view scripts/special-matrix/wilkinson.m @ 27985:9f9ac219896d

maint: Remove remaining "Author:" instances from code base. * __ftp__.cc, load-save.cc, urlwrite.cc, xnorm.cc, xnorm.h, cconv2.f, cdotc3.f, cmatm3.f, csconv2.f, dconv2.f, ddot3.f, dmatm3.f, sconv2.f, sdot3.f, smatm3.f, zconv2.f, zdconv2.f, zdotc3.f, zmatm3.f, crsf2csf.f, zrsf2csf.f, oct-norm.cc, oct-norm.h, lin2mu.m, mu2lin.m, bincoeff.m, blkdiag.m, deal.m, gradient.m, interpft.m, nextpow2.m, postpad.m, prepad.m, repmat.m, shift.m, xor.m, griddata.m, rotx.m, roty.m, rotz.m, voronoin.m, getappdata.m, isappdata.m, rmappdata.m, setappdata.m, colormap.m, gray.m, gray2ind.m, im2double.m, image.m, imagesc.m, imread.m, imshow.m, ind2gray.m, ind2rgb.m, ocean.m, __imread__.m, rgb2ind.m, javachk.m, ClassHelper.java, usejava.m, findstr.m, commutation_matrix.m, cross.m, gls.m, housh.m, isdefinite.m, ishermitian.m, issymmetric.m, logm.m, null.m, ols.m, orth.m, qzhess.m, rref.m, dos.m, nargoutchk.m, orderfields.m, parseparams.m, __w2mpth__.m, unix.m, untar.m, unzip.m, expand_rel_paths.m, make_rel_paths.m, daspect.m, orient.m, pbaspect.m, rticks.m, thetaticks.m, xticklabels.m, xticks.m, yticklabels.m, yticks.m, zticklabels.m, zticks.m, comet.m, contourf.m, plot3.m, cla.m, copyobj.m, findfigs.m, hdl2struct.m, linkaxes.m, __ghostscript__.m, __gnuplot_get_var__.m, __gnuplot_has_feature__.m, __gnuplot_has_terminal__.m, __gnuplot_open_stream__.m, __gnuplot_print__.m, struct2hdl.m, subplot.m, compan.m, conv.m, deconv.m, mpoles.m, poly.m, polyder.m, polyfit.m, polyint.m, polyout.m, polyreduce.m, polyval.m, polyvalm.m, residue.m, roots.m, ismember.m, __parse_movargs__.m, detrend.m, fftconv.m, fftfilt.m, fftshift.m, filter2.m, movfun.m, movslice.m, ichol.m, pcg.m, beta.m, ellipke.m, lcm.m, nchoosek.m, pow2.m, primes.m, pascal.m, rosser.m, wilkinson.m, corr.m, kurtosis.m, skewness.m, base2dec.m, bin2dec.m, blanks.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m, hex2dec.m, index.m, rindex.m, strjoin.m, substr.m, untabify.m, calendar.m, datestr.m, eomday.m, now.m, weekday.m: Remove remaining "Author:" instances from code base.
author Rik <rik@octave.org>
date Tue, 21 Jan 2020 14:35:03 -0800
parents bd51beb6205e
children d8318c12d903 0a5b15007766
line wrap: on
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########################################################################
##
## Copyright (C) 1999-2020 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## 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 {} {} wilkinson (@var{n})
## Return the Wilkinson matrix of order @var{n}.
##
## Wilkinson matrices are symmetric and tridiagonal with pairs of nearly, but
## not exactly, equal eigenvalues.  They are useful in testing the behavior and
## performance of eigenvalue solvers.
##
## @seealso{rosser, eig}
## @end deftypefn

function retval = wilkinson (n)

  if (nargin != 1)
    print_usage ();
  endif

  if (! (isscalar (n) && n >= 0 && (n == fix (n))))
    error ("wilkinson: N must be a non-negative integer");
  endif

  side = ones (n-1, 1);
  center = abs (-(n-1)/2:(n-1)/2);
  retval = diag (side, -1) + diag (center) + diag (side, 1);

endfunction


%!assert (wilkinson (0), [])
%!assert (wilkinson (1), 0)
%!assert (wilkinson (2), [0.5,1;1,0.5])
%!assert (wilkinson (3), [1,1,0;1,0,1;0,1,1])
%!assert (wilkinson (4), [1.5,1,0,0;1,0.5,1,0;0,1,0.5,1;0,0,1,1.5])

## Test input validation
%!error wilkinson ()
%!error wilkinson (1,2)
%!error <N must be a non-negative integer> wilkinson (ones (2))
%!error <N must be a non-negative integer> wilkinson (-1)
%!error <N must be a non-negative integer> wilkinson (1.5)