www.gusucode.com > 语音信号处理工具箱 - Voicebox源码程序 > Voicebox\dlyapsq.m
function v=dlyapsq(a,b) % Solves the discrete Lyapunov equation AV'VA' - V'V +BB' =0 % V is upper triangular with real non-negative diagonal entries % this is equivalent to v=chol(dlyap(a,b*b')) but better conditioned numerically % Copyright (C) Mike Brookes 2002 % % Last modified Wed Jan 30 09:44:31 2002 % % 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. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [q,s]=schur(a'); [q,s]=rsf2csf(q,s); [qd,r]=qr(b'*q,0); % save r for testing r0=r; [m,n]=size(r); u=zeros(n,n); if m==1 for i=1:n-1 in=i+1:n; si=s(i,i); aa=sqrt(1-si*si'); u(i,i)=r(1)/aa; u(i,in)=(u(i,i)*si'*s(i,in)+aa*r(2:end))/(eye(n-i)-si'*s(in,in)); r=aa*(u(i,i)*s(i,in)+u(i,in)*s(in,in))-si*r(2:end); end u(n,n)=r/sqrt(1-s(n,n)*s(n,n)'); else w=zeros(m,1); w(m)=1; em=eye(m); for i=1:n-m in=i+1:n; si=s(i,i); aa=sqrt(1-si*si'); u(i,i)=r(1,1)/aa; u(i,in)=(u(i,i)*si'*s(i,in)+aa*r(1,2:end))/(eye(n-i)-si'*s(in,in)); vv=aa*(u(i,i)*s(i,in)+u(i,in)*s(in,in))-si*r(1,2:end); rr=zeros(m,n-i); rr(1:m-1,:)=r(2:end,2:end); [qq,r]=qrupdate(em,rr,w,vv'); end for i=n-m+1:n-1 in=i+1:n; si=s(i,i); aa=sqrt(1-si*si'); u(i,i)=r(1,1)/aa; u(i,in)=(u(i,i)*si'*s(i,in)+aa*r(1,2:end))/(eye(n-i)-si'*s(in,in)); vv=aa*(u(i,i)*s(i,in)+u(i,in)*s(in,in))-si*r(1,2:end); rr=zeros(n-i+1,n-i); rr(1:n-i,:)=r(2:end,2:end); [qq,rr]=qrupdate(eye(n-i+1),rr,w(m-n+i:end),vv'); r=rr(1:n-i,:); end u(n,n)=r/sqrt(1-s(n,n)*s(n,n)'); end v=triu(qr(u*q')); dv=diag(v); ix=dv~=0; v(ix,:)=diag(abs(dv(ix))./dv(ix))*v(ix,:); if isreal(a) & isreal(b) v=real(v); end