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1 # Copyright (C) 1995 John W. Eaton |
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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, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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18 |
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19 function r = roots (v) |
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20 |
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21 # usage: roots (v) |
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22 # |
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23 # For a vector v with n components, return the roots of the |
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24 # polynomial v(1) * z^(n-1) + ... + v(n-1) * z + v(n). |
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25 |
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26 # Written by KH (Kurt.Hornik@neuro.tuwien.ac.at) on Dec 24, 1993. |
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27 |
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28 [nr, nc] = size (v); |
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29 if (nr <= 1 && nc <= 1) |
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30 r = []; |
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31 return; |
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32 elseif (! ((nr == 1 && nc > 1) || (nc == 1 && nr > 1))) |
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33 usage ("roots (v), where v is a nonzero vector"); |
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34 endif |
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35 |
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36 n = nr + nc - 1; |
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37 v = reshape (v, 1, n); |
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38 |
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39 # If v = [ 0 ... 0 v(k+1) ... v(k+l) 0 ... 0 ], we can remove the |
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40 # leading k zeros and n - k - l roots of the polynomial are zero. |
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41 |
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42 f = find (v); |
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43 m = max (size (f)); |
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44 if (m > 0) |
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45 v = v (f(1):f(m)); |
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46 l = max (size (v)); |
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47 if (l > 1) |
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48 A = diag (ones (1, l-2), -1); |
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49 A (1, :) = -v (2:l) ./ v (1); |
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50 r = eig (A); |
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51 if (f (m) < n) |
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52 r = [r; (zeros(n - f(m), 1))]; |
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53 endif |
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54 else |
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55 r = zeros (n - f(m), 1); |
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56 endif |
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57 else |
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58 usage ("roots (v), where v is a nonzero vector"); |
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59 endif |
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60 |
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61 endfunction |
