annotate 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
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 1999-2020 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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11 ## under the terms of the GNU General Public License as published by
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12 ## the Free Software Foundation, either version 3 of the License, or
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13 ## (at your option) any later version.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 ## GNU General Public License for more details.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23 ##
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24 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {} wilkinson (@var{n})
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28 ## Return the Wilkinson matrix of order @var{n}.
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29 ##
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30 ## Wilkinson matrices are symmetric and tridiagonal with pairs of nearly, but
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31 ## not exactly, equal eigenvalues. They are useful in testing the behavior and
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32 ## performance of eigenvalue solvers.
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33 ##
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34 ## @seealso{rosser, eig}
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35 ## @end deftypefn
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36
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37 function retval = wilkinson (n)
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38
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39 if (nargin != 1)
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40 print_usage ();
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41 endif
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42
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43 if (! (isscalar (n) && n >= 0 && (n == fix (n))))
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44 error ("wilkinson: N must be a non-negative integer");
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45 endif
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46
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47 side = ones (n-1, 1);
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48 center = abs (-(n-1)/2:(n-1)/2);
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49 retval = diag (side, -1) + diag (center) + diag (side, 1);
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50
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51 endfunction
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52
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54 %!assert (wilkinson (0), [])
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55 %!assert (wilkinson (1), 0)
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56 %!assert (wilkinson (2), [0.5,1;1,0.5])
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57 %!assert (wilkinson (3), [1,1,0;1,0,1;0,1,1])
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58 %!assert (wilkinson (4), [1.5,1,0,0;1,0.5,1,0;0,1,0.5,1;0,0,1,1.5])
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59
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60 ## Test input validation
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61 %!error wilkinson ()
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62 %!error wilkinson (1,2)
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63 %!error <N must be a non-negative integer> wilkinson (ones (2))
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64 %!error <N must be a non-negative integer> wilkinson (-1)
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65 %!error <N must be a non-negative integer> wilkinson (1.5)