class TestProductManifold(unittest.TestCase):
def setUp(self):
self.m = m = 100
self.n = n = 50
self.euclidean = Euclidean(m, n)
self.sphere = Sphere(n)
self.man = Product([self.euclidean, self.sphere])
def test_dim(self):
np_testing.assert_equal(self.man.dim, self.m*self.n+self.n-1)
def test_typicaldist(self):
np_testing.assert_equal(self.man.typicaldist,
np.sqrt((self.m*self.n)+np.pi**2))
def test_dist(self):
X = self.man.rand()
Y = self.man.rand()
np_testing.assert_equal(self.man.dist(X, Y),
np.sqrt(
self.euclidean.dist(X[0], Y[0])**2 +
self.sphere.dist(X[1], Y[1])**2))
# def test_inner(self):
# def test_proj(self):
# def test_ehess2rhess(self):
# def test_retr(self):
# def test_egrad2rgrad(self):
# def test_norm(self):
# def test_rand(self):
# def test_randvec(self):
# def test_transp(self):
def test_exp_log_inverse(self):
s = self.man
X = s.rand()
Y = s.rand()
Yexplog = s.exp(X, s.log(X, Y))
np_testing.assert_almost_equal(s.dist(Y, Yexplog), 0)
def test_log_exp_inverse(self):
s = self.man
X = s.rand()
U = s.randvec(X)
Ulogexp = s.log(X, s.exp(X, U))
np_testing.assert_array_almost_equal(U[0], Ulogexp[0])
np_testing.assert_array_almost_equal(U[1], Ulogexp[1])
def test_pairmean(self):
s = self.man
X = s.rand()
Y = s.rand()
Z = s.pairmean(X, Y)
np_testing.assert_array_almost_equal(s.dist(X, Z), s.dist(Y, Z))
class TestProductManifold(unittest.TestCase):
def setUp(self):
self.m = m = 100
self.n = n = 50
self.euclidean = Euclidean(m, n)
self.sphere = Sphere(n)
self.man = Product([self.euclidean, self.sphere])
def test_dim(self):
np_testing.assert_equal(self.man.dim, self.m * self.n + self.n - 1)
def test_typicaldist(self):
np_testing.assert_equal(self.man.typicaldist,
np.sqrt((self.m * self.n) + np.pi**2))
def test_dist(self):
X = self.man.rand()
Y = self.man.rand()
np_testing.assert_equal(
self.man.dist(X, Y),
np.sqrt(
self.euclidean.dist(X[0], Y[0])**2 +
self.sphere.dist(X[1], Y[1])**2))
def test_tangent_vector_multiplication(self):
# Regression test for https://github.com/pymanopt/pymanopt/issues/49.
man = Product((Euclidean(12), Grassmann(12, 3)))
x = man.rand()
eta = man.randvec(x)
np.float64(1.0) * eta
# def test_inner(self):
# def test_proj(self):
# def test_ehess2rhess(self):
# def test_retr(self):
# def test_egrad2rgrad(self):
# def test_norm(self):
# def test_rand(self):
# def test_randvec(self):
# def test_transp(self):
def test_exp_log_inverse(self):
s = self.man
X = s.rand()
Y = s.rand()
Yexplog = s.exp(X, s.log(X, Y))
np_testing.assert_almost_equal(s.dist(Y, Yexplog), 0)
def test_log_exp_inverse(self):
s = self.man
X = s.rand()
U = s.randvec(X)
Ulogexp = s.log(X, s.exp(X, U))
np_testing.assert_array_almost_equal(U[0], Ulogexp[0])
np_testing.assert_array_almost_equal(U[1], Ulogexp[1])
def test_pairmean(self):
s = self.man
X = s.rand()
Y = s.rand()
Z = s.pairmean(X, Y)
np_testing.assert_array_almost_equal(s.dist(X, Z), s.dist(Y, Z))
class TestProductManifold(unittest.TestCase):
def setUp(self):
self.m = m = 100
self.n = n = 50
self.euclidean = Euclidean(m, n)
self.sphere = Sphere(n)
self.man = Product([self.euclidean, self.sphere])
def test_dim(self):
np_testing.assert_equal(self.man.dim, self.m * self.n + self.n - 1)
def test_typicaldist(self):
np_testing.assert_equal(self.man.typicaldist,
np.sqrt((self.m * self.n) + np.pi**2))
def test_dist(self):
X = self.man.rand()
Y = self.man.rand()
np_testing.assert_equal(
self.man.dist(X, Y),
np.sqrt(
self.euclidean.dist(X[0], Y[0])**2 +
self.sphere.dist(X[1], Y[1])**2))
# def test_inner(self):
# def test_proj(self):
# def test_ehess2rhess(self):
# def test_retr(self):
# def test_egrad2rgrad(self):
# def test_norm(self):
# def test_rand(self):
# def test_randvec(self):
# def test_transp(self):
def test_exp_log_inverse(self):
s = self.man
X = s.rand()
Y = s.rand()
Yexplog = s.exp(X, s.log(X, Y))
np_testing.assert_almost_equal(s.dist(Y, Yexplog), 0)
def test_log_exp_inverse(self):
s = self.man
X = s.rand()
U = s.randvec(X)
Ulogexp = s.log(X, s.exp(X, U))
np_testing.assert_array_almost_equal(U[0], Ulogexp[0])
np_testing.assert_array_almost_equal(U[1], Ulogexp[1])
def test_pairmean(self):
s = self.man
X = s.rand()
Y = s.rand()
Z = s.pairmean(X, Y)
np_testing.assert_array_almost_equal(s.dist(X, Z), s.dist(Y, Z))
class TestProductManifold(ManifoldTestCase):
def setUp(self):
self.m = m = 100
self.n = n = 50
self.euclidean = Euclidean(m, n)
self.sphere = Sphere(n)
self.manifold = Product([self.euclidean, self.sphere])
point = self.manifold.random_point()
@pymanopt.function.autograd(self.manifold)
def cost(*x):
return np.sum([np.linalg.norm(a - b)**2 for a, b in zip(x, point)])
self.cost = cost
def test_dim(self):
np_testing.assert_equal(self.manifold.dim,
self.m * self.n + self.n - 1)
def test_typical_dist(self):
np_testing.assert_equal(self.manifold.typical_dist,
np.sqrt((self.m * self.n) + np.pi**2))
def test_dist(self):
X = self.manifold.random_point()
Y = self.manifold.random_point()
np_testing.assert_equal(
self.manifold.dist(X, Y),
np.sqrt(
self.euclidean.dist(X[0], Y[0])**2 +
self.sphere.dist(X[1], Y[1])**2),
)
def test_tangent_vector_multiplication(self):
# Regression test for https://github.com/pymanopt/pymanopt/issues/49.
manifold = Product((Euclidean(12), Grassmann(12, 3)))
x = manifold.random_point()
eta = manifold.random_tangent_vector(x)
np.float64(1.0) * eta
# def test_inner_product(self):
# def test_projection(self):
# def test_euclidean_to_riemannian_hessian(self):
# def test_retraction(self):
def test_first_order_function_approximation(self):
self.run_gradient_approximation_test()
def test_second_order_function_approximation(self):
self.run_hessian_approximation_test()
# def test_norm(self):
# def test_random_point(self):
# def test_random_tangent_vector(self):
# def test_transport(self):
def test_exp_log_inverse(self):
s = self.manifold
X = s.random_point()
Y = s.random_point()
Yexplog = s.exp(X, tangent_vector=s.log(X, Y))
np_testing.assert_almost_equal(s.dist(point_a=Y, point_b=Yexplog), 0)
def test_log_exp_inverse(self):
s = self.manifold
X = s.random_point()
U = s.random_tangent_vector(X)
Ulogexp = s.log(X, s.exp(X, U))
np_testing.assert_array_almost_equal(U[0], Ulogexp[0])
np_testing.assert_array_almost_equal(U[1], Ulogexp[1])
def test_pair_mean(self):
s = self.manifold
X = s.random_point()
Y = s.random_point()
Z = s.pair_mean(X, Y)
np_testing.assert_array_almost_equal(s.dist(X, Z), s.dist(Y, Z))
