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# -*- coding: utf-8 -*-
# CCP in Tomographic Imaging (CCPi) Core Imaging Library (CIL).
# Copyright 2017 UKRI-STFC
# Copyright 2017 University of Manchester
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from __future__ import unicode_literals
from ccpi.optimisation.operators import LinearOperator
from ccpi.framework import BlockGeometry, BlockDataContainer
from ccpi.optimisation.operators import FiniteDiff
class SymmetrizedGradient(LinearOperator):
r'''Symmetrized Gradient Operator: E: V -> W
V : range of the Gradient Operator
W : range of the Symmetrized Gradient
Example (2D):
.. math::
v = (v1, v2) \\
Ev = 0.5 * ( \nabla\cdot v + (\nabla\cdot c)^{T} ) \\
\begin{matrix}
\partial_{y} v1 & 0.5 * (\partial_{x} v1 + \partial_{y} v2) \\
0.5 * (\partial_{x} v1 + \partial_{y} v2) & \partial_{x} v2
\end{matrix}
'''
CORRELATION_SPACE = "Space"
CORRELATION_SPACECHANNEL = "SpaceChannels"
def __init__(self, gm_domain, bnd_cond = 'Neumann', **kwargs):
'''creator
:param gm_domain: domain of the operator
:param bnd_cond: boundary condition, either :code:`Neumann` or :code:`Periodic`.
:type bnd_cond: str, optional, default :code:`Neumann`
:param correlation: :code:`SpaceChannel` or :code:`Channel`
:type correlation: str, optional, default :code:`Channel`
'''
super(SymmetrizedGradient, self).__init__()
self.gm_domain = gm_domain
self.bnd_cond = bnd_cond
self.correlation = kwargs.get('correlation',SymmetrizedGradient.CORRELATION_SPACE)
tmp_gm = len(self.gm_domain.geometries)*self.gm_domain.geometries
self.gm_range = BlockGeometry(*tmp_gm)
# Define FD operator. We need one geometry from the BlockGeometry of the domain
self.FD = FiniteDiff(self.gm_domain.get_item(0), direction = 0, bnd_cond = self.bnd_cond)
if self.gm_domain.shape[0]==2:
self.order_ind = [0,2,1,3]
else:
self.order_ind = [0,3,6,1,4,7,2,5,8]
def direct(self, x, out=None):
'''Returns E(v)'''
if out is None:
tmp = []
for i in range(self.gm_domain.shape[0]):
for j in range(x.shape[0]):
self.FD.direction = i
tmp.append(self.FD.adjoint(x.get_item(j)))
tmp1 = [tmp[i] for i in self.order_ind]
res = [0.5 * sum(x) for x in zip(tmp, tmp1)]
return BlockDataContainer(*res)
else:
ind = 0
for i in range(self.gm_domain.shape[0]):
for j in range(x.shape[0]):
self.FD.direction = i
self.FD.adjoint(x.get_item(j), out=out[ind])
ind+=1
out1 = BlockDataContainer(*[out[i] for i in self.order_ind])
out.fill( 0.5 * (out + out1) )
def adjoint(self, x, out=None):
if out is None:
tmp = [None]*self.gm_domain.shape[0]
i = 0
for k in range(self.gm_domain.shape[0]):
tmp1 = 0
for j in range(self.gm_domain.shape[0]):
self.FD.direction = j
tmp1 += self.FD.direct(x[i])
i+=1
tmp[k] = tmp1
return BlockDataContainer(*tmp)
else:
tmp = self.gm_domain.allocate()
i = 0
for k in range(self.gm_domain.shape[0]):
tmp1 = 0
for j in range(self.gm_domain.shape[0]):
self.FD.direction = j
self.FD.direct(x[i], out=tmp[j])
i+=1
tmp1+=tmp[j]
out[k].fill(tmp1)
def domain_geometry(self):
return self.gm_domain
def range_geometry(self):
return self.gm_range
if __name__ == '__main__':
###########################################################################
## Symmetrized Gradient Tests
from ccpi.framework import ImageGeometry
from ccpi.optimisation.operators import Gradient
import numpy as np
N, M = 2, 3
K = 2
C = 2
###########################################################################
# 2D geometry no channels
ig = ImageGeometry(N, M)
Grad = Gradient(ig)
E1 = SymmetrizedGradient(Grad.range_geometry())
np.testing.assert_almost_equal(E1.norm(), np.sqrt(8), 1e-5)
print(E1.domain_geometry().shape, E1.range_geometry().shape)
u1 = E1.domain_geometry().allocate('random_int')
w1 = E1.range_geometry().allocate('random_int', symmetry = True)
lhs = E1.direct(u1).dot(w1)
rhs = u1.dot(E1.adjoint(w1))
np.testing.assert_almost_equal(lhs, rhs)
###########################################################################
# 2D geometry with channels
ig2 = ImageGeometry(N, M, channels = C)
Grad2 = Gradient(ig2, correlation = 'Space')
E2 = SymmetrizedGradient(Grad2.range_geometry())
np.testing.assert_almost_equal(E2.norm(), np.sqrt(12), 1e-6)
print(E2.domain_geometry().shape, E2.range_geometry().shape)
u2 = E2.domain_geometry().allocate('random_int')
w2 = E2.range_geometry().allocate('random_int', symmetry = True)
#
lhs2 = E2.direct(u2).dot(w2)
rhs2 = u2.dot(E2.adjoint(w2))
np.testing.assert_almost_equal(lhs2, rhs2)
###########################################################################
# 3D geometry no channels
ig3 = ImageGeometry(N, M, K)
Grad3 = Gradient(ig3, correlation = 'Space')
E3 = SymmetrizedGradient(Grad3.range_geometry())
np.testing.assert_almost_equal(E3.norm(), np.sqrt(12), 1e-6)
print(E3.domain_geometry().shape, E3.range_geometry().shape)
u3 = E3.domain_geometry().allocate('random_int')
w3 = E3.range_geometry().allocate('random_int', symmetry = True)
#
lhs3 = E3.direct(u3).dot(w3)
rhs3 = u3.dot(E3.adjoint(w3))
np.testing.assert_almost_equal(lhs3, rhs3)
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