def xstep(self):
r"""Minimise Augmented Lagrangian with respect to :math:`\mathbf{x}`."""
self.X = np.asarray(sl.lu_solve_ATAI(
self.D, self.rho, self.DTS + self.rho * (self.Y - self.U), self.lu,
self.piv),
dtype=self.dtype)
def xstep(self):
r"""Minimise Augmented Lagrangian with respect to
:math:`\mathbf{x}`.
"""
YU = self.Y - self.U
self.X = np.asarray(sl.lu_solve_ATAI(self.D, 1.0, self.block_sep0(YU) +
self.D.T.dot(self.block_sep1(YU)), self.lu, self.piv),
dtype=self.dtype)
def xistep(self, i):
r"""
Minimise Augmented Lagrangian with respect to :math:`\mathbf{x}`
component :math:`\mathbf{x}_i`.
"""
self.X[..., i] = spl.lu_solve_ATAI(self.A[i], self.rho,
self.ATS[i] + self.rho*(self.Y - self.U[..., i]),
self.lu[i], self.piv[i])
def xistep(self, i):
r"""
Minimise Augmented Lagrangian with respect to :math:`\mathbf{x}`
component :math:`\mathbf{x}_i`.
"""
self.X[..., i] = spl.lu_solve_ATAI(self.A[i], self.rho,
self.ATS[i] + self.rho*(self.Y - self.U[..., i]),
self.lu[i], self.piv[i])
def test_02(self):
rho = 1e-1
N = 128
M = 64
K = 32
D = np.random.randn(N, M)
X = np.random.randn(M, K)
S = D.dot(X)
Z = (D.T.dot(D).dot(X) + rho*X - D.T.dot(S)) / rho
lu, piv = linalg.lu_factor(D, rho)
Xslv = linalg.lu_solve_ATAI(D, rho, D.T.dot(S) + rho*Z, lu, piv)
assert(linalg.rrs(D.T.dot(D).dot(Xslv) + rho*Xslv,
D.T.dot(S) + rho*Z) < 1e-14)
def test_02(self):
rho = 1e-1
N = 128
M = 64
K = 32
D = np.random.randn(N, M)
X = np.random.randn(M, K)
S = D.dot(X)
Z = (D.T.dot(D).dot(X) + rho*X - D.T.dot(S)) / rho
lu, piv = linalg.lu_factor(D, rho)
Xslv = linalg.lu_solve_ATAI(D, rho, D.T.dot(S) + rho*Z, lu, piv)
assert(linalg.rrs(D.T.dot(D).dot(Xslv) + rho*Xslv,
D.T.dot(S) + rho*Z) < 1e-14)
def xstep(self):
r"""Minimise Augmented Lagrangian with respect to :math:`\mathbf{x}`."""
self.X = np.asarray(sl.lu_solve_ATAI(
self.D, self.rho, self.DTS + self.rho * (self.Y - self.U), self.lu,
self.piv),
dtype=self.dtype)
if self.opt['LinSolveCheck']:
b = self.DTS + self.rho * (self.Y - self.U)
ax = self.D.T.dot(self.D.dot(self.X)) + self.rho * self.X
self.xrrs = sl.rrs(ax, b)
else:
self.xrrs = None
def xstep(self):
self.extra_timer.start('xstep')
rhs = self.cnst_A0T(self._Y0 - self._U0) + \
self.gamma * (self.gamma * self._Y1 - self._U1)
# NOTE:
# Here we solve the sparse code X for each batch index i, since X is
# organized as [batch_size, num_atoms, num_signals]. This interface
# may be modified for online setting.
for i in range(self.X.shape[0]):
self.X[i] = np.asarray(
sl.lu_solve_ATAI(self.D, self.gamma**2, rhs[i], self.lu, self.piv),
dtype=self.dtype
)
self.extra_timer.stop('xstep')
