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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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1 ## Copyright (C) 1993-2015 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}.
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22 ##
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23 ## The @math{i,j} element of a Hilbert matrix is defined as
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24 ## @tex
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25 ## $$
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26 ## H(i, j) = {1 \over (i + j - 1)}
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27 ## $$
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28 ## @end tex
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29 ## @ifnottex
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30 ##
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31 ## @example
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32 ## H(i, j) = 1 / (i + j - 1)
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33 ## @end example
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34 ##
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35 ## @end ifnottex
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36 ##
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37 ## Hilbert matrices are close to being singular which make them difficult to
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38 ## invert with numerical routines. Comparing the condition number of a random
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39 ## matrix 5x5 matrix with that of a Hilbert matrix of order 5 reveals just how
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40 ## difficult the problem is.
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41 ##
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42 ## @example
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43 ## @group
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44 ## cond (rand (5))
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45 ## @result{} 14.392
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46 ## cond (hilb (5))
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47 ## @result{} 4.7661e+05
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48 ## @end group
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49 ## @end example
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50 ##
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51 ## @seealso{invhilb}
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52 ## @end deftypefn
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54 ## Author: jwe
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55
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56 function retval = hilb (n)
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58 if (nargin != 1)
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59 print_usage ();
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60 elseif (! isscalar (n))
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61 error ("hilb: N must be a scalar integer");
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62 endif
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63
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64 retval = zeros (n);
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65 tmp = 1:n;
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66 for i = 1:n
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67 retval(i, :) = 1.0 ./ tmp;
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68 tmp++;
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69 endfor
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71 endfunction
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74 %!assert (hilb (2), [1, 1/2; 1/2, 1/3])
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75 %!assert (hilb (3), [1, 1/2, 1/3; 1/2, 1/3, 1/4; 1/3, 1/4, 1/5])
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76
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77 %!error hilb ()
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78 %!error hilb (1, 2)
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79 %!error <N must be a scalar integer> hilb (ones (2))
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