def __init__(self, kernel_type, projection=False, **params):
self.kernel_type = kernel_type
self.projection = projection
self.params_keys = set(params.keys())
self.__check_args_coherence()
# Sampling
self.sampling_mode = 'GS' # Gram-Schmidt
self.list_of_samples = []
# when using .sample_k_dpp_*
self.size_k_dpp = 0
self.E_poly = None # evaluation of the
# Attributes relative to K correlation kernel:
# K, K_eig_vals, K_eig_vecs, A_zono
self.K = is_symmetric(params.get('K', None))
if self.projection:
self.K = is_projection(self.K)
e_vals, e_vecs = params.get('K_eig_dec', [None, None])
if self.projection:
self.K_eig_vals = is_equal_to_O_or_1(e_vals)
else:
self.K_eig_vals = is_in_01(e_vals)
self.eig_vecs = is_orthonormal_columns(e_vecs)
self.A_zono = is_full_row_rank(params.get('A_zono', None))
# Attributes relative to L likelihood kernel:
# L, L_eig_vals, L_eig_vecs, L_gram_factor, L_dual, L_dual_eig_vals, L_dual_eig_vecs
self.L = is_symmetric(params.get('L', None))
if self.projection:
self.L = is_projection(self.L)
e_vals, e_vecs = params.get('L_eig_dec', [None, None])
if self.projection:
self.L_eig_vals = is_equal_to_O_or_1(e_vals)
else:
self.L_eig_vals = is_geq_0(e_vals)
if self.eig_vecs is None: # K_eig_vecs = L_eig_vecs
self.eig_vecs = is_orthonormal_columns(e_vecs)
# L' "dual" likelihood kernel, L' = Phi Phi.T, Phi = L_gram_factor
self.L_gram_factor = params.get('L_gram_factor', None)
self.L_dual = None
self.L_dual_eig_vals = None
self.L_dual_eig_vecs = None
if self.L_gram_factor is not None:
Phi = self.L_gram_factor
d, N = Phi.shape
if d < N:
self.L_dual = Phi.dot(Phi.T)
print('L_dual = Phi Phi.T was computed: Phi (dxN) with d<N')
else:
if self.L is None:
self.L = Phi.T.dot(Phi)
print('L = Phi.T Phi was computed: Phi (dxN) with d>=N')
def test_kernel_evaluations(self):
N = 100
dims = np.arange(2, 5)
for d in dims:
with self.subTest(dimension=d):
jacobi_params = 0.5 - np.random.rand(d, 2)
jacobi_params[0, :] = -0.5
dpp = MultivariateJacobiOPE(N, jacobi_params)
X = np.random.rand(20, d)
Y = np.random.rand(20, d)
K_XX = is_symmetric(dpp.K(X, X))
K_xx = np.diag(K_XX)
K_xy = np.ravel([dpp.K(x, y) for x, y in zip(X, Y)])
checks = ((dpp.K(X), K_XX),
(dpp.K(X, X, eval_pointwise=True), K_xx),
(dpp.K(X, Y, eval_pointwise=True), K_xy))
for idx, (a, b) in enumerate(checks):
with self.subTest(idx=idx):
self.assertTrue(np.allclose(a, b),
'a={}, b={}'.format(a, b))
def test_symmetric(self):
N = 20
X = rndm.randn(N, N)
list_of_inputs = [(True, None), (False, X), (True, X.T + X),
(True, X.T.dot(X))]
for idx, (flag, _input) in enumerate(list_of_inputs):
with self.subTest(index=idx, is_symmetric=flag):
if flag:
self.assertTrue(utils.is_symmetric(_input) is _input)
else:
with self.assertRaises(ValueError) as context:
utils.is_symmetric(_input)
self.assertIn('M.T != M', str(context.exception))
def test_symmetric(self):
self.assertIsNone(utils.is_symmetric(None))
X = rndm.randn(20, 20)
sym_part = 0.5 * (X + X.T)
self.assertTrue(np.allclose(utils.is_symmetric(sym_part), sym_part))
with self.assertRaises(ValueError) as context:
utils.is_symmetric(X)
self.assertTrue('M.T != M' in str(context.exception))
Y = rndm.randn(20, 30)
cov = Y.T.dot(Y)
self.assertTrue(np.allclose(utils.is_symmetric(cov), cov))
with self.assertRaises(ValueError) as context:
utils.is_symmetric(Y)
self.assertTrue('M.T != M' in str(context.exception))
def __init__(self, kernel_type, projection=False, **params):
self.kernel_type = kernel_type
self.projection = projection
self.params_keys = set(params.keys())
self.__check_args_coherence()
# Sampling
self.sampling_mode = 'GS' # Gram-Schmidt
self.list_of_samples = []
# when using .sample_k_dpp_*
self.size_k_dpp = 0
self.E_poly = None # evaluation of the
# Attributes relative to K correlation kernel:
# K, K_eig_vals, K_eig_vecs, A_zono
self.K = is_symmetric(params.get('K', None))
if self.projection:
self.K = is_projection(self.K)
e_vals, e_vecs = params.get('K_eig_dec', [None, None])
if self.projection:
self.K_eig_vals = is_equal_to_O_or_1(e_vals)
else:
self.K_eig_vals = is_in_01(e_vals)
self.eig_vecs = is_orthonormal_columns(e_vecs)
self.A_zono = is_full_row_rank(params.get('A_zono', None))
# Attributes relative to L likelihood kernel:
# L, L_eig_vals, L_eig_vecs, L_gram_factor, L_dual
self.L = is_symmetric(params.get('L', None))
if self.projection:
self.L = is_projection(self.L)
e_vals, e_vecs = params.get('L_eig_dec', [None, None])
if self.projection:
self.L_eig_vals = is_equal_to_O_or_1(e_vals)
else:
self.L_eig_vals = is_geq_0(e_vals)
if self.eig_vecs is None: # K_eig_vecs = L_eig_vecs
self.eig_vecs = is_orthonormal_columns(e_vecs)
# L' "dual" likelihood kernel, L' = Phi Phi.T, Phi = L_gram_factor
self.L_gram_factor = params.get('L_gram_factor', None)
self.L_dual = None
if self.L_gram_factor is not None:
Phi = self.L_gram_factor
d, N = Phi.shape
if d < N:
self.L_dual = Phi.dot(Phi.T)
print('L_dual = Phi Phi.T was computed: Phi (dxN) with d<N')
else:
if self.L is None:
self.L = Phi.T.dot(Phi)
print('L = Phi.T Phi was computed: Phi (dxN) with d>=N')
# L likelihood function representation
# eval_L(X, Y) = L(X, Y)
# eval_L(X) = L(X, X)
self.eval_L, self.X_data = params.get('L_eval_X_data', [None, None])
self.intermediate_sample_info = None
if self.eval_L is not None:
if not callable(self.eval_L):
raise ValueError(
'eval_L should be a positive semi-definite kernel function'
)
if self.X_data is not None:
if not (self.X_data.size and self.X_data.ndim == 2):
err_print = [
'Wrong shape = {}'.format(self.X_data.shape),
'X_data should be a non empty (N x d) ndarray'
]
raise ValueError('\n'.join(err_print))