## Copyright (C) 2015 Lachlan Andrew
##
## 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
## .
## -*- texinfo -*-
## @deftypefn {Function File} {} mahal (@var{y}, @var{x})
## 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
## answer(i) = (@var{y}(i,:)-mean (@var{x})) * inv (A) * (@var{y}(i,:)-mean (@var{x}))'
## 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
## 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 ("mahalanobis: X and Y must be numeric matrices or vectors");
endif
if (ndims (x) != 2 || ndims (y) != 2)
error ("mahalanobis: X and Y must be 2-D matrices or vectors");
endif
[xr, xc] = size (x);
[yr, yc] = size (y);
if (xc != yc)
error ("mahalanobis: X and Y must have the same number of columns");
endif
if (isinteger (x))
x = double (x);
endif
xm = mean (x);
## 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 mahalanobis ()
%!error mahalanobis (1, 2, 3)
%!error mahalanobis ('A', 'B')
%!error mahalanobis ([1, 2], ['A', 'B'])
%!error mahalanobis (ones (2,2,2))
%!error mahalanobis (ones (2,2), ones (2,2,2))
%!error mahalanobis (ones (2,2), ones (2,3))
%X = [1 0; 0 1; 1 1; 0 0];
%assert (mahal (X,X), [1.5; 1.5; 1.5; 1.5])