www.gusucode.com > 语音信号处理工具箱 - Voicebox源码程序 > Voicebox\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;