--- /dev/null
+function Q=quantile(Y,q,DIM,method)
+% QUANTILE calculates the quantiles of histograms and sample arrays.
+%
+% Q = quantile(Y,q)
+% Q = quantile(Y,q,DIM)
+% returns the q-th quantile along dimension DIM of sample array Y.
+% size(Q) is equal size(Y) except for dimension DIM which is size(Q,DIM)=length(Q)
+%
+% Q = quantile(HIS,q)
+% returns the q-th quantile from the histogram HIS.
+% HIS must be a HISTOGRAM struct as defined in HISTO2 or HISTO3.
+% If q is a vector, the each row of Q returns the q(i)-th quantile
+%
+% see also: HISTO2, HISTO3, PERCENTILE
+
+
+% $Id: quantile.m 9601 2012-02-09 14:14:36Z schloegl $
+% Copyright (C) 1996-2003,2005,2006,2007,2009,2011 by Alois Schloegl <alois.schloegl@gmail.com>
+% This function is part of the NaN-toolbox
+% http://pub.ist.ac.at/~schloegl/matlab/NaN/
+
+% This program 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.
+%
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+if nargin<3,
+ DIM = [];
+end;
+if isempty(DIM),
+ DIM = find(size(Y)>1,1);
+ if isempty(DIM), DIM = 1; end;
+end;
+
+
+if nargin<2,
+ help quantile
+
+else
+ [q, rix] = sort(q(:)'); % sort quantile values
+ [tmp,rix] = sort(rix); % generate reverse index
+
+ SW = isstruct(Y);
+ if SW, SW = isfield(Y,'datatype'); end;
+ if SW, SW = strcmp(Y.datatype,'HISTOGRAM'); end;
+ if SW,
+ [yr, yc] = size(Y.H);
+ Q = repmat(nan,length(q),yc);
+ if ~isfield(Y,'N');
+ Y.N = sum(Y.H,1);
+ end;
+
+ for k1 = 1:yc,
+ tmp = Y.H(:,k1)>0;
+ h = full(Y.H(tmp,k1));
+ t = Y.X(tmp,min(size(Y.X,2),k1));
+
+ N = Y.N(k1);
+ t2(1:2:2*length(t)) = t;
+ t2(2:2:2*length(t)) = t;
+ x2 = cumsum(h);
+ x(1)=0;
+ x(2:2:2*length(t)) = x2;
+ x(3:2:2*length(t)) = x2(1:end-1);
+
+ % Q(q < 0 | 1 < q,:) = NaN; % already done at initialization
+ Q(q==0,k1) = t2(1);
+ Q(q==1,k1) = t2(end);
+ n = 1;
+ for k2 = find( (0 < q) & (q < 1) )
+ while (q(k2)*N > x(n)),
+ n=n+1;
+ end;
+
+ if q(k2)*N==x(n)
+ % mean of upper and lower bound
+ Q(k2,k1) = (t2(n)+t2(n+1))/2;
+ else
+ Q(k2,k1) = t2(n);
+ end;
+ end;
+ Q = Q(rix,:); % order resulting quantiles according to original input q
+ end;
+
+
+ elseif isnumeric(Y),
+ sz = size(Y);
+ if DIM>length(sz),
+ sz = [sz,ones(1,DIM-length(sz))];
+ end;
+
+ f = zeros(1,length(q));
+ f( (q < 0) | (1 < q) ) = NaN;
+ D1 = prod(sz(1:DIM-1));
+ D3 = prod(sz(DIM+1:length(sz)));
+ Q = repmat(nan,[sz(1:DIM-1),length(q),sz(DIM+1:length(sz))]);
+ for k = 0:D1-1,
+ for l = 0:D3-1,
+ xi = k + l * D1*sz(DIM) + 1 ;
+ xo = k + l * D1*length(q) + 1;
+ t = Y(xi:D1:xi+D1*sz(DIM)-1);
+ t = t(~isnan(t));
+ N = length(t);
+
+ if (N==0)
+ f(:) = NaN;
+ else
+ t = sort(t);
+ t2(1:2:2*length(t)) = t;
+ t2(2:2:2*length(t)) = t;
+ x = floor((1:2*length(t))/2);
+ %f(q < 0 | 1 < q) = NaN; % for efficiency its defined outside loop
+ f(q==0) = t2(1);
+ f(q==1) = t2(end);
+
+ n = 1;
+ for k2 = find( (0 < q) & (q < 1) )
+ while (q(k2)*N > x(n)),
+ n = n+1;
+ end;
+
+ if q(k2)*N==x(n)
+ % mean of upper and lower bound
+ f(k2) = (t2(n) + t2(n+1))/2;
+ else
+ f(k2) = t2(n);
+ end;
+ end;
+ end;
+ Q(xo:D1:xo + D1*length(q) - 1) = f(rix);
+ end;
+ end;
+
+ else
+ fprintf(2,'Error QUANTILES: invalid input argument\n');
+ return;
+ end;
+
+end;
+
+%!assert(quantile(1:10,[.2,.5]),[2.5, 5.5])
+
+
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