def f_Y(Y_in):
Y = np.reshape(Y_in, (k, n))
L = np.dot(U, Y)
loss_data = grslra.lpnorm(X - L)
E = (L - hankel.orth_proj(L))
loss_lambda = -innerprod(Lambda, E) / (m * n)
loss_structure = rho / 2.0 * np.linalg.norm(E, 'fro')**2 / (m * n)
return loss_data + loss_lambda + loss_structure
def prepare(self, iteration):
G_old = self.G
H_old = self.H
self.prepare_grad()
if not (iteration % self.params["direction_reset_rate"]):
# set search direction as negative gradient at initialization or when reset due
self.H = self.space.get_H(self.G, 0.0, 0.0)
else:
tauG = self.space.transport(G_old, self.X_old, H_old, self.t)
tauH = self.space.transport(H_old, self.X_old, H_old, self.t)
gamma_HS = innerprod(self.G - tauG, self.G) / (innerprod(self.G - tauG, tauH) + 1E-16) # Hestenes-Stiefel update
gamma_HS = np.maximum(gamma_HS, 0)
# gamma_DY = innerprod(self.G, self.G) / (innerprod(self.G - tauG, tauH)) # Dai-Yuan update
# gamma_FR = innerprod(self.G, self.G) / innerprod(tauG, tauG) # Fletcher-Reeves update
# gamma_PR = np.maximum(innerprod(self.G, self.G - tauG) / innerprod(tauG, tauG), 0.0) # Polak-Ribiere update
self.H = self.space.get_H(self.G, gamma_HS, tauH)
self.GH = innerprod(self.G, self.H)
if self.GH > 0:
self.H = self.space.get_H(self.G, 0.0, 0.0)
self.GH = innerprod(self.G, self.H)
def f_Lambda_U(U_in):
U = np.reshape(U_in, (m, k))
L = np.dot(U, Y)
E = (L - hankel.orth_proj(L))
loss_lambda = -innerprod(Lambda, E) / (m * n)
return loss_lambda
def f_Lambda_Y(Y_in):
Y = np.reshape(Y_in, (k, n))
L = np.dot(U, Y)
E = (L - hankel.orth_proj(L))
loss_lambda = -innerprod(Lambda, E) / (m * n)
return loss_lambda
def prepare(self, iteration):
self.prepare_grad()
self.H = self.space.get_H(self.G, 0.0, 0.0)
self.GH = innerprod(self.G, self.H)