def dist(self, x, y):
# Adapted from equation 6.13 of "Positive definite matrices". Chol
# decomp gives the same result as matrix sqrt. There may be a more
# efficient way to compute this!
c = np.linalg.cholesky(x)
c_inv = np.linalg.inv(c)
l = multilog(multiprod(multiprod(c_inv, y), multitransp(c_inv)),
pos_def=True)
return la.norm(multiprod(multiprod(c, l), c_inv))
def dist(self, x, y):
# Adapted from equation 6.13 of "Positive definite matrices". The
# Cholesky decomposition gives the same result as matrix sqrt. There
# may be more efficient ways to compute this.
c = la.cholesky(x)
c_inv = la.inv(c)
logm = multilog(multiprod(multiprod(c_inv, y), multitransp(c_inv)),
pos_def=True)
return la.norm(logm)
def dist(self, x, y):
# Adapted from equation 6.13 of "Positive definite matrices". Chol
# decomp gives the same result as matrix sqrt. There may be a more
# efficient way to compute this!
c = np.linalg.cholesky(x)
c_inv = np.linalg.inv(c)
l = multilog(multiprod(multiprod(c_inv, y), multitransp(c_inv)),
pos_def=True)
return la.norm(multiprod(multiprod(c, l), c_inv))
def test_multilog(self):
A = np.zeros((self.k, self.m, self.m))
L = np.zeros((self.k, self.m, self.m))
for i in range(self.k):
a = np.diag(rnd.rand(self.m))
q, r = la.qr(rnd.randn(self.m, self.m))
A[i] = q.dot(a.dot(q.T))
L[i] = logm(A[i])
np_testing.assert_allclose(multilog(A, pos_def=True), L)
def test_multilog(self):
A = np.zeros((self.k, self.m, self.m))
l = np.zeros((self.k, self.m, self.m))
for i in range(self.k):
a = np.diag(rnd.rand(self.m))
q, r = la.qr(rnd.randn(self.m, self.m))
A[i] = q.dot(a.dot(q.T))
l[i] = logm(A[i])
np_testing.assert_allclose(multilog(A, pos_def=True), l)
def dist(self, x, y):
c = la.cholesky(x)
c_inv = la.inv(c)
logm = multilog(multiprod(multiprod(c_inv, y), multihconj(c_inv)),
pos_def=True)
return np.real(la.norm(logm))
def log(self, x, y):
c = la.cholesky(x)
c_inv = la.inv(c)
logm = multilog(multiprod(multiprod(c_inv, y), multitransp(c_inv)),
pos_def=True)
return multiprod(multiprod(c, logm), multitransp(c))
def log(self, x, y):
c = la.cholesky(x)
c_inv = la.inv(c)
l = multilog(multiprod(multiprod(c_inv, y), multitransp(c_inv)),
pos_def=True)
return multiprod(multiprod(c, l), multitransp(c))
def test_multilog_singlemat(self):
a = np.diag(rnd.rand(self.m))
q, r = la.qr(rnd.randn(self.m, self.m))
# A is a positive definite matrix
A = q.dot(a.dot(q.T))
np_testing.assert_allclose(multilog(A, pos_def=True), logm(A))
def test_multilog_singlemat(self):
a = np.diag(rnd.rand(self.m))
q, r = la.qr(rnd.randn(self.m, self.m))
# A is a positive definite matrix
A = q.dot(a.dot(q.T))
np_testing.assert_allclose(multilog(A, pos_def=True), logm(A))
