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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 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} vander (@var{c}) |
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22 ## Return the Vandermonde matrix whose next to last column is @var{c}. |
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23 ## |
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24 ## A Vandermonde matrix has the form |
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25 ## @iftex |
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26 ## @tex |
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27 ## $$ |
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28 ## \left[\matrix{c_0^n & \ldots & c_0^2 & c_0 & 1\cr |
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29 ## c_1^n & \ldots & c_1^2 & c_1 & 1\cr |
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30 ## \vdots & & \vdots & \vdots & \vdots\cr |
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31 ## c_n^n & \ldots & c_n^2 & c_n & 1}\right]. |
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32 ## $$ |
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33 ## @end tex |
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34 ## @end iftex |
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35 ## @ifinfo |
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36 ## |
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37 ## @example |
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38 ## @group |
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39 ## c(0)^n ... c(0)^2 c(0) 1 |
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40 ## c(1)^n ... c(1)^2 c(1) 1 |
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41 ## . . . . |
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42 ## . . . . |
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43 ## . . . . |
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44 ## |
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45 ## c(n)^n ... c(n)^2 c(n) 1 |
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46 ## @end group |
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47 ## @end example |
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48 ## @end ifinfo |
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49 ## @end deftypefn |
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50 ## @seealso{hankel, sylvester_matrix, hilb, invhilb, and toeplitz} |
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51 |
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52 ## Author: jwe |
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53 |
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54 function retval = vander (c) |
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55 |
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56 if (nargin != 1) |
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57 usage ("vander (c)"); |
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58 endif |
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59 |
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60 nr = rows (c); |
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61 nc = columns (c); |
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62 if (nr == 1 && nc == 1) |
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63 retval = 1; |
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64 elseif (nr == 1 || nc == 1) |
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65 n = length (c); |
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66 if (n > 0) |
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67 retval = zeros (n, n); |
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68 for i = 1:n |
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69 tmp = c(i); |
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70 for j = 1:n |
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71 retval (i, j) = tmp ^ (n - j); |
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72 endfor |
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73 endfor |
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74 endif |
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75 else |
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76 error ("vander: argument must be a vector"); |
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77 endif |
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78 |
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79 endfunction |
