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1 ## Copyright (C) 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2002, |
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2 ## 2004, 2005, 2006, 2007, 2008 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} {} 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 ## $$ |
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28 ## \left[\matrix{c_1^{n-1} & \cdots & c_1^2 & c_1 & 1 \cr |
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29 ## c_2^{n-1} & \cdots & c_2^2 & c_2 & 1 \cr |
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30 ## \vdots & \ddots & \vdots & \vdots & \vdots \cr |
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31 ## c_n^{n-1} & \cdots & c_n^2 & c_n & 1 }\right] |
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32 ## $$ |
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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(1)^(n-1) ... c(1)^2 c(1) 1 |
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40 ## c(2)^(n-1) ... c(2)^2 c(2) 1 |
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41 ## . . . . . |
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42 ## . . . . . |
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43 ## . . . . . |
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44 ## c(n)^(n-1) ... c(n)^2 c(n) 1 |
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45 ## @end group |
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46 ## @end example |
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47 ## @end ifinfo |
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48 ## @seealso{hankel, sylvester_matrix, hilb, invhilb, toeplitz} |
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49 ## @end deftypefn |
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50 |
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51 ## Author: jwe |
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52 |
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53 function retval = vander (c) |
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54 |
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55 if (nargin != 1) |
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56 print_usage (); |
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57 endif |
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58 |
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59 if (isvector (c)) |
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60 n = length (c); |
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61 retval = (c(:) * ones (1, n)) .^ (ones (n, 1) * (n-1:-1:0)); |
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62 else |
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63 error ("vander: argument must be a vector"); |
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64 endif |
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65 |
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66 endfunction |
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67 |
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68 %!test |
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69 %! c = [0,1,2,3]; |
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70 %! expect = [0,0,0,1; 1,1,1,1; 8,4,2,1; 27,9,3,1]; |
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71 %! result = vander(c); |
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72 %! assert(expect, result); |
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73 |
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74 %!assert((vander (1) == 1 && vander ([1, 2, 3]) == vander ([1; 2; 3]) |
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75 %! && vander ([1, 2, 3]) == [1, 1, 1; 4, 2, 1; 9, 3, 1] |
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76 %! && vander ([1, 2, 3]*i) == [-1, i, 1; -4, 2i, 1; -9, 3i, 1])); |
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77 |
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78 %!error vander ([1, 2; 3, 4]); |
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79 |
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80 %!error vander (); |
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81 |
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82 %!error vander (1, 2); |
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83 |
