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# loglcmat

## PURPOSE log-Likelihood of cycle matrix.

## SYNOPSIS logL = logLcmat(Fobs,F,def)

## DESCRIPTION ```  LOGLCMAT  log-Likelihood of cycle matrix.

computes the log-Likelihood of an observed
cycle matrix Fobs which has the expected cycle matrix F.

The log-Likelihood is
logL = C + D,
C = log(N!)-sum(log(N_ij!)),  D = sum(N_ij*log(g_ij))

logL = logLcmat(Fobs,F,def)

Fobs  = Observation of cycle matrix
F     = Expected cycle matrix
def   = 0: Don't compute constant part, logL=D, (default)
1: Compute constant part, logL=C+D```

## CROSS-REFERENCE INFORMATION This function calls:
This function is called by:
 f_smctp Auxiliary function used by ESTSMCTP

## SOURCE CODE ```001 function logL = logLcmat(Fobs,F,def)
002 % LOGLCMAT  log-Likelihood of cycle matrix.
003 %
004 % computes the log-Likelihood of an observed
005 %   cycle matrix Fobs which has the expected cycle matrix F.
006 %
007 % The log-Likelihood is
008 %   logL = C + D,
009 %   C = log(N!)-sum(log(N_ij!)),  D = sum(N_ij*log(g_ij))
010 %
011 % logL = logLcmat(Fobs,F,def)
012 %
013 % Fobs  = Observation of cycle matrix
014 % F     = Expected cycle matrix
015 % def   = 0: Don't compute constant part, logL=D, (default)
016 %         1: Compute constant part, logL=C+D
017
018 if nargin<3, def=0; end
019
020 F = flipud(F)';       % Convert to PJ-def
021 Fobs = flipud(Fobs)'; % Convert to PJ-def
022
023 n = length(F);
024 N = sum(sum(Fobs));
025
026 F = F / sum(sum(F));
027
028 FF = F(:);
029 FFobs = Fobs(:);
030 FI = find(FF>0 & FFobs>0);
031 FIobs = find(FFobs>0);
032
033 % Copmute constant part of log-Likelihood (part C)
034
035 if def == 1
036   logL = sum(log(1:N));
037   for k = 1:length(FIobs)
038     logL = logL - sum(log( 1:FFobs(FIobs(k)) ));
039   end
040 else
041   logL = 0;
042 end
043
044 % Copmute log-Likelihood (part D)
045
046 logL = logL + sum(FFobs(FI).*log(FF(FI)));
047
048```

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

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