l1median_VaZh_z.m

function [y] = l1median_VaZh_z(X, maxiter, tol, zerotol, medIn)
%{
To calculate the L1_median of X  with the l1median_VaZh method

Inputs:
X       ---the number of the records is the number of rows
maxiter ---the max number of iteration
tol     ---the tolerance of iteration
zerotol ---the tolerance of vector to zero
medIn   ---a row vector representing initial median of X

Outputs:
y       ---the median of X
%}

%% To discuss the parameters
if (nargin > 5)
    error ('Too many input arguments.') ;
elseif (nargin < 5)
    medIn = median(X);
    if(nargin < 4)
        zerotol = 1e-15 ;
        if (nargin < 3)
            tol = 0.01 ;
            if (nargin < 2)
                maxiter = 200 ;
                if (nargin < 1)
                    error ('Data matrix X is missing.') ;
                end
            end
        end
    end
end

[rn,vn] = size(X);
iterdis = 1;
iter = 0;
y = medIn;

%% Begin the iteration
while (iterdis > 0) && (iter < maxiter)
    Tnum=zeros(1,vn);
    R = zeros(1,vn);
    Tden=0;
    yita = 0;
    for i=1:rn
        dist = norm(X(i,:)-y);
        if dist >= zerotol
            Tnum = Tnum + X(i,:)/dist;
            Tden=Tden + 1/dist;
            R = R + (X(i,:)-y)/dist;
        else
            yita = 1;
        end
    end
    if Tden == 0
        T=0;
    else
       T=Tnum/Tden;
    end
    if norm(R) == 0
        r = 0;
    else
        r = min(1,yita/norm(R));
    end
    Ty = (1-r)*T + r*y;
    iterdis = norm((Ty-y),1) - tol*norm(y,1);
    iter = iter + 1;
    y=Ty;     
end