Mercurial > octave-nkf
annotate scripts/linear-algebra/qzhess.m @ 11593:1577c6f80926
Use non-breaking spaces between certain adjectives and their nouns in docstrings.
author | Rik <octave@nomad.inbox5.com> |
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date | Thu, 20 Jan 2011 20:19:29 -0800 |
parents | fd0a3ac60b0e |
children | c5c94b63931f |
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11523 | 1 ## Copyright (C) 1993-2011 John W. Eaton |
2313 | 2 ## |
3 ## This file is part of Octave. | |
4 ## | |
5 ## Octave is free software; you can redistribute it and/or modify it | |
6 ## under the terms of the GNU General Public License as published by | |
7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
8 ## your option) any later version. | |
2313 | 9 ## |
10 ## Octave is distributed in the hope that it will be useful, but | |
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
13 ## General Public License for more details. | |
14 ## | |
15 ## You should have received a copy of the GNU General Public License | |
7016 | 16 ## along with Octave; see the file COPYING. If not, see |
17 ## <http://www.gnu.org/licenses/>. | |
245 | 18 |
3372 | 19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {[@var{aa}, @var{bb}, @var{q}, @var{z}] =} qzhess (@var{A}, @var{B}) |
3372 | 21 ## Compute the Hessenberg-triangular decomposition of the matrix pencil |
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22 ## @code{(@var{A}, @var{B})}, returning |
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23 ## @code{@var{aa} = @var{q} * @var{A} * @var{z}}, |
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24 ## @code{@var{bb} = @var{q} * @var{B} * @var{z}}, with @var{q} and @var{z} |
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25 ## orthogonal. For example: |
3426 | 26 ## |
3372 | 27 ## @example |
28 ## @group | |
29 ## [aa, bb, q, z] = qzhess ([1, 2; 3, 4], [5, 6; 7, 8]) | |
30 ## @result{} aa = [ -3.02244, -4.41741; 0.92998, 0.69749 ] | |
31 ## @result{} bb = [ -8.60233, -9.99730; 0.00000, -0.23250 ] | |
32 ## @result{} q = [ -0.58124, -0.81373; -0.81373, 0.58124 ] | |
33 ## @result{} z = [ 1, 0; 0, 1 ] | |
34 ## @end group | |
35 ## @end example | |
3426 | 36 ## |
3372 | 37 ## The Hessenberg-triangular decomposition is the first step in |
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38 ## Moler and Stewart's QZ@tie{}decomposition algorithm. |
3426 | 39 ## |
3372 | 40 ## Algorithm taken from Golub and Van Loan, @cite{Matrix Computations, 2nd |
41 ## edition}. | |
42 ## @end deftypefn | |
29 | 43 |
2312 | 44 ## Author: A. S. Hodel <scotte@eng.auburn.edu> |
45 ## Created: August 1993 | |
46 ## Adapted-By: jwe | |
29 | 47 |
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48 function [aa, bb, q, z] = qzhess (A, B) |
72 | 49 |
54 | 50 if (nargin != 2) |
6046 | 51 print_usage (); |
54 | 52 endif |
53 | |
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54 [na, ma] = size (A); |
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55 [nb, mb] = size (B); |
54 | 56 if (na != ma || na != nb || nb != mb) |
57 error ("qzhess: incompatible dimensions"); | |
58 endif | |
59 | |
2303 | 60 ## Reduce to hessenberg-triangular form. |
29 | 61 |
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62 [q, bb] = qr (B); |
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63 aa = q' * A; |
54 | 64 q = q'; |
65 z = eye (na); | |
66 for j = 1:(na-2) | |
67 for i = na:-1:(j+2) | |
68 | |
2303 | 69 ## disp (["zero out aa(", num2str(i), ",", num2str(j), ")"]) |
54 | 70 |
71 rot = givens (aa (i-1, j), aa (i, j)); | |
72 aa ((i-1):i, :) = rot *aa ((i-1):i, :); | |
73 bb ((i-1):i, :) = rot *bb ((i-1):i, :); | |
74 q ((i-1):i, :) = rot *q ((i-1):i, :); | |
75 | |
2303 | 76 ## disp (["now zero out bb(", num2str(i), ",", num2str(i-1), ")"]) |
54 | 77 |
78 rot = givens (bb (i, i), bb (i, i-1))'; | |
79 bb (:, (i-1):i) = bb (:, (i-1):i) * rot'; | |
80 aa (:, (i-1):i) = aa (:, (i-1):i) * rot'; | |
81 z (:, (i-1):i) = z (:, (i-1):i) * rot'; | |
82 | |
83 endfor | |
29 | 84 endfor |
85 | |
54 | 86 bb (2, 1) = 0.0; |
87 for i = 3:na | |
88 bb (i, 1:(i-1)) = zeros (1, i-1); | |
89 aa (i, 1:(i-2)) = zeros (1, i-2); | |
90 endfor | |
91 | |
29 | 92 endfunction |