Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / statistics-1.1.3 / nanstd.m

diff --git a/octave_packages/statistics-1.1.3/nanstd.m b/octave_packages/statistics-1.1.3/nanstd.m
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+## Copyright (C) 2001 Paul Kienzle <pkienzle@users.sf.net>
+##
+## 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/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{v} =} nanstd (@var{X})
+## @deftypefnx{Function File} {@var{v} =} nanstd (@var{X}, @var{opt})
+## @deftypefnx{Function File} {@var{v} =} nanstd (@var{X}, @var{opt}, @var{dim})
+## Compute the standard deviation while ignoring NaN values.
+##
+## @code{nanstd} is identical to the @code{std} function except that NaN values are
+## ignored.  If all values are NaN, the standard deviation is returned as NaN.
+## If there is only a single non-NaN value, the deviation is returned as 0. 
+##
+## The argument @var{opt} determines the type of normalization to use. Valid values
+## are
+##
+## @table @asis 
+## @item 0:
+##   normalizes with @math{N-1}, provides the square root of best unbiased estimator of 
+##   the variance [default]
+## @item 1:
+##   normalizes with @math{N}, this provides the square root of the second moment around 
+##   the mean
+## @end table
+##
+## The third argument @var{dim} determines the dimension along which the standard
+## deviation is calculated.
+##
+## @seealso{std, nanmin, nanmax, nansum, nanmedian, nanmean}
+## @end deftypefn
+
+function v = nanstd (X, opt, varargin)
+  if nargin < 1
+    print_usage;
+  else
+    if nargin < 3
+      dim = min(find(size(X)>1));
+      if isempty(dim), dim=1; endif;
+    else
+      dim = varargin{1};
+    endif
+    if ((nargin < 2) || isempty(opt))
+      opt = 0;
+    endif
+
+    ## determine the number of non-missing points in each data set
+    n = sum (!isnan(X), varargin{:});
+    
+    ## replace missing data with zero and compute the mean
+    X(isnan(X)) = 0;
+    meanX = sum (X, varargin{:}) ./ n;
+    
+    ## subtract the mean from the data and compute the sum squared
+    sz = ones(1,length(size(X)));
+    sz(dim) = size(X,dim);
+    v = sumsq (X - repmat(meanX,sz), varargin{:});
+    
+    ## because the missing data was set to zero each missing data
+    ## point will contribute (-meanX)^2 to sumsq, so remove these
+    v = v - (meanX .^ 2) .* (size(X,dim) - n);
+    
+    if (opt == 0)
+      ## compute the standard deviation from the corrected sumsq using
+      ## max(n-1,1) in the denominator so that the std for a single point is 0
+      v = sqrt ( v ./ max(n - 1, 1) );
+    elseif (opt == 1)
+      ## compute the standard deviation from the corrected sumsq
+      v = sqrt ( v ./ n );
+    else
+      error ("std: unrecognized normalization type");
+    endif
+
+  endif
+endfunction