|
3431
|
1 ## Copyright (C) 1996, 1998 Auburn University. All rights reserved. |
|
|
2 ## |
|
|
3 ## This file is part of Octave. |
|
|
4 ## |
|
|
5 ## Octave is free software; you can redistribute it and/or modify it |
|
7016
|
6 ## under the terms of the GNU General Public License as published by |
|
|
7 ## the Free Software Foundation; either version 3 of the License, or (at |
|
|
8 ## your option) any later version. |
|
3431
|
9 ## |
|
7016
|
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. |
|
3431
|
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/>. |
|
3431
|
18 |
|
|
19 ## -*- texinfo -*- |
|
5016
|
20 ## @deftypefn {Function File} {@var{y} =} zgfmul (@var{a}, @var{b}, @var{c}, @var{d}, @var{x}) |
|
|
21 ## Compute product of @var{zgep} incidence matrix @math{F} with vector @var{x}. |
|
|
22 ## Used by @command{zgepbal} (in @command{zgscal}) as part of generalized conjugate gradient |
|
3431
|
23 ## iteration. |
|
|
24 ## @end deftypefn |
|
|
25 |
|
|
26 ## References: |
|
|
27 ## ZGEP: Hodel, "Computation of Zeros with Balancing," 1992, submitted to LAA |
|
|
28 ## Generalized CG: Golub and Van Loan, "Matrix Computations, 2nd ed" 1989 |
|
|
29 |
|
|
30 ## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> |
|
|
31 ## Conversion to Octave July 3, 1994 |
|
|
32 |
|
|
33 function y = zgfmul (a, b, c, d, x) |
|
|
34 |
|
|
35 [n,m] = size(b); |
|
|
36 [p,m1] = size(c); |
|
|
37 nm = n+m; |
|
|
38 y = zeros(nm+p,1); |
|
|
39 |
|
|
40 ## construct F column by column |
|
|
41 for jj=1:n |
|
|
42 Fj = zeros(nm+p,1); |
|
|
43 |
|
|
44 ## rows 1:n: F1 |
|
|
45 aridx = complement(jj,find(a(jj,:) != 0)); |
|
|
46 acidx = complement(jj,find(a(:,jj) != 0)); |
|
|
47 bidx = find(b(jj,:) != 0); |
|
|
48 cidx = find(c(:,jj) != 0); |
|
|
49 |
|
|
50 Fj(aridx) = Fj(aridx) - 1; # off diagonal entries of F1 |
|
|
51 Fj(acidx) = Fj(acidx) - 1; |
|
|
52 ## diagonal entry of F1 |
|
|
53 Fj(jj) = length(aridx)+length(acidx) + length(bidx) + length(cidx); |
|
|
54 |
|
|
55 if(!isempty(bidx)) Fj(n+bidx) = 1; endif # B' incidence |
|
|
56 if(!isempty(cidx)) Fj(n+m+cidx) = -1; endif # -C incidence |
|
|
57 y = y + x(jj)*Fj; # multiply by corresponding entry of x |
|
|
58 endfor |
|
|
59 |
|
|
60 for jj=1:m |
|
|
61 Fj = zeros(nm+p,1); |
|
|
62 bidx = find(b(:,jj) != 0); |
|
|
63 if(!isempty(bidx)) Fj(bidx) = 1; endif # B incidence |
|
|
64 didx = find(d(:,jj) != 0); |
|
|
65 if(!isempty(didx)) Fj(n+m+didx) = 1; endif # D incidence |
|
|
66 Fj(n+jj) = length(bidx) + length(didx); # F2 is diagonal |
|
|
67 y = y + x(n+jj)*Fj; # multiply by corresponding entry of x |
|
|
68 endfor |
|
|
69 |
|
|
70 for jj=1:p |
|
|
71 Fj = zeros(nm+p,1); |
|
|
72 cidx = find(c(jj,:) != 0); |
|
|
73 if(!isempty(cidx)) Fj(cidx) = -1; endif # -C' incidence |
|
|
74 didx = find(d(jj,:) != 0); |
|
|
75 if(!isempty(didx)) Fj(n+didx) = 1; endif # D' incidence |
|
|
76 Fj(n+m+jj) = length(cidx) + length(didx); # F2 is diagonal |
|
|
77 y = y + x(n+m+jj)*Fj; # multiply by corresponding entry of x |
|
|
78 endfor |
|
|
79 |
|
|
80 endfunction |
