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chi2cmat

PURPOSE ^

Chi-square distance of cycle matrix.

SYNOPSIS ^

chi2 = chi2cmat(Fobs,F)

DESCRIPTION ^

  CHI2CMAT  Chi-square distance of cycle matrix.
 
  Computes the chi-square distance between the observed
  cycle matrix Fobs and the expected cycle matrix F.
 
  The chi-square distance is defined as
    chi2 = sum( (N_ij - N*g_ij)^2 ./ (N*g_ij) );
 
  chi2 = chi2cmat(Fobs,F)
 
  Fobs  = Observation of cycle matrix
  F     = Expected cycle matrix

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

01 function chi2 = chi2cmat(Fobs,F)
02 % CHI2CMAT  Chi-square distance of cycle matrix.
03 %
04 % Computes the chi-square distance between the observed
05 % cycle matrix Fobs and the expected cycle matrix F.
06 %
07 % The chi-square distance is defined as
08 %   chi2 = sum( (N_ij - N*g_ij)^2 ./ (N*g_ij) );
09 %
10 % chi2 = chi2cmat(Fobs,F)
11 %
12 % Fobs  = Observation of cycle matrix
13 % F     = Expected cycle matrix
14 
15 F = flipud(F)';       % Convert to PJ-def
16 Fobs = flipud(Fobs)'; % Convert to PJ-def
17 
18 n = length(F);
19 N = sum(sum(Fobs));
20 
21 F = F / sum(sum(F));
22 
23 FF = F(:);
24 FFobs = Fobs(:);
25 FI = find(F>0);
26 
27 % Compute chi-square quantity
28 
29 chi2 = sum( (FFobs(FI) - N*FF(FI)).^2 ./ (N*FF(FI)) );
30 
31

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

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