# HG changeset patch
# User jwe
# Date 745018965 0
# Node ID 69497d3b3b75dc10f11c0d597c1d797b93ba3999
# Parent  969b6494a10ca3c8c86f7fe42c64961be35975c1
[project @ 1993-08-10 21:42:45 by jwe]
Initial revision

diff -r 969b6494a10c -r 69497d3b3b75 scripts/linear-algebra/qzhess.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/scripts/linear-algebra/qzhess.m	Tue Aug 10 21:42:45 1993 +0000
@@ -0,0 +1,45 @@
+function [aa,bb,q,z] = qzhess(a,b)
+
+% compute the qz decomposition of the matrix pencil (a - lambda b)
+% result: (for MATLAB compatibility):
+%	q*a*z = aa, q*b*z = bb
+%	q, z orthogonal, 
+%	v = matrix of generalized eigenvectors
+%
+% This ought to be done in a compiled program
+% Algorithm taken from Golub and Van Loan, MATRIX COMPUTATIONS, 2nd ed.
+
+[na,ma] = size(a);
+[nb,mb] = size(b);
+if( (na ~= ma) | (na ~= nb) | (nb ~= mb) ) 
+  disp('qz: incompatible dimensions');
+  return;
+endif
+
+% reduce to hessenberg-triangular form
+[q,bb] = qr(b);
+aa = q'*a;
+q = q';
+z = eye(na);
+for j=1:(na-2)
+  for i=na:-1:(j+2)
+    %disp(['zero out aa(',num2str(i),',',num2str(j),')'])
+    rot= givens(aa(i-1,j),aa(i,j));
+    aa((i-1):i,:) = rot*aa((i-1):i,:);
+    bb((i-1):i,:) = rot*bb((i-1):i,:);
+    q( (i-1):i,:) = rot*q( (i-1):i,:);
+    
+    %disp(['now zero out bb(',num2str(i),',',num2str(i-1),')'])
+    rot = givens(bb(i,i),bb(i,i-1))';
+    bb(:,(i-1):i) = bb(:,(i-1):i)*rot';
+    aa(:,(i-1):i) = aa(:,(i-1):i)*rot';
+    z(:, (i-1):i) = z(:, (i-1):i)*rot';
+  endfor
+endfor
+
+bb(2,1) = 0;
+for i=3:na
+  bb(i,1:(i-1)) = zeros(1,i-1);
+  aa(i,1:(i-2)) = zeros(1,i-2);
+endfor
+endfunction