/usr/share/octave/packages/3.2/nan-2.4.4/std.m is in octave-nan 2.4.4-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 | 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;
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