Mercurial > hg > octave-lyh
annotate scripts/special-matrix/hilb.m @ 8817:03b7f618ab3d
include docstrings for new functions in the manual
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Thu, 19 Feb 2009 15:39:19 -0500 |
| parents | 81d6ab3ac93c |
| children | eb63fbe60fab |
| rev | line source |
|---|---|
| 7017 | 1 ## Copyright (C) 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2004, |
| 2 ## 2005, 2006, 2007 John W. Eaton | |
| 2313 | 3 ## |
| 4 ## This file is part of Octave. | |
| 5 ## | |
| 6 ## Octave is free software; you can redistribute it and/or modify it | |
| 7 ## under the terms of the GNU General Public License as published by | |
| 7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
| 9 ## your option) any later version. | |
| 2313 | 10 ## |
| 11 ## Octave is distributed in the hope that it will be useful, but | |
| 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 14 ## General Public License for more details. | |
| 15 ## | |
| 16 ## You should have received a copy of the GNU General Public License | |
| 7016 | 17 ## along with Octave; see the file COPYING. If not, see |
| 18 ## <http://www.gnu.org/licenses/>. | |
| 245 | 19 |
| 3369 | 20 ## -*- texinfo -*- |
| 21 ## @deftypefn {Function File} {} hilb (@var{n}) | |
| 22 ## Return the Hilbert matrix of order @var{n}. The | |
| 23 ## @iftex | |
| 24 ## @tex | |
| 25 ## $i,\,j$ | |
| 26 ## @end tex | |
| 27 ## @end iftex | |
|
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28 ## @ifnottex |
| 3369 | 29 ## i, j |
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changeset
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30 ## @end ifnottex |
| 3369 | 31 ## element of a Hilbert matrix is defined as |
| 32 ## @iftex | |
| 33 ## @tex | |
| 34 ## $$ | |
| 35 ## H (i, j) = {1 \over (i + j - 1)} | |
| 36 ## $$ | |
| 37 ## @end tex | |
| 38 ## @end iftex | |
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8517
81d6ab3ac93c
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sh@sh-laptop
parents:
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diff
changeset
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39 ## @ifnottex |
| 3426 | 40 ## |
| 3369 | 41 ## @example |
| 42 ## H (i, j) = 1 / (i + j - 1) | |
| 43 ## @end example | |
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44 ## @end ifnottex |
| 5642 | 45 ## @seealso{hankel, vander, sylvester_matrix, invhilb, toeplitz} |
| 3369 | 46 ## @end deftypefn |
| 4 | 47 |
| 2314 | 48 ## Author: jwe |
| 49 | |
| 2311 | 50 function retval = hilb (n) |
| 4 | 51 |
| 52 | |
| 53 if (nargin != 1) | |
| 6046 | 54 print_usage (); |
| 4 | 55 endif |
| 56 | |
| 57 nmax = length (n); | |
| 58 if (nmax == 1) | |
| 59 retval = zeros (n); | |
| 556 | 60 tmp = 1:n; |
| 61 for i = 1:n | |
| 62 retval (i, :) = 1.0 ./ (tmp + (i - 1)); | |
| 4 | 63 endfor |
| 64 else | |
| 65 error ("hilb: expecting scalar argument, found something else"); | |
| 66 endif | |
| 67 | |
| 68 endfunction | |
| 7411 | 69 |
| 70 %!assert((hilb (2) == [1, 1/2; 1/2, 1/3] | |
| 71 %! && hilb (3) == [1, 1/2, 1/3; 1/2, 1/3, 1/4; 1/3, 1/4, 1/5])); | |
| 72 | |
| 73 %!error hilb (); | |
| 74 | |
| 75 %!error hilb (1, 2); | |
| 76 |