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1 ## Copyright (C) 1996, 1997 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: polyvalm (c, x) |
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21 ## |
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22 ## Evaluate a polynomial in the matrix sense. |
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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 ## polyvalm(c,X) will evaluate the polynomial in the matrix sense, i.e. matrix |
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31 ## multiplication is used instead of element by element multiplication as is |
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32 ## used in polyval. |
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33 ## |
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34 ## X must be a square matrix. |
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35 ## |
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36 ## SEE ALSO: polyval, poly, roots, conv, deconv, residue, filter, |
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37 ## polyderiv, polyinteg |
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38 |
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39 ## Author: Tony Richardson <arichard@stark.cc.oh.us> |
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40 ## Created: June 1994 |
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41 ## Adapted-By: jwe |
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42 |
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43 function y = polyvalm (c, x) |
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44 |
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45 if (nargin != 2) |
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46 usage ("polyvalm (c, x)"); |
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47 endif |
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48 |
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49 if (! (is_vector (c) || isempty (c))) |
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50 error ("polyvalm: first argument must be a vector."); |
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51 endif |
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52 |
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53 if (! is_square (x)) |
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54 error("polyvalm: second argument must be a square matrix."); |
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55 endif |
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56 |
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57 if (isempty (c)) |
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58 y = []; |
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59 return; |
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60 endif |
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61 |
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62 [v, d] = eig (x); |
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63 |
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64 if (is_symmetric (x)) |
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65 y = v * diag (polyval (c, diag (d))) * v'; |
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66 else |
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67 y = v * (diag (polyval (c, diag (d))) / v); |
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68 endif |
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69 |
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70 endfunction |
