def xstep(self):
r"""Minimise Augmented Lagrangian with respect to
:math:`\mathbf{x}`."""
self.X = sl.idctii(self.Gamma*sl.dctii(self.Y + self.S - self.U,
axes=self.axes), axes=self.axes)
if self.opt['LinSolveCheck']:
self.xrrs = sl.rrs(self.X + (self.lmbda/self.rho) *
sl.idctii((self.Alpha**2)*sl.dctii(self.X, axes=self.axes),
axes=self.axes), self.Y + self.S - self.U)
else:
self.xrrs = None
def xstep(self):
r"""Minimise Augmented Lagrangian with respect to
:math:`\mathbf{x}`."""
self.X = sl.idctii(self.Gamma*sl.dctii(self.Y + self.S - self.U,
axes=self.axes), axes=self.axes)
if self.opt['LinSolveCheck']:
self.xrrs = sl.rrs(
self.X + (self.lmbda/self.rho) *
sl.idctii((self.Alpha**2) *
sl.dctii(self.X, axes=self.axes),
axes=self.axes), self.Y + self.S - self.U)
else:
self.xrrs = None
def eval_objfn(self):
r"""Compute components of objective function as well as total
contribution to objective function. Data fidelity term is
:math:`(1/2) \| \mathbf{x} - \mathbf{s} \|_2^2` and
regularisation term is :math:`\| D \mathbf{x} \|_2^2`.
"""
gvr = self.obfn_gvar()
dfd = np.sum(np.abs(self.Wdf * gvr))
reg = 0.5*linalg.norm(sl.idctii(self.Alpha*sl.dctii(self.X,
axes=self.axes), axes=self.axes))**2
obj = dfd + self.lmbda*reg
return (obj, dfd, reg)
def eval_objfn(self):
r"""Compute components of objective function as well as total
contribution to objective function. Data fidelity term is
:math:`(1/2) \| \mathbf{x} - \mathbf{s} \|_2^2` and
regularisation term is :math:`\| D \mathbf{x} \|_2^2`.
"""
gvr = self.obfn_gvar()
dfd = np.sum(np.abs(self.Wdf * gvr))
reg = 0.5*np.linalg.norm(
sl.idctii(self.Alpha*sl.dctii(self.X, axes=self.axes),
axes=self.axes))**2
obj = dfd + self.lmbda*reg
return (obj, dfd, reg)