MG1_G_ETAQA.m

function G = MG1_G_ETAQA(An)
% MG1_G_ETAQA computes the G matrix for M/G/1-Type Markov Chains [Bini, Meini]
%
%
%   Discrete case:
%   G = MG1_G_ETAQA(An) computes the minimal nonnegative solution to the 
%   matrix equation G = A0 + A1 G + A2 G^2 + A3 G^3 + ... + A_max G^max,
%   a nonnegative matrix, with (A0+A1+A2+...+A_max) irreducible and
%   stochastic
%
%   Continuous case:
%   G = MG1_G_ETAQA(An) computes the minimal nonnegative solution to the
%   matrix equation 0 = A0 + A1 G + A2 G^2 + A3 G^3 + ... + A_max G^max,
%   a nonnegative matrix, with (A0+A1+A2+...+A_max) irreducible and
%       stochastic 
 
r = size(An,1);
s = size(An,2);
b = s/r;
psize = r;
Gtemp = zeros(psize,psize);
 
 
% check if the matrix is stochastic
 
rowsum = sum(An,2);
isdiscrete = 0;
for i=1:r
    if (rowsum(i) < 1e-16)
        
    else
        isdicrete = 1;
    end
end
 
if (isdiscrete == 0)
    L = An(:,r+1:2*r);
    t = min(diag(L));
    if (t > 0)
        error('This is not stochastic matrix, neither continuous nor discrete! \n Please make sure every row sum up to 0 or 1');    
    end
    An = An/(-t);
    An(:,r+1:2*r) = An(:,r+1:2*r) + eye(r);
 
end
 
 
G = MG1_CR(An);
 
 
%while max(max(abs(G-Gtemp))) > 1e-15
%   Gtemp = G;
%   G = zeros(psize,psize);
%    E=eye(psize);
%   for i = 1:s
%       G = G + An{i}*E;
%        E=E*Gtemp;
%   end
%end
 
 
 
 
end