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1 ## Copyright (C) 1996, 1997 Auburn University. All rights reserved. |
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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 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} lyap (@var{a}, @var{b}, @var{c}) |
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22 ## @deftypefnx {Function File} {} lyap (@var{a}, @var{b}) |
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23 ## Solve the Lyapunov (or Sylvester) equation via the Bartels-Stewart |
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24 ## algorithm (Communications of the ACM, 1972). |
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25 ## |
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26 ## If @var{a}, @var{b}, and @var{c} are specified, then @code{lyap} returns |
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27 ## the solution of the Sylvester equation |
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28 ## @iftex |
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29 ## @tex |
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30 ## $$ A X + X B + C = 0 $$ |
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31 ## @end tex |
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32 ## @end iftex |
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33 ## @ifinfo |
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34 ## @example |
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35 ## a x + x b + c = 0 |
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36 ## @end example |
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37 ## @end ifinfo |
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38 ## If only @code{(a, b)} are specified, then @code{lyap} returns the |
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39 ## solution of the Lyapunov equation |
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40 ## @iftex |
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41 ## @tex |
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42 ## $$ A^T X + X A + B = 0 $$ |
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43 ## @end tex |
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44 ## @end iftex |
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45 ## @ifinfo |
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46 ## @example |
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47 ## a' x + x a + b = 0 |
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48 ## @end example |
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49 ## @end ifinfo |
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50 ## If @var{b} is not square, then @code{lyap} returns the solution of either |
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51 ## @iftex |
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52 ## @tex |
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53 ## $$ A^T X + X A + B^T B = 0 $$ |
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54 ## @end tex |
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55 ## @end iftex |
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56 ## @ifinfo |
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57 ## @example |
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58 ## a' x + x a + b' b = 0 |
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59 ## @end example |
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60 ## @end ifinfo |
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61 ## @noindent |
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62 ## or |
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63 ## @iftex |
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64 ## @tex |
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65 ## $$ A X + X A^T + B B^T = 0 $$ |
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66 ## @end tex |
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67 ## @end iftex |
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68 ## @ifinfo |
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69 ## @example |
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70 ## a x + x a' + b b' = 0 |
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71 ## @end example |
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72 ## @end ifinfo |
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73 ## @noindent |
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74 ## whichever is appropriate. |
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75 ## |
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76 ## Solves by using the Bartels-Stewart algorithm (1972). |
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77 ## @end deftypefn |
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78 |
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79 ## Author: A. S. Hodel <scotte@eng.auburn.edu> |
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80 ## Created: August 1993 |
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81 ## Adapted-By: jwe |
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82 |
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83 function x = lyap (a, b, c) |
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84 |
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85 if (nargin != 3 && nargin != 2) |
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86 usage ("lyap (a, b {,c})"); |
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87 endif |
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88 |
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89 if ((n = is_square(a)) == 0) |
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90 error ("lyap: a is not square"); |
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91 endif |
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92 |
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93 if (nargin == 2) |
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94 |
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95 ## Transform Lyapunov equation to Sylvester equation form. |
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96 |
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97 if ((m = is_square (b)) == 0) |
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98 if ((m = rows (b)) == n) |
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99 |
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100 ## solve a x + x a' + b b' = 0 |
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101 |
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102 b = b * b'; |
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103 a = a'; |
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104 else |
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105 |
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106 ## Try to solve a'x + x a + b' b = 0. |
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107 |
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108 m = columns (b); |
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109 b = b' * b; |
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110 endif |
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111 |
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112 if (m != n) |
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113 error ("lyap: a, b not conformably dimensioned"); |
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114 endif |
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115 endif |
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116 |
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117 ## Set up Sylvester equation. |
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118 |
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119 c = b; |
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120 b = a; |
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121 a = b'; |
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122 |
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123 else |
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124 |
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125 ## Check dimensions. |
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126 |
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127 if ((m = is_square (b)) == 0) |
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128 error ("lyap: b must be square in a sylvester equation"); |
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129 endif |
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130 |
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131 [n1, m1] = size(c); |
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132 |
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133 if (n != n1 || m != m1) |
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134 error("lyap: a,b,c not conformably dimensioned"); |
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135 endif |
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136 endif |
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137 |
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138 ## Call octave built-in function. |
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139 |
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140 x = syl (a, b, c); |
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141 |
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142 endfunction |
