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smctp2joint

PURPOSE ^

Calculates the joint MCTP for a SMCTP.

SYNOPSIS ^

[Q,QQ] = smctp2joint(P,F)

DESCRIPTION ^

 SMCTP2JOINT  Calculates the joint MCTP for a SMCTP. 
  
  CALL: [Q,QQ] = smctp2joint(P,F) 
  
  Q      = Cell array of min-max and max-min transition  
           matrices for joint MCTP.                   {1x2} 
  QQ     = Cell array of min-max and max-min transition  
           matrices matrices for SMCTP.               {rx2} 
  
  P      = Transition matrix for regime process.      [rxr] 
  F      = Cell array of min-Max and Max-min matrices {rx2} 
  F{i,1} = min-Max matrix, process i                  [nxn] 
  F{i,2} = Max-min matrix, process i                  [nxn] 
  
  If a matrix F{i,2}=[], then the process will 
  be assumed to be time-reversible. 
  
  See also  smctp2stat, mctp2stat

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function [Q,QQ] = smctp2joint(P,F) 
002 %SMCTP2JOINT  Calculates the joint MCTP for a SMCTP. 
003 % 
004 % CALL: [Q,QQ] = smctp2joint(P,F) 
005 % 
006 % Q      = Cell array of min-max and max-min transition  
007 %          matrices for joint MCTP.                   {1x2} 
008 % QQ     = Cell array of min-max and max-min transition  
009 %          matrices matrices for SMCTP.               {rx2} 
010 % 
011 % P      = Transition matrix for regime process.      [rxr] 
012 % F      = Cell array of min-Max and Max-min matrices {rx2} 
013 % F{i,1} = min-Max matrix, process i                  [nxn] 
014 % F{i,2} = Max-min matrix, process i                  [nxn] 
015 % 
016 % If a matrix F{i,2}=[], then the process will 
017 % be assumed to be time-reversible. 
018 % 
019 % See also  smctp2stat, mctp2stat 
020  
021 % Tested  on Matlab  5.3 
022 % 
023 % History: 
024 % Updated by PJ 18-May-2000 
025 %   updated for WAFO 
026 % Created by PJ (Pär Johannesson) 1999 
027  
028 % Check input arguments 
029  
030 ni = nargin; 
031 no = nargout; 
032 error(nargchk(2,2,ni)); 
033  
034 % Define  
035  
036 r = length(P);   % Number of regime states 
037 n = length(F{1,1});  % Number of levels 
038  
039 % Check that the rowsums of P are equal to 1 
040  
041 P = mat2tmat(P); 
042  
043 % Normalize the rowsums of F{1,1},...,F{r,1} to 1 
044 %  ==>  QQ{1,1},...,QQ{r,1} 
045  
046 for i = 1:r 
047   QQ{i,1} = F{i,1}; 
048   QQ{i,1} = mat2tmat(QQ{i,1},1); 
049 end 
050  
051 % Normalize the rowsums of F{1,2},...,F{r,2} to 1 
052 %  ==>  QQ{1,2},...,QQ{r,2} 
053  
054 for i = 1:r 
055    
056   if isempty(F{i,2})        % Time-reversible 
057     QQ{i,2} = F{i,1}'; 
058   else                   % F{i,2} is given 
059     QQ{i,2} = F{i,2};  
060   end 
061      
062   QQ{i,2} = mat2tmat(QQ{i,2},-1); 
063  
064 end 
065  
066 Q = cell(1,2); 
067  
068 % Make the transition matrix Q for the joint min-Max process 
069  
070 Q{1,1} = zeros(n*r,n*r); 
071 I = 0:r:(n-1)*r; 
072 for z=1:r 
073   Q0 = kron(QQ{z,1},P); 
074   Q{1,1}(I+z,:) = Q0(I+z,:); 
075 end 
076  
077  
078 % Make the transition matrix Qh for the joint Max-min process 
079  
080 Q{1,2} = zeros(n*r,n*r); 
081 I = 0:r:(n-1)*r; 
082 for z=1:r 
083   Q0 = kron(QQ{z,2},P); 
084   Q{1,2}(I+z,:) = Q0(I+z,:); 
085 end 
086

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

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