def test_inner_product(self, n, tangent_vec_a, tangent_vec_b, base_point,
expected):
metric = SPDMetricBuresWasserstein(n)
result = metric.inner_product(gs.array(tangent_vec_a),
gs.array(tangent_vec_b),
gs.array(base_point))
self.assertAllClose(result, gs.array(expected))
def test_bureswasserstein_inner_product(self):
"""Test of SPDMetricBuresWasserstein.inner_product method."""
base_point = gs.array([[1., 0., 0.], [0., 1.5, .5], [0., .5, 1.5]])
tangent_vec_a = gs.array([[2., 1., 1.], [1., .5, .5], [1., .5, .5]])
tangent_vec_b = gs.array([[1., 2., 4.], [2., 3., 8.], [4., 8., 5.]])
metric = SPDMetricBuresWasserstein(3)
result = metric.inner_product(tangent_vec_a, tangent_vec_b, base_point)
expected = gs.array(4.)
self.assertAllClose(result, expected)
class TestQuotientMetric(geomstats.tests.TestCase):
def setup_method(self):
gs.random.seed(0)
n = 3
self.bundle = BuresWassersteinBundle(n)
self.base = self.bundle.base
self.base_metric = SPDMetricBuresWasserstein(n)
self.quotient_metric = QuotientMetric(self.bundle)
def test_belongs(self):
point = self.base.random_point()
result = self.bundle.belongs(point)
self.assertTrue(result)
def test_riemannian_submersion(self):
mat = self.bundle.random_point()
point = self.bundle.riemannian_submersion(mat)
result = self.bundle.belongs(point)
self.assertTrue(result)
def test_lift_and_riemannian_submersion(self):
point = self.base.random_point()
mat = self.bundle.lift(point)
result = self.bundle.riemannian_submersion(mat)
self.assertAllClose(result, point)
def test_tangent_riemannian_submersion(self):
mat = self.bundle.random_point()
point = self.bundle.riemannian_submersion(mat)
vec = self.bundle.random_point()
tangent_vec = self.bundle.tangent_riemannian_submersion(vec, point)
result = self.base.is_tangent(tangent_vec, point)
self.assertTrue(result)
def test_horizontal_projection(self):
mat = self.bundle.random_point()
vec = self.bundle.random_point()
horizontal_vec = self.bundle.horizontal_projection(vec, mat)
product = Matrices.mul(horizontal_vec, GeneralLinear.inverse(mat))
is_horizontal = Matrices.is_symmetric(product)
self.assertTrue(is_horizontal)
def test_vertical_projection(self):
mat = self.bundle.random_point()
vec = self.bundle.random_point()
vertical_vec = self.bundle.vertical_projection(vec, mat)
result = self.bundle.tangent_riemannian_submersion(vertical_vec, mat)
expected = gs.zeros_like(result)
self.assertAllClose(result, expected, atol=1e-5)
def test_horizontal_lift_and_tangent_riemannian_submersion(self):
mat = self.bundle.random_point()
tangent_vec = Matrices.to_symmetric(self.bundle.random_point())
horizontal = self.bundle.horizontal_lift(tangent_vec, fiber_point=mat)
result = self.bundle.tangent_riemannian_submersion(horizontal, mat)
self.assertAllClose(result, tangent_vec)
def test_is_horizontal(self):
mat = self.bundle.random_point()
tangent_vec = Matrices.to_symmetric(self.bundle.random_point())
horizontal = self.bundle.horizontal_lift(tangent_vec, fiber_point=mat)
result = self.bundle.is_horizontal(horizontal, mat)
self.assertTrue(result)
def test_is_vertical(self):
mat = self.bundle.random_point()
tangent_vec = self.bundle.random_point()
vertical = self.bundle.vertical_projection(tangent_vec, mat)
result = self.bundle.is_vertical(vertical, mat)
self.assertTrue(result)
@geomstats.tests.autograd_tf_and_torch_only
def test_align(self):
point = self.bundle.random_point(2)
aligned = self.bundle.align(point[0], point[1], tol=1e-10)
result = self.bundle.is_horizontal(point[1] - aligned,
point[1],
atol=1e-4)
self.assertTrue(result)
def test_inner_product(self):
mat = self.bundle.random_point()
point = self.bundle.riemannian_submersion(mat)
tangent_vecs = Matrices.to_symmetric(self.bundle.random_point(2)) / 10
result = self.quotient_metric.inner_product(tangent_vecs[0],
tangent_vecs[1],
fiber_point=mat)
expected = self.base_metric.inner_product(tangent_vecs[0],
tangent_vecs[1], point)
self.assertAllClose(result, expected)
def test_exp(self):
mat = self.bundle.random_point()
point = self.bundle.riemannian_submersion(mat)
tangent_vec = Matrices.to_symmetric(self.bundle.random_point()) / 5
result = self.quotient_metric.exp(tangent_vec, point)
expected = self.base_metric.exp(tangent_vec, point)
self.assertAllClose(result, expected)
@geomstats.tests.autograd_tf_and_torch_only
def test_log(self):
mats = self.bundle.random_point(2)
points = self.bundle.riemannian_submersion(mats)
result = self.quotient_metric.log(points[1], points[0])
expected = self.base_metric.log(points[1], points[0])
self.assertAllClose(result, expected, atol=3e-4)
@geomstats.tests.autograd_tf_and_torch_only
def test_squared_dist(self):
mats = self.bundle.random_point(2)
points = self.bundle.riemannian_submersion(mats)
result = self.quotient_metric.squared_dist(points[1],
points[0],
tol=1e-10)
expected = self.base_metric.squared_dist(points[1], points[0])
self.assertAllClose(result, expected)
def test_integrability_tensor(self):
mat = self.bundle.random_point()
point = self.bundle.riemannian_submersion(mat)
tangent_vec = Matrices.to_symmetric(self.bundle.random_point()) / 5
with pytest.raises(NotImplementedError):
self.bundle.integrability_tensor(tangent_vec, tangent_vec, point)
class TestQuotientMetric(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(0)
n = 3
self.base = SPDMatrices(n)
self.base_metric = SPDMetricBuresWasserstein(n)
self.group = SpecialOrthogonal(n)
self.bundle = FiberBundle(GeneralLinear(n),
base=self.base,
group=self.group)
self.quotient_metric = QuotientMetric(self.bundle,
ambient_metric=MatricesMetric(
n, n))
def submersion(point):
return GeneralLinear.mul(point, GeneralLinear.transpose(point))
def tangent_submersion(tangent_vec, base_point):
product = GeneralLinear.mul(base_point,
GeneralLinear.transpose(tangent_vec))
return 2 * GeneralLinear.to_symmetric(product)
def horizontal_lift(tangent_vec, point, base_point=None):
if base_point is None:
base_point = submersion(point)
sylvester = gs.linalg.solve_sylvester(base_point, base_point,
tangent_vec)
return GeneralLinear.mul(sylvester, point)
self.bundle.submersion = submersion
self.bundle.tangent_submersion = tangent_submersion
self.bundle.horizontal_lift = horizontal_lift
self.bundle.lift = gs.linalg.cholesky
def test_belongs(self):
point = self.base.random_uniform()
result = self.bundle.belongs(point)
self.assertTrue(result)
def test_submersion(self):
mat = self.bundle.total_space.random_uniform()
point = self.bundle.submersion(mat)
result = self.bundle.belongs(point)
self.assertTrue(result)
def test_lift_and_submersion(self):
point = self.base.random_uniform()
mat = self.bundle.lift(point)
result = self.bundle.submersion(mat)
self.assertAllClose(result, point)
def test_tangent_submersion(self):
mat = self.bundle.total_space.random_uniform()
point = self.bundle.submersion(mat)
vec = self.bundle.total_space.random_uniform()
tangent_vec = self.bundle.tangent_submersion(vec, point)
result = self.base.is_tangent(tangent_vec, point)
self.assertTrue(result)
def test_horizontal_projection(self):
mat = self.bundle.total_space.random_uniform()
vec = self.bundle.total_space.random_uniform()
horizontal_vec = self.bundle.horizontal_projection(vec, mat)
product = GeneralLinear.mul(horizontal_vec, GeneralLinear.inverse(mat))
is_horizontal = GeneralLinear.is_symmetric(product)
self.assertTrue(is_horizontal)
def test_vertical_projection(self):
mat = self.bundle.total_space.random_uniform()
vec = self.bundle.total_space.random_uniform()
vertical_vec = self.bundle.vertical_projection(vec, mat)
result = self.bundle.tangent_submersion(vertical_vec, mat)
expected = gs.zeros_like(result)
self.assertAllClose(result, expected, atol=1e-5)
def test_horizontal_lift_and_tangent_submersion(self):
mat = self.bundle.total_space.random_uniform()
tangent_vec = GeneralLinear.to_symmetric(
self.bundle.total_space.random_uniform())
horizontal = self.bundle.horizontal_lift(tangent_vec, mat)
result = self.bundle.tangent_submersion(horizontal, mat)
self.assertAllClose(result, tangent_vec)
def test_is_horizontal(self):
mat = self.bundle.total_space.random_uniform()
tangent_vec = GeneralLinear.to_symmetric(
self.bundle.total_space.random_uniform())
horizontal = self.bundle.horizontal_lift(tangent_vec, mat)
result = self.bundle.is_horizontal(horizontal, mat)
self.assertTrue(result)
def test_is_vertical(self):
mat = self.bundle.total_space.random_uniform()
tangent_vec = self.bundle.total_space.random_uniform()
vertical = self.bundle.vertical_projection(tangent_vec, mat)
result = self.bundle.is_vertical(vertical, mat)
self.assertTrue(result)
def test_align(self):
point = self.bundle.total_space.random_uniform(2)
aligned = self.bundle.align(point[0], point[1], tol=1e-10)
result = self.bundle.is_horizontal(point[1] - aligned,
point[1],
atol=1e-5)
self.assertTrue(result)
def test_inner_product(self):
mat = self.bundle.total_space.random_uniform()
point = self.bundle.submersion(mat)
tangent_vecs = GeneralLinear.to_symmetric(
self.bundle.total_space.random_uniform(2)) / 10
result = self.quotient_metric.inner_product(tangent_vecs[0],
tangent_vecs[1],
point=mat)
expected = self.base_metric.inner_product(tangent_vecs[0],
tangent_vecs[1], point)
self.assertAllClose(result, expected)
def test_exp(self):
mat = self.bundle.total_space.random_uniform()
point = self.bundle.submersion(mat)
tangent_vec = GeneralLinear.to_symmetric(
self.bundle.total_space.random_uniform()) / 5
result = self.quotient_metric.exp(tangent_vec, point)
expected = self.base_metric.exp(tangent_vec, point)
self.assertAllClose(result, expected)
def test_log(self):
mats = self.bundle.total_space.random_uniform(2)
points = self.bundle.submersion(mats)
result = self.quotient_metric.log(points[1], points[0], tol=1e-10)
expected = self.base_metric.log(points[1], points[0])
self.assertAllClose(result, expected, atol=3e-4)
def test_squared_dist(self):
mats = self.bundle.total_space.random_uniform(2)
points = self.bundle.submersion(mats)
result = self.quotient_metric.squared_dist(points[1],
points[0],
tol=1e-10)
expected = self.base_metric.squared_dist(points[1], points[0])
self.assertAllClose(result, expected, atol=1e-5)