def function_and_gradient(self, x):
if not np.all(x >= self.lower_bounds):
raise_or_warn(
'Optimizer violated the lower bounds for rate matrix elements.',
self.on_error)
# compute function
K = np.zeros((self.N, self.N))
K[self.I, self.J] = x / self.pi[self.I]
K[self.J, self.I] = x / self.pi[self.J]
np.fill_diagonal(K, -sum1(K))
# compute eigendecomposition
lam, A, Ainv = eigen_decomposition(K, self.pi)
# T = kdot(kdot(A,np.diag(np.exp(self.tau*lam))),Ainv)
T = sp.linalg.expm(self.dt * K)
T[self.
zero_C] = 1.0 # set unused elements to dummy to avoid division by 0
# check T!=0 for C!=0
if np.any(np.abs(T[self.nonzero_C]) <= 1E-20):
warnings.warn(
'Warning: during iteration T_ij became very small while C(tau)_ij > 0. Regularizing T.',
NotConnectedWarning)
for i, j in zip(*self.nonzero_C):
if T[i, j] <= 1E-20:
T[i, j] = 1E-20
f = ksum(self.C * np.log(T))
if self.verbose:
logging.info('iteration=%d, log L=%f' % (self.count, f))
self.count += 1
V = getV(lam, self.dt)
# M = Ainv.dot(Ctau.T/T.T).dot(A)*V.T
M = kdot(kdot(Ainv, np.ascontiguousarray(self.C.T / T.T)),
A) * np.ascontiguousarray(V.T)
# H = A.dot(M).dot(Ainv)
H = kdot(kdot(A, M), Ainv)
grad = np.zeros(len(x))
for i in range(len(x)):
Di = self.D[i]
grad[i] = vdot(H[Di.col, Di.row],
Di.data) # this is (H.T*Di).sum()
return (-f, -grad)
def test_kdot(self):
d0 = np.random.randint(1, high=100)
d1 = np.random.randint(1, high=100)
d2 = np.random.randint(1, high=100)
a = np.random.randn(d0, d1)
b = np.random.randn(d1, d2)
assert np.allclose(a.dot(b), kahandot.kdot(a, b))
def vdot(a, b):
# Kahan summation scalar product
n = a.shape[0]
return kdot(a.reshape((1, n)), b.reshape((n, 1)))[0, 0]