function [ X,iterations ] = SVT_sr(M,P,T,delta,itermax,tol)
%Single value thresholding algorithm，SVT
% function：solve the following optimization problem
%                  min  ||X||*
%               s.t. P(X-M) = 0
% X: recovered matrix
% M: observed matrix
% P: sampling set
% T: single value threshold

% output：X,iterations
 
% initialization
[n1,n2]=size(M);
% Y = zeros(size(M));
Y = P.*M;
iterations = 0;

eta = 1.1; % convergence control parameter
% lambda = 0.001; % regularization parameter

if nargin < 3
    T = mean(M(M~=0)); % for speed
%     T = sqrt(n1*n2)/0.1;  % for accuracy
end
if nargin < 4
    delta = 2;  % delta: step size
end
if nargin < 5
    itermax = 100 ;
end
if nargin < 6
    tol = 1.25e-4;
end


for ii = 1:itermax
    % singular value threshold operation
    [U, S, V] = svd(Y, 'econ') ;
    S = sign(S) .*max(abs(S) - T, 0) ; %   
    X = U*S*V';
    % update auxiliary matrix Y
    Y = Y + delta* P.* (M-X);
    Y = P.*Y ;
    % update delta
    delta = delta/eta;
    % computer error
    error = norm( P.* (M-X),'fro' )/norm( P.* M,'fro' );
    disp([ii, error]);
    if error<tol
        break;
    end
    % update iterations
    iterations = ii ;
end
end