GM1StationaryDistr.m

%  pi = GM1StationaryDistr (B, R, K)
%  
%  Returns the stationary distribution of the G/M/1 type
%  Markov chain up to a given level K.
%  
%  Parameters
%  ----------
%  A : length(M) list of matrices of shape (N,N)
%      Matrix blocks of the G/M/1 type generator in the 
%      regular part, from 0 to M-1.
%  B : length(M) list of matrices of shape (N,N)
%      Matrix blocks of the G/M/1 type generator at the
%  R : matrix, shape (N,N)
%      Matrix R of the G/M/1 type Markov chain
%  K : integer
%      The stationary distribution is returned up to
%      this level.
%  
%  Returns
%  -------
%  pi : array, shape (1,(K+1)*N)
%      The stationary probability vector up to level K
 
function pi = GM1StationaryDistr (B, R, K)
 
    global BuToolsVerbose;
 
    M = size(B{1},2);
    N = size(B{2},1);    
    Bm = zeros(M+(N-1)*length(B),M);
    Bm(1:M,1:M) = B{1};
    for i=2:length(B)
        Bm(M+(i-2)*N+1:M+(i-1)*N,:) = B{i};
    end
 
    pi = GIM1_pi(Bm,R,'MaxNumComp', K+1, 'Verbose', BuToolsVerbose);
end