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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 Operator
import numpy
class LinearOperator(Operator):
'''A Linear Operator that maps from a space X <-> Y'''
def __init__(self):
super(LinearOperator, self).__init__()
def is_linear(self):
'''Returns if the operator is linear'''
return True
def adjoint(self,x, out=None):
'''returns the adjoint/inverse operation
only available to linear operators'''
raise NotImplementedError
@staticmethod
def PowerMethod(operator, iterations, x_init=None):
'''Power method to calculate iteratively the Lipschitz constant
:param operator: input operator
:type operator: :code:`LinearOperator`
:param iterations: number of iterations to run
:type iteration: int
:param x_init: starting point for the iteration in the operator domain
:returns: tuple with: L, list of L at each iteration, the data the iteration worked on.
'''
# Initialise random
if x_init is None:
x0 = operator.domain_geometry().allocate('random')
else:
x0 = x_init.copy()
x1 = operator.domain_geometry().allocate()
y_tmp = operator.range_geometry().allocate()
s = numpy.zeros(iterations)
# Loop
for it in numpy.arange(iterations):
operator.direct(x0,out=y_tmp)
operator.adjoint(y_tmp,out=x1)
x1norm = x1.norm()
if hasattr(x0, 'squared_norm'):
s[it] = x1.dot(x0) / x0.squared_norm()
else:
x0norm = x0.norm()
s[it] = x1.dot(x0) / (x0norm * x0norm)
x1.multiply((1.0/x1norm), out=x0)
return numpy.sqrt(s[-1]), numpy.sqrt(s), x0
def calculate_norm(self, **kwargs):
'''Returns the norm of the LinearOperator as calculated by the PowerMethod'''
x0 = kwargs.get('x0', None)
iterations = kwargs.get('iterations', 25)
s1, sall, svec = LinearOperator.PowerMethod(self, iterations, x_init=x0)
return s1
@staticmethod
def dot_test(operator, domain_init=None, range_init=None, verbose=False):
r'''Does a dot linearity test on the operator
Evaluates if the following equivalence holds
.. math::
Ax\times y = y \times A^Tx
:param operator: operator to test
:param range_init: optional initialisation container in the operator range
:param domain_init: optional initialisation container in the operator domain
:returns: boolean, True if the test is passed.
'''
if range_init is None:
y = operator.range_geometry().allocate('random_int')
else:
y = range_init
if domain_init is None:
x = operator.domain_geometry().allocate('random_int')
else:
x = domain_init
fx = operator.direct(x)
by = operator.adjoint(y)
a = fx.dot(y)
b = by.dot(x)
if verbose:
print ('Left hand side {}, \nRight hand side {}'.format(a, b))
try:
numpy.testing.assert_almost_equal(abs((a-b)/a), 0, decimal=4)
return True
except AssertionError as ae:
print (ae)
return False
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