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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
import scipy.sparse as sp
import numpy as np
from ccpi.framework import ImageData
class SparseFiniteDiff(object):
'''Create Sparse Matrices for the Finite Difference Operator'''
def __init__(self, domain_geometry, range_geometry=None,
direction=0, bnd_cond = 'Neumann'):
super(SparseFiniteDiff, self).__init__(domain_geometry=domain_geometry,
range_geometry=range_geometry)
self.direction = direction
self.bnd_cond = bnd_cond
if self.range_geometry is None:
self.range_geometry = self.domain_geometry
self.get_dims = [i for i in gm_domain.shape]
if self.direction + 1 > len(self.gm_domain.shape):
raise ValueError('Gradient directions more than geometry domain')
def matrix(self):
i = self.direction
mat = sp.spdiags(np.vstack([-np.ones((1,self.get_dims[i])),np.ones((1,self.get_dims[i]))]), [0,1], self.get_dims[i], self.get_dims[i], format = 'lil')
if self.bnd_cond == 'Neumann':
mat[-1,:] = 0
elif self.bnd_cond == 'Periodic':
mat[-1,0] = 1
tmpGrad = mat if i == 0 else sp.eye(self.get_dims[0])
for j in range(1, self.gm_domain.length):
tmpGrad = sp.kron(mat, tmpGrad ) if j == i else sp.kron(sp.eye(self.get_dims[j]), tmpGrad )
return tmpGrad
def T(self):
return self.matrix().T
def direct(self, x):
x_asarr = x.as_array()
res = np.reshape( self.matrix() * x_asarr.flatten('F'), self.gm_domain.shape, 'F')
return type(x)(res)
def adjoint(self, x):
x_asarr = x.as_array()
res = np.reshape( self.matrix().T * x_asarr.flatten('F'), self.gm_domain.shape, 'F')
return type(x)(res)
def sum_abs_row(self):
res = np.array(np.reshape(abs(self.matrix()).sum(axis=0), self.gm_domain.shape, 'F'))
#res[res==0]=0
return ImageData(res)
def sum_abs_col(self):
res = np.array(np.reshape(abs(self.matrix()).sum(axis=1), self.gm_domain.shape, 'F') )
#res[res==0]=0
return ImageData(res)
if __name__ == '__main__':
from ccpi.framework import ImageGeometry
from ccpi.optimisation.operators import FiniteDiff
# 2D
M, N= 2, 3
ig = ImageGeometry(M, N)
arr = ig.allocate('random_int')
for i in [0,1]:
# Neumann
sFD_neum = SparseFiniteDiff(ig, direction=i, bnd_cond='Neumann')
G_neum = FiniteDiff(ig, direction=i, bnd_cond='Neumann')
# Periodic
sFD_per = SparseFiniteDiff(ig, direction=i, bnd_cond='Periodic')
G_per = FiniteDiff(ig, direction=i, bnd_cond='Periodic')
u_neum_direct = G_neum.direct(arr)
u_neum_sp_direct = sFD_neum.direct(arr)
np.testing.assert_array_almost_equal(u_neum_direct.as_array(), u_neum_sp_direct.as_array(), decimal=4)
u_neum_adjoint = G_neum.adjoint(arr)
u_neum_sp_adjoint = sFD_neum.adjoint(arr)
np.testing.assert_array_almost_equal(u_neum_adjoint.as_array(), u_neum_sp_adjoint.as_array(), decimal=4)
u_per_direct = G_neum.direct(arr)
u_per_sp_direct = sFD_neum.direct(arr)
np.testing.assert_array_almost_equal(u_per_direct.as_array(), u_per_sp_direct.as_array(), decimal=4)
u_per_adjoint = G_per.adjoint(arr)
u_per_sp_adjoint = sFD_per.adjoint(arr)
np.testing.assert_array_almost_equal(u_per_adjoint.as_array(), u_per_sp_adjoint.as_array(), decimal=4)
# 3D
M, N, K = 2, 3, 4
ig3D = ImageGeometry(M, N, K)
arr3D = ig3D.allocate('random_int')
for i in [0,1,2]:
# Neumann
sFD_neum3D = SparseFiniteDiff(ig3D, direction=i, bnd_cond='Neumann')
G_neum3D = FiniteDiff(ig3D, direction=i, bnd_cond='Neumann')
# Periodic
sFD_per3D = SparseFiniteDiff(ig3D, direction=i, bnd_cond='Periodic')
G_per3D = FiniteDiff(ig3D, direction=i, bnd_cond='Periodic')
u_neum_direct3D = G_neum3D.direct(arr3D)
u_neum_sp_direct3D = sFD_neum3D.direct(arr3D)
np.testing.assert_array_almost_equal(u_neum_direct3D.as_array(), u_neum_sp_direct3D.as_array(), decimal=4)
u_neum_adjoint3D = G_neum3D.adjoint(arr3D)
u_neum_sp_adjoint3D = sFD_neum3D.adjoint(arr3D)
np.testing.assert_array_almost_equal(u_neum_adjoint3D.as_array(), u_neum_sp_adjoint3D.as_array(), decimal=4)
u_per_direct3D = G_neum3D.direct(arr3D)
u_per_sp_direct3D = sFD_neum3D.direct(arr3D)
np.testing.assert_array_almost_equal(u_per_direct3D.as_array(), u_per_sp_direct3D.as_array(), decimal=4)
u_per_adjoint3D = G_per3D.adjoint(arr3D)
u_per_sp_adjoint3D = sFD_per3D.adjoint(arr3D)
np.testing.assert_array_almost_equal(u_per_adjoint3D.as_array(), u_per_sp_adjoint3D.as_array(), decimal=4)
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