diff options
Diffstat (limited to 'Wrappers')
| -rwxr-xr-x | Wrappers/Python/ccpi/optimisation/operators/CompositeOperator.py | 1464 |
1 files changed, 818 insertions, 646 deletions
diff --git a/Wrappers/Python/ccpi/optimisation/operators/CompositeOperator.py b/Wrappers/Python/ccpi/optimisation/operators/CompositeOperator.py index be2d525..77abb8c 100755 --- a/Wrappers/Python/ccpi/optimisation/operators/CompositeOperator.py +++ b/Wrappers/Python/ccpi/optimisation/operators/CompositeOperator.py @@ -1,647 +1,819 @@ -# -*- coding: utf-8 -*-
-"""
-Created on Thu Feb 14 12:36:40 2019
-
-@author: ofn77899
-"""
-#from ccpi.optimisation.ops import Operator
-import numpy
-from numbers import Number
-import functools
-from ccpi.framework import AcquisitionData, ImageData
-
-class Operator(object):
- '''Operator that maps from a space X -> Y'''
- def __init__(self, **kwargs):
- self.scalar = 1
- def is_linear(self):
- '''Returns if the operator is linear'''
- return False
- def direct(self,x, out=None):
- raise NotImplementedError
- def size(self):
- # To be defined for specific class
- raise NotImplementedError
- def norm(self):
- raise NotImplementedError
- def allocate_direct(self):
- '''Allocates memory on the Y space'''
- raise NotImplementedError
- def allocate_adjoint(self):
- '''Allocates memory on the X space'''
- raise NotImplementedError
- def range_dim(self):
- raise NotImplementedError
- def domain_dim(self):
- raise NotImplementedError
- def __rmul__(self, other):
- assert isinstance(other, Number)
- self.scalar = other
- return self
-
-class LinearOperator(Operator):
- '''Operator that maps from a space X -> Y'''
- def is_linear(self):
- '''Returns if the operator is linear'''
- return True
- def adjoint(self,x, out=None):
- raise NotImplementedError
-
-# this should go in the framework
-
-class CompositeDataContainer(object):
- '''Class to hold a composite operator'''
- def __init__(self, *args, shape=None):
- '''containers must be passed row by row'''
- self.containers = args
- self.index = 0
- if shape is None:
- shape = (len(args),1)
- self.shape = shape
- n_elements = functools.reduce(lambda x,y: x*y, shape, 1)
- if len(args) != n_elements:
- raise ValueError(
- 'Dimension and size do not match: expected {} got {}'
- .format(n_elements,len(args)))
-# for i in range(shape[0]):
-# b.append([])
-# for j in range(shape[1]):
-# b[-1].append(args[i*shape[1]+j])
-# indices.append(i*shape[1]+j)
-# self.containers = b
-
- def __iter__(self):
- return self
- def next(self):
- '''python2 backwards compatibility'''
- return self.__next__()
- def __next__(self):
- try:
- out = self[self.index]
- except IndexError as ie:
- raise StopIteration()
- self.index+=1
- return out
-
- def is_compatible(self, other):
- '''basic check if the size of the 2 objects fit'''
- if isinstance(other, Number):
- return True
- elif isinstance(other, list) or isinstance(other, numpy.ndarray):
- # TODO look elements should be numbers
- for ot in other:
- if not isinstance(ot, Number):
- raise ValueError('List/ numpy array can only contain numbers')
- return len(self.containers) == len(other)
- return len(self.containers) == len(other.containers)
- def get_item(self, row, col=0):
- if row > self.shape[0]:
- raise ValueError('Requested row {} > max {}'.format(row, self.shape[0]))
- if col > self.shape[1]:
- raise ValueError('Requested col {} > max {}'.format(col, self.shape[1]))
-
- index = row*self.shape[1]+col
- return self.containers[index]
-
- def add(self, other, out=None, *args, **kwargs):
- assert self.is_compatible(other)
- if isinstance(other, Number):
- return type(self)(*[ el.add(other, out, *args, **kwargs) for el in self.containers])
- elif isinstance(other, list):
- return type(self)(*[ el.add(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other)])
- return type(self)(*[ el.add(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other.containers)])
-
- def subtract(self, other, out=None , *args, **kwargs):
- assert self.is_compatible(other)
- if isinstance(other, Number):
- return type(self)(*[ el.subtract(other, out, *args, **kwargs) for el in self.containers])
- elif isinstance(other, list):
- return type(self)(*[ el.subtract(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other)])
- return type(self)(*[ el.subtract(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other.containers)])
-
- def multiply(self, other , out=None, *args, **kwargs):
- assert self.is_compatible(other)
- if isinstance(other, Number):
- return type(self)(*[ el.multiply(other, out, *args, **kwargs) for el in self.containers])
- elif isinstance(other, list):
- return type(self)(*[ el.multiply(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other)])
- return type(self)(*[ el.multiply(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other.containers)])
-
- def divide(self, other , out=None ,*args, **kwargs):
- assert self.is_compatible(other)
- if isinstance(other, Number):
- return type(self)(*[ el.divide(other, out, *args, **kwargs) for el in self.containers])
- elif isinstance(other, list):
- return type(self)(*[ el.divide(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other)])
- return type(self)(*[ el.divide(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other.containers)])
-
- def power(self, other , out=None, *args, **kwargs):
- assert self.is_compatible(other)
- if isinstance(other, Number):
- return type(self)(*[ el.power(other, out, *args, **kwargs) for el in self.containers])
- elif isinstance(other, list):
- return type(self)(*[ el.power(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other)])
- return type(self)(*[ el.power(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other.containers)])
-
- def maximum(self,other, out=None, *args, **kwargs):
- assert self.is_compatible(other)
- if isinstance(other, Number):
- return type(self)(*[ el.maximum(other, out, *args, **kwargs) for el in self.containers])
- elif isinstance(other, list):
- return type(self)(*[ el.maximum(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other)])
- return type(self)(*[ el.maximum(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other.containers)])
-
- ## unary operations
- def abs(self, out=None, *args, **kwargs):
- return type(self)(*[ el.abs(out, *args, **kwargs) for el in self.containers])
- def sign(self, out=None, *args, **kwargs):
- return type(self)(*[ el.sign(out, *args, **kwargs) for el in self.containers])
- def sqrt(self, out=None, *args, **kwargs):
- return type(self)(*[ el.sqrt(out, *args, **kwargs) for el in self.containers])
-
- ## reductions
- def sum(self, out=None, *args, **kwargs):
- return numpy.asarray([ el.sum(*args, **kwargs) for el in self.containers])
-
- def copy(self):
- '''alias of clone'''
- return self.clone()
- def clone(self):
- return type(self)(*[el.copy() for el in self.containers])
-
- def __add__(self, other):
- return self.add( other )
- # __radd__
-
- def __sub__(self, other):
- return self.subtract( other )
- # __rsub__
-
- def __mul__(self, other):
- return self.multiply(other)
- # __rmul__
-
- def __div__(self, other):
- return self.divide(other)
- # __rdiv__
- def __truediv__(self, other):
- return self.divide(other)
-
- def __pow__(self, other):
- return self.power(other)
- # reverse operand
- def __radd__(self, other):
- return self + other
- # __radd__
-
- def __rsub__(self, other):
- return (-1 * self) + other
- # __rsub__
-
- def __rmul__(self, other):
- return self * other
- # __rmul__
-
- def __rdiv__(self, other):
- print ("call __rdiv__")
- return pow(self / other, -1)
- # __rdiv__
- def __rtruediv__(self, other):
- return self.__rdiv__(other)
-
- def __rpow__(self, other):
- return other.power(self)
-
- def __iadd__(self, other):
- if isinstance (other, CompositeDataContainer):
- for el,ot in zip(self.containers, other.containers):
- el += ot
- elif isinstance(other, Number):
- for el in self.containers:
- el += other
- elif isinstance(other, list) or isinstance(other, numpy.ndarray):
- assert self.is_compatible(other)
- for el,ot in zip(self.containers, other):
- el += ot
- return self
- # __radd__
-
- def __isub__(self, other):
- if isinstance (other, CompositeDataContainer):
- for el,ot in zip(self.containers, other.containers):
- el -= ot
- elif isinstance(other, Number):
- for el in self.containers:
- el -= other
- elif isinstance(other, list) or isinstance(other, numpy.ndarray):
- assert self.is_compatible(other)
- for el,ot in zip(self.containers, other):
- el -= ot
- return self
- # __rsub__
-
- def __imul__(self, other):
- if isinstance (other, CompositeDataContainer):
- for el,ot in zip(self.containers, other.containers):
- el *= ot
- elif isinstance(other, Number):
- for el in self.containers:
- el *= other
- elif isinstance(other, list) or isinstance(other, numpy.ndarray):
- assert self.is_compatible(other)
- for el,ot in zip(self.containers, other):
- el *= ot
- return self
- # __imul__
-
- def __idiv__(self, other):
- if isinstance (other, CompositeDataContainer):
- for el,ot in zip(self.containers, other.containers):
- el /= ot
- elif isinstance(other, Number):
- for el in self.containers:
- el /= other
- elif isinstance(other, list) or isinstance(other, numpy.ndarray):
- assert self.is_compatible(other)
- for el,ot in zip(self.containers, other):
- el /= ot
- return self
- # __rdiv__
- def __itruediv__(self, other):
- return self.__idiv__(other)
- def norm(self):
- y = numpy.asarray([el.norm().sum() for el in self.containers])
- return y.sum()
-
-class CompositeOperator(Operator):
- '''Class to hold a composite operator'''
- def __init__(self, *args, shape=None):
- self.operators = args
- if shape is None:
- shape = (len(args),1)
- self.shape = shape
- n_elements = functools.reduce(lambda x,y: x*y, shape, 1)
- if len(args) != n_elements:
- raise ValueError(
- 'Dimension and size do not match: expected {} got {}'
- .format(n_elements,len(args)))
- def get_item(self, row, col):
- if row > self.shape[0]:
- raise ValueError('Requested row {} > max {}'.format(row, self.shape[0]))
- if col > self.shape[1]:
- raise ValueError('Requested col {} > max {}'.format(col, self.shape[1]))
-
- index = row*self.shape[1]+col
- return self.operators[index]
-
- def norm(self):
- norm = [op.norm() for op in self.operators]
- b = []
- for i in range(self.shape[0]):
- b.append([])
- for j in range(self.shape[1]):
- b[-1].append(norm[i*self.shape[1]+j])
- return numpy.asarray(b)
-
- def direct(self, x, out=None):
- shape = self.get_output_shape(x.shape)
- res = []
- for row in range(self.shape[0]):
- for col in range(self.shape[1]):
- if col == 0:
- prod = self.get_item(row,col).direct(x.get_item(col))
- else:
- prod += self.get_item(row,col).direct(x.get_item(col))
- res.append(prod)
- print ("len res" , len(res))
- return CompositeDataContainer(*res, shape=shape)
-
- def adjoint(self, x, out=None):
- shape = self.get_output_shape(x.shape, adjoint=True)
- res = []
- for row in range(self.shape[1]):
- for col in range(self.shape[0]):
- if col == 0:
- prod = self.get_item(row,col).adjoint(x.get_item(col))
- else:
- prod += self.get_item(row,col).adjoint(x.get_item(col))
- res.append(prod)
- return CompositeDataContainer(*res, shape=shape)
-
- def get_output_shape(self, xshape, adjoint=False):
- print ("operator shape {} data shape {}".format(self.shape, xshape))
- sshape = self.shape[1]
- oshape = self.shape[0]
- if adjoint:
- sshape = self.shape[0]
- oshape = self.shape[1]
- if sshape != xshape[0]:
- raise ValueError('Incompatible shapes {} {}'.format(self.shape, xshape))
- print ((oshape, xshape[-1]))
- return (oshape, xshape[-1])
-if __name__ == '__main__':
- #from ccpi.optimisation.Algorithms import GradientDescent
- from ccpi.plugins.ops import CCPiProjectorSimple
- from ccpi.optimisation.ops import PowerMethodNonsquare
- from ccpi.optimisation.ops import TomoIdentity
- from ccpi.optimisation.funcs import Norm2sq, Norm1
- from ccpi.framework import ImageGeometry, AcquisitionGeometry
- from ccpi.optimisation.Algorithms import CGLS
- import matplotlib.pyplot as plt
-
- ig0 = ImageGeometry(2,3,4)
- ig1 = ImageGeometry(12,42,55,32)
-
- data0 = ImageData(geometry=ig0)
- data1 = ImageData(geometry=ig1) + 1
-
- data2 = ImageData(geometry=ig0) + 2
- data3 = ImageData(geometry=ig1) + 3
-
- cp0 = CompositeDataContainer(data0,data1)
- cp1 = CompositeDataContainer(data2,data3)
-#
- a = [ (el, ot) for el,ot in zip(cp0.containers,cp1.containers)]
- print (a[0][0].shape)
- #cp2 = CompositeDataContainer(*a)
- cp2 = cp0.add(cp1)
- assert (cp2.get_item(0,0).as_array()[0][0][0] == 2.)
- assert (cp2.get_item(1,0).as_array()[0][0][0] == 4.)
-
- cp2 = cp0 + cp1
- assert (cp2.get_item(0,0).as_array()[0][0][0] == 2.)
- assert (cp2.get_item(1,0).as_array()[0][0][0] == 4.)
- cp2 = cp0 + 1
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 1. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 2., decimal = 5)
- cp2 = cp0 + [1 ,2]
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 1. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 3., decimal = 5)
- cp2 += cp1
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , +3. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , +6., decimal = 5)
-
- cp2 += 1
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , +4. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , +7., decimal = 5)
-
- cp2 += [-2,-1]
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 2. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 6., decimal = 5)
-
-
- cp2 = cp0.subtract(cp1)
- assert (cp2.get_item(0,0).as_array()[0][0][0] == -2.)
- assert (cp2.get_item(1,0).as_array()[0][0][0] == -2.)
- cp2 = cp0 - cp1
- assert (cp2.get_item(0,0).as_array()[0][0][0] == -2.)
- assert (cp2.get_item(1,0).as_array()[0][0][0] == -2.)
-
- cp2 = cp0 - 1
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , -1. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 0, decimal = 5)
- cp2 = cp0 - [1 ,2]
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , -1. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , -1., decimal = 5)
-
- cp2 -= cp1
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , -3. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , -4., decimal = 5)
-
- cp2 -= 1
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , -4. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , -5., decimal = 5)
-
- cp2 -= [-2,-1]
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , -2. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , -4., decimal = 5)
-
-
- cp2 = cp0.multiply(cp1)
- assert (cp2.get_item(0,0).as_array()[0][0][0] == 0.)
- assert (cp2.get_item(1,0).as_array()[0][0][0] == 3.)
- cp2 = cp0 * cp1
- assert (cp2.get_item(0,0).as_array()[0][0][0] == 0.)
- assert (cp2.get_item(1,0).as_array()[0][0][0] == 3.)
-
- cp2 = cp0 * 2
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 2, decimal = 5)
- cp2 = cp0 * [3 ,2]
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 2., decimal = 5)
-
- cp2 *= cp1
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0 , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , +6., decimal = 5)
-
- cp2 *= 1
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , +6., decimal = 5)
-
- cp2 *= [-2,-1]
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , -6., decimal = 5)
-
-
- cp2 = cp0.divide(cp1)
- assert (cp2.get_item(0,0).as_array()[0][0][0] == 0.)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0], 1./3., decimal=4)
- cp2 = cp0/cp1
- assert (cp2.get_item(0,0).as_array()[0][0][0] == 0.)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0], 1./3., decimal=4)
-
- cp2 = cp0 / 2
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 0.5, decimal = 5)
- cp2 = cp0 / [3 ,2]
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 0.5, decimal = 5)
-
- cp2 += 1
- cp2 /= cp1
- # TODO fix inplace division
-
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 1./2 , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 1.5/3., decimal = 5)
-
- cp2 /= 1
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0.5 , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 0.5, decimal = 5)
-
- cp2 /= [-2,-1]
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , -0.5/2. , decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , -0.5, decimal = 5)
- ####
-
- cp2 = cp0.power(cp1)
- assert (cp2.get_item(0,0).as_array()[0][0][0] == 0.)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0], 1., decimal=4)
- cp2 = cp0**cp1
- assert (cp2.get_item(0,0).as_array()[0][0][0] == 0.)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0], 1., decimal=4)
-
- cp2 = cp0 ** 2
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0., decimal=5)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 1., decimal = 5)
-
- cp2 = cp0.maximum(cp1)
- assert (cp2.get_item(0,0).as_array()[0][0][0] == cp1.get_item(0,0).as_array()[0][0][0])
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0], cp2.get_item(1,0).as_array()[0][0][0], decimal=4)
-
-
- cp2 = cp0.abs()
- numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0], 0., decimal=4)
- numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0], 1., decimal=4)
-
- cp2 = cp0.subtract(cp1)
- s = cp2.sign()
- numpy.testing.assert_almost_equal(s.get_item(0,0).as_array()[0][0][0], -1., decimal=4)
- numpy.testing.assert_almost_equal(s.get_item(1,0).as_array()[0][0][0], -1., decimal=4)
-
- cp2 = cp0.add(cp1)
- s = cp2.sqrt()
- numpy.testing.assert_almost_equal(s.get_item(0,0).as_array()[0][0][0], numpy.sqrt(2), decimal=4)
- numpy.testing.assert_almost_equal(s.get_item(1,0).as_array()[0][0][0], numpy.sqrt(4), decimal=4)
-
- s = cp0.sum()
- numpy.testing.assert_almost_equal(s[0], 0, decimal=4)
- s0 = 1
- s1 = 1
- for i in cp0.get_item(0,0).shape:
- s0 *= i
- for i in cp0.get_item(1,0).shape:
- s1 *= i
-
- numpy.testing.assert_almost_equal(s[1], cp0.get_item(0,0).as_array()[0][0][0]*s0 +cp0.get_item(1,0).as_array()[0][0][0]*s1, decimal=4)
-
- # Set up phantom size N x N x vert by creating ImageGeometry, initialising the
- # ImageData object with this geometry and empty array and finally put some
- # data into its array, and display one slice as image.
-
- # Image parameters
- N = 128
- vert = 4
-
- # Set up image geometry
- ig = ImageGeometry(voxel_num_x=N,
- voxel_num_y=N,
- voxel_num_z=vert)
-
- # Set up empty image data
- Phantom = ImageData(geometry=ig,
- dimension_labels=['horizontal_x',
- 'horizontal_y',
- 'vertical'])
-
- # Populate image data by looping over and filling slices
- i = 0
- while i < vert:
- if vert > 1:
- x = Phantom.subset(vertical=i).array
- else:
- x = Phantom.array
- x[round(N/4):round(3*N/4),round(N/4):round(3*N/4)] = 0.5
- x[round(N/8):round(7*N/8),round(3*N/8):round(5*N/8)] = 0.98
- if vert > 1 :
- Phantom.fill(x, vertical=i)
- i += 1
-
- # Display slice of phantom
- if vert > 1:
- plt.imshow(Phantom.subset(vertical=0).as_array())
- else:
- plt.imshow(Phantom.as_array())
- plt.show()
-
-
- # Set up AcquisitionGeometry object to hold the parameters of the measurement
- # setup geometry: # Number of angles, the actual angles from 0 to
- # pi for parallel beam, set the width of a detector
- # pixel relative to an object pixe and the number of detector pixels.
- angles_num = 20
- det_w = 1.0
- det_num = N
-
- angles = numpy.linspace(0,numpy.pi,angles_num,endpoint=False,dtype=numpy.float32)*\
- 180/numpy.pi
-
- # Inputs: Geometry, 2D or 3D, angles, horz detector pixel count,
- # horz detector pixel size, vert detector pixel count,
- # vert detector pixel size.
- ag = AcquisitionGeometry('parallel',
- '3D',
- angles,
- N,
- det_w,
- vert,
- det_w)
-
- # Set up Operator object combining the ImageGeometry and AcquisitionGeometry
- # wrapping calls to CCPi projector.
- A = CCPiProjectorSimple(ig, ag)
-
- # Forward and backprojection are available as methods direct and adjoint. Here
- # generate test data b and do simple backprojection to obtain z. Display all
- # data slices as images, and a single backprojected slice.
- b = A.direct(Phantom)
- z = A.adjoint(b)
-
- for i in range(b.get_dimension_size('vertical')):
- plt.imshow(b.subset(vertical=i).array)
- plt.show()
-
- plt.imshow(z.subset(vertical=0).array)
- plt.title('Backprojected data')
- plt.show()
-
- # Using the test data b, different reconstruction methods can now be set up as
- # demonstrated in the rest of this file. In general all methods need an initial
- # guess and some algorithm options to be set. Note that 100 iterations for
- # some of the methods is a very low number and 1000 or 10000 iterations may be
- # needed if one wants to obtain a converged solution.
- x_init = ImageData(geometry=ig,
- dimension_labels=['horizontal_x','horizontal_y','vertical'])
- X_init = CompositeDataContainer(x_init)
- B = CompositeDataContainer(b,
- ImageData(geometry=ig, dimension_labels=['horizontal_x','horizontal_y','vertical']))
-
- # setup a tomo identity
- I = 0.3 * TomoIdentity(geometry=ig)
-
- # composite operator
- K = CompositeOperator(A, I, shape=(2,1))
-
- out = K.direct(X_init)
-
- f = Norm2sq(K,B)
- f.L = 0.1
-
- cg = CGLS()
- cg.set_up(X_init, K, B )
- cg.max_iteration = 1
-
- cgs = CGLS()
- cgs.set_up(x_init, A, b )
- cgs.max_iteration = 2
-
- out.__isub__(B)
- out2 = K.adjoint(out)
-
- #(2.0*self.c)*self.A.adjoint( self.A.direct(x) - self.b )
-
- for _ in cg:
- print ("iteration {} {}".format(cg.iteration, cg.get_current_loss()))
-
- fig = plt.figure()
- plt.imshow(cg.get_output().get_item(0,0).subset(vertical=0).as_array())
- plt.title('Composite CGLS')
- plt.show()
-
- for _ in cgs:
- print ("iteration {} {}".format(cgs.iteration, cgs.get_current_loss()))
-
- fig = plt.figure()
- plt.imshow(cgs.get_output().subset(vertical=0).as_array())
- plt.title('Simple CGLS')
+# -*- coding: utf-8 -*- +""" +Created on Thu Feb 14 12:36:40 2019 + +@author: ofn77899 +""" +#from ccpi.optimisation.ops import Operator +import numpy +from numbers import Number +import functools +from ccpi.framework import AcquisitionData, ImageData + +class Operator(object): + '''Operator that maps from a space X -> Y''' + def __init__(self, **kwargs): + self.scalar = 1 + def is_linear(self): + '''Returns if the operator is linear''' + return False + def direct(self,x, out=None): + raise NotImplementedError + def size(self): + # To be defined for specific class + raise NotImplementedError + def norm(self): + raise NotImplementedError + def allocate_direct(self): + '''Allocates memory on the Y space''' + raise NotImplementedError + def allocate_adjoint(self): + '''Allocates memory on the X space''' + raise NotImplementedError + def range_dim(self): + raise NotImplementedError + def domain_dim(self): + raise NotImplementedError + def __rmul__(self, other): + assert isinstance(other, Number) + self.scalar = other + return self + +class LinearOperator(Operator): + '''Operator that maps from a space X -> Y''' + def is_linear(self): + '''Returns if the operator is linear''' + return True + def adjoint(self,x, out=None): + raise NotImplementedError + +# this should go in the framework + +class CompositeDataContainer(object): + '''Class to hold a composite operator''' + __array_priority__ = 1 + def __init__(self, *args, shape=None): + '''containers must be passed row by row''' + self.containers = args + self.index = 0 + if shape is None: + shape = (len(args),1) + self.shape = shape + n_elements = functools.reduce(lambda x,y: x*y, shape, 1) + if len(args) != n_elements: + raise ValueError( + 'Dimension and size do not match: expected {} got {}' + .format(n_elements,len(args))) +# for i in range(shape[0]): +# b.append([]) +# for j in range(shape[1]): +# b[-1].append(args[i*shape[1]+j]) +# indices.append(i*shape[1]+j) +# self.containers = b + + def __iter__(self): + return self + def next(self): + '''python2 backwards compatibility''' + return self.__next__() + def __next__(self): + try: + out = self[self.index] + except IndexError as ie: + raise StopIteration() + self.index+=1 + return out + + def is_compatible(self, other): + '''basic check if the size of the 2 objects fit''' + if isinstance(other, Number): + return True + elif isinstance(other, list): + # TODO look elements should be numbers + for ot in other: + if not isinstance(ot, (Number,\ + numpy.int, numpy.int8, numpy.int16, numpy.int32, numpy.int64,\ + numpy.float, numpy.float16, numpy.float32, numpy.float64, \ + numpy.complex)): + raise ValueError('List/ numpy array can only contain numbers {}'\ + .format(type(ot))) + return len(self.containers) == len(other) + elif isinstance(other, numpy.ndarray): + return self.shape == other.shape + return len(self.containers) == len(other.containers) + def get_item(self, row, col=0): + if row > self.shape[0]: + raise ValueError('Requested row {} > max {}'.format(row, self.shape[0])) + if col > self.shape[1]: + raise ValueError('Requested col {} > max {}'.format(col, self.shape[1])) + + index = row*self.shape[1]+col + return self.containers[index] + + def add(self, other, out=None, *args, **kwargs): + assert self.is_compatible(other) + if isinstance(other, Number): + return type(self)(*[ el.add(other, out, *args, **kwargs) for el in self.containers]) + elif isinstance(other, list) or isinstance(other, numpy.ndarray): + return type(self)(*[ el.add(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other)]) + return type(self)(*[ el.add(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other.containers)]) + + def subtract(self, other, out=None , *args, **kwargs): + assert self.is_compatible(other) + if isinstance(other, Number): + return type(self)(*[ el.subtract(other, out, *args, **kwargs) for el in self.containers]) + elif isinstance(other, list) or isinstance(other, numpy.ndarray): + return type(self)(*[ el.subtract(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other)]) + return type(self)(*[ el.subtract(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other.containers)]) + + def multiply(self, other , out=None, *args, **kwargs): + self.is_compatible(other) + if isinstance(other, Number): + return type(self)(*[ el.multiply(other, out, *args, **kwargs) for el in self.containers]) + elif isinstance(other, list): + return type(self)(*[ el.multiply(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other)]) + elif isinstance(other, numpy.ndarray): + return type(self)(*[ el.multiply(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other)]) + return type(self)(*[ el.multiply(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other.containers)]) + + def divide(self, other , out=None ,*args, **kwargs): + self.is_compatible(other) + if isinstance(other, Number): + return type(self)(*[ el.divide(other, out, *args, **kwargs) for el in self.containers]) + elif isinstance(other, list) or isinstance(other, numpy.ndarray): + return type(self)(*[ el.divide(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other)]) + return type(self)(*[ el.divide(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other.containers)]) + + def power(self, other , out=None, *args, **kwargs): + assert self.is_compatible(other) + if isinstance(other, Number): + return type(self)(*[ el.power(other, out, *args, **kwargs) for el in self.containers]) + elif isinstance(other, list) or isinstance(other, numpy.ndarray): + return type(self)(*[ el.power(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other)]) + return type(self)(*[ el.power(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other.containers)]) + + def maximum(self,other, out=None, *args, **kwargs): + assert self.is_compatible(other) + if isinstance(other, Number): + return type(self)(*[ el.maximum(other, out, *args, **kwargs) for el in self.containers]) + elif isinstance(other, list) or isinstance(other, numpy.ndarray): + return type(self)(*[ el.maximum(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other)]) + return type(self)(*[ el.maximum(ot, out, *args, **kwargs) for el,ot in zip(self.containers,other.containers)]) + + ## unary operations + def abs(self, out=None, *args, **kwargs): + return type(self)(*[ el.abs(out, *args, **kwargs) for el in self.containers]) + def sign(self, out=None, *args, **kwargs): + return type(self)(*[ el.sign(out, *args, **kwargs) for el in self.containers]) + def sqrt(self, out=None, *args, **kwargs): + return type(self)(*[ el.sqrt(out, *args, **kwargs) for el in self.containers]) + def conjugate(self, out=None): + return type(self)(*[el.conjugate() for el in self.containers]) + + ## reductions + def sum(self, out=None, *args, **kwargs): + return numpy.asarray([ el.sum(*args, **kwargs) for el in self.containers]) + def norm(self): + y = numpy.asarray([el**2 for el in self.containers]) + return y.sum() + def copy(self): + '''alias of clone''' + return self.clone() + def clone(self): + return type(self)(*[el.copy() for el in self.containers]) + + def __add__(self, other): + return self.add( other ) + # __radd__ + + def __sub__(self, other): + return self.subtract( other ) + # __rsub__ + + def __mul__(self, other): + return self.multiply(other) + # __rmul__ + + def __div__(self, other): + return self.divide(other) + # __rdiv__ + def __truediv__(self, other): + return self.divide(other) + + def __pow__(self, other): + return self.power(other) + # reverse operand + def __radd__(self, other): + return self + other + # __radd__ + + def __rsub__(self, other): + return (-1 * self) + other + # __rsub__ + + def __rmul__(self, other): + '''Reverse multiplication + + to make sure that this method is called rather than the __mul__ of a numpy array + the class constant __array_priority__ must be set > 0 + https://docs.scipy.org/doc/numpy-1.15.1/reference/arrays.classes.html#numpy.class.__array_priority__ + ''' + return self * other + # __rmul__ + + def __rdiv__(self, other): + return pow(self / other, -1) + # __rdiv__ + def __rtruediv__(self, other): + return self.__rdiv__(other) + + def __rpow__(self, other): + return other.power(self) + + def __iadd__(self, other): + if isinstance (other, CompositeDataContainer): + for el,ot in zip(self.containers, other.containers): + el += ot + elif isinstance(other, Number): + for el in self.containers: + el += other + elif isinstance(other, list) or isinstance(other, numpy.ndarray): + self.is_compatible(other) + for el,ot in zip(self.containers, other): + el += ot + return self + # __radd__ + + def __isub__(self, other): + if isinstance (other, CompositeDataContainer): + for el,ot in zip(self.containers, other.containers): + el -= ot + elif isinstance(other, Number): + for el in self.containers: + el -= other + elif isinstance(other, list) or isinstance(other, numpy.ndarray): + assert self.is_compatible(other) + for el,ot in zip(self.containers, other): + el -= ot + return self + # __rsub__ + + def __imul__(self, other): + if isinstance (other, CompositeDataContainer): + for el,ot in zip(self.containers, other.containers): + el *= ot + elif isinstance(other, Number): + for el in self.containers: + el *= other + elif isinstance(other, list) or isinstance(other, numpy.ndarray): + assert self.is_compatible(other) + for el,ot in zip(self.containers, other): + el *= ot + return self + # __imul__ + + def __idiv__(self, other): + if isinstance (other, CompositeDataContainer): + for el,ot in zip(self.containers, other.containers): + el /= ot + elif isinstance(other, Number): + for el in self.containers: + el /= other + elif isinstance(other, list) or isinstance(other, numpy.ndarray): + assert self.is_compatible(other) + for el,ot in zip(self.containers, other): + el /= ot + return self + # __rdiv__ + def __itruediv__(self, other): + return self.__idiv__(other) + + + +class CompositeOperator(Operator): + '''Class to hold a composite operator''' + def __init__(self, *args, shape=None): + self.operators = args + if shape is None: + shape = (len(args),1) + self.shape = shape + n_elements = functools.reduce(lambda x,y: x*y, shape, 1) + if len(args) != n_elements: + raise ValueError( + 'Dimension and size do not match: expected {} got {}' + .format(n_elements,len(args))) + def get_item(self, row, col): + if row > self.shape[0]: + raise ValueError('Requested row {} > max {}'.format(row, self.shape[0])) + if col > self.shape[1]: + raise ValueError('Requested col {} > max {}'.format(col, self.shape[1])) + + index = row*self.shape[1]+col + return self.operators[index] + + def norm(self): + norm = [op.norm() for op in self.operators] + b = [] + for i in range(self.shape[0]): + b.append([]) + for j in range(self.shape[1]): + b[-1].append(norm[i*self.shape[1]+j]) + return numpy.asarray(b) + + def direct(self, x, out=None): + shape = self.get_output_shape(x.shape) + res = [] + for row in range(self.shape[0]): + for col in range(self.shape[1]): + if col == 0: + prod = self.get_item(row,col).direct(x.get_item(col)) + else: + prod += self.get_item(row,col).direct(x.get_item(col)) + res.append(prod) + return CompositeDataContainer(*res, shape=shape) + + def adjoint(self, x, out=None): + shape = self.get_output_shape(x.shape, adjoint=True) + res = [] + for row in range(self.shape[1]): + for col in range(self.shape[0]): + if col == 0: + prod = self.get_item(row,col).adjoint(x.get_item(col)) + else: + prod += self.get_item(row,col).adjoint(x.get_item(col)) + res.append(prod) + return CompositeDataContainer(*res, shape=shape) + + def get_output_shape(self, xshape, adjoint=False): + sshape = self.shape[1] + oshape = self.shape[0] + if adjoint: + sshape = self.shape[0] + oshape = self.shape[1] + if sshape != xshape[0]: + raise ValueError('Incompatible shapes {} {}'.format(self.shape, xshape)) + return (oshape, xshape[-1]) + +''' + def direct(self, x, out=None): + + out = [None]*self.dimension[0] + for i in range(self.dimension[0]): + z1 = ImageData(np.zeros(self.compMat[i][0].range_dim())) + for j in range(self.dimension[1]): + z1 += self.compMat[i][j].direct(x[j]) + out[i] = z1 + + return out + + + def adjoint(self, x, out=None): + + out = [None]*self.dimension[1] + for i in range(self.dimension[1]): + z2 = ImageData(np.zeros(self.compMat[0][i].domain_dim())) + for j in range(self.dimension[0]): + z2 += self.compMat[j][i].adjoint(x[j]) + out[i] = z2 +''' +from ccpi.optimisation.Algorithms import Algorithm +from collections.abc import Iterable +class CGLS(Algorithm): + + '''Conjugate Gradient Least Squares algorithm + + Parameters: + x_init: initial guess + operator: operator for forward/backward projections + data: data to operate on + ''' + def __init__(self, **kwargs): + super(CGLS, self).__init__() + self.x = kwargs.get('x_init', None) + self.operator = kwargs.get('operator', None) + self.data = kwargs.get('data', None) + if self.x is not None and self.operator is not None and \ + self.data is not None: + print ("Calling from creator") + return self.set_up(x_init =kwargs['x_init'], + operator=kwargs['operator'], + data =kwargs['data']) + + def set_up(self, x_init, operator , data ): + + self.r = data.copy() + self.x = x_init.copy() + + self.operator = operator + self.d = operator.adjoint(self.r) + + + self.normr2 = (self.d * self.d).sum() + if isinstance(self.normr2, Iterable): + self.normr2 = sum(self.normr2) + #self.normr2 = numpy.sqrt(self.normr2) + print ("set_up" , self.normr2) + + def should_stop(self): + '''stopping cryterion, currently only based on number of iterations''' + return self.iteration >= self.max_iteration + + def update(self): + + Ad = self.operator.direct(self.d) + norm = (Ad*Ad).sum() + if isinstance(norm, Iterable): + norm = sum(norm) + #norm = numpy.sqrt(norm) + print (norm) + alpha = self.normr2/norm + self.x += (self.d * alpha) + self.r -= (Ad * alpha) + s = self.operator.adjoint(self.r) + + normr2_new = (s*s).sum() + if isinstance(normr2_new, Iterable): + normr2_new = sum(normr2_new) + #normr2_new = numpy.sqrt(normr2_new) + print (normr2_new) + + beta = normr2_new/self.normr2 + self.normr2 = normr2_new + self.d = s + beta*self.d + + def update_objective(self): + self.loss.append((self.r*self.r).sum()) + + def run(self, iterations, callback=None): + self.max_iteration += iterations + for _ in self: + if callback is not None: + callback(self.iteration, self.get_current_loss()) + + +if __name__ == '__main__': + #from ccpi.optimisation.Algorithms import GradientDescent + from ccpi.plugins.ops import CCPiProjectorSimple + from ccpi.optimisation.ops import PowerMethodNonsquare + from ccpi.optimisation.ops import TomoIdentity + from ccpi.optimisation.funcs import Norm2sq, Norm1 + from ccpi.framework import ImageGeometry, AcquisitionGeometry + from ccpi.optimisation.Algorithms import GradientDescent + #from ccpi.optimisation.Algorithms import CGLS + import matplotlib.pyplot as plt + + ig0 = ImageGeometry(2,3,4) + ig1 = ImageGeometry(12,42,55,32) + + data0 = ImageData(geometry=ig0) + data1 = ImageData(geometry=ig1) + 1 + + data2 = ImageData(geometry=ig0) + 2 + data3 = ImageData(geometry=ig1) + 3 + + cp0 = CompositeDataContainer(data0,data1) + cp1 = CompositeDataContainer(data2,data3) +# + a = [ (el, ot) for el,ot in zip(cp0.containers,cp1.containers)] + print (a[0][0].shape) + #cp2 = CompositeDataContainer(*a) + cp2 = cp0.add(cp1) + assert (cp2.get_item(0,0).as_array()[0][0][0] == 2.) + assert (cp2.get_item(1,0).as_array()[0][0][0] == 4.) + + cp2 = cp0 + cp1 + assert (cp2.get_item(0,0).as_array()[0][0][0] == 2.) + assert (cp2.get_item(1,0).as_array()[0][0][0] == 4.) + cp2 = cp0 + 1 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 1. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 2., decimal = 5) + cp2 = cp0 + [1 ,2] + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 1. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 3., decimal = 5) + cp2 += cp1 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , +3. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , +6., decimal = 5) + + cp2 += 1 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , +4. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , +7., decimal = 5) + + cp2 += [-2,-1] + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 2. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 6., decimal = 5) + + + cp2 = cp0.subtract(cp1) + assert (cp2.get_item(0,0).as_array()[0][0][0] == -2.) + assert (cp2.get_item(1,0).as_array()[0][0][0] == -2.) + cp2 = cp0 - cp1 + assert (cp2.get_item(0,0).as_array()[0][0][0] == -2.) + assert (cp2.get_item(1,0).as_array()[0][0][0] == -2.) + + cp2 = cp0 - 1 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , -1. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 0, decimal = 5) + cp2 = cp0 - [1 ,2] + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , -1. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , -1., decimal = 5) + + cp2 -= cp1 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , -3. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , -4., decimal = 5) + + cp2 -= 1 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , -4. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , -5., decimal = 5) + + cp2 -= [-2,-1] + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , -2. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , -4., decimal = 5) + + + cp2 = cp0.multiply(cp1) + assert (cp2.get_item(0,0).as_array()[0][0][0] == 0.) + assert (cp2.get_item(1,0).as_array()[0][0][0] == 3.) + cp2 = cp0 * cp1 + assert (cp2.get_item(0,0).as_array()[0][0][0] == 0.) + assert (cp2.get_item(1,0).as_array()[0][0][0] == 3.) + + cp2 = cp0 * 2 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 2, decimal = 5) + cp2 = 2 * cp0 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 2, decimal = 5) + cp2 = cp0 * [3 ,2] + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 2., decimal = 5) + cp2 = cp0 * numpy.asarray([3 ,2]) + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 2., decimal = 5) + + cp2 = [3,2] * cp0 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 2., decimal = 5) + cp2 = numpy.asarray([3,2]) * cp0 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 2., decimal = 5) + cp2 = [3,2,3] * cp0 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 2., decimal = 5) + + cp2 *= cp1 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0 , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , +6., decimal = 5) + + cp2 *= 1 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , +6., decimal = 5) + + cp2 *= [-2,-1] + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , -6., decimal = 5) + + + cp2 = cp0.divide(cp1) + assert (cp2.get_item(0,0).as_array()[0][0][0] == 0.) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0], 1./3., decimal=4) + cp2 = cp0/cp1 + assert (cp2.get_item(0,0).as_array()[0][0][0] == 0.) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0], 1./3., decimal=4) + + cp2 = cp0 / 2 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 0.5, decimal = 5) + cp2 = cp0 / [3 ,2] + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 0.5, decimal = 5) + cp2 = cp0 / numpy.asarray([3 ,2]) + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 0.5, decimal = 5) + cp3 = numpy.asarray([3 ,2]) / (cp0+1) + numpy.testing.assert_almost_equal(cp3.get_item(0,0).as_array()[0][0][0] , 3. , decimal=5) + numpy.testing.assert_almost_equal(cp3.get_item(1,0).as_array()[0][0][0] , 1, decimal = 5) + + cp2 += 1 + cp2 /= cp1 + # TODO fix inplace division + + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 1./2 , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 1.5/3., decimal = 5) + + cp2 /= 1 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0.5 , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 0.5, decimal = 5) + + cp2 /= [-2,-1] + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , -0.5/2. , decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , -0.5, decimal = 5) + #### + + cp2 = cp0.power(cp1) + assert (cp2.get_item(0,0).as_array()[0][0][0] == 0.) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0], 1., decimal=4) + cp2 = cp0**cp1 + assert (cp2.get_item(0,0).as_array()[0][0][0] == 0.) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0], 1., decimal=4) + + cp2 = cp0 ** 2 + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0] , 0., decimal=5) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0] , 1., decimal = 5) + + cp2 = cp0.maximum(cp1) + assert (cp2.get_item(0,0).as_array()[0][0][0] == cp1.get_item(0,0).as_array()[0][0][0]) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0], cp2.get_item(1,0).as_array()[0][0][0], decimal=4) + + + cp2 = cp0.abs() + numpy.testing.assert_almost_equal(cp2.get_item(0,0).as_array()[0][0][0], 0., decimal=4) + numpy.testing.assert_almost_equal(cp2.get_item(1,0).as_array()[0][0][0], 1., decimal=4) + + cp2 = cp0.subtract(cp1) + s = cp2.sign() + numpy.testing.assert_almost_equal(s.get_item(0,0).as_array()[0][0][0], -1., decimal=4) + numpy.testing.assert_almost_equal(s.get_item(1,0).as_array()[0][0][0], -1., decimal=4) + + cp2 = cp0.add(cp1) + s = cp2.sqrt() + numpy.testing.assert_almost_equal(s.get_item(0,0).as_array()[0][0][0], numpy.sqrt(2), decimal=4) + numpy.testing.assert_almost_equal(s.get_item(1,0).as_array()[0][0][0], numpy.sqrt(4), decimal=4) + + s = cp0.sum() + numpy.testing.assert_almost_equal(s[0], 0, decimal=4) + s0 = 1 + s1 = 1 + for i in cp0.get_item(0,0).shape: + s0 *= i + for i in cp0.get_item(1,0).shape: + s1 *= i + + numpy.testing.assert_almost_equal(s[1], cp0.get_item(0,0).as_array()[0][0][0]*s0 +cp0.get_item(1,0).as_array()[0][0][0]*s1, decimal=4) + + # Set up phantom size N x N x vert by creating ImageGeometry, initialising the + # ImageData object with this geometry and empty array and finally put some + # data into its array, and display one slice as image. + + # Image parameters + N = 128 + vert = 4 + + # Set up image geometry + ig = ImageGeometry(voxel_num_x=N, + voxel_num_y=N, + voxel_num_z=vert) + + # Set up empty image data + Phantom = ImageData(geometry=ig, + dimension_labels=['horizontal_x', + 'horizontal_y', + 'vertical']) + Phantom += 0.05 + # Populate image data by looping over and filling slices + i = 0 + while i < vert: + if vert > 1: + x = Phantom.subset(vertical=i).array + else: + x = Phantom.array + x[round(N/4):round(3*N/4),round(N/4):round(3*N/4)] = 0.5 + x[round(N/8):round(7*N/8),round(3*N/8):round(5*N/8)] = 0.94 + if vert > 1 : + Phantom.fill(x, vertical=i) + i += 1 + + + perc = 0.02 + # Set up empty image data + noise = ImageData(numpy.random.normal(loc = 0.04 , + scale = perc , + size = Phantom.shape), geometry=ig, + dimension_labels=['horizontal_x', + 'horizontal_y', + 'vertical']) + Phantom += noise + + # Set up AcquisitionGeometry object to hold the parameters of the measurement + # setup geometry: # Number of angles, the actual angles from 0 to + # pi for parallel beam, set the width of a detector + # pixel relative to an object pixe and the number of detector pixels. + angles_num = 20 + det_w = 1.0 + det_num = N + + angles = numpy.linspace(0,numpy.pi,angles_num,endpoint=False,dtype=numpy.float32)*\ + 180/numpy.pi + + # Inputs: Geometry, 2D or 3D, angles, horz detector pixel count, + # horz detector pixel size, vert detector pixel count, + # vert detector pixel size. + ag = AcquisitionGeometry('parallel', + '3D', + angles, + N, + det_w, + vert, + det_w) + + # Set up Operator object combining the ImageGeometry and AcquisitionGeometry + # wrapping calls to CCPi projector. + A = CCPiProjectorSimple(ig, ag) + + # Forward and backprojection are available as methods direct and adjoint. Here + # generate test data b and some noise + + b = A.direct(Phantom) + + + #z = A.adjoint(b) + + + # Using the test data b, different reconstruction methods can now be set up as + # demonstrated in the rest of this file. In general all methods need an initial + # guess and some algorithm options to be set. Note that 100 iterations for + # some of the methods is a very low number and 1000 or 10000 iterations may be + # needed if one wants to obtain a converged solution. + x_init = ImageData(geometry=ig, + dimension_labels=['horizontal_x','horizontal_y','vertical']) + X_init = CompositeDataContainer(x_init) + B = CompositeDataContainer(b, + ImageData(geometry=ig, dimension_labels=['horizontal_x','horizontal_y','vertical'])) + + # setup a tomo identity + Ibig = 1e5 * TomoIdentity(geometry=ig) + Ismall = 1e-5 * TomoIdentity(geometry=ig) + + # composite operator + Kbig = CompositeOperator(A, Ibig, shape=(2,1)) + Ksmall = CompositeOperator(A, Ismall, shape=(2,1)) + + #out = K.direct(X_init) + + f = Norm2sq(Kbig,B) + f.L = 0.00003 + + fsmall = Norm2sq(Ksmall,B) + f.L = 0.00003 + + simplef = Norm2sq(A, b) + simplef.L = 0.00003 + + gd = GradientDescent( x_init=x_init, objective_function=simplef, + rate=simplef.L) + gd.max_iteration = 10 + + cg = CGLS() + cg.set_up(X_init, Kbig, B ) + cg.max_iteration = 1 + + cgsmall = CGLS() + cgsmall.set_up(X_init, Ksmall, B ) + cgsmall.max_iteration = 1 + + + cgs = CGLS() + cgs.set_up(x_init, A, b ) + cgs.max_iteration = 6 +# + #out.__isub__(B) + #out2 = K.adjoint(out) + + #(2.0*self.c)*self.A.adjoint( self.A.direct(x) - self.b ) + + for _ in gd: + print ("iteration {} {}".format(gd.iteration, gd.get_current_loss())) + + cg.run(10, lambda it,val: print ("iteration {} objective {}".format(it,val))) + + cgs.run(10, lambda it,val: print ("iteration {} objective {}".format(it,val))) + + cgsmall.run(10, lambda it,val: print ("iteration {} objective {}".format(it,val))) + cgsmall.run(10, lambda it,val: print ("iteration {} objective {}".format(it,val))) +# for _ in cg: +# print ("iteration {} {}".format(cg.iteration, cg.get_current_loss())) +# +# fig = plt.figure() +# plt.imshow(cg.get_output().get_item(0,0).subset(vertical=0).as_array()) +# plt.title('Composite CGLS') +# plt.show() +# +# for _ in cgs: +# print ("iteration {} {}".format(cgs.iteration, cgs.get_current_loss())) +# + fig = plt.figure() + plt.subplot(1,5,1) + plt.imshow(Phantom.subset(vertical=0).as_array()) + plt.title('Simulated Phantom') + plt.subplot(1,5,2) + plt.imshow(gd.get_output().subset(vertical=0).as_array()) + plt.title('Simple Gradient Descent') + plt.subplot(1,5,3) + plt.imshow(cgs.get_output().subset(vertical=0).as_array()) + plt.title('Simple CGLS') + plt.subplot(1,5,4) + plt.imshow(cg.get_output().get_item(0,0).subset(vertical=0).as_array()) + plt.title('Composite CGLS\nbig lambda') + plt.subplot(1,5,5) + plt.imshow(cgsmall.get_output().get_item(0,0).subset(vertical=0).as_array()) + plt.title('Composite CGLS\nsmall lambda') plt.show()
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