# Copyright 2024 United Kingdom Research and Innovation
# Copyright 2024 The University of Manchester
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# Licensed under the Apache License, Version 2.0 (the "License");
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# Authors:
# CIL Developers, listed at: https://github.com/TomographicImaging/CIL/blob/master/NOTICE.txt
from cil.optimisation.algorithms import Algorithm
from cil.optimisation.functions import ZeroFunction
import logging
import warnings
[docs]
class PD3O(Algorithm):
r"""Primal Dual Three Operator Splitting (PD3O) algorithm, see "A New Primal–Dual Algorithm for Minimizing the Sum
of Three Functions with a Linear Operator". This is a primal dual algorithm for minimising :math:`f(x)+g(x)+h(Ax)` where all functions are proper, lower semi-continuous and convex,
:math:`f` should be differentiable with a Lipschitz continuous gradient and :math:`A` is a bounded linear operator.
Parameters
----------
f : Function
A smooth function with Lipschitz continuous gradient.
g : Function
A convex function with a computationally computable proximal.
h : Function
A composite convex function.
operator: Operator
Bounded linear operator
delta: Float, optional, default is `1./(gamma*operator.norm()**2)`
The dual step-size
gamma: Float, optional, default is `2.0/f.L`
The primal step size
initial : DataContainer, optional default is a container of zeros, in the domain of the operator
Initial point for the algorithm.
Reference
---------
Yan, M. A New Primal–Dual Algorithm for Minimizing the Sum of Three Functions with a Linear Operator. J Sci Comput 76, 1698–1717 (2018). https://doi.org/10.1007/s10915-018-0680-3
"""
def __init__(self, f, g, h, operator, delta=None, gamma=None, initial=None, **kwargs):
super(PD3O, self).__init__(**kwargs)
self.set_up(f=f, g=g, h=h, operator=operator, delta=delta, gamma=gamma, initial=initial, **kwargs)
[docs]
def set_up(self, f, g, h, operator, delta=None, gamma=None, initial=None,**kwargs):
logging.info("{} setting up".format(self.__class__.__name__, ))
self.f = f # smooth function
if isinstance(self.f, ZeroFunction):
warnings.warn(" If self.f is the ZeroFunction, then PD3O = PDHG. Please use PDHG instead. Otherwise, select a relatively small parameter gamma ", UserWarning)
if gamma is None:
gamma = 1.0/operator.norm()
self.g = g # proximable
self.h = h # composite
self.operator = operator
if gamma is None:
gamma = 0.99*2.0/self.f.L
if delta is None :
delta = 0.99/(gamma*self.operator.norm()**2)
self.gamma = gamma
self.delta = delta
if initial is None:
self.x = self.operator.domain_geometry().allocate(0)
else:
self.x = initial.copy()
self.x_old = self.x.copy()
self.s_old = self.operator.range_geometry().allocate(0)
self.s = self.operator.range_geometry().allocate(0)
self.grad_f = self.operator.domain_geometry().allocate(0)
self.configured = True
logging.info("{} configured".format(self.__class__.__name__, ))
# initial proximal conjugate step
self.operator.direct(self.x_old, out=self.s)
self.s_old.sapyb(1, self.s, self.delta, out=self.s_old)
self.h.proximal_conjugate(self.s_old, self.delta, out=self.s)
[docs]
def update(self):
r""" Performs a single iteration of the PD3O algorithm
"""
# Following equations 4 in https://link.springer.com/article/10.1007/s10915-018-0680-3
# in this case order of proximal steps we recover the (primal) PDHG, when f=0
tmp = self.x_old
self.x_old = self.x
self.x = tmp
# proximal step
self.f.gradient(self.x_old, out=self.grad_f)
self.x_old.sapyb(1., self.grad_f, -self.gamma, out = self.grad_f) # x_old - gamma * grad_f(x_old)
self.operator.adjoint(self.s, out=self.x_old)
self.x_old.sapyb(-self.gamma, self.grad_f, 1.0, out=self.x_old)
self.g.proximal(self.x_old, self.gamma, out = self.x)
# update step
self.f.gradient(self.x, out=self.x_old)
self.x_old *= self.gamma
self.grad_f += self.x_old
self.x.sapyb(2, self.grad_f, -1.0, out=self.x_old) # 2*x - x_old + gamma*(grad_f_x_old) - gamma*(grad_f_x)
tmp = self.s_old
self.s_old = self.s
self.s = tmp
# proximal conjugate step
self.operator.direct(self.x_old, out=self.s)
self.s_old.sapyb(1, self.s, self.delta, out=self.s_old)
self.h.proximal_conjugate(self.s_old, self.delta, out=self.s)
[docs]
def update_objective(self):
"""
Evaluates the primal objective
"""
self.operator.direct(self.x, out=self.s_old)
fun_h = self.h(self.s_old)
fun_g = self.g(self.x)
fun_f = self.f(self.x)
p1 = fun_f + fun_g + fun_h
self.loss.append(p1)
