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1 ## Copyright (C) 1996, 1998 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 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, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301 USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {@var{y} =} zgfmul (@var{a}, @var{b}, @var{c}, @var{d}, @var{x}) |
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22 ## Compute product of @var{zgep} incidence matrix @math{F} with vector @var{x}. |
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23 ## Used by @command{zgepbal} (in @command{zgscal}) as part of generalized conjugate gradient |
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24 ## iteration. |
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25 ## @end deftypefn |
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26 |
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27 ## References: |
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28 ## ZGEP: Hodel, "Computation of Zeros with Balancing," 1992, submitted to LAA |
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29 ## Generalized CG: Golub and Van Loan, "Matrix Computations, 2nd ed" 1989 |
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30 |
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31 ## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> |
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32 ## Conversion to Octave July 3, 1994 |
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33 |
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34 function y = zgfmul (a, b, c, d, x) |
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35 |
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36 [n,m] = size(b); |
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37 [p,m1] = size(c); |
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38 nm = n+m; |
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39 y = zeros(nm+p,1); |
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40 |
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41 ## construct F column by column |
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42 for jj=1:n |
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43 Fj = zeros(nm+p,1); |
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44 |
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45 ## rows 1:n: F1 |
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46 aridx = complement(jj,find(a(jj,:) != 0)); |
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47 acidx = complement(jj,find(a(:,jj) != 0)); |
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48 bidx = find(b(jj,:) != 0); |
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49 cidx = find(c(:,jj) != 0); |
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50 |
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51 Fj(aridx) = Fj(aridx) - 1; # off diagonal entries of F1 |
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52 Fj(acidx) = Fj(acidx) - 1; |
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53 ## diagonal entry of F1 |
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54 Fj(jj) = length(aridx)+length(acidx) + length(bidx) + length(cidx); |
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55 |
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56 if(!isempty(bidx)) Fj(n+bidx) = 1; endif # B' incidence |
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57 if(!isempty(cidx)) Fj(n+m+cidx) = -1; endif # -C incidence |
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58 y = y + x(jj)*Fj; # multiply by corresponding entry of x |
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59 endfor |
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60 |
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61 for jj=1:m |
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62 Fj = zeros(nm+p,1); |
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63 bidx = find(b(:,jj) != 0); |
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64 if(!isempty(bidx)) Fj(bidx) = 1; endif # B incidence |
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65 didx = find(d(:,jj) != 0); |
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66 if(!isempty(didx)) Fj(n+m+didx) = 1; endif # D incidence |
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67 Fj(n+jj) = length(bidx) + length(didx); # F2 is diagonal |
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68 y = y + x(n+jj)*Fj; # multiply by corresponding entry of x |
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69 endfor |
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70 |
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71 for jj=1:p |
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72 Fj = zeros(nm+p,1); |
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73 cidx = find(c(jj,:) != 0); |
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74 if(!isempty(cidx)) Fj(cidx) = -1; endif # -C' incidence |
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75 didx = find(d(jj,:) != 0); |
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76 if(!isempty(didx)) Fj(n+didx) = 1; endif # D' incidence |
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77 Fj(n+m+jj) = length(cidx) + length(didx); # F2 is diagonal |
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78 y = y + x(n+m+jj)*Fj; # multiply by corresponding entry of x |
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79 endfor |
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80 |
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81 endfunction |
