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Import.
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 % CRANK calculate ranks for Spearman correlation
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Daniele Nicolodi <nicolodi@science.unitn.it>
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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 % Given the data series w
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Daniele Nicolodi <nicolodi@science.unitn.it>
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4 % Calculate:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % rw: the ranks (ties are treated by midranking)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 % s: the sum(fk^3 - fk), where fk are the number of kth group of ties
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 % References:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % [1] W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery,
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 % Numerical Recipes 3rd Edition: The Art of Scientific Computing,
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 % Cambridge University Press; 3 edition (September 10, 2007)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 % L Ferraioli 06-12-2010
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 % $Id: crank.m,v 1.1 2011/03/07 10:46:53 luigi Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 function [rw,s] = crank(w)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 [sw,idx] = sort(w);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 n = numel(sw);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 s = 0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 jj = 2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 while jj < n+1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 if sw(jj) ~= sw(jj-1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 sw(jj-1) = jj-1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 jj = jj+1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 jt = jj+1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 while jt<=n+1 && sw(jt-1)==sw(jj-1)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 jt = jt + 1;
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34 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 rnk = 0.5*(jj+jt-3);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 for ji=jj:jt-1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 sw(ji-1)=rnk;
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38 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 t = jt-jj;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 s = s + (t*t*t-t);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 jj = jt;
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42 end
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43 end
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44
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 if jj==n+1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46 sw(n)=n+1;
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47 end
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48
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 rw = zeros(size(sw));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 for ii=1:numel(sw)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 rw(idx(ii)) = sw(ii);
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52 end
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53
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54 end