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annotate scripts/special-matrix/hilb.m @ 11523:fd0a3ac60b0e
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| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Fri, 14 Jan 2011 05:47:45 -0500 |
| parents | 693e22af08ae |
| children | 4d777e05d47c |
| rev | line source |
|---|---|
| 11523 | 1 ## Copyright (C) 1993-2011 John W. Eaton |
| 2313 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 2313 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 245 | 18 |
| 3369 | 19 ## -*- texinfo -*- |
| 20 ## @deftypefn {Function File} {} hilb (@var{n}) | |
| 21 ## Return the Hilbert matrix of order @var{n}. The | |
| 22 ## @tex | |
| 23 ## $i,\,j$ | |
| 24 ## @end tex | |
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25 ## @ifnottex |
| 3369 | 26 ## i, j |
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27 ## @end ifnottex |
| 3369 | 28 ## element of a Hilbert matrix is defined as |
| 29 ## @tex | |
| 30 ## $$ | |
| 31 ## H (i, j) = {1 \over (i + j - 1)} | |
| 32 ## $$ | |
| 33 ## @end tex | |
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34 ## @ifnottex |
| 3426 | 35 ## |
| 3369 | 36 ## @example |
| 37 ## H (i, j) = 1 / (i + j - 1) | |
| 38 ## @end example | |
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Rik <octave@nomad.inbox5.com>
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39 ## |
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40 ## @end ifnottex |
| 5642 | 41 ## @seealso{hankel, vander, sylvester_matrix, invhilb, toeplitz} |
| 3369 | 42 ## @end deftypefn |
| 4 | 43 |
| 2314 | 44 ## Author: jwe |
| 45 | |
| 2311 | 46 function retval = hilb (n) |
| 4 | 47 |
| 48 | |
| 49 if (nargin != 1) | |
| 6046 | 50 print_usage (); |
| 4 | 51 endif |
| 52 | |
| 53 nmax = length (n); | |
| 54 if (nmax == 1) | |
| 55 retval = zeros (n); | |
| 556 | 56 tmp = 1:n; |
| 57 for i = 1:n | |
| 58 retval (i, :) = 1.0 ./ (tmp + (i - 1)); | |
| 4 | 59 endfor |
| 60 else | |
| 61 error ("hilb: expecting scalar argument, found something else"); | |
| 62 endif | |
| 63 | |
| 64 endfunction | |
| 7411 | 65 |
| 66 %!assert((hilb (2) == [1, 1/2; 1/2, 1/3] | |
| 67 %! && hilb (3) == [1, 1/2, 1/3; 1/2, 1/3, 1/4; 1/3, 1/4, 1/5])); | |
| 68 | |
| 69 %!error hilb (); | |
| 70 | |
| 71 %!error hilb (1, 2); | |
| 72 |