def test_multiexpm_conjugate_symmetric(self):
shape = (self.k, self.m, self.m)
A = np.random.normal(size=shape) + 1j * np.random.normal(size=shape)
A = 0.5 * (A + multihconj(A))
# Compare fast path for conjugate symmetric matrices vs. general slow
# one.
np_testing.assert_allclose(multiexpm(A, symmetric=True),
multiexpm(A, symmetric=False))
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 geodesic(point_a, point_b, alpha):
if alpha < 0 or 1 < alpha:
raise ValueError("Exponent must be in [0,1]")
c = np.linalg.cholesky(point_a)
c_inv = np.linalg.inv(c)
log_cbc = multilogm(
c_inv @ point_b @ multitransp(c_inv),
positive_definite=True,
)
powm = multiexpm(alpha * log_cbc, symmetric=False)
return c @ powm @ multitransp(c)
def test_multiexpm(self):
A = multisym(np.random.normal(size=(self.k, self.m, self.m)))
e = np.zeros((self.k, self.m, self.m))
for i in range(self.k):
e[i] = expm(A[i])
np_testing.assert_allclose(multiexpm(A, symmetric=True), e)
def test_multiexpm_singlemat(self):
# A is a positive definite matrix
A = np.random.normal(size=(self.m, self.m))
A = A + A.T
np_testing.assert_allclose(multiexpm(A, symmetric=True), expm(A))
def exp(self, point, tangent_vector):
p_inv_tv = np.linalg.solve(point, tangent_vector)
return point @ multiexpm(p_inv_tv, symmetric=False)
def exp(self, point, tangent_vector):
return point @ multiexpm(tangent_vector)