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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: compan (c) |
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21 ## |
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22 ## Compute the companion matrix corresponding to polynomial vector c. |
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23 ## |
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24 ## In octave a polynomial is represented by it's coefficients (arranged |
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25 ## in descending order). For example a vector c of length n+1 corresponds |
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26 ## to the following nth order polynomial |
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27 ## |
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28 ## p(x) = c(1) x^n + ... + c(n) x + c(n+1). |
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29 ## |
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30 ## The corresponding companion matrix is |
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31 ## _ _ |
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32 ## | -c(2)/c(1) -c(3)/c(1) ... -c(n)/c(1) -c(n+1)/c(1) | |
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33 ## | 1 0 ... 0 0 | |
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34 ## | 0 1 ... 0 0 | |
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35 ## A = | . . . . . | |
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36 ## | . . . . . | |
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37 ## | . . . . . | |
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38 ## |_ 0 0 ... 1 0 _| |
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39 ## |
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40 ## The eigenvalues of the companion matrix are equal to the roots of the |
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41 ## polynomial. |
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42 ## |
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43 ## SEE ALSO: poly, roots, residue, conv, deconv, polyval, polyderiv, polyinteg |
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44 |
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45 ## Author: Tony Richardson <amr@mpl.ucsd.edu> |
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46 ## Created: June 1994 |
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47 ## Adapted-By: jwe |
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48 |
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49 function A = compan (c) |
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50 |
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51 if (nargin != 1) |
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52 usage ("compan (vector)"); |
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53 endif |
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54 |
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55 if(is_matrix (c)) |
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56 error("compan: expecting a vector argument."); |
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57 endif |
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58 |
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59 ## Ensure that c is a row vector. |
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60 |
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61 if(rows(c) > 1) |
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62 c = c.'; |
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63 endif |
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64 |
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65 n = length (c); |
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66 A = diag (ones (n-2, 1), -1); |
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67 A (1, :) = -c (2:n) /c (1); |
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68 |
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69 endfunction |
