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1 ## Copyright (C) 1996 John W. Eaton |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 2, or (at your option) |
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8 ## any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, write to the Free |
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17 ## Software Foundation, 59 Temple Place - Suite 330, Boston, MA |
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18 ## 02111-1307, USA. |
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19 |
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20 ## Usage: [aa, bb, q, z] = qzhess (a, b) |
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21 ## |
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22 ## Compute the qz decomposition of the matrix pencil (a - lambda b) |
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23 ## |
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24 ## result: (for Matlab compatibility): |
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25 ## |
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26 ## aa = q*a*z and bb = q*b*z, with q, z orthogonal, and |
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27 ## v = matrix of generalized eigenvectors. |
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28 ## |
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29 ## This ought to be done in a compiled program |
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30 ## |
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31 ## Algorithm taken from Golub and Van Loan, Matrix Computations, 2nd ed. |
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32 |
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33 ## Author: A. S. Hodel <scotte@eng.auburn.edu> |
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34 ## Created: August 1993 |
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35 ## Adapted-By: jwe |
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36 |
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37 function [aa, bb, q, z] = qzhess (a, b) |
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38 |
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39 if (nargin != 2) |
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40 error ("usage: [aa, bb, q, z] = qzhess (a, b)"); |
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41 endif |
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42 |
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43 [na, ma] = size (a); |
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44 [nb, mb] = size (b); |
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45 if (na != ma || na != nb || nb != mb) |
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46 error ("qzhess: incompatible dimensions"); |
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47 endif |
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48 |
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49 ## Reduce to hessenberg-triangular form. |
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50 |
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51 [q, bb] = qr (b); |
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52 aa = q' * a; |
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53 q = q'; |
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54 z = eye (na); |
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55 for j = 1:(na-2) |
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56 for i = na:-1:(j+2) |
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57 |
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58 ## disp (["zero out aa(", num2str(i), ",", num2str(j), ")"]) |
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59 |
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60 rot = givens (aa (i-1, j), aa (i, j)); |
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61 aa ((i-1):i, :) = rot *aa ((i-1):i, :); |
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62 bb ((i-1):i, :) = rot *bb ((i-1):i, :); |
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63 q ((i-1):i, :) = rot *q ((i-1):i, :); |
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64 |
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65 ## disp (["now zero out bb(", num2str(i), ",", num2str(i-1), ")"]) |
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66 |
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67 rot = givens (bb (i, i), bb (i, i-1))'; |
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68 bb (:, (i-1):i) = bb (:, (i-1):i) * rot'; |
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69 aa (:, (i-1):i) = aa (:, (i-1):i) * rot'; |
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70 z (:, (i-1):i) = z (:, (i-1):i) * rot'; |
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71 |
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72 endfor |
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73 endfor |
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74 |
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75 bb (2, 1) = 0.0; |
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76 for i = 3:na |
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77 bb (i, 1:(i-1)) = zeros (1, i-1); |
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78 aa (i, 1:(i-2)) = zeros (1, i-2); |
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79 endfor |
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80 |
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81 endfunction |
