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view scripts/special-matrix/hilb.m @ 27898:4d6d21839dfd
remove Author: jwe and Adapted-by: jwe lines from source files
These lines have little meaning now in the age of modern version
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Files affected: url-transfer.cc, url-transfer.h, acot.m, acoth.m,
acsc.m, acsch.m, asec.m, asech.m, cot.m, coth.m, csc.m, csch.m, sec.m,
sech.m, cart2pol.m, cart2sph.m, deal.m, fliplr.m, flipud.m, int2str.m,
logspace.m, num2str.m, pol2cart.m, rot90.m, sortrows.m, sph2cart.m,
waitbar.m, doc.m, hsv2rgb.m, rgb2hsv.m, beep.m, isstr.m, setstr.m,
strmatch.m, cond.m, rank.m, trace.m, bug_report.m, cast.m, delete.m,
dir.m, list_primes.m, ls.m, ls_command.m, menu.m, pack.m, recycle.m,
substruct.m, version.m, glpk.m, axis.m, box.m, grid.m,
__axis_label__.m, text.m, title.m, view.m, xlabel.m, ylabel.m,
zlabel.m, bar.m, barh.m, comet3.m, hist.m, line.m, loglog.m, mesh.m,
patch.m, plot.m, polar.m, __bar__.m, __line__.m, __plt__.m,
__stem__.m, semilogx.m, semilogy.m, sombrero.m, stairs.m, stem.m,
surface.m, __default_plot_options__.m, __gnuplot_drawnow__.m,
__next_line_color__.m, __plt_get_axis_arg__.m, __pltopt__.m, clf.m,
closereq.m, gca.m, gnuplot_binary.in.m, isfigure.m, meshgrid.m,
__gnuplot_draw_axes__.m, __gnuplot_draw_figure__.m, shg.m, addpref.m,
getpref.m, ispref.m, loadprefs.m, prefsfile.m, saveprefs.m, rmpref.m,
setpref.m, ismember.m, setdiff.m, union.m, hankel.m, hilb.m, vander.m,
median.m, std.m, cstrcat.m, isletter.m, str2num.m, strcat.m,
oruntests.m, rundemos.m, asctime.m, clock.m, ctime.m, date.m, etime.m,
is_leap_year.m.
author | John W. Eaton <jwe@octave.org> |
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date | Thu, 02 Jan 2020 15:43:01 -0500 |
parents | 00f796120a6d |
children | b442ec6dda5c |
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## Copyright (C) 1993-2019 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 ## <https://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {} {} 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 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 += 1; 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))