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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 ccpi.optimisation.functions import Function
import numpy
class IndicatorBox(Function):
r'''Indicator function for box constraint
.. math::
f(x) = \mathbb{I}_{[a, b]} = \begin{cases}
0, if x\in[a, b]
\infty, otherwise
\end{cases}
'''
def __init__(self,lower=-numpy.inf,upper=numpy.inf):
super(IndicatorBox, self).__init__()
self.lower = lower
self.upper = upper
def __call__(self,x):
'''Evaluates IndicatorBox at x'''
if (numpy.all(x.array>=self.lower) and
numpy.all(x.array <= self.upper) ):
val = 0
else:
val = numpy.inf
return val
def gradient(self,x):
return ValueError('Not Differentiable')
def convex_conjugate(self,x):
'''Convex conjugate of IndicatorBox at x'''
return x.maximum(0).sum()
def proximal(self, x, tau, out=None):
r'''Proximal operator of IndicatorBox at x
.. math:: prox_{\tau * f}(x)
'''
if out is None:
return (x.maximum(self.lower)).minimum(self.upper)
else:
x.maximum(self.lower, out=out)
out.minimum(self.upper, out=out)
def proximal_conjugate(self, x, tau, out=None):
r'''Proximal operator of the convex conjugate of IndicatorBox at x:
..math:: prox_{\tau * f^{*}}(x)
'''
if out is None:
return x - tau * self.proximal(x/tau, tau)
else:
self.proximal(x/tau, tau, out=out)
out *= -1*tau
out += x
if __name__ == '__main__':
from ccpi.framework import ImageGeometry, BlockDataContainer
N, M = 2,3
ig = ImageGeometry(voxel_num_x = N, voxel_num_y = M)
u = ig.allocate('random_int')
tau = 2
f = IndicatorBox(2, 3)
lower = 10
upper = 30
z1 = f.proximal(u, tau)
z2 = f.proximal_conjugate(u/tau, 1/tau)
z = z1 + tau * z2
numpy.testing.assert_array_equal(z.as_array(), u.as_array())
out1 = ig.allocate()
out2 = ig.allocate()
f.proximal(u, tau, out=out1)
f.proximal_conjugate(u/tau, 1/tau, out = out2)
p = out1 + tau * out2
numpy.testing.assert_array_equal(p.as_array(), u.as_array())
d = f.convex_conjugate(u)
print(d)
# what about n-dimensional Block
#uB = BlockDataContainer(u,u,u)
#lowerB = BlockDataContainer(1,2,3)
#upperB = BlockDataContainer(10,21,30)
#fB = IndicatorBox(lowerB, upperB)
#z1B = fB.proximal(uB, tau)
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