def test_rand(self):
# Just make sure that things generated are on the manifold and that
# if you generate two they are not equal.
X = self.man.rand()
np_testing.assert_allclose(multiprod(multitransp(X), X), multieye(self.k, self.n), atol=1e-10)
Y = self.man.rand()
assert np.linalg.norm(X - Y) > 1e-6
def test_rand(self):
# Just make sure that things generated are on the manifold and that
# if you generate two they are not equal.
X = self.man.rand()
np_testing.assert_allclose(multiprod(multitransp(X), X),
multieye(self.k, self.n), atol=1e-10)
Y = self.man.rand()
assert np.linalg.norm(X - Y) > 1e-6
def test_random_point(self):
# Just make sure that things generated are on the manifold and that
# if you generate two they are not equal.
X = self.manifold.random_point()
np_testing.assert_allclose(multihconj(X) @ X,
multieye(self.k, self.n),
atol=1e-10)
Y = self.manifold.random_point()
assert np.linalg.norm(X - Y) > 1e-6
assert np.iscomplex(X).all()
def test_exp(self):
# Check that exp lies on the manifold and that exp of a small vector u
# is close to x + u.
s = self.man
x = s.rand()
u = s.randvec(x)
xexpu = s.exp(x, u)
np_testing.assert_allclose(multiprod(multitransp(xexpu), xexpu), multieye(self.k, self.n), atol=1e-10)
u = u * 1e-6
xexpu = s.exp(x, u)
np_testing.assert_allclose(xexpu, x + u)
def test_retr(self):
# Test that the result is on the manifold and that for small
# tangent vectors it has little effect.
x = self.man.rand()
u = self.man.randvec(x)
xretru = self.man.retr(x, u)
np_testing.assert_allclose(multiprod(multitransp(xretru), xretru), multieye(self.k, self.n), atol=1e-10)
u = u * 1e-6
xretru = self.man.retr(x, u)
np_testing.assert_allclose(xretru, x + u)
def test_exp(self):
# Check that exp lies on the manifold and that exp of a small vector u
# is close to x + u.
s = self.man
x = s.rand()
u = s.randvec(x)
xexpu = s.exp(x, u)
np_testing.assert_allclose(multiprod(multitransp(xexpu), xexpu),
multieye(self.k, self.n), atol=1e-10)
u = u * 1e-6
xexpu = s.exp(x, u)
np_testing.assert_allclose(xexpu, x + u)
def test_retr(self):
# Test that the result is on the manifold and that for small
# tangent vectors it has little effect.
x = self.man.rand()
u = self.man.randvec(x)
xretru = self.man.retr(x, u)
np_testing.assert_allclose(multiprod(multitransp(xretru), xretru),
multieye(self.k, self.n),
atol=1e-10)
u = u * 1e-6
xretru = self.man.retr(x, u)
np_testing.assert_allclose(xretru, x + u)
def test_retraction(self):
# Test that the result is on the manifold and that for small
# tangent vectors it has little effect.
x = self.manifold.random_point()
u = self.manifold.random_tangent_vector(x)
xretru = self.manifold.retraction(x, u)
np_testing.assert_allclose(
multitransp(xretru) @ xretru,
multieye(self.k, self.n),
atol=1e-10,
)
u = u * 1e-6
xretru = self.manifold.retraction(x, u)
np_testing.assert_allclose(xretru, x + u)
def test_random_point(self):
point = self.so.random_point()
assert point.shape == (self.n, self.n)
np_testing.assert_almost_equal(point.T @ point - point @ point.T, 0)
np_testing.assert_almost_equal(point.T @ point, np.eye(self.n))
assert np.allclose(np.linalg.det(point), 1)
point = self.so_product.random_point()
assert point.shape == (self.k, self.n, self.n)
np_testing.assert_almost_equal(
multitransp(point) @ point - point @ multitransp(point),
0,
)
np_testing.assert_almost_equal(
multitransp(point) @ point, multieye(self.k, self.n)
)
assert np.allclose(np.linalg.det(point), 1)
def test_exp(self):
# Check that exp lies on the manifold and that exp of a small vector u
# is close to x + u.
s = self.manifold
x = s.random_point()
u = s.random_tangent_vector(x)
xexpu = s.exp(x, u)
np_testing.assert_allclose(
multitransp(xexpu) @ xexpu,
multieye(self.k, self.n),
atol=1e-10,
)
u = u * 1e-6
xexpu = s.exp(x, u)
np_testing.assert_allclose(xexpu, x + u)
def exp(self, point, tangent_vector):
pt_tv = multitransp(point) @ tangent_vector
if self._k == 1:
identity = np.eye(self._p)
else:
identity = multieye(self._k, self._p)
a = np.block([point, tangent_vector])
b = multiexpm(
np.block([
[
pt_tv,
-multitransp(tangent_vector) @ tangent_vector,
],
[identity, pt_tv],
]))[..., :self._p]
c = multiexpm(-pt_tv)
return a @ (b @ c)
def test_multieye(self):
A = np.zeros((self.k, self.n, self.n))
for i in range(self.k):
A[i] = np.eye(self.n)
np_testing.assert_allclose(A, multieye(self.k, self.n))
def test_multieye(self):
A = np.zeros((self.k, self.n, self.n))
for i in range(self.k):
A[i] = np.eye(self.n)
np_testing.assert_allclose(A, multieye(self.k, self.n))
