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## Copyright (C) 1995-2013 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} {} spearman (@var{x})
## @deftypefnx {Function File} {} spearman (@var{x}, @var{y})
## @cindex Spearman's Rho
## Compute Spearman's rank correlation coefficient @var{rho}.
##
## For two data vectors @var{x} and @var{y}, Spearman's @var{rho} is the
## correlation coefficient of the ranks of @var{x} and @var{y}.
##
## If @var{x} and @var{y} are drawn from independent distributions,
## @var{rho} has zero mean and variance @code{1 / (n - 1)}, and is
## asymptotically normally distributed.
##
## @code{spearman (@var{x})} is equivalent to @code{spearman (@var{x},
## @var{x})}.
## @seealso{ranks, kendall}
## @end deftypefn
## Author: KH <Kurt.Hornik@wu-wien.ac.at>
## Description: Spearman's rank correlation rho
function rho = spearman (x, y = [])
if (nargin < 1 || nargin > 2)
print_usage ();
endif
if ( ! (isnumeric (x) || islogical (x))
|| ! (isnumeric (y) || islogical (y)))
error ("spearman: X and Y must be numeric matrices or vectors");
endif
if (ndims (x) != 2 || ndims (y) != 2)
error ("spearman: X and Y must be 2-D matrices or vectors");
endif
if (isrow (x))
x = x.';
endif
if (nargin == 1)
rho = corr (ranks (x));
else
if (isrow (y))
y = y.';
endif
if (rows (x) != rows (y))
error ("spearman: X and Y must have the same number of observations");
endif
rho = corr (ranks (x), ranks (y));
endif
## Restore class cleared by ranks
if (isa (x, "single") || isa (y, "single"))
rho = single (rho);
endif
endfunction
%!test
%! x = 1:10;
%! y = exp (x);
%! assert (spearman (x,y), 1, 5*eps);
%! assert (spearman (x,-y), -1, 5*eps);
%!assert (spearman ([1 2 3], [-1 1 -2]), -0.5, 5*eps)
%% Test input validation
%!error spearman ()
%!error spearman (1, 2, 3)
%!error spearman (['A'; 'B'])
%!error spearman (ones (1,2), {1, 2})
%!error spearman (ones (2,2,2))
%!error spearman (ones (2,2), ones (2,2,2))
%!error spearman (ones (2,2), ones (3,2))
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