Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / nan-2.5.5 / std.m

diff --git a/octave_packages/nan-2.5.5/std.m b/octave_packages/nan-2.5.5/std.m
new file mode 100644 (file)
index 0000000..b199821
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+++ b/octave_packages/nan-2.5.5/std.m
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+function [o,v]=std(x,opt,DIM,W)
+% STD calculates the standard deviation.
+% 
+% [y,v] = std(x [, opt[, DIM [, W]]])
+% 
+% opt   option 
+%      0:  normalizes with N-1 [default]
+%              provides the square root of best unbiased estimator of the variance
+%      1:  normalizes with N, 
+%              this provides the square root of the second moment around the mean
+%      otherwise: 
+%               best unbiased estimator of the standard deviation (see [1])      
+%
+% DIM  dimension
+%      N STD of  N-th dimension 
+%      default or []: first DIMENSION, with more than 1 element
+% W    weights to compute weighted s.d. (default: [])
+%      if W=[], all weights are 1. 
+%      number of elements in W must match size(x,DIM) 
+%
+% y    estimated standard deviation
+%
+% features:
+% - provides an unbiased estimation of the S.D. 
+% - can deal with NaN's (missing values)
+% - weighting of data 
+% - dimension argument also in Octave
+% - compatible to Matlab and Octave
+%
+% see also: RMS, SUMSKIPNAN, MEAN, VAR, MEANSQ,
+%
+%
+% References(s):
+% [1] http://mathworld.wolfram.com/StandardDeviationDistribution.html
+
+
+%    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/>.
+
+%      $Id: std.m 8223 2011-04-20 09:16:06Z schloegl $
+%      Copyright (C) 2000-2003,2006,2009,2010 by Alois Schloegl <alois.schloegl@gmail.com>     
+%       This is part of the NaN-toolbox for Octave and Matlab 
+%       http://pub.ist.ac.at/~schloegl/matlab/NaN/
+
+if nargin<4,
+       W = []; 
+end;
+if nargin<3,
+       DIM = []; 
+end;
+if isempty(DIM), 
+        DIM = find(size(x)>1,1);
+        if isempty(DIM), DIM=1; end;
+end;
+
+
+[y,n,ssq] = sumskipnan(x,DIM,W);
+if all(ssq(:).*n(:) > 2*(y(:).^2))
+       %% rounding error is neglectable 
+       y = ssq - y.*y./n;
+else
+       %% rounding error is not neglectable 
+       szx = size(x);
+       szy = size(y);
+       if length(szy)<length(szx);
+               szy(length(szy)+1:length(szx)) = 1;
+       end;
+       [y,n] = sumskipnan((x-repmat(y./n,szx./szy)).^2,DIM,W);
+end;
+
+
+if nargin<2,
+        opt = 0;
+end;
+if isempty(opt),
+        opt = 0;
+end;
+
+
+if opt==0, 
+        % square root if the best unbiased estimator of the variance 
+        ib = inf;
+        o  = sqrt(y./max(n-1,0));      % normalize
+        
+elseif opt==1, 
+       ib = NaN;        
+        o  = sqrt(y./n);
+
+else
+        % best unbiased estimator of the mean
+        if exist('unique','file'), 
+               % usually only a few n's differ
+                [N,tmp,tix] = unique(n(:));    % compress n and calculate ib(n)
+               ib = sqrt(N/2).*gamma((N-1)./2)./gamma(N./2);   %inverse b(n) [1]
+               ib = ib(reshape(tix,size(y)));  % expand ib to correct size
+                
+        elseif exist('histo3','file'), 
+               % usually only a few n's differ
+                [N,tix] = histo3(n(:)); N = N.X;
+                ib = sqrt(N/2).*gamma((N-1)./2)./gamma(N./2);  %inverse b(n) [1]
+               ib = ib(reshape(tix,size(y)));  % expand ib to correct size
+                
+        else   % gamma is called prod(size(n)) times 
+                ib = sqrt(n/2).*gamma((n-1)./2)./gamma(n./2);  %inverse b(n) [1]
+        end;   
+        ib = reshape(ib,size(y));
+        o  = sqrt(y./n).*ib;
+end;
+
+if nargout>1,
+       v = y.*((max(n-1,0)./(n.*n))-1./(n.*ib.*ib)); % variance of the estimated S.D. ??? needs further checks
+end;
+
+