1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
|
# -*- 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.operators import Operator
from ccpi.framework import ImageGeometry
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'''
# Initialise random
if x_init is None:
x0 = operator.domain_geometry().allocate(type(operator.domain_geometry()).RANDOM_INT)
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()
s[it] = x1.dot(x0) / x0.squared_norm()
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
|
