function [sol, info] = pocs(x_0,F, param)
%POCS Projection onto convex sets
% Usage: sol = pocs(x_0,F, param);
% sol = pocs(x_0,F);
% [sol,info] = pocs(...);
%
% Input parameters:
% x_0 : Starting point of the algorithm
% F : Array of function to minimize
% param : Optional parameter
% Output parameters:
% sol : Solution
% info : Structure summarizing informations at convergence
%
% POCS solves:
%
% sol = argmin || x - x_0 ||_2 for x belong to R^N and belonging to all sets
%
% where x are the optimization variables.
%
% F is a cell array of structures representing the indicative functions
% of all sets. F{ii}.eval contains an anonymous function that evaluate
% how far is the point x to the set ii. F{ii}.prox project the point x to
% the set ii. This .prox notation is kept for compatibility reason.
%
% This function is kept for backward compatibility and is not recommended
% to be used.
%
% Url: https://epfl-lts2.github.io/unlocbox-html/doc/solver/pocs.html
% Copyright (C) 2012-2016 Nathanael Perraudin.
% This file is part of UNLOCBOX version 1.7.4
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
param.algo = 'POCS';
if ~iscell(F)
F = {F};
end
[sol, info] = solvep(x_0,F,param);
% Author: Nathanael Perraudin
% Date: 14 dec 2012
% Testing: not done!
end
% function [sol, info,objective] = pocs(x_0,F, param)
% %POCS Projection onto convex sets
% % Usage: sol = pocs(x_0,F, param);
% % sol = pocs(x_0,F);
% % [sol,info,objective] = pocs(...);
% %
% % Input parameters:
% % x_0 : Starting point of the algorithm
% % F : Array of function to minimize
% % param : Optional parameter
% % Output parameters:
% % sol : Solution
% % info : Structure summarizing informations at convergence
% % objective: vector (evaluation of the objective function each iteration)
% %
% % `backard_backward` solves:
% %
% % .. sol = argmin || x - x_0 ||_2 for x belong to R^N and belonging to all sets
% %
% % .. math:: sol = arg \min_x \|x-x_0\| \hspace{1cm} for \hspace{1cm} x\in \cap_i \mathcal{C}_i
% %
% % where *x* is the variable.
% %
% % * *x_0* is the starting point.
% %
% % * *F* is an array of structures representing functions containing
% % operators inside and eventually the norm. The prox: *F(i).prox* and
% % the function: *F(i).eval* are defined in the same way as in the
% % Forward-backward and Douglas-Rachford algorithms F(i).prox should
% % perform the projection. This .prox notation is kept for compatibility
% % reason.
% %
% % * *param* a Matlab structure containing the following fields:
% %
% % General parameters:
% %
% % * *param.tol* : is stop criterion for the loop. The algorithm stops if
% %
% % .. ( n(t) - n(t-1) ) / n(t) < tol,
% %
% % .. math:: \frac{ n(t) - n(t-1) }{ n(t)} < tol,
% %
% % where $n(t) = f_1(x)+f_2(x)$ is the objective function at iteration *t*
% % by default, `tol=10e-4`.
% %
% % * *param.maxit* : is the maximum number of iteration. By default, it is 200.
% %
% % * *param.verbose* : 0 no log, 1 print main steps, 2 print all steps.
% %
% % * *param.abs_tol* : If activated, this stopping critterion is the
% % objectiv function smaller than *param.tol*. By default 1.
% %
% %
% % info is a Matlab structure containing the following fields:
% %
% % * *info.algo* : Algorithm used
% %
% % * *info.iter* : Number of iteration
% %
% % * *info.time* : Time of exectution of the function in sec.
% %
% % * *info.final_eval* : Final evaluation of the objectivs functions
% %
% % * *info.crit* : Stopping critterion used
% %
% % * *info.rel_norm* : Relative norm at convergence
% %
% %
% % See also: backward_backward generalized_forward_backward
%
%
%
% % Author: Nathanael Perraudin
% % Date: 14 dec 2012
%
% % Start the time counter
% t1 = tic;
%
% % test the evaluate function
% [F] = test_eval(F);
%
% % number of function
% m = size(F,2);
%
% % Optional input arguments
% if nargin<3, param=struct; end
%
% if ~isfield(param, 'tol'), param.tol=10e-4 ; end
% if ~isfield(param, 'maxit'), param.maxit=200; end
% if ~isfield(param, 'verbose'), param.verbose=1 ; end
% if ~isfield(param, 'abs_tol'), param.abs_tol=1 ; end
%
%
%
%
%
% % Initialization
% curr_norm = 0;
% for ii = 1:m
% curr_norm = F{ii}.eval(x_0)+curr_norm;
% end
% [~,~,prev_norm,iter,objective,~] = convergence_test(curr_norm);
%
% sol=x_0;
%
% % Main loop
% while 1
%
% %
% if param.verbose >= 2
% fprintf('Iteration %i:\n', iter);
% end
%
%
%
% for ii = 1:m
% sol = F{ii}.prox(sol,0);
% end
%
%
% % Global stopping criterion
% curr_norm=0;
% for ii = 1:m
% curr_norm = F{ii}.eval(sol)+curr_norm;
% end
% [stop,rel_norm,prev_norm,iter,objective,crit] = convergence_test(curr_norm,prev_norm,iter,objective,param);
% [sol,param]=post_process(sol,iter,curr_norm,prev_norm,param);
% if stop
% break;
% end
% if param.verbose >= 2
% fprintf(' ||f|| = %e, rel_norm = %e\n', ...
% curr_norm, rel_norm);
% end
%
%
% end
%
% % Log
% if param.verbose>1
% % Print norm
% fprintf('\n Solution found:\n');
% fprintf(' Final residue:%e Final relative norm: %e\n',curr_norm, rel_norm );
%
%
% % Stopping criterion
% fprintf(' %i iterations\n', iter);
% fprintf(' Stopping criterion: %s \n\n', crit);
%
% end
%
% if param.verbose==1
% % single line print
% fprintf(' POCS: ||f||=%e, REL_OBJ=%e, iter=%i, crit: %s \n',curr_norm, rel_norm,iter,crit );
% end
%
%
% info.algo=mfilename;
% info.iter=iter;
% info.final_eval=curr_norm;
% info.crit=crit;
% info.time=toc(t1);
% info.rel_norm=rel_norm;
%
% end