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doc: Use Octave coding conventions in @example blocks of docstrings. * accumarray.m, accumdim.m, bar.m, base2dec.m, bincoeff.m, bitcmp.m, bitset.m, celldisp.m, chop.m, clabel.m, cloglog.m, colon.m, compass.m, computer.m, contour3.m, contourc.m, corr.m, cstrcat.m, ctime.m, cylinder.m, date.m, dec2base.m, demo.m, dir.m, dlmwrite.m, expm.m, ezcontourf.m, ezcontour.m, ezmeshc.m, ezmesh.m, ezplot.m, ezsurfc.m, ezsurf.m, feather.m, findobj.m, flipdim.m, fplot.m, genvarname.m, getfield.m, hankel.m, hilb.m, hist.m, idivide.m, index.m, int2str.m, interp1.m, is_leap_year.m, ismember.m, isocolors.m, isonormals.m, isosurface.m, kurtosis.m, legendre.m, linkprop.m, logit.m, logm.m, __makeinfo__.m, __marching_cube__.m, median.m, mkoctfile.m, moment.m, mpoles.m, orderfields.m, pcg.m, pcr.m, plot3.m, plotmatrix.m, polyaffine.m, polygcd.m, poly.m, polyout.m, print.m, qp.m, quadgk.m, qzhess.m, randi.m, rat.m, refreshdata.m, residue.m, rose.m, rot90.m, saveas.m, saveobj.m, shiftdim.m, skewness.m, spaugment.m, spdiags.m, sqp.m, stem.m, str2num.m, strcat.m, strjust.m, strread.m, strsplit.m, structfun.m, subplot.m, subsindex.m, substruct.m, surfl.m, surfnorm.m, svds.m, uimenu.m, union.m, voronoi.m, warning_ids.m, wblpdf.m: Use Octave coding conventions in @example blocks of docstrings.
author Rik <octave@nomad.inbox5.com>
date Sat, 04 Feb 2012 22:12:50 -0800
parents 72c96de7a403
children f3d52523cde1
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1 ## Copyright (C) 1993-2012 John W. Eaton
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} hilb (@var{n})
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21 ## Return the Hilbert matrix of order @var{n}. The @math{i,j} element
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22 ## of a Hilbert matrix is defined as
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23 ## @tex
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24 ## $$
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25 ## H(i, j) = {1 \over (i + j - 1)}
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26 ## $$
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27 ## @end tex
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28 ## @ifnottex
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29 ##
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30 ## @example
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31 ## H(i, j) = 1 / (i + j - 1)
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32 ## @end example
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33 ##
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34 ## @end ifnottex
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35 ##
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36 ## Hilbert matrices are close to being singular which make them difficult to
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37 ## invert with numerical routines.
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38 ## Comparing the condition number of a random matrix 5x5 matrix with that of
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39 ## a Hilbert matrix of order 5 reveals just how difficult the problem is.
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40 ##
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41 ## @example
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42 ## @group
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43 ## cond (rand (5))
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44 ## @result{} 14.392
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45 ## cond (hilb (5))
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46 ## @result{} 4.7661e+05
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47 ## @end group
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48 ## @end example
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49 ##
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50 ## @seealso{invhilb}
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51 ## @end deftypefn
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53 ## Author: jwe
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54
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55 function retval = hilb (n)
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57 if (nargin != 1)
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58 print_usage ();
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59 elseif (! isscalar (n))
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60 error ("hilb: N must be a scalar integer");
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61 endif
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62
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63 retval = zeros (n);
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64 tmp = 1:n;
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65 for i = 1:n
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66 retval(i, :) = 1.0 ./ tmp;
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67 tmp++;
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68 endfor
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70 endfunction
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73 %!assert (hilb (2), [1, 1/2; 1/2, 1/3])
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74 %!assert (hilb (3), [1, 1/2, 1/3; 1/2, 1/3, 1/4; 1/3, 1/4, 1/5])
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75
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76 %!error hilb ()
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77 %!error hilb (1, 2)
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78 %!error <N must be a scalar integer> hilb (ones(2))
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