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1 ## Copyright (C) 1996, 1998, 2000, 2001, 2005, 2006, 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 ## Undocumented internal function. |
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21 |
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22 ## -*- texinfo -*- |
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23 ## @deftypefn {Function File} {[@var{poly}, @var{rvals}] =} __zp2ssg2__ (@var{rvals}) |
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24 ## Used internally in @code{zp2ss} |
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25 ## Extract 2 values from @var{rvals} (if possible) and construct |
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26 ## a polynomial with those roots. |
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27 ## @end deftypefn |
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28 |
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29 ## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> |
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30 ## Created: August 1996 |
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31 |
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32 function [poly, rvals] = __zp2ssg2__ (rvals) |
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33 |
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34 ## locate imaginary roots (if any) |
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35 cidx = find (imag (rvals)); |
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36 |
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37 if (! isempty (cidx)) |
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38 ## select first complex root, omit from cidx |
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39 r1i = cidx(1); |
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40 r1 = rvals(r1i); |
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41 cidx = complement (r1i, cidx); |
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42 |
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43 ## locate conjugate root (must be in cidx list, just in case there's |
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44 ## roundoff) |
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45 err = abs (rvals(cidx) - r1'); |
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46 minerr = min (err); |
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47 c2i = find (err == minerr, 1); |
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48 r2i = cidx(c2i); |
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49 r2 = rvals(r2i); |
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50 cidx = complement (r2i, cidx); |
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51 |
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52 ## don't check for divide by zero, since 0 is not complex. |
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53 if (abs (r2-r1') / abs (r1) > 1e-12) |
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54 error ("r1=(%f,%f); r2=(%f,%f), not conjugates.", |
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55 real (r1), imag (r1), real (r2), imag(r2)); |
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56 endif |
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57 |
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58 ## complex conjugate pair |
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59 poly = [1, -2*real(r1), real(r1)^2+imag(r1)^2]; |
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60 else |
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61 ## select two roots (they're all real) |
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62 r1 = rvals(1); |
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63 r2 = rvals(2); |
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64 poly = [1, -(r1+r2), (r1*r2)]; |
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65 r1i = 1; |
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66 r2i = 2; |
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67 endif |
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68 |
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69 ## remove roots used |
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70 idx = complement ([r1i, r2i], 1:length(rvals)); |
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71 rvals = rvals(idx); |
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72 |
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73 endfunction |
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74 |
