/usr/share/octave/packages/statistics-1.3.0/mahal.m is in octave-statistics 1.3.0-1.
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##
## 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; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} mahal (@var{y}, @var{x})
## Mahalanobis' D-square distance.
##
## Return the Mahalanobis' D-square distance of the points in
## @var{y} from the distribution implied by points @var{x}.
##
## Specifically, it uses a Cholesky decomposition to set
##
## @example
## answer(i) = (@var{y}(i,:) - mean (@var{x})) * inv (A) * (@var{y}(i,:)-mean (@var{x}))'
## @end example
##
## where A is the covariance of @var{x}.
##
## The data @var{x} and @var{y} must have the same number of components
## (columns), but may have a different number of observations (rows).
##
## @end deftypefn
## Author: Lachlan Andrew <lachlanbis@gmail.com>
## Created: September 2015
## Based on function mahalanobis by Friedrich Leisch
function retval = mahal (y, x)
if (nargin != 2)
print_usage ();
endif
if (! (isnumeric (x) || islogical (x)) || ! (isnumeric (y) || islogical (y)))
error ("mahal: X and Y must be numeric matrices or vectors");
endif
if (! ismatrix (x) || ! ismatrix (y))
error ("mahal: X and Y must be 2-D matrices or vectors");
endif
[xr, xc] = size (x);
[yr, yc] = size (y);
if (xc != yc)
error ("mahal: X and Y must have the same number of columns");
endif
if (isinteger (x))
x = double (x);
endif
xm = mean (x, 1);
## Center data by subtracting mean of x
x = bsxfun (@minus, x, xm);
y = bsxfun (@minus, y, xm);
w = (x' * x) / (xr - 1);
retval = sumsq (y / chol (w), 2);
endfunction
## Test input validation
%!error mahal ()
%!error mahal (1, 2, 3)
%!error mahal ("A", "B")
%!error <must be numeric> mahal ([1, 2], ["A", "B"])
%!error mahal (ones (2, 2, 2))
%!error <must be 2-D matrices> mahal (ones (2, 2), ones (2, 2, 2))
%!error <same number of columns> mahal (ones (2, 2), ones (2, 3))
%!test
%! X = [1 0; 0 1; 1 1; 0 0];
%! assert (mahal (X, X), [1.5; 1.5; 1.5; 1.5], eps)
%! assert (mahal (X, X+1), [7.5; 7.5; 1.5; 13.5], eps)
%!assert (mahal ([true; true], [false; true]), [0.5; 0.5], eps)
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