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# tr_x2p

## PURPOSE

Transforms a vector X to a transition matrix P.

## SYNOPSIS

P = tr_x2p(X,trans)

## DESCRIPTION

```  TR_X2P  Transforms a vector X to a transition matrix P.

CALL: P = tr_x2p(X,trans)

P     = transition matrix.           [rxr]

X     = Vector of length n=r*(r-1).  [nx1]
trans = 0: No transformation. (default)
1: inverse log-odds-transformation.
x = 1/(exp(-y)+1)

## CROSS-REFERENCE INFORMATION

This function calls:
 error Display message and abort function. num2str Convert number to string. (Fast version)
This function is called by:
 estsmctp Estimate SMCTP model from an observed rainflow matrix. f_smctp Auxiliary function used by ESTSMCTP

## SOURCE CODE

```001 function P = tr_x2p(X,trans)
002 % TR_X2P  Transforms a vector X to a transition matrix P.
003 %
004 % CALL: P = tr_x2p(X,trans)
005 %
006 % P     = transition matrix.           [rxr]
007 %
008 % X     = Vector of length n=r*(r-1).  [nx1]
009 % trans = 0: No transformation. (default)
010 %         1: inverse log-odds-transformation.
011 %              x = 1/(exp(-y)+1)
012 %
014
015 if nargin<2, trans=[]; end
016 if isempty(trans), trans=0; end
017
018 r=(1+sqrt(1+4*length(X)))/2;
019
020 switch trans
021
022 case 0  % No transformation
023
024 case 1  % inverse-log-odds-transformation
025
026   X = invlogOdds(X);
027
028 otherwise
029
030   error(['Transformation ' num2str(trans) ' not defined.']);
031
032 end % switch
033
034 E= eye(r);
035 EE = E(:);
036 IE = find(EE==0);
037 Y = zeros(r*r,1);
038 Y(IE) = X;
039 P = reshape(Y,r,r)';
040 for i = 1:r
041   P(i,i) = 1-sum(P(i,:));
042 end
043
044 %
045 % inverse of log-odds
046 %
047
048 function x=invlogOdds(y)
049
050 x=1./(exp(-y)+1);
051
052```

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

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