update packages

[CreaPhase.git] / octave_packages / m / statistics / base / cov.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} {} cov (@var{x})
+## @deftypefnx {Function File} {} cov (@var{x}, @var{opt})
+## @deftypefnx {Function File} {} cov (@var{x}, @var{y})
+## @deftypefnx {Function File} {} cov (@var{x}, @var{y}, @var{opt})
+## Compute the covariance matrix.
+##
+## If each row of @var{x} and @var{y} is an observation, and each column is
+## a variable, then the @w{(@var{i}, @var{j})-th} entry of
+## @code{cov (@var{x}, @var{y})} is the covariance between the @var{i}-th
+## variable in @var{x} and the @var{j}-th variable in @var{y}.
+## @tex
+## $$
+## \sigma_{ij} = {1 \over N-1} \sum_{i=1}^N (x_i - \bar{x})(y_i - \bar{y})
+## $$
+## where $\bar{x}$ and $\bar{y}$ are the mean values of $x$ and $y$.
+## @end tex
+## @ifnottex
+##
+## @example
+## cov (x) = 1/N-1 * SUM_i (x(i) - mean(x)) * (y(i) - mean(y))
+## @end example
+##
+## @end ifnottex
+##
+## If called with one argument, compute @code{cov (@var{x}, @var{x})}, the
+## covariance between the columns of @var{x}.
+##
+## 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
+## covariance [default]
+##
+## @item 1:
+##   normalize with @math{N}, this provides the second moment around the mean
+## @end table
+## @seealso{corr}
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Description: Compute covariances
+
+function c = cov (x, y = [], opt = 0)
+
+  if (nargin < 1 || nargin > 3)
+    print_usage ();
+  endif
+
+  if (   ! (isnumeric (x) || islogical (x))
+      || ! (isnumeric (y) || islogical (y)))
+    error ("cov: X and Y must be numeric matrices or vectors");
+  endif
+
+  if (ndims (x) != 2 || ndims (y) != 2)
+    error ("cov: X and Y must be 2-D matrices or vectors");
+  endif
+
+  if (nargin == 2 && isscalar (y))
+    opt = y;
+  endif
+
+  if (opt != 0 && opt != 1)
+    error ("cov: normalization OPT must be 0 or 1");
+  endif
+
+  ## Special case, scalar has zero covariance
+  if (isscalar (x))
+    if (isa (x, 'single'))
+      c = single (0);
+    else
+      c = 0;
+    endif
+    return;
+  endif
+
+  if (isrow (x))
+    x = x.';
+  endif
+  n = rows (x);
+
+  if (nargin == 1 || isscalar (y))
+    x = center (x, 1);
+    c = conj (x' * x / (n - 1 + opt));
+  else
+    if (isrow (y))
+      y = y.';
+    endif
+    if (rows (y) != n)
+      error ("cov: X and Y must have the same number of observations");
+    endif
+    x = center (x, 1);
+    y = center (y, 1);
+    c = conj (x' * y / (n - 1 + opt));
+  endif
+
+endfunction
+
+
+%!test
+%! x = rand (10);
+%! cx1 = cov (x);
+%! cx2 = cov (x, x);
+%! assert(size (cx1) == [10, 10] && size (cx2) == [10, 10]);
+%! assert(cx1, cx2, 1e1*eps);
+
+%!test
+%! x = [1:3]';
+%! y = [3:-1:1]';
+%! assert (cov (x,y), -1, 5*eps)
+%! assert (cov (x,flipud (y)), 1, 5*eps)
+%! assert (cov ([x, y]), [1 -1; -1 1], 5*eps)
+
+%!test
+%! x = single ([1:3]');
+%! y = single ([3:-1:1]');
+%! assert (cov (x,y), single (-1), 5*eps)
+%! assert (cov (x,flipud (y)), single (1), 5*eps)
+%! assert (cov ([x, y]), single ([1 -1; -1 1]), 5*eps)
+
+%!test
+%! x = [1:5];
+%! c = cov (x);
+%! assert (isscalar (c));
+%! assert (c, 2.5);
+
+%!assert(cov (5), 0);
+%!assert(cov (single(5)), single(0));
+
+%!test
+%! x = [1:5];
+%! c = cov (x, 0);
+%! assert(c, 2.5);
+%! c = cov (x, 1);
+%! assert(c, 2);
+
+%% Test input validation
+%!error cov ();
+%!error cov (1, 2, 3, 4);
+%!error cov ([1; 2], ["A", "B"]);
+%!error cov (ones (2,2,2));
+%!error cov (ones (2,2), ones (2,2,2));
+%!error cov (1, 3);
+%!error cov (ones (2,2), ones (3,2));
+