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1 ## Copyright (C) 1996, 1997, 1998, 1999, 2000, 2002, 2004, 2005, 2006, |
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2 ## 2007 John W. Eaton |
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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 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} sylvester_matrix (@var{k}) |
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22 ## Return the Sylvester matrix of order |
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23 ## @iftex |
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24 ## @tex |
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25 ## $n = 2^k$. |
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26 ## @end tex |
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27 ## @end iftex |
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28 ## @ifinfo |
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29 ## n = 2^k. |
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30 ## @end ifinfo |
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31 ## @seealso{hankel, vander, hilb, invhilb, toeplitz} |
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32 ## @end deftypefn |
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33 |
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34 ## Author: jwe |
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35 |
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36 function retval = sylvester_matrix (k) |
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37 |
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38 if (nargin != 1) |
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39 print_usage (); |
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40 endif |
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41 |
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42 if (isscalar (k)) |
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43 if (k < 1) |
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44 retval = 1; |
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45 else |
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46 tmp = sylvester_matrix (k-1); |
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47 retval = [tmp, tmp; tmp, -tmp]; |
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48 endif |
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49 else |
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50 error ("sylvester_matrix: expecting scalar argument"); |
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51 endif |
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52 |
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53 endfunction |
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54 |
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55 %!assert((sylvester_matrix (1) == [1, 1; 1, -1] |
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56 %! && (sylvester_matrix (2) |
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57 %! == [1, 1, 1, 1; 1, -1, 1, -1; 1, 1, -1, -1; 1, -1, -1, 1]))); |
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58 |
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59 %!error sylvester_matrix ([1, 2; 3, 4]); |
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60 |
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61 %!error sylvester_matrix (); |
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62 |
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63 %!error sylvester_matrix (1, 2); |
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64 |
