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mctp2stat

PURPOSE ^

Calculates the stationary distribution for a MCTP.

SYNOPSIS ^

[ro_min,ro_max,QQ]=mctp2stat(Q)

DESCRIPTION ^

 MCTP2STAT  Calculates the stationary distribution for a MCTP. 
  
  CALL: [ro_min,ro_max] = mctp2stat(F); 
  
  ro_min = Stationary distribution of minima.         [1xn] 
  ro_max = Stationary distribution of maxima.         [1xn] 
  
  F      = Cell array of min-max and max-min   
           matrices matrices for MCTP.                {1x2} 
  F{1,1} = min-Max matrix                             [nxn] 
  F{1,2} = Max-min matrix                             [nxn] 
  
  Examples:  
     [G, Gh] = mktestmat([-1 1 32],[-0.2 0.2],0.15,1); 
     [ro_min,ro_max] = mctp2stat({G Gh}); 
  
  See also

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function [ro_min,ro_max,QQ]=mctp2stat(Q) 
002 %MCTP2STAT  Calculates the stationary distribution for a MCTP. 
003 % 
004 % CALL: [ro_min,ro_max] = mctp2stat(F); 
005 % 
006 % ro_min = Stationary distribution of minima.         [1xn] 
007 % ro_max = Stationary distribution of maxima.         [1xn] 
008 % 
009 % F      = Cell array of min-max and max-min   
010 %          matrices matrices for MCTP.                {1x2} 
011 % F{1,1} = min-Max matrix                             [nxn] 
012 % F{1,2} = Max-min matrix                             [nxn] 
013 % 
014 % Examples:  
015 %    [G, Gh] = mktestmat([-1 1 32],[-0.2 0.2],0.15,1); 
016 %    [ro_min,ro_max] = mctp2stat({G Gh}); 
017 % 
018 % See also   
019  
020 % Tested  on Matlab  5.3 
021 % 
022 % History: 
023 % Updated by PJ 18-May-2000 
024 %   updated for WAFO 
025 % Created by PJ (Pär Johannesson) 1999 
026  
027 % Check input arguments 
028  
029 ni = nargin; 
030 no = nargout; 
031 error(nargchk(1,1,ni)); 
032  
033 if isempty(Q{1,2}) 
034   Q{1,2} = Q{1,1}'; 
035 end 
036  
037 % Stationary distribution (=ro) of local minima with transition matrix 
038 % Qt = Q*Qh = "Transition matrix for min-to-min" 
039  
040 Qt = Q{1,1}*Q{1,2}; 
041 ro_min = mc2stat(Qt(1:end-1,1:end-1));  % Stationary distr., row vector   
042 ro_min = [ro_min 0];  % Minimum can't reach the highest level 
043  
044 % Stationary distribution (=roh) of local maxima with transition matrix 
045 % Qt = Qh*Q = "Transition matrix for max-to-max" 
046  
047 Qth = Q{1,2}*Q{1,1}; 
048 ro_max = mc2stat(Qth(2:end,2:end));  % Stationary distr., row vector   
049 ro_max = [0 ro_max];  % Maximum can't reach the highest level 
050

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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