def __init__(self,
A,
y,
proxg,
eps,
x=None,
G=None,
max_iter=100,
tau=None,
sigma=None,
show_pbar=True):
self.y = y
self.x = x
self.y_device = backend.get_device(y)
if self.x is None:
with self.y_device:
self.x = self.y_device.xp.zeros(A.ishape, dtype=self.y.dtype)
self.x_device = backend.get_device(self.x)
if G is None:
self.max_eig_app = MaxEig(A.H * A,
dtype=self.x.dtype,
device=self.x_device,
show_pbar=show_pbar)
proxfc = prox.Conj(prox.L2Proj(A.oshape, eps, y=y))
else:
proxf1 = prox.L2Proj(A.oshape, eps, y=y)
proxf2 = proxg
proxfc = prox.Conj(prox.Stack([proxf1, proxf2]))
proxg = prox.NoOp(A.ishape)
A = linop.Vstack([A, G])
if tau is None or sigma is None:
max_eig = MaxEig(A.H * A,
dtype=self.x.dtype,
device=self.x_device,
show_pbar=show_pbar).run()
tau = 1
sigma = 1 / max_eig
with self.y_device:
self.u = self.y_device.xp.zeros(A.oshape, dtype=self.y.dtype)
alg = PrimalDualHybridGradient(proxfc,
proxg,
A,
A.H,
self.x,
self.u,
tau,
sigma,
max_iter=max_iter)
super().__init__(alg, show_pbar=show_pbar)
def _get_PrimalDualHybridGradient(self):
with self.y_device:
y = -self.y
A = self.A
if self.proxg is None:
proxg = prox.NoOp(self.x.shape)
else:
proxg = self.proxg
if self.lamda > 0:
def gradh(x):
with backend.get_device(self.x):
gradh_x = 0
if self.lamda > 0:
if self.z is None:
gradh_x += self.lamda * x
else:
gradh_x += self.lamda * (x - self.z)
return gradh_x
gamma_primal = self.lamda
else:
gradh = None
gamma_primal = 0
if self.G is None:
proxfc = prox.L2Reg(y.shape, 1, y=y)
gamma_dual = 1
else:
A = linop.Vstack([A, self.G])
proxf1c = prox.L2Reg(self.y.shape, 1, y=y)
proxf2c = prox.Conj(self.proxg)
proxfc = prox.Stack([proxf1c, proxf2c])
proxg = prox.NoOp(self.x.shape)
gamma_dual = 0
if self.tau is None:
if self.sigma is None:
self.sigma = 1
S = linop.Multiply(A.oshape, self.sigma)
AHA = A.H * S * A
max_eig = MaxEig(AHA,
dtype=self.x.dtype,
device=self.x_device,
max_iter=self.max_power_iter,
show_pbar=self.show_pbar).run()
self.tau = 1 / (max_eig + self.lamda)
else:
T = linop.Multiply(A.ishape, self.tau)
AAH = A * T * A.H
max_eig = MaxEig(AAH,
dtype=self.x.dtype,
device=self.x_device,
max_iter=self.max_power_iter,
show_pbar=self.show_pbar).run()
self.sigma = 1 / max_eig
with self.y_device:
u = self.y_device.xp.zeros(A.oshape, dtype=self.y.dtype)
self.alg = PrimalDualHybridGradient(proxfc,
proxg,
A,
A.H,
self.x,
u,
self.tau,
self.sigma,
gamma_primal=gamma_primal,
gamma_dual=gamma_dual,
gradh=gradh,
max_iter=self.max_iter)
def _get_PrimalDualHybridGradient(self):
with self.y_device:
A = self.A
if self.lamda > 0:
gamma_primal = self.lamda
proxg = prox.L2Reg(self.x.shape,
self.lamda,
y=self.z,
proxh=self.proxg)
else:
gamma_primal = 0
if self.proxg is None:
proxg = prox.NoOp(self.x.shape)
else:
proxg = self.proxg
if self.G is None:
proxfc = prox.L2Reg(self.y.shape, 1, y=-self.y)
gamma_dual = 1
else:
A = linop.Vstack([A, self.G])
proxf1c = prox.L2Reg(self.y.shape, 1, y=-self.y)
proxf2c = prox.Conj(proxg)
proxfc = prox.Stack([proxf1c, proxf2c])
proxg = prox.NoOp(self.x.shape)
gamma_dual = 0
if self.tau is None:
if self.sigma is None:
self.sigma = 1
S = linop.Multiply(A.oshape, self.sigma)
AHA = A.H * S * A
max_eig = MaxEig(AHA,
dtype=self.x.dtype,
device=self.x_device,
max_iter=self.max_power_iter,
show_pbar=self.show_pbar).run()
self.tau = 1 / max_eig
elif self.sigma is None:
T = linop.Multiply(A.ishape, self.tau)
AAH = A * T * A.H
max_eig = MaxEig(AAH,
dtype=self.x.dtype,
device=self.x_device,
max_iter=self.max_power_iter,
show_pbar=self.show_pbar).run()
self.sigma = 1 / max_eig
with self.y_device:
u = self.y_device.xp.zeros(A.oshape, dtype=self.y.dtype)
self.alg = PrimalDualHybridGradient(proxfc,
proxg,
A,
A.H,
self.x,
u,
self.tau,
self.sigma,
gamma_primal=gamma_primal,
gamma_dual=gamma_dual,
max_iter=self.max_iter)