function [x,R] = admm(x, K, ProxF, ProxKG, options)
% admm - Alternating Directions Method of Multipliers algorithm
%
%    [x,R] = admm(x, K, ProxF, ProxKG, options);
%
%   Solves 
%       min_x F(K*x) + G(x)
%   where F and G are proper closed convex functions, 
%   and K is a linear operator such that K^*K is invertible.
%   F is supposed simple and G is also simple in the metric K^*K, i.e.
%   prox^K_{ga*G}(x) = argmin_y 1/2||x-K y||^2 + ga*G(x) is easy to compute.
%   
%
%   INPUTS:
%   ProxF(y,ga) computes Prox_{ga*F}(y)
%   ProxKG(x,ga) computes Prox^K_{ga*G}(x)
%   K is the handle to the linear operator.
%   options.ga > 0 is the ADMM parameter.
%   options.verb=0 suppress display of progression.
%   options.niter is the number of iterations.
%   options.report(x) is a function to fill in R.
%
%   OUTPUTS:
%   x is the final solution.
%   R(i) = options.report(x) at iteration i.
%

report = getoptions(options, 'report', @(x)0);
niter = getoptions(options, 'niter', 100);
theta = getoptions(options, 'theta', 1);
verb = getoptions(options, 'verb', 1);


if isnumeric(K)
    K = @(x)K*x;
end        


R = [];
u = K(x);
w = u;
for i=1:niter    
    if verb
        progressbar(i,niter);
    end
    % record energies
    R(i) = report(x);
    % update
    x = ProxKG( u - w, gamma);
    s = K(x) + w;
    u = ProxF(  s, gamma);
    w = s - u;
end