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    Metadata details:
    filename: tvqc_logbarrier.m
    path of file: ./repos/CS_MoCo_LAB/reconstruction/matlab/CS_LAB_matlab/@L1_Magic/private
    
    the code of the file until where you have to start completion: % tvqc_logbarrier.m
%
% Solve quadractically constrained TV minimization
% min TV(x)  s.t.  ||Ax-b||_2 <= epsilon.
%
% Recast as the SOCP
% min sum(t) s.t.  ||D_{ij}x||_2 <= t,  i,j=1,...,n
%                  ||Ax - b||_2 <= epsilon
% and use a log barrier algorithm.
%
% Usage:  xp = tvqc_logbarrier(x0, A, At, b, epsilon, lbtol, mu, cgtol, cgmaxiter)
%
% x0 - Nx1 vector, initial point.
%
% A - Either a handle to a function that takes a N vector and returns a K 
%     vector , or a KxN matrix.  If A is a function handle, the algorithm
%     operates in "largescale" mode, solving the Newton systems via the
%     Conjugate Gradients algorithm.
%
% At - Handle to a function that takes a K vector and returns an N vector.
%      If A is a KxN
    
function that takes a N vector and returns a K 
%     vector , or a KxN matrix.  If A is a function handle, the algorithm
%     operates in "largescale" mode, solving the Newton systems via the
%     Conjugate Gradients algorithm.
%
% At - Handle to a function that takes a K vector and returns an N vector.
%      If A is a KxN matrix, At is ignored.
%
% b - Kx1 vector of observations.
%
% epsilon - scalar, constraint relaxation parameter
%
% lbtol - The log barrier algorithm terminates when the duality gap <= lbtol.
%         Also, the number of log barrier iterations is completely
%         determined by lbtol.
%         Default = 1e-3.
%
% mu - Factor by which to increase the barrier constant at each iteration.
%      Default = 10.
%
% cgtol - Tolerance for Conjugate Gradients; ignored if A is a matrix.
%     Default = 1e-8.
%
% cgmaxiter - Maximum number of iterations for Conjugate Gradients; ignored
%     if A is a matrix.
%     Default = 200.
%
% Written by: Justin Romberg, Caltech
% Email: jrom@acm.caltech.edu
% Created: October 2005
%


function [xp, tp] = tvqc_logbarrier(x0, A, At, b, epsilon, lbtol, mu, cgtol, cgmaxiter, bComplex, sz)  

largescale = isa(A,'function_handle'); 

if (nargin < 6), lbtol = 1e-3; end