def test_geigh_Lsym_bp():
Xs = [
np.random.uniform(size=(4, 5)),
np.random.uniform(size=(5, 5)),
np.random.uniform(size=(5, 1))
]
for X in Xs:
Lsym = get_sym_laplacian_bp(X)
true_evals, true_evecs = eigh_wrapper(Lsym, rank=None)
for rank in range(1, sum(X.shape) + 1):
gevals, gevecs = geigh_Lsym_bp(X,
rank=rank,
zero_tol=1e-10,
end='largest')
check_geigh_Lsym_internal_no_zeros(X, gevals, gevecs, rank)
assert np.allclose(gevals[:rank], true_evals[:rank])
gevals, gevecs = geigh_Lsym_bp(X,
rank=rank,
zero_tol=1e-10,
end='smallest')
check_geigh_Lsym_internal_no_zeros(X, gevals, gevecs, rank)
assert np.allclose(gevals[:rank], true_evals[-rank:])
rank = None
gevals, gevecs = geigh_Lsym_bp(X,
rank=rank,
zero_tol=1e-10,
end='largest')
check_geigh_Lsym_internal_no_zeros(X, gevals, gevecs, rank)
gevals, gevecs = geigh_Lsym_bp(X,
rank=rank,
zero_tol=1e-10,
end='smallest')
check_geigh_Lsym_internal_no_zeros(X, gevals, gevecs, rank)
# test with zero rows/cols
X = deepcopy(Xs)[0]
X[0, :] = 0
X[:, 0] = 0
true_gevals, true_zero_mask = true_gevals_Lsym(X)
for rank in range(1, 7 + 1):
# make sure gen evals are correct
gevals, gevecs = geigh_Lsym_bp(X,
rank=rank,
zero_tol=1e-10,
end='largest')
# check_geigh_Lsym_internal(X, gevals, gevecs, rank=rank)
assert np.allclose(gevals, true_gevals[:rank])
# check gen evecs have correct zero rows
assert np.allclose(abs(gevecs[true_zero_mask]).sum(), 0)
def check_vs_internal_smallest_eigh_Lsym_bp_from_Tsym_no_zeros(X, rank):
"""
Checks internal consistency
"""
evals, evecs = smallest_eigh_Lsym_bp_from_Tsym_no_zeros(X, rank=rank)
if rank is None:
rank = min(X.shape)
Lsym = get_sym_laplacian_bp(X)
assert len(evals) == rank
assert evecs.shape[0] == sum(X.shape)
assert evecs.shape[1] == rank
for k in range(rank):
v = evecs[:, k]
q = Lsym @ v / v
# check that v is an eigenvector
# note 0 entries give infs so we ignore these for checking
idx = np.where(abs(v) > 1e-10)[0][0] # for non nan
for i in range(len(q)):
assert np.allclose(v[i], 0) or np.allclose(q[i], q[idx])
# make sure the empirical eval is equal to the returned evals
assert np.allclose(q[idx], evals[k])
assert np.allclose(evecs.T @ evecs, np.eye(rank))
def true_gevals_Lsym(X, zero_tol=1e-10):
Lsym = get_sym_laplacian_bp(X)
true_evals, true_evecs = eigh_wrapper(Lsym, rank=None)
zero_row_mask = np.linalg.norm(X, axis=1) < zero_tol
zero_col_mask = np.linalg.norm(X, axis=0) < zero_tol
n_iso_verts = sum(zero_row_mask) + sum(zero_col_mask)
meow = max(X.shape) - n_iso_verts
true_gevals = np.concatenate([
true_evals[0:meow], [1] * (max(X.shape) - min(X.shape)),
true_evals[-meow:]
])
true_gevals = np.sort(true_gevals)[::-1]
true_zero_mask = np.concatenate([zero_row_mask, zero_col_mask])
return true_gevals, true_zero_mask
def check_eigh_Lsym_bp_from_Tsym(X, rank=None):
"""
Checks the output of get_sym_laplacian_bp
"""
Lsym = get_sym_laplacian_bp(X)
true_evals, true_evecs = eigh_wrapper(Lsym)
if rank is None:
_rank = min(X.shape)
else:
_rank = rank
# check largest eigenvectors
evals, evecs = eigh_Lsym_bp_from_Tsym(X, end='largest', rank=rank)
for k in range(len(evals)):
# check the evals are correct
assert np.allclose(evals[k], true_evals[k])
if not np.allclose(evals[k], 1): # non-unique subspace for 1 evals
# check eigenvectors point in the same direction
a = angle(true_evecs[:, k], evecs[:, k], subspace=True)
assert a < 1e-4
# check normalization
assert np.allclose(evecs.T @ evecs, np.eye(evecs.shape[1]))
# check smallest eigenvectors
evals, evecs = eigh_Lsym_bp_from_Tsym(X, end='smallest', rank=rank)
base_idx = sum(X.shape) - min(X.shape) + (min(X.shape) - _rank)
for k in range(len(evals)):
# check the evals are correct
assert np.allclose(evals[k], true_evals[base_idx + k])
if not np.allclose(evals[k], 1): # non-unique subspace for 1 evals
# check eigenvectors point in the same direction
a = angle(true_evecs[:, base_idx + k], evecs[:, k], subspace=True)
assert a < 1e-4
# check normalization
assert np.allclose(evecs.T @ evecs, np.eye(evecs.shape[1]))
def check_vs_truth_smallest_eigh_Lsym_bp_from_Tsym_no_zeros(X, rank):
"""
Check against ground truth
"""
evals, evecs = smallest_eigh_Lsym_bp_from_Tsym_no_zeros(X, rank=rank)
if rank is None:
rank = min(X.shape)
Lsym = get_sym_laplacian_bp(X)
evals_true, evecs_true = eigh_wrapper(A=Lsym)
evals_true = evals_true[-rank:]
evecs_true = evecs_true[:, -rank:]
# check gevals match true gecals
assert np.allclose(evals, evals_true)
# check evecs span the correct space
for k in range(rank):
# ignore 1 evals since the evecs are non-unique
if not np.allclose(evals[k], 1):
assert angle(evecs[:, k], evecs_true[:, k], subspace=True) < 1e-4