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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:
 f_smctp Auxiliary function used by ESTSMCTP

## 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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