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1 ## Copyright (C) 1996, 1998, 2000, 2005, 2007 |
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2 ## Auburn University. All rights reserved. |
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3 ## |
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4 ## This file is part of Octave. |
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5 ## |
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6 ## Octave is free software; you can redistribute it and/or modify it |
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7 ## under the terms of the GNU General Public License as published by |
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8 ## the Free Software Foundation; either version 3 of the License, or (at |
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9 ## your option) any later version. |
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10 ## |
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11 ## Octave is distributed in the hope that it will be useful, but |
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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14 ## General Public License for more details. |
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15 ## |
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16 ## You should have received a copy of the GNU General Public License |
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17 ## along with Octave; see the file COPYING. If not, see |
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18 ## <http://www.gnu.org/licenses/>. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} zgfslv (@var{n}, @var{m}, @var{p}, @var{b}) |
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22 ## Solve system of equations for dense zgep problem. |
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23 ## @end deftypefn |
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24 |
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25 ## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> |
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26 ## Converted to Octave by R Bruce Tenison, July 3, 1994 |
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27 |
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28 function x = zgfslv (n, m, p, b) |
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29 |
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30 nmp = n+m+p; |
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31 gam1 = (2*n)+m+p; gam2 = n+p; gam3 = n+m; |
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32 |
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33 G1 = givens(sqrt(m),-sqrt(p))'; |
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34 G2 = givens(m+p,sqrt(n*(m+p)))'; |
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35 |
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36 x = b; |
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37 |
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38 ## 1) U1 e^n = sqrt(n)e_1^n |
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39 ## 2) U2 e^m = sqrt(m)e_1^m |
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40 ## 3) U3 e^p = sqrt(p)e_1^p |
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41 xdx1 = 1:n; xdx2 = n+(1:m); xdx3 = n+m+(1:p); |
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42 x(xdx1,1) = zgshsr(x(xdx1,1)); |
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43 x(xdx2,1) = zgshsr(x(xdx2,1)); |
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44 x(xdx3,1) = zgshsr(x(xdx3,1)); |
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45 |
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46 ## 4) Givens rotations to reduce stray non-zero elements |
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47 idx1 = [n+1,n+m+1]; idx2 = [1,n+1]; |
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48 x(idx1) = G1'*x(idx1); |
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49 x(idx2) = G2'*x(idx2); |
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50 |
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51 ## 6) Scale x, then back-transform to get x |
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52 en = ones(n,1); em = ones(m,1); ep = ones(p,1); |
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53 lam = [gam1*en;gam2*em;gam3*ep]; |
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54 lam(1) = n+m+p; |
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55 lam(n+1) = 1; # dummy value to avoid divide by zero |
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56 lam(n+m+1)=n+m+p; |
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57 |
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58 x = x ./ lam; x(n+1) = 0; # minimum norm solution |
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59 |
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60 ## back transform now. |
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61 x(idx2) = G2*x(idx2); |
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62 x(idx1) = G1*x(idx1); |
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63 x(xdx3,1) = zgshsr(x(xdx3,1)); |
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64 x(xdx2,1) = zgshsr(x(xdx2,1)); |
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65 x(xdx1,1) = zgshsr(x(xdx1,1)); |
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66 |
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67 endfunction |
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68 |
