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comparison scripts/linear-algebra/qzhess.m @ 3372:f16c2ce14886

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[project @ 1999-11-23 19:07:09 by jwe]
author jwe
date Tue, 23 Nov 1999 19:07:18 +0000
parents 8b262e771614
children f8dde1807dee
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3371:86873384cd10 3372:f16c2ce14886
15 ## You should have received a copy of the GNU General Public License 15 ## You should have received a copy of the GNU General Public License
16 ## along with Octave; see the file COPYING. If not, write to the Free 16 ## along with Octave; see the file COPYING. If not, write to the Free
17 ## Software Foundation, 59 Temple Place - Suite 330, Boston, MA 17 ## Software Foundation, 59 Temple Place - Suite 330, Boston, MA
18 ## 02111-1307, USA. 18 ## 02111-1307, USA.
19 19
20 ## Usage: [aa, bb, q, z] = qzhess (a, b) 20 ## -*- texinfo -*-
21 ## 21 ## @deftypefn {Function File} {[@var{aa}, @var{bb}, @var{q}, @var{z}] =} qzhess (@var{a}, @var{b})
22 ## Compute the qz decomposition of the matrix pencil (a - lambda b) 22 ## Compute the Hessenberg-triangular decomposition of the matrix pencil
23 ## 23 ## @code{(@var{a}, @var{b})}, returning
24 ## result: (for Matlab compatibility): 24 ## @code{@var{aa} = @var{q} * @var{a} * @var{z}},
25 ## 25 ## @code{@var{bb} = @var{q} * @var{b} * @var{z}}, with @var{q} and @var{z}
26 ## aa = q*a*z and bb = q*b*z, with q, z orthogonal, and 26 ## orthogonal. For example,
27 ## v = matrix of generalized eigenvectors. 27 ##
28 ## 28 ## @example
29 ## This ought to be done in a compiled program 29 ## @group
30 ## 30 ## [aa, bb, q, z] = qzhess ([1, 2; 3, 4], [5, 6; 7, 8])
31 ## Algorithm taken from Golub and Van Loan, Matrix Computations, 2nd ed. 31 ## @result{} aa = [ -3.02244, -4.41741; 0.92998, 0.69749 ]
32 ## @result{} bb = [ -8.60233, -9.99730; 0.00000, -0.23250 ]
33 ## @result{} q = [ -0.58124, -0.81373; -0.81373, 0.58124 ]
34 ## @result{} z = [ 1, 0; 0, 1 ]
35 ## @end group
36 ## @end example
37 ##
38 ## The Hessenberg-triangular decomposition is the first step in
39 ## Moler and Stewart's QZ decomposition algorithm.
40 ##
41 ## Algorithm taken from Golub and Van Loan, @cite{Matrix Computations, 2nd
42 ## edition}.
43 ## @end deftypefn
32 44
33 ## Author: A. S. Hodel <scotte@eng.auburn.edu> 45 ## Author: A. S. Hodel <scotte@eng.auburn.edu>
34 ## Created: August 1993 46 ## Created: August 1993
35 ## Adapted-By: jwe 47 ## Adapted-By: jwe
36 48