update packages

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

diff --git a/octave_packages/m/statistics/base/std.m b/octave_packages/m/statistics/base/std.m
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+## Copyright (C) 1996-2012 John W. Eaton
+##
+## 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} {} std (@var{x})
+## @deftypefnx {Function File} {} std (@var{x}, @var{opt})
+## @deftypefnx {Function File} {} std (@var{x}, @var{opt}, @var{dim})
+## Compute the standard deviation of the elements of the vector @var{x}.
+## @tex
+## $$
+## {\rm std} (x) = \sigma = \sqrt{{\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1}}
+## $$
+## where $\bar{x}$ is the mean value of $x$ and $N$ is the number of elements.
+## @end tex
+## @ifnottex
+##
+## @example
+## @group
+## std (x) = sqrt ( 1/(N-1) SUM_i (x(i) - mean(x))^2 )
+## @end group
+## @end example
+##
+## @noindent
+## where @math{N} is the number of elements.
+## @end ifnottex
+##
+## If @var{x} is a matrix, compute the standard deviation 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 square root of the best unbiased
+## estimator of the variance [default]
+##
+## @item 1:
+##   normalize with @math{N}, this provides the square root of the second
+## moment around the mean
+## @end table
+##
+## If the optional argument @var{dim} is given, operate along this dimension.
+## @seealso{var, range, iqr, mean, median}
+## @end deftypefn
+
+## Author: jwe
+
+function retval = std (x, opt = 0, dim)
+
+  if (nargin < 1 || nargin > 3)
+    print_usage ();
+  endif
+
+  if (! (isnumeric (x) || islogical (x)))
+    error ("std: X must be a numeric vector or matrix");
+  endif
+
+  if (isempty (opt))
+    opt = 0;
+  endif
+  if (opt != 0 && opt != 1)
+    error ("std: 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 ("std: DIM must be an integer and a valid dimension");
+    endif
+  endif
+
+  n = sz(dim);
+  if (n == 1 || isempty (x))
+    if (isa (x, 'single'))
+      retval = zeros (sz, 'single');
+    else
+      retval = zeros (sz);
+    endif
+  else
+    retval = sqrt (sumsq (center (x, dim), dim) / (n - 1 + opt));
+  endif
+
+endfunction
+
+
+%!test
+%! x = ones (10, 2);
+%! y = [1, 3];
+%! assert(std (x) == [0, 0]);
+%! assert(std (y), sqrt (2), sqrt (eps));
+%! assert(std (x, 0, 2), zeros (10, 1));
+
+%!assert(std (ones (3, 1, 2), 0, 2), zeros (3, 1, 2));
+%!assert(std ([1 2], 0), sqrt(2)/2, 5*eps);
+%!assert(std ([1 2], 1), 0.5, 5*eps);
+%!assert(std(1), 0);
+%!assert(std(single(1)), single(0));
+%!assert(std([]), []);
+%!assert(std(ones (1,3,0,2)), ones (1,3,0,2));
+
+%% Test input validation
+%!error std ();
+%!error std (1, 2, 3, 4);
+%!error std (['A'; 'B'])
+%!error std (1, -1);
+