|
245
|
1 # Copyright (C) 1993 John W. Eaton |
|
|
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 the |
|
|
7 # Free Software Foundation; either version 2, or (at your option) any |
|
|
8 # later version. |
|
|
9 # |
|
|
10 # Octave is distributed in the hope that it will be useful, but WITHOUT |
|
|
11 # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
|
|
12 # FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
|
|
13 # for more details. |
|
|
14 # |
|
|
15 # You should have received a copy of the GNU General Public License |
|
|
16 # along with Octave; see the file COPYING. If not, write to the Free |
|
|
17 # Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. |
|
|
18 |
|
75
|
19 function x = dlyap (a, b) |
|
|
20 |
|
|
21 # Usage: x = dlyap (a, b) |
|
|
22 # |
|
|
23 # Solve a x a' - x + b = 0 (discrete Lyapunov equation) for square |
|
|
24 # matrices a and b. If b is not square, then the function attempts |
|
|
25 # to solve either |
|
|
26 # |
|
|
27 # a x a' - x + b b' = 0 |
|
|
28 # |
|
|
29 # or |
|
|
30 # |
|
|
31 # a' x a - x + b' b = 0 |
|
|
32 # |
|
|
33 # whichever is appropriate. Uses Schur decomposition as in Kitagawa |
|
|
34 # (1977). |
|
|
35 |
|
|
36 # Written by A. S. Hodel (scotte@eng.auburn.edu) August 1993. |
|
|
37 |
|
|
38 if ((n = is_square (a)) == 0) |
|
|
39 fprintf (stderr, "warning: dlyap: a must be square"); |
|
|
40 endif |
|
|
41 |
|
|
42 if ((m = is_square (b)) == 0) |
|
|
43 [n1, m] = size (b); |
|
|
44 if (n1 == n) |
|
|
45 b = b*b'; |
|
|
46 m = n1; |
|
|
47 else |
|
|
48 b = b'*b; |
|
|
49 a = a'; |
|
|
50 endif |
|
|
51 endif |
|
|
52 |
|
|
53 if (n != m) |
|
|
54 fprintf (stderr, "warning: dlyap: a,b not conformably dimensioned"); |
|
|
55 endif |
|
|
56 |
|
|
57 # Solve the equation column by column. |
|
|
58 |
|
|
59 [u, s] = schur (a); |
|
|
60 b = u'*b*u; |
|
|
61 |
|
|
62 j = n; |
|
|
63 while (j > 0) |
|
|
64 j1 = j; |
|
|
65 |
|
|
66 # Check for Schur block. |
|
|
67 |
|
|
68 if (j == 1) |
|
|
69 blksiz = 1; |
|
|
70 elseif (s (j, j-1) != 0) |
|
|
71 blksiz = 2; |
|
|
72 j = j - 1; |
|
|
73 else |
|
|
74 blksiz = 1; |
|
|
75 endif |
|
|
76 |
|
|
77 Ajj = kron (s (j:j1, j:j1), s) - eye (blksiz*n); |
|
|
78 |
|
|
79 rhs = reshape (b (:, j:j1), blksiz*n, 1); |
|
|
80 |
|
|
81 if (j1 < n) |
|
|
82 rhs2 = s*(x (:, (j1+1):n) * s (j:j1, (j1+1):n)'); |
|
|
83 rhs = rhs + reshape (rhs2, blksiz*n, 1); |
|
|
84 endif |
|
|
85 |
|
|
86 v = - Ajj\rhs; |
|
|
87 x (:, j) = v (1:n); |
|
|
88 |
|
|
89 if(blksiz == 2) |
|
|
90 x (:, j1) = v ((n+1):blksiz*n); |
|
|
91 endif |
|
|
92 |
|
|
93 j = j - 1; |
|
|
94 |
|
|
95 endwhile |
|
|
96 |
|
|
97 # Back-transform to original coordinates. |
|
|
98 |
|
|
99 x = u*x*u'; |
|
|
100 |
|
|
101 endfunction |
