def test_cholesky_factor(self, n, spd_mat, cf):
result = SPDMatrices.cholesky_factor(gs.array(spd_mat))
self.assertAllClose(result, gs.array(cf))
self.assertAllClose(
gs.all(PositiveLowerTriangularMatrices(n).belongs(result)),
gs.array(True),
)
def differential_cholesky_factor(cls, tangent_vec, base_point):
"""Compute the differential of the cholesky factor map.
Parameters
----------
tangent_vec : array_like, shape=[..., n, n]
Tangent vector at base point.
symmetric matrix.
base_point : array_like, shape=[..., n, n]
Base point.
spd matrix.
Returns
-------
differential_cf : array-like, shape=[..., n, n]
Differential of cholesky factor map
lower triangular matrix.
"""
cf = cls.cholesky_factor(base_point)
differential_cf = PositiveLowerTriangularMatrices.inverse_differential_gram(
tangent_vec, cf)
return differential_cf
def test_cholesky_factor_belongs(self, n, mat):
result = SPDMatrices(n).cholesky_factor(gs.array(mat))
self.assertAllClose(
gs.all(PositiveLowerTriangularMatrices(n).belongs(result)), True
)
class CholeskyMetricTestData(_RiemannianMetricTestData):
n_list = random.sample(range(2, 5), 2)
metric_args_list = [(n, ) for n in n_list]
shape_list = [(n, n) for n in n_list]
space_list = [PositiveLowerTriangularMatrices(n) for n in n_list]
n_points_list = random.sample(range(1, 5), 2)
n_tangent_vecs_list = random.sample(range(1, 5), 2)
n_points_a_list = random.sample(range(1, 5), 2)
n_points_b_list = [1]
batch_size_list = random.sample(range(2, 5), 2)
alpha_list = [1] * 2
n_rungs_list = [1] * 2
scheme_list = ["pole"] * 2
def diag_inner_product_test_data(self):
smoke_data = [
dict(
n=2,
tangent_vec_a=[[1.0, 0.0], [-2.0, -1.0]],
tangent_vec_b=[[2.0, 0.0], [-3.0, -1.0]],
base_point=[[SQRT_2, 0.0], [-3.0, 1.0]],
expected=2.0,
)
]
return self.generate_tests(smoke_data)
def strictly_lower_inner_product_test_data(self):
smoke_data = [
dict(
n=2,
tangent_vec_a=[[1.0, 0.0], [-2.0, -1.0]],
tangent_vec_b=[[2.0, 0.0], [-3.0, -1.0]],
expected=6.0,
)
]
return self.generate_tests(smoke_data)
def inner_product_test_data(self):
smoke_data = [
dict(
n=2,
tangent_vec_a=[[1.0, 0.0], [-2.0, -1.0]],
tangent_vec_b=[[2.0, 0.0], [-3.0, -1.0]],
base_point=[[SQRT_2, 0.0], [-3.0, 1.0]],
expected=8.0,
),
dict(
n=2,
tangent_vec_a=[
[[3.0, 0.0], [4.0, 2.0]],
[[-1.0, 0.0], [2.0, -4.0]],
],
tangent_vec_b=[[[4.0, 0.0], [3.0, 3.0]],
[[3.0, 0.0], [-6.0, 2.0]]],
base_point=[[[3, 0.0], [-2.0, 6.0]], [[1, 0.0], [-1.0, 1.0]]],
expected=[13.5, -23.0],
),
]
return self.generate_tests(smoke_data)
def exp_test_data(self):
smoke_data = [
dict(
n=2,
tangent_vec=[[-1.0, 0.0], [2.0, 3.0]],
base_point=[[1.0, 0.0], [2.0, 2.0]],
expected=[[1 / EULER, 0.0], [4.0, 2 * gs.exp(1.5)]],
),
dict(
n=2,
tangent_vec=[[[0.0, 0.0], [2.0, 0.0]], [[1.0, 0.0], [0.0,
0.0]]],
base_point=[[[1.0, 0.0], [2.0, 2.0]], [[1.0, 0.0], [0.0,
2.0]]],
expected=[
[[1.0, 0.0], [4.0, 2.0]],
[[gs.exp(1.0), 0.0], [0.0, 2.0]],
],
),
]
return self.generate_tests(smoke_data)
def log_test_data(self):
smoke_data = [
dict(
n=2,
point=[[EULER, 0.0], [2.0, EULER**3]],
base_point=[[EULER**3, 0.0], [4.0, EULER**4]],
expected=[[-2.0 * EULER**3, 0.0], [-2.0, -1 * EULER**4]],
),
dict(
n=2,
point=[
[[gs.exp(-2.0), 0.0], [0.0, gs.exp(2.0)]],
[[gs.exp(-3.0), 0.0], [2.0, gs.exp(3.0)]],
],
base_point=[[[1.0, 0.0], [-1.0, 1.0]], [[1.0, 0.0], [0.0,
1.0]]],
expected=[[[-2.0, 0.0], [1.0, 2.0]], [[-3.0, 0.0], [2.0,
3.0]]],
),
]
return self.generate_tests(smoke_data)
def squared_dist_test_data(self):
smoke_data = [
dict(
n=2,
point_a=[[EULER, 0.0], [2.0, EULER**3]],
point_b=[[EULER**3, 0.0], [4.0, EULER**4]],
expected=9,
),
dict(
n=2,
point_a=[
[[EULER, 0.0], [2.0, EULER**3]],
[[EULER, 0.0], [4.0, EULER**3]],
],
point_b=[
[[EULER**3, 0.0], [4.0, EULER**4]],
[[EULER**3, 0.0], [7.0, EULER**4]],
],
expected=[9, 14],
),
]
return self.generate_tests(smoke_data)
def exp_shape_test_data(self):
return self._exp_shape_test_data(self.metric_args_list,
self.space_list, self.shape_list)
def log_shape_test_data(self):
return self._log_shape_test_data(self.metric_args_list,
self.space_list)
def squared_dist_is_symmetric_test_data(self):
return self._squared_dist_is_symmetric_test_data(
self.metric_args_list,
self.space_list,
self.n_points_a_list,
self.n_points_b_list,
atol=gs.atol * 1000,
)
def exp_belongs_test_data(self):
return self._exp_belongs_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
belongs_atol=gs.atol * 1000,
)
def log_is_tangent_test_data(self):
return self._log_is_tangent_test_data(
self.metric_args_list,
self.space_list,
self.n_points_list,
is_tangent_atol=gs.atol * 1000,
)
def geodesic_ivp_belongs_test_data(self):
return self._geodesic_ivp_belongs_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_points_list,
belongs_atol=gs.atol * 1000,
)
def geodesic_bvp_belongs_test_data(self):
return self._geodesic_bvp_belongs_test_data(
self.metric_args_list,
self.space_list,
self.n_points_list,
belongs_atol=gs.atol * 1000,
)
def exp_after_log_test_data(self):
return self._exp_after_log_test_data(
self.metric_args_list,
self.space_list,
self.n_points_list,
rtol=gs.rtol * 100,
atol=gs.atol * 10000,
)
def log_after_exp_test_data(self):
return self._log_after_exp_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
rtol=gs.rtol * 100,
atol=gs.atol * 10000,
)
def exp_ladder_parallel_transport_test_data(self):
return self._exp_ladder_parallel_transport_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
self.n_rungs_list,
self.alpha_list,
self.scheme_list,
)
def exp_geodesic_ivp_test_data(self):
return self._exp_geodesic_ivp_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
self.n_points_list,
rtol=gs.rtol * 100000,
atol=gs.atol * 100000,
)
def parallel_transport_ivp_is_isometry_test_data(self):
return self._parallel_transport_ivp_is_isometry_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
is_tangent_atol=gs.atol * 1000,
atol=gs.atol * 1000,
)
def parallel_transport_bvp_is_isometry_test_data(self):
return self._parallel_transport_bvp_is_isometry_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
is_tangent_atol=gs.atol * 1000,
atol=gs.atol * 1000,
)
def dist_is_symmetric_test_data(self):
return self._dist_is_symmetric_test_data(
self.metric_args_list,
self.space_list,
self.n_points_a_list,
self.n_points_b_list,
)
def dist_is_positive_test_data(self):
return self._dist_is_positive_test_data(
self.metric_args_list,
self.space_list,
self.n_points_a_list,
self.n_points_b_list,
)
def squared_dist_is_positive_test_data(self):
return self._squared_dist_is_positive_test_data(
self.metric_args_list,
self.space_list,
self.n_points_a_list,
self.n_points_b_list,
)
def dist_is_norm_of_log_test_data(self):
return self._dist_is_norm_of_log_test_data(
self.metric_args_list,
self.space_list,
self.n_points_a_list,
self.n_points_b_list,
)
def dist_point_to_itself_is_zero_test_data(self):
return self._dist_point_to_itself_is_zero_test_data(
self.metric_args_list, self.space_list, self.n_points_list)
def inner_product_is_symmetric_test_data(self):
return self._inner_product_is_symmetric_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
)
def retraction_lifting_test_data(self):
return self._log_after_exp_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
rtol=gs.rtol * 100,
atol=gs.atol * 10000,
)
