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1 # Copyright (C) 1993 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 the |
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7 # Free Software Foundation; either version 2, or (at your option) any |
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8 # later version. |
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9 # |
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10 # Octave is distributed in the hope that it will be useful, but WITHOUT |
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11 # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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12 # FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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13 # 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, 675 Mass Ave, Cambridge, MA 02139, USA. |
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18 |
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19 function x = lyap (a, b, c) |
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20 |
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21 # Usage: x = lyap (a, b {,c}) |
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22 # |
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23 # If (a, b, c) are specified, then lyap returns the solution of the |
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24 # Sylvester equation |
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25 # |
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26 # a x + x b + c = 0 |
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27 # |
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28 # If only (a, b) are specified, then lyap returns the solution of the |
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29 # Lyapunov equation |
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30 # |
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31 # a' x + x a + b = 0 |
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32 # |
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33 # If b is not square, then lyap returns the solution of either |
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34 # |
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35 # a' x + x a + b' b = 0 |
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36 # |
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37 # or |
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38 # |
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39 # a x + x a' + b b' = 0 |
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40 # |
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41 # whichever is appropriate. |
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42 # |
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43 # Solves by using the Bartels-Stewart algorithm (1972). |
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44 |
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45 # Written by A. S. Hodel (scotte@eng.auburn.edu) August 1993. |
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46 |
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47 |
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48 if (nargin != 3 && nargin != 2) |
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49 error ("usage: lyap (a, b {,c})"); |
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50 endif |
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51 |
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52 if ((n = is_square(a)) == 0) |
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53 error ("lyap: a is not square"); |
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54 endif |
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55 |
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56 if (nargin == 2) |
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57 |
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58 # Transform Lyapunov equation to Sylvester equation form. |
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59 |
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60 if ((m = is_square (b)) == 0) |
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61 if ((m = rows (b)) == n) |
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62 |
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63 # solve a x + x a' + b b' = 0 |
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64 |
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65 b = b * b'; |
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66 a = a'; |
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67 else |
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68 |
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69 # Try to solve a'x + x a + b' b = 0. |
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70 |
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71 m = columns (b); |
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72 b = b' * b; |
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73 endif |
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74 |
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75 if (m != n) |
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76 error ("lyap: a, b not conformably dimensioned"); |
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77 endif |
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78 endif |
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79 |
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80 # Set up Sylvester equation. |
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81 |
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82 c = b; |
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83 b = a; |
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84 a = b' |
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85 |
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86 else |
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87 |
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88 # Check dimensions. |
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89 |
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90 if ((m = is_square (b)) == 0) |
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91 error ("lyap: b must be square in a sylvester equation"); |
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92 endif |
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93 |
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94 [n1, m1] = size(c); |
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95 |
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96 if (n != n1 || m != m1) |
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97 error("lyap: a,b,c not conformably dimensioned"); |
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98 endif; |
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99 endif |
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100 |
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101 # Call octave built-in function. |
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102 |
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103 x = syl (a, b, c); |
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104 |
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105 endfunction |
