% The following matlab function is used for claculation of Simpson's Index of
% Diversity and 95% Confidence Interval
%
% Copyright (C) 2009 UMMI@IMM
%
% This file is part of Comparing Partitions website .
% Comparing Partitions website is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
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% You should have received a copy of the GNU General Public License
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%
function [SID,CI,s]=SimpsonDivIndex(invec)
%function SID=SimpsonDivIndex(invec)
%invec= vector with data cluster defined
%Joao Carrico 10 August 2005
%jcarrico@algos.inesc-id.pt
[a,b,c]=unique(invec);
N=length(invec);%total strains in population
s=length(a);%Total types in population
tc=histc(c,[1:max(c)]);%Total strains per type
SumTc=sum(tc.*(tc-1));
SID=1-(SumTc/(N*(N-1)));%Simpson's Index of Diversity
fTc=tc./N;%type frequency
SumfTc3=sum(fTc.^3);
SumfTc2=sum(fTc.^2);
s2=(4/N)*(SumfTc3-SumfTc2^2);%variance for SID values
CI=[SID-2*sqrt(s2) SID+2*sqrt(s2)];%95% Confidence Interval