1function [A,B,Q,Z] = qzswitch(i,A,B,Q,Z) 2%function [A,B,Q,Z] = qzswitch(i,A,B,Q,Z) 3% 4% Takes U.T. matrices A, B, orthonormal matrices Q,Z, interchanges 5% diagonal elements i and i+1 of both A and B, while maintaining 6% Q'AZ' and Q'BZ' unchanged. If diagonal elements of A and B 7% are zero at matching positions, the returned A will have zeros at both 8% positions on the diagonal. This is natural behavior if this routine is used 9% to drive all zeros on the diagonal of A to the lower right, but in this case 10% the qz transformation is not unique and it is not possible simply to switch 11% the positions of the diagonal elements of both A and B. 12 13% Original file downloaded from: 14% http://sims.princeton.edu/yftp/gensys/mfiles/qzswitch.m 15 16% Copyright (C) 1993-2007 Christopher Sims 17% Copyright (C) 2008-2011 Dynare Team 18% 19% This file is part of Dynare. 20% 21% Dynare is free software: you can redistribute it and/or modify 22% it under the terms of the GNU General Public License as published by 23% the Free Software Foundation, either version 3 of the License, or 24% (at your option) any later version. 25% 26% Dynare is distributed in the hope that it will be useful, 27% but WITHOUT ANY WARRANTY; without even the implied warranty of 28% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 29% GNU General Public License for more details. 30% 31% You should have received a copy of the GNU General Public License 32% along with Dynare. If not, see <http://www.gnu.org/licenses/>. 33 34realsmall=sqrt(eps)*10; 35%realsmall=1e-3; 36a = A(i,i); d = B(i,i); b = A(i,i+1); e = B(i,i+1); 37c = A(i+1,i+1); f = B(i+1,i+1); 38% A(i:i+1,i:i+1)=[a b; 0 c]; 39% B(i:i+1,i:i+1)=[d e; 0 f]; 40if (abs(c)<realsmall && abs(f)<realsmall) 41 if abs(a)<realsmall 42 % l.r. coincident 0's with u.l. of A=0; do nothing 43 return 44 else 45 % l.r. coincident zeros; put 0 in u.l. of a 46 wz=[b; -a]; 47 wz=wz/sqrt(wz'*wz); 48 wz=[wz [wz(2)';-wz(1)'] ]; 49 xy=eye(2); 50 end 51elseif (abs(a)<realsmall && abs(d)<realsmall) 52 if abs(c)<realsmall 53 % u.l. coincident zeros with l.r. of A=0; do nothing 54 return 55 else 56 % u.l. coincident zeros; put 0 in l.r. of A 57 wz=eye(2); 58 xy=[c -b]; 59 xy=xy/sqrt(xy*xy'); 60 xy=[[xy(2)' -xy(1)'];xy]; 61 end 62else 63 % usual case 64 wz = [c*e-f*b, (c*d-f*a)']; 65 xy = [(b*d-e*a)', (c*d-f*a)']; 66 n = sqrt(wz*wz'); 67 m = sqrt(xy*xy'); 68 if m<eps*100 69 % all elements of A and B proportional 70 return 71 end 72 wz = n\wz; 73 xy = m\xy; 74 wz = [wz; -wz(2)', wz(1)']; 75 xy = [xy;-xy(2)', xy(1)']; 76end 77A(i:i+1,:) = xy*A(i:i+1,:); 78B(i:i+1,:) = xy*B(i:i+1,:); 79A(:,i:i+1) = A(:,i:i+1)*wz; 80B(:,i:i+1) = B(:,i:i+1)*wz; 81Z(:,i:i+1) = Z(:,i:i+1)*wz; 82Q(i:i+1,:) = xy*Q(i:i+1,:);