def xstep(self):
r"""Minimise Augmented Lagrangian with respect to
:math:`\mathbf{x}`.
"""
self.YU[:] = self.Y - self.U
self.block_sep0(self.YU)[:] += self.S
Zf = sl.rfftn(self.YU, None, self.cri.axisN)
Z0f = self.block_sep0(Zf)
Z1f = self.block_sep1(Zf)
DZ0f = np.conj(self.Df) * Z0f
DZ0fBQ = sl.dot(self.B.dot(self.Q).T, DZ0f, axis=self.cri.axisC)
Z1fQ = sl.dot(self.Q.T, Z1f, axis=self.cri.axisC)
b = DZ0fBQ + Z1fQ
Xh = sl.solvedbd_sm(self.gDf, (self.mu / self.rho) * self.GHGf + 1.0,
b, self.c, axis=self.cri.axisM)
self.Xf[:] = sl.dot(self.Q, Xh, axis=self.cri.axisC)
self.X = sl.irfftn(self.Xf, self.cri.Nv, self.cri.axisN)
if self.opt['LinSolveCheck']:
DDXf = np.conj(self.Df) * sl.inner(self.Df, self.Xf,
axis=self.cri.axisM)
DDXfBB = sl.dot(self.B.T.dot(self.B), DDXf, axis=self.cri.axisC)
ax = self.rho * (DDXfBB + self.Xf) + \
self.mu * self.GHGf * self.Xf
b = self.rho * (sl.dot(self.B.T, DZ0f, axis=self.cri.axisC)
+ Z1f)
self.xrrs = sl.rrs(ax, b)
else:
self.xrrs = None
def xstep(self):
r"""Minimise Augmented Lagrangian with respect to
:math:`\mathbf{x}`.
"""
self.YU[:] = self.Y - self.U
self.block_sep0(self.YU)[:] += self.S
Zf = sl.rfftn(self.YU, None, self.cri.axisN)
Z0f = self.block_sep0(Zf)
Z1f = self.block_sep1(Zf)
DZ0f = np.conj(self.Df) * Z0f
DZ0fBQ = sl.dot(self.B.dot(self.Q).T, DZ0f, axis=self.cri.axisC)
Z1fQ = sl.dot(self.Q.T, Z1f, axis=self.cri.axisC)
b = DZ0fBQ + Z1fQ
Xh = sl.solvedbd_sm(self.gDf, (self.mu / self.rho) * self.GHGf + 1.0,
b, self.c, axis=self.cri.axisM)
self.Xf[:] = sl.dot(self.Q, Xh, axis=self.cri.axisC)
self.X = sl.irfftn(self.Xf, self.cri.Nv, self.cri.axisN)
if self.opt['LinSolveCheck']:
DDXf = np.conj(self.Df) * sl.inner(self.Df, self.Xf,
axis=self.cri.axisM)
DDXfBB = sl.dot(self.B.T.dot(self.B), DDXf, axis=self.cri.axisC)
ax = self.rho * (DDXfBB + self.Xf) + \
self.mu * self.GHGf * self.Xf
b = self.rho * (sl.dot(self.B.T, DZ0f, axis=self.cri.axisC)
+ Z1f)
self.xrrs = sl.rrs(ax, b)
else:
self.xrrs = None
def test_10(self):
N = 32
M = 16
K = 8
D = util.complex_randn(N, N, 1, 1, M)
X = util.complex_randn(N, N, 1, K, M)
S = np.sum(D*X, axis=4, keepdims=True)
d = 1e-1 * (np.random.randn(N, N, 1, 1, M).astype('complex') +
np.random.randn(N, N, 1, 1, M).astype('complex') * 1.0j)
Z = (D.conj()*np.sum(D*X, axis=4, keepdims=True) +
d*X - D.conj()*S) / d
Xslv = linalg.solvedbd_sm(D, d, D.conj()*S + d*Z)
assert(linalg.rrs(D.conj()*np.sum(D*Xslv, axis=4, keepdims=True) +
d*Xslv, D.conj()*S + d*Z) < 1e-11)
def test_10(self):
N = 32
M = 16
K = 8
D = util.complex_randn(N, N, 1, 1, M)
X = util.complex_randn(N, N, 1, K, M)
S = np.sum(D*X, axis=4, keepdims=True)
d = 1e-1 * (np.random.randn(N, N, 1, 1, M).astype('complex') +
np.random.randn(N, N, 1, 1, M).astype('complex') * 1.0j)
Z = (D.conj()*np.sum(D*X, axis=4, keepdims=True) +
d*X - D.conj()*S) / d
Xslv = linalg.solvedbd_sm(D, d, D.conj()*S + d*Z)
assert(linalg.rrs(D.conj()*np.sum(D*Xslv, axis=4, keepdims=True) +
d*Xslv, D.conj()*S + d*Z) < 1e-11)