def objective(self, x, use_ad=False):
# unpack variable
beta = x[self.idx_beta]
gamma = x[self.idx_gamma]
delta = x[self.idx_delta]
# trimming option
if self.use_trimming:
sqrt_w = np.sqrt(self.w)
sqrt_W = sqrt_w.reshape(self.N, 1)
F_beta = self.F(beta) * sqrt_w
Y = self.Y * sqrt_w
Z = self.Z * sqrt_W
if self.std_flag == 0:
V = self.V**self.w
elif self.std_flag == 1:
V = np.repeat(delta[0], self.N)**self.w
elif self.std_flag == 2:
V = np.repeat(delta, self.n)**self.w
else:
F_beta = self.F(beta)
Y = self.Y
Z = self.Z
if self.std_flag == 0:
V = self.V
elif self.std_flag == 1:
V = np.repeat(delta[0], self.N)
elif self.std_flag == 2:
V = np.repeat(delta, self.n)
# residual and variance
R = Y - F_beta
D = utils.VarMat(V, Z, gamma, self.n)
val = 0.5 * self.N * np.log(2.0 * np.pi)
if use_ad:
# should only use when testing
varmat = D
D = varmat.varMat()
inv_D = varmat.invVarMat()
val += 0.5 * np.log(np.linalg.det(D))
val += 0.5 * R.dot(inv_D.dot(R))
else:
val += 0.5 * D.logDet()
val += 0.5 * R.dot(D.invDot(R))
# add gpriors
if self.use_regularizer:
val += 0.5 * self.hw.dot((self.H(x) - self.hm)**2)
if self.use_gprior:
val += 0.5 * self.gw.dot((x - self.gm)**2)
if self.use_lprior:
val += self.lw.dot(x[self.k:])
return val
def degree_of_freedom(self):
"""Compute the degree of freedom of the model
only considered in term of beta
"""
if self.soln is None:
print("Please fit the data first.")
if self.use_trimming:
sqrt_w = np.sqrt(self.w)
sqrt_W = sqrt_w.reshape(self.N, 1)
F_beta = self.F(self.beta) * sqrt_w
JF_beta = self.JF(self.beta) * sqrt_W
Y = self.Y * sqrt_w
Z = self.Z * sqrt_W
if self.std_flag == 0:
V = self.V**self.w
elif self.std_flag == 1:
V = np.repeat(delta[0], self.N)**self.w
elif self.std_flag == 2:
V = np.repeat(delta, self.n)**self.w
else:
F_beta = self.F(self.beta)
JF_beta = self.JF(self.beta)
Y = self.Y
Z = self.Z
if self.std_flag == 0:
V = self.V
elif self.std_flag == 1:
V = np.repeat(delta[0], self.N)
elif self.std_flag == 2:
V = np.repeat(delta, self.n)
D = utils.VarMat(V, Z, self.gamma, self.n)
# compute the Hessian matrix
hess = JF_beta.T.dot(D.invDot(JF_beta))
if self.use_regularizer:
JH_beta = self.JH(self.soln)[:, self.idx_beta]
hess += (JH_beta.T * self.hw).dot(JH_beta)
# substract the active constraints
lb_beta = self.lb[self.idx_beta]
ub_beta = self.ub[self.idx_beta]
JC_beta = np.eye(self.k_beta)
active_id = (np.abs(self.beta - lb_beta) < 1e-7) |\
(np.abs(self.beta - ub_beta) < 1e-7)
if np.any(active_id):
JC_beta = JC_beta[active_id]
else:
JC_beta = np.array([]).reshape(0, self.k_beta)
if self.use_constraints:
JC_beta_more = self.JC(self.soln)[:, self.idx_beta]
active_id = (np.abs(self.C(self.soln) - self.cl) < 1e-7) |\
(np.abs(self.C(self.soln) - self.cu) < 1e-7)
if np.any(active_id):
JC_beta_more = JC_beta_more[active_id]
else:
JC_beta_more = np.array([]).reshape(0, self.k_beta)
JC_beta = np.vstack((JC_beta, JC_beta_more))
if JC_beta.size != 0:
cw = np.repeat(1e15, JC_beta.shape[0])
hess += (JC_beta.T * cw).dot(JC_beta)
hat_mat = JF_beta.dot(np.linalg.pinv(hess)).dot(D.invDot(JF_beta).T)
df = np.trace(hat_mat)
return df
def gradient(self, x, use_ad=False, eps=1e-12):
if use_ad:
# should only use when testing
g = np.zeros(self.k_total)
z = x + 0j
for i in range(self.k_total):
z[i] += eps * 1j
g[i] = self.objective(z, use_ad=use_ad).imag / eps
z[i] -= eps * 1j
return g
# unpack variable
beta = x[self.idx_beta]
gamma = x[self.idx_gamma]
delta = x[self.idx_delta]
gamma[gamma <= 0.0] = 0.0
# trimming option
if self.use_trimming:
sqrt_w = np.sqrt(self.w)
sqrt_W = sqrt_w.reshape(self.N, 1)
F_beta = self.F(beta) * sqrt_w
JF_beta = self.JF(beta) * sqrt_W
Y = self.Y * sqrt_w
Z = self.Z * sqrt_W
if self.std_flag == 0:
V = self.V**self.w
elif self.std_flag == 1:
V = np.repeat(delta[0], self.N)**self.w
elif self.std_flag == 2:
V = np.repeat(delta, self.n)**self.w
else:
F_beta = self.F(beta)
JF_beta = self.JF(beta)
Y = self.Y
Z = self.Z
if self.std_flag == 0:
V = self.V
elif self.std_flag == 1:
V = np.repeat(delta[0], self.N)
elif self.std_flag == 2:
V = np.repeat(delta, self.n)
# residual and variance
R = Y - F_beta
D = utils.VarMat(V, Z, gamma, self.n)
# gradient for beta
DR = D.invDot(R)
g_beta = -JF_beta.T.dot(DR)
# gradient for gamma
DZ = D.invDot(Z)
g_gamma = 0.5*np.sum(Z*DZ, axis=0) -\
0.5*np.sum(
np.add.reduceat(DZ.T*R, self.idx_split, axis=1)**2,
axis=1)
# gradient for delta
if self.std_flag == 0:
g_delta = np.array([])
elif self.std_flag == 1:
d = -DR**2 + D.invDiag()
if self.use_trimming:
v = np.repeat(delta[0], self.N)
d *= self.w * (v**(self.w - 1.0))
g_delta = 0.5 * np.array([np.sum(d)])
elif self.std_flag == 2:
d = -DR**2 + D.invDiag()
if self.use_trimming:
v = np.repeat(delta, self.n)
d *= self.w * (v**(self.w - 1.0))
g_delta = 0.5 * (np.add.reduceat(d, self.idx_split))
g = np.hstack((g_beta, g_gamma, g_delta))
# add gradient from the regularizer
if self.use_regularizer:
g += self.JH(x).T.dot((self.H(x) - self.hm) * self.hw)
# add gradient from the gprior
if self.use_gprior:
g += (x[:self.k] - self.gm) * self.gw
# add gradient from the lprior
if self.use_lprior:
g = np.hstack((g, self.lw))
return g
def get_varmat(model: LimeTr):
S = model.S**model.w
Z = model.Z * np.sqrt(model.w)[:, None]
n = model.n
gamma = model.gamma
return utils.VarMat(S**2, Z, gamma, n)