www.pudn.com > voicebox2.zip > DUALDIAG.M

function [a,d]=dualdiag(w,b) 
%DUALDIAG Simultaneous diagonalisation of two hermitian matrices [A,D]=(W,B) 
% Given two hermitian matrices W and B with W positive definite, this routine 
% calculates A such that A'*W*A=I and A'*B*A=diag(D). The D will be in descending order. 
% 
% Suppose we have several N-dimensional data row-vectors arising from each of C different classes of data. 
% for each class, c, we can form the mean data vector m(c) and the within-class covariance matrix W(c) 
% We can then form the between class covariance matrix B by taking the covariance of the mean vectors m(1), m(2), ... 
% and also the averaged within-class covariance matrix W by averaging W(1), W(2), ... 
% If we then take A=dualdiag(W,B) and postmultiply all our original data vectors by A, we obtain new 
% data vectors for which the average within-class covariance matrix is the identity and for which 
% the first few components contain most of the information that is useful in discriminating between classes. 
 
% An alternative algorithm that is 20% faster but slightly less accurate is: 
% n=size(w,1); 
% [v,l]=eig(w\b); 
% [s,i]=sort(-diag(l)); 
% s=-s; 
% d=l(i*(n+1)-n); 
% q=sqrt(diag(v'*w*v))'.^(-1); 
% a=v(:,i).*q(ones(n,1),i); 
 
 
%      Copyright (C) Mike Brookes 1997 
% 
%      Last modified Fri Dec 17 07:57:42 1999 
% 
%   VOICEBOX is a MATLAB toolbox for speech processing. Home page is at 
%   http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%   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 2 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 can obtain a copy of the GNU General Public License from 
%   ftp://prep.ai.mit.edu/pub/gnu/COPYING-2.0 or by writing to 
%   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
[y,l]=eig(w+w'); 
z=y*diag(sqrt(diag(l*0.5)).^(-1)); 
[u,s,v]=svd(z'*(b+b')*z); 
d=diag(s)*0.5; 
a=z*u;