## 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])