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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)

CROSS-REFERENCE INFORMATION

This function calls:
 smc2rfm Calculates the rainflow matrix/intensity for a switching Markov chain. error Display message and abort function.
This function is called by:
 rfcdemo1 Demo for switching AR(1)-processes. test_markov Quick test of the routines in module 'markov'

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 %
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

Comments or corrections to the WAFO group

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