, v0=v0
)
indices = eigvals_arpack.argsort()[::-1]
# eigenvalues
eigvals_arpack = eigvals_arpack[indices]
assert_array_almost_equal(eigvals_lapack, eigvals_arpack, decimal=10)
# eigenvectors
eigvecs_arpack = eigvecs_arpack[:, indices]
eigvecs_arpack, _ = svd_flip(eigvecs_arpack, dummy_vecs)
assert_array_almost_equal(eigvecs_arpack, eigvecs_lapack, decimal=8)
