def spatial_vfield_gradient(self, i):
if self.alpha == 0:
return ZeroOperator(self.space, range=self.vf_space)
else:
functional = self
i -= self.N
if i == self.N - 1:
return ZeroOperator(self.space, self.vf_space)
else:
class VfieldDerivative(Operator):
def __init__(self):
super(VfieldDerivative,
self).__init__(functional.space,
functional.vf_space)
def _call(self, x, out):
xim = x[:functional.N]
xvf = x[functional.N:]
res = functional.residual(xim[i + 1], xim[i], xvf[i])
dhuber = functional.huber.gradient(res)
tmp = functional.tau * functional.grad(
xim[i + 1]) * dhuber
tmp *= functional.alpha
out.assign(tmp)
return VfieldDerivative()
def spatial_vfield_gradient(self, i):
functional = self
i -= self.N
if i == self.N - 1:
return ZeroOperator(self.space, self.vf_space)
else:
class VfieldDerivative(Operator):
def __init__(self):
super(VfieldDerivative,
self).__init__(functional.space, functional.vf_space)
def _call(self, x, out):
xim = x[:functional.N]
ret = functional.grad(xim[i + 1]) * functional.lagr_mult[i]
out.assign(ret)
return VfieldDerivative()
def spatial_image_gradient(self, i):
if self.alpha[i] == 0:
return ZeroOperator(self.space, range=self.image_space)
else:
functional = self
class auxOperator(Operator):
def __init__(self):
super(auxOperator, self).__init__(functional.space,
functional.image_space)
def _call(self, x, out):
xim = x[:functional.N]
xi = xim[i]
ret = functional.alpha[i] * (
functional.forward.adjoint *
(functional.forward -
ConstantOperator(functional.data[i])))(xi)
out.assign(ret)
return auxOperator()
def __getitem__(self, index):
"""Get sub-operator by index.
Parameters
----------
index : int or tuple of int
A pair of integers given as (row, col).
Returns
-------
suboperator : `ReductionOperator`, `Operator` or ``0``
If index is an integer, return the row given by the index.
If index is a tuple, it must have two elements.
if there is an operator at ``(row, col)``, the operator is
returned, otherwise ``0``.
Examples
--------
>>> r3 = odl.rn(3)
>>> pspace = odl.ProductSpace(r3, r3)
>>> I = odl.IdentityOperator(r3)
>>> prod_op = ProductSpaceOperator([[0, I],
... [0, 0]],
... domain=pspace, range=pspace)
>>> prod_op[0, 0]
0
>>> prod_op[0, 1]
IdentityOperator(rn(3))
>>> prod_op[1, 0]
0
>>> prod_op[1, 1]
0
By accessing single indices, a row is extracted as a
`ReductionOperator`:
>>> prod_op[0]
ReductionOperator(ZeroOperator(rn(3)), IdentityOperator(rn(3)))
"""
if isinstance(index, tuple):
row, col = index
linear_index = np.flatnonzero((self.ops.row == row)
& (self.ops.col == col))
if linear_index.size == 0:
return 0
else:
return self.ops.data[int(linear_index)]
else:
index = int(index)
ops = [None] * len(self.domain)
for op, col, row in zip(self.ops.data, self.ops.col, self.ops.row):
if row == index:
ops[col] = op
for i in range(len(self.domain)):
if ops[i] is None:
ops[i] = ZeroOperator(self.domain[i])
return ReductionOperator(*ops)
def spatial_image_gradient(self, i):
if self.alpha == 0:
return ZeroOperator(self.space, range=self.image_space)
else:
functional = self
if i == 0:
class FirstImageDerivative(Operator):
def __init__(self):
super(FirstImageDerivative,
self).__init__(functional.space,
functional.image_space)
def _call(self, x, out):
xim = x[:functional.N]
xvf = x[functional.N:]
res = -functional.huber.gradient(
functional.residual(xim[1], xim[0], xvf[0]))
res *= functional.alpha
out.assign(res)
return FirstImageDerivative()
if i == self.N - 1:
class LastImageDerivative(Operator):
def __init__(self):
super(LastImageDerivative,
self).__init__(functional.space,
functional.image_space)
def _call(self, x, out):
xim = x[:functional.N]
xvf = x[functional.N:]
res = functional.residual(xim[-1], xim[-2], xvf[-2])
dhuber = functional.huber.gradient(res)
P = PointwiseInner(functional.vf_space, xvf[-2])
tmp = dhuber - functional.tau * (
P(functional.grad(dhuber)) -
functional.grad.adjoint(xvf[-2]) * dhuber)
tmp *= functional.alpha
out.assign(tmp)
return LastImageDerivative()
if 0 < i < self.N - 1:
class IntermediateImageDerivative(Operator):
def __init__(self):
super(IntermediateImageDerivative,
self).__init__(functional.space,
functional.image_space)
def _call(self, x, out):
xim = x[:functional.N]
xvf = x[functional.N:]
resi = functional.residual(xim[i], xim[i - 1],
xvf[i - 1])
resii = functional.residual(xim[i + 1], xim[i], xvf[i])
dhuberi = functional.huber.gradient(resi)
dhuberii = functional.huber.gradient(resii)
P = PointwiseInner(functional.vf_space, xvf[i - 1])
tmp = dhuberi - functional.tau * (
P(functional.grad(dhuberi)) -
functional.grad.adjoint(xvf[i - 1]) * dhuberi)
tmp -= dhuberii
tmp *= functional.alpha
out.assign(tmp)
return IntermediateImageDerivative()
else:
raise ValueError('time index out of range')
def spatial_vfield_gradient(self, i):
i -= self.N
return ZeroOperator(self.space, range=self.vf_space)