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# smctp2stat

## PURPOSE

Stationary distributions for a switching MCTP.

## SYNOPSIS

[ro,ro_min,ro_max,Ro_min,Ro_max,QQ] = mctp2stat(P,F)

## DESCRIPTION

```  SMCTP2STAT  Stationary distributions for a switching MCTP.

CALL: [ro,ro_min,ro_max] = smctp2stat(P,F);
[ro,ro_min,ro_max,Ro_min,Ro_max] = smctp2stat(P,F);

ro     = Stationary distribution of regime process.   [1xr]
ro_min = Stationary distr. of minima for subloads. {r}[1xn]
ro_max = Stationary distr. of maxima for subloads. {r}[1xn]
Ro_min = Stationary distr. of minima for joint MCTP.  [1xnr]
Ro_max = Stationary distr. of maxima for joint MCTP.  [1xnr]

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]

## CROSS-REFERENCE INFORMATION

This function calls:
 mat2tmat Converts a matrix to a transition matrix. mc2stat Calculates the stationary distribution for a Markov chain. mctp2stat Calculates the stationary distribution for a MCTP. smctp2joint Calculates the joint MCTP for a SMCTP. error Display message and abort function.
This function is called by:
 test_markov Quick test of the routines in module 'markov'

## SOURCE CODE

```001 function [ro,ro_min,ro_max,Ro_min,Ro_max,QQ] = mctp2stat(P,F)
002 % SMCTP2STAT  Stationary distributions for a switching MCTP.
003 %
004 % CALL: [ro,ro_min,ro_max] = smctp2stat(P,F);
005 %       [ro,ro_min,ro_max,Ro_min,Ro_max] = smctp2stat(P,F);
006 %
007 % ro     = Stationary distribution of regime process.   [1xr]
008 % ro_min = Stationary distr. of minima for subloads. {r}[1xn]
009 % ro_max = Stationary distr. of maxima for subloads. {r}[1xn]
010 % Ro_min = Stationary distr. of minima for joint MCTP.  [1xnr]
011 % Ro_max = Stationary distr. of maxima for joint MCTP.  [1xnr]
012 %
013 % P      = Transition matrix for regime process.        [rxr]
014 % F      = Cell array of min-Max and Max-min matrices   {rx2}
015 % F{i,1} = min-Max matrix, process i                    [nxn]
016 % F{i,2} = Max-min matrix, process i                    [nxn]
017 %
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(2,2,ni));
032
033 % Define
034
035 r = length(P);   % Number of regime states
036 n = length(F{1,1});  % Number of levels
037
038 % Check that the rowsums of P are equal to 1
039
040 P = mat2tmat(P);
041
042 % Normalize the rowsums of F{1,1},...,F{r,1} to 1
043 %  ==>  QQ{1,1},...,QQ{r,1}
044
045 for i = 1:r
046   QQ{i,1} = F{i,1};
047   QQ{i,1} = mat2tmat(QQ{i,1},1);
048 end
049
050 % Normalize the rowsums of F{1,2},...,F{r,2} to 1
051 %  ==>  QQ{1,2},...,QQ{r,2}
052
053 for i = 1:r
054
055   if isempty(F{i,2})        % Time-reversible
056     QQ{i,2} = F{i,1}';
057   else                   % F{i,2} is given
058     QQ{i,2} = F{i,2};
059   end
060
061   QQ{i,2} = mat2tmat(QQ{i,2},-1);
062
063 end
064
065 % Stationary distribution (=ro) for regime process.
066
067 ro = mc2stat(P);
068
069 % Stationary distribution (=ro) of local minima with transition matrix
070 % Qt = Q*Qh = "Transition matrix for min-to-min"
071
072 for i = 1:r
073   [ro_min{i},ro_max{i}] = mctp2stat(F(i,:));
074 end
075
076 [Q,QQ] = smctp2joint(P,F)
077
078 [Ro_min,Ro_max] = mctp2stat(Q);
079
080
081```

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

Comments or corrections to the WAFO group

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