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mc2rfm

PURPOSE ^

Calculates the rainflow matrix/intensity for a Markov chain.

SYNOPSIS ^

[F_rfc,mu_rfc] = mc2rfm(Q,def)

DESCRIPTION ^

  MC2RFM  Calculates the rainflow matrix/intensity for a Markov chain.
 
  CALL: [F_rfc,mu_rfc] = mc2rfc(Q,1);
        [F_rfc,mu_rfc] = mc2rfc(Q,[2 h]);
 
  F_rfc  = Rainflow matrix / Rainflow intensity     [NxN]
  mu_rfc = Rainflow counting intensity              [NxN]
 
  Q      = Transition matrix for Markov chain       [nxn]
  def    = Definition 1: Markov chain  (default),    N=n
                      2: Discretized Markov chain,   N=n+1
  h      = Discretization step (ONLY Def 2!)
 
  Calculates 
    (1) the rainflow matrix for a Markov chain OR
    (2) the rainflow intensity for a discretized Markov chain.
 
  Example: 
    F = magic(5)
    Q = mat2tmat(F)
    Frfc = mc2rfm(Q)
 
  See also  smc2rfm, mctp2rfm, mc2stat, mc2reverse, cmatplot

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function [F_rfc,mu_rfc] = mc2rfm(Q,def)
002 % MC2RFM  Calculates the rainflow matrix/intensity for a Markov chain.
003 %
004 % CALL: [F_rfc,mu_rfc] = mc2rfc(Q,1);
005 %       [F_rfc,mu_rfc] = mc2rfc(Q,[2 h]);
006 %
007 % F_rfc  = Rainflow matrix / Rainflow intensity     [NxN]
008 % mu_rfc = Rainflow counting intensity              [NxN]
009 %
010 % Q      = Transition matrix for Markov chain       [nxn]
011 % def    = Definition 1: Markov chain  (default),    N=n
012 %                     2: Discretized Markov chain,   N=n+1
013 % h      = Discretization step (ONLY Def 2!)
014 %
015 % Calculates 
016 %   (1) the rainflow matrix for a Markov chain OR
017 %   (2) the rainflow intensity for a discretized Markov chain.
018 %
019 % Example: 
020 %   F = magic(5)
021 %   Q = mat2tmat(F)
022 %   Frfc = mc2rfm(Q)
023 %
024 % See also  smc2rfm, mctp2rfm, mc2stat, mc2reverse, cmatplot
025 
026 % References
027 %  
028 %  P. Johannesson (1999):
029 %  Rainflow Analysis of Switching Markov Loads.
030 %  PhD thesis, Mathematical Statistics, Centre for Mathematical Sciences,
031 %  Lund Institute of Technology.
032 %  
033 %  P. Johannesson (1998):
034 %  Rainflow Cycles for Switching Processes with Markov Structure.
035 %  Probability in the Engineering and Informational Sciences, 
036 %  Vol. 12, No. 2, pp. 143-175.
037   
038 % Tested  on Matlab  5.3
039 %
040 % History:
041 % Revised by PJ  23-Nov-1999
042 %   updated for WAFO
043 % Created by PJ (Pär Johannesson) 1997
044 %   Copyright (c) 1997 by Pär Johannesson
045 %   Toolbox: Rainflow Cycles for Switching Processes V.1.0, 2-Oct-1997
046 
047 % Check input arguments
048 
049 ni = nargin;
050 no = nargout;
051 error(nargchk(1,2,ni));
052 
053 if ni<2, def = []; end
054 if isempty(def), def = 1; end
055 
056 
057 [F_rfc,mu_rfc] = smc2rfm(1,{Q},def);
058 
059

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

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