# -*- coding: utf-8 -*-
# Copyright 2019 United Kingdom Research and Innovation
# Copyright 2019 The 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.
#
# Authors:
# CIL Developers, listed at: https://github.com/TomographicImaging/CIL/blob/master/NOTICE.txt
from cil.optimisation.functions import Function
from cil.framework import DataContainer
from cil.optimisation.operators import DiagonalOperator
[docs]class L2NormSquared(Function):
r""" L2NormSquared function: :math:`F(x) = \| x\|^{2}_{2} = \underset{i}{\sum}x_{i}^{2}`
Following cases are considered:
a) :math:`F(x) = \|x\|^{2}_{2}`
b) :math:`F(x) = \|x - b\|^{2}_{2}`
.. note:: For case b) case we can use :code:`F = L2NormSquared().centered_at(b)`,
see *TranslateFunction*.
:Example:
>>> F = L2NormSquared()
>>> F = L2NormSquared(b=b)
>>> F = L2NormSquared().centered_at(b)
"""
[docs] def __init__(self, **kwargs):
'''creator
Cases considered (with/without data):
a) .. math:: f(x) = \|x\|^{2}_{2}
b) .. math:: f(x) = \|\|x - b\|\|^{2}_{2}
:param b: translation of the function
:type b: :code:`DataContainer`, optional
'''
super(L2NormSquared, self).__init__(L = 2)
self.b = kwargs.get('b',None)
[docs] def __call__(self, x):
r"""Returns the value of the L2NormSquared function at x.
Following cases are considered:
a) :math:`F(x) = \|x\|^{2}_{2}`
b) :math:`F(x) = \|x - b\|^{2}_{2}`
:param: :math:`x`
:returns: :math:`\underset{i}{\sum}x_{i}^{2}`
"""
y = x
if self.b is not None:
y = x - self.b
try:
return y.squared_norm()
except AttributeError as ae:
# added for compatibility with SIRF
return (y.norm()**2)
[docs] def gradient(self, x, out=None):
r"""Returns the value of the gradient of the L2NormSquared function at x.
Following cases are considered:
a) :math:`F'(x) = 2x`
b) :math:`F'(x) = 2(x-b)`
"""
if self.b is None:
ret = x.multiply(2, out=out)
else:
ret = x.sapyb(2, self.b, -2, out=out)
if out is None:
return ret
[docs] def convex_conjugate(self, x):
r"""Returns the value of the convex conjugate of the L2NormSquared function at x.
Consider the following cases:
a) .. math:: F^{*}(x^{*}) = \frac{1}{4}\|x^{*}\|^{2}_{2}
b) .. math:: F^{*}(x^{*}) = \frac{1}{4}\|x^{*}\|^{2}_{2} + <x^{*}, b>
"""
tmp = 0
if self.b is not None:
tmp = x.dot(self.b)
return 0.25 * x.squared_norm() + tmp
[docs] def proximal(self, x, tau, out = None):
r"""Returns the value of the proximal operator of the L2NormSquared function at x.
Consider the following cases:
a) .. math:: \mathrm{prox}_{\tau F}(x) = \frac{x}{1+2\tau}
b) .. math:: \mathrm{prox}_{\tau F}(x) = \frac{x-b}{1+2\tau} + b
"""
mult = 1/(1+2*tau)
if self.b is None:
ret = x.multiply(mult, out=out)
else:
ret = x.sapyb(mult, self.b, (1-mult), out=out)
if out is None:
return ret
[docs]class WeightedL2NormSquared(Function):
r""" WeightedL2NormSquared function: :math:`F(x) = \| x\|_{w}^{2}_{2} = \underset{i}{\sum}w_{i}*x_{i}^{2} = <x, w*x> = x^{T}*w*x`
"""
[docs] def __init__(self, **kwargs):
# Weight can be either a scalar or a DataContainer
# Lispchitz constant L = 2 *||weight||
self.weight = kwargs.get('weight', 1.0)
self.b = kwargs.get('b', None)
tmp_norm = 1.0
self.tmp_space = self.weight*0.
if isinstance(self.weight, DataContainer):
self.operator_weight = DiagonalOperator(self.weight)
tmp_norm = self.operator_weight.norm()
self.tmp_space = self.operator_weight.domain_geometry().allocate()
if (self.weight<0).any():
raise ValueError('Weigth contains negative values')
super(WeightedL2NormSquared, self).__init__(L = 2 * tmp_norm )
[docs] def __call__(self, x):
self.operator_weight.direct(x, out = self.tmp_space)
y = x.dot(self.tmp_space)
if self.b is not None:
self.operator_weight.direct(x - self.b, out = self.tmp_space)
y = (x - self.b).dot(self.tmp_space)
return y
[docs] def gradient(self, x, out=None):
if out is not None:
out.fill(x)
if self.b is not None:
out -= self.b
self.operator_weight.direct(out, out=out)
out *= 2
else:
y = x
if self.b is not None:
y = x - self.b
return 2*self.weight*y
[docs] def convex_conjugate(self, x):
tmp = 0
if self.b is not None:
tmp = x.dot(self.b)
return (1./4) * (x/self.weight.sqrt()).squared_norm() + tmp
[docs] def proximal(self, x, tau, out = None):
if out is None:
if self.b is None:
return x/(1+2*tau*self.weight)
else:
tmp = x.subtract(self.b)
tmp /= (1+2*tau*self.weight)
tmp += self.b
return tmp
else:
if self.b is not None:
x.subtract(self.b, out=out)
out /= (1+2*tau*self.weight)
out += self.b
else:
x.divide((1+2*tau*self.weight), out=out)