mahalanobis.m

JAVA 数学程序库 提供常规的数值计算程序包

## Copyright (C) 1996, 1997 John W. Eaton
##
## 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 2, or (at your option)
## any later version.
##
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## 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, write to the Free
## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
## 02110-1301, USA.

## -*- texinfo -*-
## @deftypefn {Function File} {} mahalanobis (@var{x}, @var{y})
## Return the Mahalanobis' D-square distance between the multivariate
## samples @var{x} and @var{y}, which must have the same number of
## components (columns), but may have a different number of observations
## (rows).
## @end deftypefn

## Author: Friedrich Leisch <[e-mail]>
## Created: July 1993
## Adapted-By: jwe

function retval = mahalanobis (X, Y)

  if (nargin != 2)
    print_usage ();
  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

  Xm = sum (X) / xr;
  Ym = sum (Y) / yr;

  X = X - ones (xr, 1) * Xm;
  Y = Y - ones (yr, 1) * Ym;

  W = (X' * X + Y' * Y) / (xr + yr - 2)

  Winv = inv (W);

  retval = (Xm - Ym) * Winv * (Xm - Ym)';

endfunction