# ITE / code / shared / embedded / E4 / bkjordan.m

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54``` ```function [P, Q, U1, U2, iR, iS] = bkjordan(A, cut) % bkjordan - Computes the decomposition A = [U1 U2]*diag(P,Q)*inv([U1 U2]) % [P, Q, U1, U2, iR, iS] = bkjordan(A, cut) % P stores the eigenvalues of A greater or equal that cut, and Q the % eigenvalues that do not meet this condition. % inv([U1 U2]) = [iR; iS] iR*U1=I iS*U2=I iR*U2=0 iS*U1=0. % % 5/3/97 % Copyright (C) 1997 Jaime Terceiro % % 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, 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 should have received a copy of the GNU General Public License % along with this file. If not, write to the Free Software Foundation, % 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. [T, U, iU, eigen] = bkdiag(A); k1 = abs(eigen) >= cut; k2 = ~k1; sk1 = sum(k1); sk2 = sum(k2); if sk1 & sk2 P = T(k1,k1); U1 = U(:,k1); iR = iU(k1,:); Q = T(k2,k2); U2 = U(:,k2); iS = iU(k2,:); elseif sk2 P = []; U1= []; iR= []; Q = A; U2 = eye(size(A)); iS = U2; else Q = []; U2= []; iS= []; P = A; U1 = eye(size(A)); iR = U1; end ```