update packages

[CreaPhase.git] / octave_packages / m / statistics / base / var.m

diff --git a/octave_packages/m/statistics/base/var.m b/octave_packages/m/statistics/base/var.m
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+## Copyright (C) 1995-2012 Kurt Hornik
+##
+## This file is part of Octave.
+##
+## Octave 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.
+##
+## Octave 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 Octave; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn  {Function File} {} var (@var{x})
+## @deftypefnx {Function File} {} var (@var{x}, @var{opt})
+## @deftypefnx {Function File} {} var (@var{x}, @var{opt}, @var{dim})
+## Compute the variance of the elements of the vector @var{x}.
+## @tex
+## $$
+## {\rm var} (x) = \sigma^2 = {\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1}
+## $$
+## where $\bar{x}$ is the mean value of $x$.
+## @end tex
+## @ifnottex
+##
+## @example
+## @group
+## var (x) = 1/(N-1) SUM_i (x(i) - mean(x))^2
+## @end group
+## @end example
+##
+## @end ifnottex
+## If @var{x} is a matrix, compute the variance for each column
+## and return them in a row vector.
+##
+## The argument @var{opt} determines the type of normalization to use.
+## Valid values are
+##
+## @table @asis
+## @item 0:
+##   normalize with @math{N-1}, provides the best unbiased estimator of the
+## variance [default]
+##
+## @item 1:
+##   normalizes with @math{N}, this provides the second moment around the mean
+## @end table
+##
+## If the optional argument @var{dim} is given, operate along this dimension.
+## @seealso{cov, std, skewness, kurtosis, moment}
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Description: Compute variance
+
+function retval = var (x, opt = 0, dim)
+
+  if (nargin < 1 || nargin > 3)
+    print_usage ();
+  endif
+
+  if (! (isnumeric (x) || islogical (x)))
+    error ("var: X must be a numeric vector or matrix");
+  endif
+
+  if (isempty (opt))
+    opt = 0;
+  endif
+  if (opt != 0 && opt != 1)
+    error ("var: normalization OPT must be 0 or 1");
+  endif
+
+  nd = ndims (x);
+  sz = size (x);
+  if (nargin < 3)
+    ## Find the first non-singleton dimension.
+    (dim = find (sz > 1, 1)) || (dim = 1);
+  else
+    if (!(isscalar (dim) && dim == fix (dim))
+        || !(1 <= dim && dim <= nd))
+      error ("var: DIM must be an integer and a valid dimension");
+    endif
+  endif
+
+  n = sz(dim);
+  if (n == 1)
+    if (isa (x, 'single'))
+      retval = zeros (sz, 'single');
+    else
+      retval = zeros (sz);
+    endif
+  elseif (numel (x) > 0)
+    retval = sumsq (center (x, dim), dim) / (n - 1 + opt);
+  else
+    error ("var: X must not be empty");
+  endif
+
+endfunction
+
+
+%!assert(var (13), 0);
+%!assert(var (single(13)), single(0));
+%!assert(var ([1,2,3]), 1);
+%!assert(var ([1,2,3], 1), 2/3, eps);
+%!assert(var ([1,2,3], [], 1), [0,0,0]);
+
+%% Test input validation
+%!error var ()
+%!error var (1,2,3,4)
+%!error var (['A'; 'B'])
+%!error var (1, -1);
+%!error var ([],1)
+