You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: inexact_alm_rlr.m
    path of file: ./repos/lrslibrary/algorithms/lrr/ROSL
    
    the code of the file until where you have to start completion: function [alpha, E, A] = inexact_alm_rlr(X, K, D, tol, maxIter) 

% This matlab code implements the inexact augmented Lagrange multiplier 
% method for Robust linear regresion with known alpha
%
% alpha- k x n matrix of known coefficients
%
% X - m x n matrix of observations/data (required input)
%
% tol - tolerance for stopping criterion.
%
% maxIter - maximum number of iterations
%  
% 
% min_D \|E\|_1, s.t. X = D*alpha +E;
% 
% The laplacian function: L(A,E,Y,u) =  |E|_1  + \mu/2* |X- D*alpha-E+Y/mu|_F^2;
%
%
% Xianbiao Shu (xshu2@illinois.edu)
% Copyright: Mitsubishi Electric Research Lab
% Reference: X. Shu, F. Porikli, N. Ahujia "Robust Orthonormal Subspace Learning: Efficient Recovery of Corrupted Low-rank Matrices". CVPR 2014; 

addpath PROPACK;


[m, n] = size(X);

% initialize
% alpha   % Low-rank coeffs

E = zeros(size(X)); % sparse innovation
A = X;


Z = 0; % Z = Y/mu

norm_inf = norm(X(:), inf); 
d_norm = norm(X, 'fro');

mu = 10*5e-2/norm_inf; % this parameter can be tuned
rho = 1.5;       %1.3    % this parameter can be tuned
mu_bar = mu * 1e7;



iter = 0;
Iteration = 0;
converged = false;


while ~converged    

    iter = iter + 1;
    
    E_temp = X - A + Z; 

    


    %% Intensity threshold
    E = max(abs(E_temp) - 1/mu, 0).*sign(E_temp);   




    
    %% Sparse Representation
    A_ini = X -E + Z;
    
    

%%   given D and A
    
    [U, S, V] = svd(D, 0); 
    diag_S = diag(S);
    SV = length(diag_S(diag_S>0));
    
    alpha = V(:, 1:SV)*diag(1./diag_S(1:SV))*(U(:, 1:SV))'*A_ini;
    A = D*alpha;
    

    
function [alpha, E, A] = inexact_alm_rlr(X, K, D, tol, maxIter) 

% This matlab code implements the inexact augmented Lagrange multiplier 
% method for Robust linear regresion with known alpha
%
% alpha- k x n matrix of known coefficients
%
% X - m x n matrix of observations/data (required input)
%
% tol - tolerance for stopping criterion.
%
% maxIter - maximum number of iterations
%  
% 
% min_D \|E\|_1, s.t. X = D*alpha +E;
% 
% The laplacian function: L(A,E,Y,u) =  |E|_1  + \mu/2* |X- D*alpha-E+Y/mu|_F^2;
%
%
% Xianbiao Shu (xshu2@illinois.edu)
% Copyright: Mitsubishi Electric Research Lab
% Reference: X. Shu, F. Porikli, N. Ahujia "Robust Orthonormal Subspace Learning: Efficient Recovery of Corrupted Low-rank Matrices". CVPR 2014; 

addpath PROPACK;


[m, n] = size(X);

% initialize
% alpha   % Low-rank coeffs

E = zeros(size(X)); % sparse innovation
A = X;


Z = 0; % Z = Y/mu

norm_inf = norm(X(:), inf); 
d_norm = norm(X, 'fro');

mu = 10*5e-2/norm_inf; % this parameter can be tuned
rho = 1.5;       %1.3    % this parameter can be tuned
mu_bar = mu * 1e7;



iter = 0;
Iteration = 0;
converged = false;


while ~converged    

    iter = iter + 1;
    
    E_temp = X - A + Z; 

    


    %% Intensity threshold
    E = max(abs(E_temp) - 1/mu, 0).*sign(E_temp);   




    
    %% Sparse Representation
    A_ini = X -E + Z;
    
    

%%   given D and A
    
    [U, S, V] = svd(D, 0); 
    diag_S = diag(S);
    SV = length(diag_S(diag_S>0));
    
    alpha = V(:, 1:SV)*diag(1./diag_S(1:SV))*(U(:, 1:SV))'*A_ini;
    A = D*alpha;
    
    
        

    
    Iteration = Iteration + 1;
    
    Error = X - A - E;
    Z = (Z + Error)/rho;  


    mu = min(mu*rho, mu_bar);

        
    %% stop Criterion    
    stopCriterion = norm(Error, 'fro') / d_norm;
    if stopCriterion < tol || iter >= maxIter
        converged = true;
    end