Mercurial > octave-antonio
view scripts/special-matrix/hilb.m @ 20162:2645f9ef8c88 stable
doc: Update more docstrings to have one sentence summary as first line.
Reviewed specfun, special-matrix, testfun, and time script directories.
* scripts/specfun/expint.m, scripts/specfun/isprime.m,
scripts/specfun/legendre.m, scripts/specfun/primes.m,
scripts/specfun/reallog.m, scripts/specfun/realsqrt.m,
scripts/special-matrix/gallery.m, scripts/special-matrix/hadamard.m,
scripts/special-matrix/hankel.m, scripts/special-matrix/hilb.m,
scripts/special-matrix/invhilb.m, scripts/special-matrix/magic.m,
scripts/special-matrix/pascal.m, scripts/special-matrix/rosser.m,
scripts/special-matrix/toeplitz.m, scripts/special-matrix/vander.m,
scripts/special-matrix/wilkinson.m, scripts/testfun/assert.m,
scripts/testfun/demo.m, scripts/testfun/example.m, scripts/testfun/fail.m,
scripts/testfun/rundemos.m, scripts/testfun/runtests.m,
scripts/testfun/speed.m, scripts/time/asctime.m, scripts/time/calendar.m,
scripts/time/clock.m, scripts/time/ctime.m, scripts/time/datenum.m,
scripts/time/datestr.m, scripts/time/datevec.m, scripts/time/etime.m,
scripts/time/is_leap_year.m, scripts/time/now.m, scripts/time/weekday.m:
Update more docstrings to have one sentence summary as first line.
author | Rik <rik@octave.org> |
---|---|
date | Sun, 03 May 2015 17:00:11 -0700 |
parents | 4197fc428c7d |
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))