def test_inner_product(self, n, power_euclidean, tangent_vec_a,
tangent_vec_b, base_point, expected):
metric = SPDMetricEuclidean(n, power_euclidean)
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_power_euclidean_inner_product(self):
base_point = gs.array([[1., 0., 0.], [0., 2.5, 1.5], [0., 1.5, 2.5]])
tangent_vec = gs.array([[2., 1., 1.], [1., .5, .5], [1., .5, .5]])
metric = SPDMetricEuclidean(3, power_euclidean=.5)
result = metric.inner_product(tangent_vec, tangent_vec, base_point)
expected = [[3472 / 576]]
self.assertAllClose(result, expected)
def test_log_and_exp_euclidean_p05(self):
"""Test of SPDMetricEuclidean.log and exp methods for power_euclidean=0.5."""
base_point = gs.array([[5.0, 0.0, 0.0], [0.0, 7.0, 2.0], [0.0, 2.0, 8.0]])
point = gs.array([[9.0, 0.0, 0.0], [0.0, 5.0, 0.0], [0.0, 0.0, 1.0]])
metric = SPDMetricEuclidean(3, power_euclidean=0.5)
log = metric.log(point=point, base_point=base_point)
result = metric.exp(tangent_vec=log, base_point=base_point)
expected = point
self.assertAllClose(result, expected)
def setUp(self):
warnings.simplefilter('ignore', category=ImportWarning)
gs.random.seed(1234)
self.n = 3
self.space = SPDMatrices(n=self.n)
self.metric_affine = SPDMetricAffine(n=self.n)
self.metric_procrustes = SPDMetricProcrustes(n=self.n)
self.metric_euclidean = SPDMetricEuclidean(n=self.n)
self.metric_logeuclidean = SPDMetricLogEuclidean(n=self.n)
self.n_samples = 4
def setUp(self):
"""Set up the test."""
warnings.simplefilter('ignore', category=ImportWarning)
gs.random.seed(1234)
self.n = 3
self.space = SPDMatrices(n=self.n)
self.metric_affine = SPDMetricAffine(n=self.n)
self.metric_bureswasserstein = SPDMetricBuresWasserstein(n=self.n)
self.metric_euclidean = SPDMetricEuclidean(n=self.n)
self.metric_logeuclidean = SPDMetricLogEuclidean(n=self.n)
self.n_samples = 4
def setUp_alt(self, n=3, n_samples=4):
"""Set up the test, flexible parameters."""
warnings.simplefilter('ignore', category=ImportWarning)
gs.random.seed(1234)
self.n = n
self.space = SPDMatrices(n=self.n)
self.metric_affine = SPDMetricAffine(n=self.n)
self.metric_procrustes = SPDMetricProcrustes(n=self.n)
self.metric_euclidean = SPDMetricEuclidean(n=self.n)
self.metric_logeuclidean = SPDMetricLogEuclidean(n=self.n)
self.n_samples = n_samples
def test_power_euclidean_inner_product(self):
"""Test of SPDMetricEuclidean.inner_product method."""
base_point = gs.array([[1., 0., 0.], [0., 2.5, 1.5], [0., 1.5, 2.5]])
tangent_vec = gs.array([[2., 1., 1.], [1., .5, .5], [1., .5, .5]])
metric = SPDMetricEuclidean(3, power_euclidean=.5)
result = metric.inner_product(tangent_vec, tangent_vec, base_point)
expected = 3472 / 576
self.assertAllClose(result, expected)
result = self.metric_euclidean.inner_product(tangent_vec, tangent_vec,
base_point)
expected = MatricesMetric(3, 3).inner_product(tangent_vec, tangent_vec)
self.assertAllClose(result, expected)
def test_parallel_transport(
self, n, power_euclidean, tangent_vec_a, base_point, tangent_vec_b
):
metric = SPDMetricEuclidean(n, power_euclidean)
result = metric.parallel_transport(tangent_vec_a, base_point, tangent_vec_b)
self.assertAllClose(result, tangent_vec_a)
def test_squared_dist_is_symmetric(self, n, power_euclidean, point_a, point_b):
metric = SPDMetricEuclidean(n, power_euclidean)
sd_a_b = metric.squared_dist(point_a, point_b)
sd_b_a = metric.squared_dist(point_b, point_a)
self.assertAllClose(sd_a_b, sd_b_a, atol=gs.atol * 100)
def test_log_then_exp(self, n, power_euclidean, point, base_point):
metric = SPDMetricEuclidean(n, power_euclidean)
log = metric.log(gs.array(point), base_point=gs.array(base_point))
result = metric.exp(tangent_vec=log, base_point=gs.array(base_point))
self.assertAllClose(result, point, atol=gs.atol * 1000)
def test_log(self, n, power_euclidean, point, base_point, expected):
metric = SPDMetricEuclidean(n)
result = metric.log(gs.array(point), gs.array(base_point))
self.assertAllClose(result, gs.array(expected))
def test_exp_domain(self, n, power_euclidean, tangent_vec, base_point, expected):
metric = SPDMetricEuclidean(n, power_euclidean)
result = metric.exp_domain(
gs.array(tangent_vec), gs.array(base_point), expected
)
self.assertAllClose(result, gs.array(expected))