Mercurial > octave-nkf
view scripts/special-matrix/hilb.m @ 20651:e54ecb33727e
lo-array-gripes.cc: Remove FIXME's related to buffer size.
* lo-array-gripes.cc: Remove FIXME's related to buffer size. Shorten sprintf
buffers from 100 to 64 characters (still well more than 19 required).
Use 'const' decorator on constant value for clarity. Remove extra space
between variable and array bracket.
author | Rik <rik@octave.org> |
---|---|
date | Mon, 12 Oct 2015 21:13:47 -0700 |
parents | 2645f9ef8c88 |
children |
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## Copyright (C) 1993-2015 John W. Eaton ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {} hilb (@var{n}) ## Return the Hilbert matrix of order @var{n}. ## ## The @math{i,j} element of a Hilbert matrix is defined as ## @tex ## $$ ## H(i, j) = {1 \over (i + j - 1)} ## $$ ## @end tex ## @ifnottex ## ## @example ## H(i, j) = 1 / (i + j - 1) ## @end example ## ## @end ifnottex ## ## Hilbert matrices are close to being singular which make them difficult to ## invert with numerical routines. Comparing the condition number of a random ## matrix 5x5 matrix with that of a Hilbert matrix of order 5 reveals just how ## difficult the problem is. ## ## @example ## @group ## cond (rand (5)) ## @result{} 14.392 ## cond (hilb (5)) ## @result{} 4.7661e+05 ## @end group ## @end example ## ## @seealso{invhilb} ## @end deftypefn ## Author: jwe function retval = hilb (n) if (nargin != 1) print_usage (); elseif (! isscalar (n)) error ("hilb: N must be a scalar integer"); endif retval = zeros (n); tmp = 1:n; for i = 1:n retval(i, :) = 1.0 ./ tmp; tmp++; endfor endfunction %!assert (hilb (2), [1, 1/2; 1/2, 1/3]) %!assert (hilb (3), [1, 1/2, 1/3; 1/2, 1/3, 1/4; 1/3, 1/4, 1/5]) %!error hilb () %!error hilb (1, 2) %!error <N must be a scalar integer> hilb (ones (2))