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| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Mon, 26 Jul 2010 21:25:36 -0700 |
| parents | a1dbe9d80eee |
| children | 994e2a93a8e2 |
| rev | line source |
|---|---|
| 7017 | 1 ## Copyright (C) 1993, 1995, 1996, 1997, 1999, 2000, 2005, 2006, 2007 |
| 2 ## John W. Eaton | |
| 2313 | 3 ## |
| 4 ## This file is part of Octave. | |
| 5 ## | |
| 6 ## Octave is free software; you can redistribute it and/or modify it | |
| 7 ## under the terms of the GNU General Public License as published by | |
| 7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
| 9 ## your option) any later version. | |
| 2313 | 10 ## |
| 11 ## Octave is distributed in the hope that it will be useful, but | |
| 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 14 ## General Public License for more details. | |
| 15 ## | |
| 16 ## You should have received a copy of the GNU General Public License | |
| 7016 | 17 ## along with Octave; see the file COPYING. If not, see |
| 18 ## <http://www.gnu.org/licenses/>. | |
| 245 | 19 |
| 3372 | 20 ## -*- texinfo -*- |
| 21 ## @deftypefn {Function File} {[@var{aa}, @var{bb}, @var{q}, @var{z}] =} qzhess (@var{a}, @var{b}) | |
| 22 ## Compute the Hessenberg-triangular decomposition of the matrix pencil | |
| 23 ## @code{(@var{a}, @var{b})}, returning | |
| 3426 | 24 ## @code{@var{aa} = @var{q} * @var{a} * @var{z}}, |
| 3372 | 25 ## @code{@var{bb} = @var{q} * @var{b} * @var{z}}, with @var{q} and @var{z} |
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10821
693e22af08ae
Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents:
7017
diff
changeset
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26 ## orthogonal. For example: |
| 3426 | 27 ## |
| 3372 | 28 ## @example |
| 29 ## @group | |
| 30 ## [aa, bb, q, z] = qzhess ([1, 2; 3, 4], [5, 6; 7, 8]) | |
| 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 | |
| 3426 | 37 ## |
| 3372 | 38 ## The Hessenberg-triangular decomposition is the first step in |
| 39 ## Moler and Stewart's QZ decomposition algorithm. | |
| 3426 | 40 ## |
| 3372 | 41 ## Algorithm taken from Golub and Van Loan, @cite{Matrix Computations, 2nd |
| 42 ## edition}. | |
| 43 ## @end deftypefn | |
| 29 | 44 |
| 2312 | 45 ## Author: A. S. Hodel <scotte@eng.auburn.edu> |
| 46 ## Created: August 1993 | |
| 47 ## Adapted-By: jwe | |
| 29 | 48 |
| 2312 | 49 function [aa, bb, q, z] = qzhess (a, b) |
| 72 | 50 |
| 54 | 51 if (nargin != 2) |
| 6046 | 52 print_usage (); |
| 54 | 53 endif |
| 54 | |
| 55 [na, ma] = size (a); | |
| 56 [nb, mb] = size (b); | |
| 57 if (na != ma || na != nb || nb != mb) | |
| 58 error ("qzhess: incompatible dimensions"); | |
| 59 endif | |
| 60 | |
| 2303 | 61 ## Reduce to hessenberg-triangular form. |
| 29 | 62 |
| 54 | 63 [q, bb] = qr (b); |
| 64 aa = q' * a; | |
| 65 q = q'; | |
| 66 z = eye (na); | |
| 67 for j = 1:(na-2) | |
| 68 for i = na:-1:(j+2) | |
| 69 | |
| 2303 | 70 ## disp (["zero out aa(", num2str(i), ",", num2str(j), ")"]) |
| 54 | 71 |
| 72 rot = givens (aa (i-1, j), aa (i, j)); | |
| 73 aa ((i-1):i, :) = rot *aa ((i-1):i, :); | |
| 74 bb ((i-1):i, :) = rot *bb ((i-1):i, :); | |
| 75 q ((i-1):i, :) = rot *q ((i-1):i, :); | |
| 76 | |
| 2303 | 77 ## disp (["now zero out bb(", num2str(i), ",", num2str(i-1), ")"]) |
| 54 | 78 |
| 79 rot = givens (bb (i, i), bb (i, i-1))'; | |
| 80 bb (:, (i-1):i) = bb (:, (i-1):i) * rot'; | |
| 81 aa (:, (i-1):i) = aa (:, (i-1):i) * rot'; | |
| 82 z (:, (i-1):i) = z (:, (i-1):i) * rot'; | |
| 83 | |
| 84 endfor | |
| 29 | 85 endfor |
| 86 | |
| 54 | 87 bb (2, 1) = 0.0; |
| 88 for i = 3:na | |
| 89 bb (i, 1:(i-1)) = zeros (1, i-1); | |
| 90 aa (i, 1:(i-2)) = zeros (1, i-2); | |
| 91 endfor | |
| 92 | |
| 29 | 93 endfunction |