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1 ### Copyright (C) 1996 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 |
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7 ### the Free Software Foundation; either version 2, or (at your option) |
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8 ### any later version. |
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9 ### |
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10 ### Octave is distributed in the hope that it will be useful, but |
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11 ### WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ### General Public License 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 |
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18 ### 02111-1307, USA. |
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19 |
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20 ## usage: roots (v) |
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21 ## |
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22 ## For a vector v with n components, return the roots of the |
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23 ## polynomial v(1) * z^(n-1) + ... + v(n-1) * z + v(n). |
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24 |
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25 function r = roots (v) |
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26 |
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27 ## Written by KH (Kurt.Hornik@ci.tuwien.ac.at) on Dec 24, 1993 |
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28 ## Updated by KH on Nov 25, 1994 |
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29 |
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30 if (min (size (v)) > 1 || nargin != 1) |
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31 usage ("roots (v), where v is a vector"); |
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32 endif |
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33 |
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34 n = length (v); |
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35 v = reshape (v, 1, n); |
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36 |
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37 ## If v = [ 0 ... 0 v(k+1) ... v(k+l) 0 ... 0 ], we can remove the |
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38 ## leading k zeros and n - k - l roots of the polynomial are zero. |
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39 |
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40 f = find (v); |
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41 m = max (size (f)); |
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42 |
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43 if (m > 0 && n > 1) |
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44 v = v(f(1):f(m)); |
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45 l = max (size (v)); |
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46 if (l > 1) |
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47 A = diag (ones (1, l-2), -1); |
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48 A(1,:) = -v(2:l) ./ v(1); |
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49 r = eig (A); |
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50 if (f(m) < n) |
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51 tmp = zeros (n - f(m), 1); |
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52 r = [r; tmp]; |
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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 r = []; |
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59 endif |
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60 |
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61 endfunction |
