def sum1(M):
# 1-D Kahan summation along axis 1
n, m = M.shape
x = np.zeros(n)
for i in range(n):
x[i] = ksum(np.reshape(M[i, :], (1, m)))
return x
def function(self, x):
self.count += 1
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))
T = sp.linalg.expm(self.dt * K) # use eigendecomposition instead?
T[self.
zero] = 1.0 # set unused elements to dummy to avoid division by 0
# check T!=0 for C!=0
nonzero_C = np.where(self.C != 0)
if np.any(np.abs(T[nonzero_C]) <= 1E-20):
warnings.warn(
'Warning: during iteration T_ij became very small while C(tau)_ij > 0.',
NotConnectedWarning)
f = ksum(self.C * np.log(T))
if self.verbose:
logging.info('iteration=%d, log L=%f' % (self.count, f))
return -f
def function(self, x):
self.count += 1
if self.sparsity is None:
assert np.all(x >= 0)
else:
assert np.all(x > 0)
# 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))
T = sp.linalg.expm(self.dt * K) # use eigendecomposition instead?
T[self.
zero] = 1.0 # set unused elements to dummy to avoid division by 0
# check T!=0 for C!=0
nonzero_C = np.where(self.C != 0)
if np.any(np.abs(T[nonzero_C]) <= 1E-15):
warnings.warn(
'Warning: during iteration T_ij became very small while C(tau)_ij > 0.',
NotConnectedWarning)
f = ksum(self.C * np.log(T))
if self.verbose:
logging.info('iteration=%d, log L=%f' % (self.count, f))
return -f
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)