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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
import numpy as np
class FiniteDiff(LinearOperator):
'''Finite Difference Operator:
Computes first-order forward/backward differences
on 2D, 3D, 4D ImageData
under Neumann/Periodic boundary conditions
Order of the Gradient ( ImageGeometry may contain channels ):
Grad_order = ['channels', 'direction_z', 'direction_y', 'direction_x']
Grad_order = ['channels', 'direction_y', 'direction_x']
Grad_order = ['direction_z', 'direction_y', 'direction_x']
Grad_order = ['channels', 'direction_z', 'direction_y', 'direction_x']
'''
def __init__(self, gm_domain, gm_range=None, direction=0, bnd_cond = 'Neumann'):
super(FiniteDiff, self).__init__()
self.gm_domain = gm_domain
self.gm_range = gm_range
self.direction = direction
self.bnd_cond = bnd_cond
# Domain Geometry = Range Geometry if not stated
if self.gm_range is None:
self.gm_range = self.gm_domain
# check direction and "length" of geometry
if self.direction + 1 > len(self.gm_domain.shape):
raise ValueError('Gradient directions more than geometry domain')
#self.voxel_size = kwargs.get('voxel_size',1)
# this wrongly assumes a homogeneous voxel size
# self.voxel_size = self.gm_domain.voxel_size_x
def direct(self, x, out=None):
x_asarr = x.as_array()
x_sz = len(x.shape)
outnone = False
if out is None:
outnone = True
ret = self.domain_geometry().allocate()
outa = ret.as_array()
else:
outa = out.as_array()
outa[:]=0
######################## Direct for 2D ###############################
if x_sz == 2:
if self.direction == 1:
np.subtract( x_asarr[:,1:], x_asarr[:,0:-1], out = outa[:,0:-1] )
if self.bnd_cond == 'Neumann':
pass
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[:,0], x_asarr[:,-1], out = outa[:,-1] )
else:
raise ValueError('No valid boundary conditions')
if self.direction == 0:
np.subtract( x_asarr[1:], x_asarr[0:-1], out = outa[0:-1,:] )
if self.bnd_cond == 'Neumann':
pass
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[0,:], x_asarr[-1,:], out = outa[-1,:] )
else:
raise ValueError('No valid boundary conditions')
######################## Direct for 3D ###############################
elif x_sz == 3:
if self.direction == 0:
np.subtract( x_asarr[1:,:,:], x_asarr[0:-1,:,:], out = outa[0:-1,:,:] )
if self.bnd_cond == 'Neumann':
pass
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[0,:,:], x_asarr[-1,:,:], out = outa[-1,:,:] )
else:
raise ValueError('No valid boundary conditions')
if self.direction == 1:
np.subtract( x_asarr[:,1:,:], x_asarr[:,0:-1,:], out = outa[:,0:-1,:] )
if self.bnd_cond == 'Neumann':
pass
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[:,0,:], x_asarr[:,-1,:], out = outa[:,-1,:] )
else:
raise ValueError('No valid boundary conditions')
if self.direction == 2:
np.subtract( x_asarr[:,:,1:], x_asarr[:,:,0:-1], out = outa[:,:,0:-1] )
if self.bnd_cond == 'Neumann':
pass
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[:,:,0], x_asarr[:,:,-1], out = outa[:,:,-1] )
else:
raise ValueError('No valid boundary conditions')
######################## Direct for 4D ###############################
elif x_sz == 4:
if self.direction == 0:
np.subtract( x_asarr[1:,:,:,:], x_asarr[0:-1,:,:,:], out = outa[0:-1,:,:,:] )
if self.bnd_cond == 'Neumann':
pass
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[0,:,:,:], x_asarr[-1,:,:,:], out = outa[-1,:,:,:] )
else:
raise ValueError('No valid boundary conditions')
if self.direction == 1:
np.subtract( x_asarr[:,1:,:,:], x_asarr[:,0:-1,:,:], out = outa[:,0:-1,:,:] )
if self.bnd_cond == 'Neumann':
pass
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[:,0,:,:], x_asarr[:,-1,:,:], out = outa[:,-1,:,:] )
else:
raise ValueError('No valid boundary conditions')
if self.direction == 2:
np.subtract( x_asarr[:,:,1:,:], x_asarr[:,:,0:-1,:], out = outa[:,:,0:-1,:] )
if self.bnd_cond == 'Neumann':
pass
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[:,:,0,:], x_asarr[:,:,-1,:], out = outa[:,:,-1,:] )
else:
raise ValueError('No valid boundary conditions')
if self.direction == 3:
np.subtract( x_asarr[:,:,:,1:], x_asarr[:,:,:,0:-1], out = outa[:,:,:,0:-1] )
if self.bnd_cond == 'Neumann':
pass
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[:,:,:,0], x_asarr[:,:,:,-1], out = outa[:,:,:,-1] )
else:
raise ValueError('No valid boundary conditions')
else:
raise NotImplementedError
# res = out #/self.voxel_size
#return type(x)(out)
if outnone:
ret.fill(outa)
return ret
def adjoint(self, x, out=None):
x_asarr = x.as_array()
x_sz = len(x.shape)
outnone = False
if out is None:
outnone = True
ret = self.range_geometry().allocate()
outa = ret.as_array()
#out = np.zeros_like(x_asarr)
else:
outa = out.as_array()
outa[:]=0
######################## Adjoint for 2D ###############################
if x_sz == 2:
if self.direction == 1:
np.subtract( x_asarr[:,1:], x_asarr[:,0:-1], out = outa[:,1:] )
if self.bnd_cond == 'Neumann':
np.subtract( x_asarr[:,0], 0, out = outa[:,0] )
np.subtract( -x_asarr[:,-2], 0, out = outa[:,-1] )
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[:,0], x_asarr[:,-1], out = outa[:,0] )
else:
raise ValueError('No valid boundary conditions')
if self.direction == 0:
np.subtract( x_asarr[1:,:], x_asarr[0:-1,:], out = outa[1:,:] )
if self.bnd_cond == 'Neumann':
np.subtract( x_asarr[0,:], 0, out = outa[0,:] )
np.subtract( -x_asarr[-2,:], 0, out = outa[-1,:] )
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[0,:], x_asarr[-1,:], out = outa[0,:] )
else:
raise ValueError('No valid boundary conditions')
######################## Adjoint for 3D ###############################
elif x_sz == 3:
if self.direction == 0:
np.subtract( x_asarr[1:,:,:], x_asarr[0:-1,:,:], out = outa[1:,:,:] )
if self.bnd_cond == 'Neumann':
np.subtract( x_asarr[0,:,:], 0, out = outa[0,:,:] )
np.subtract( -x_asarr[-2,:,:], 0, out = outa[-1,:,:] )
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[0,:,:], x_asarr[-1,:,:], out = outa[0,:,:] )
else:
raise ValueError('No valid boundary conditions')
if self.direction == 1:
np.subtract( x_asarr[:,1:,:], x_asarr[:,0:-1,:], out = outa[:,1:,:] )
if self.bnd_cond == 'Neumann':
np.subtract( x_asarr[:,0,:], 0, out = outa[:,0,:] )
np.subtract( -x_asarr[:,-2,:], 0, out = outa[:,-1,:] )
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[:,0,:], x_asarr[:,-1,:], out = outa[:,0,:] )
else:
raise ValueError('No valid boundary conditions')
if self.direction == 2:
np.subtract( x_asarr[:,:,1:], x_asarr[:,:,0:-1], out = outa[:,:,1:] )
if self.bnd_cond == 'Neumann':
np.subtract( x_asarr[:,:,0], 0, out = outa[:,:,0] )
np.subtract( -x_asarr[:,:,-2], 0, out = outa[:,:,-1] )
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[:,:,0], x_asarr[:,:,-1], out = outa[:,:,0] )
else:
raise ValueError('No valid boundary conditions')
######################## Adjoint for 4D ###############################
elif x_sz == 4:
if self.direction == 0:
np.subtract( x_asarr[1:,:,:,:], x_asarr[0:-1,:,:,:], out = outa[1:,:,:,:] )
if self.bnd_cond == 'Neumann':
np.subtract( x_asarr[0,:,:,:], 0, out = outa[0,:,:,:] )
np.subtract( -x_asarr[-2,:,:,:], 0, out = outa[-1,:,:,:] )
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[0,:,:,:], x_asarr[-1,:,:,:], out = outa[0,:,:,:] )
else:
raise ValueError('No valid boundary conditions')
if self.direction == 1:
np.subtract( x_asarr[:,1:,:,:], x_asarr[:,0:-1,:,:], out = outa[:,1:,:,:] )
if self.bnd_cond == 'Neumann':
np.subtract( x_asarr[:,0,:,:], 0, out = outa[:,0,:,:] )
np.subtract( -x_asarr[:,-2,:,:], 0, out = outa[:,-1,:,:] )
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[:,0,:,:], x_asarr[:,-1,:,:], out = outa[:,0,:,:] )
else:
raise ValueError('No valid boundary conditions')
if self.direction == 2:
np.subtract( x_asarr[:,:,1:,:], x_asarr[:,:,0:-1,:], out = outa[:,:,1:,:] )
if self.bnd_cond == 'Neumann':
np.subtract( x_asarr[:,:,0,:], 0, out = outa[:,:,0,:] )
np.subtract( -x_asarr[:,:,-2,:], 0, out = outa[:,:,-1,:] )
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[:,:,0,:], x_asarr[:,:,-1,:], out = outa[:,:,0,:] )
else:
raise ValueError('No valid boundary conditions')
if self.direction == 3:
np.subtract( x_asarr[:,:,:,1:], x_asarr[:,:,:,0:-1], out = outa[:,:,:,1:] )
if self.bnd_cond == 'Neumann':
np.subtract( x_asarr[:,:,:,0], 0, out = outa[:,:,:,0] )
np.subtract( -x_asarr[:,:,:,-2], 0, out = outa[:,:,:,-1] )
elif self.bnd_cond == 'Periodic':
np.subtract( x_asarr[:,:,:,0], x_asarr[:,:,:,-1], out = outa[:,:,:,0] )
else:
raise ValueError('No valid boundary conditions')
else:
raise NotImplementedError
outa *= -1 #/self.voxel_size
if outnone:
ret.fill(outa)
return ret
#else:
# out.fill(outa)
def range_geometry(self):
'''
Returns the range_geometry of FiniteDiff
'''
return self.gm_range
def domain_geometry(self):
'''
Returns the domain_geometry of FiniteDiff
'''
return self.gm_domain
if __name__ == '__main__':
from ccpi.framework import ImageGeometry
import numpy
N, M = 2, 3
ig = ImageGeometry(N, M)
FD = FiniteDiff(ig, direction = 1, bnd_cond = 'Neumann')
u = FD.domain_geometry().allocate('random_int')
res = FD.domain_geometry().allocate()
res1 = FD.range_geometry().allocate()
FD.direct(u, out=res)
z = FD.direct(u)
# print(z.as_array(), res.as_array())
for i in range(10):
#
z1 = FD.direct(u)
FD.direct(u, out=res)
u = ig.allocate('random_int')
res = u
z1 = u
numpy.testing.assert_array_almost_equal(z1.as_array(), \
res.as_array(), decimal=4)
# print(z1.as_array(), res.as_array())
z2 = FD.adjoint(z1)
FD.adjoint(z1, out=res1)
numpy.testing.assert_array_almost_equal(z2.as_array(), \
res1.as_array(), decimal=4)
# w = G.range_geometry().allocate('random_int')
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