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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 9fc020886ae9
children
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1 ## Copyright (C) 1999-2015 Peter Ekberg
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2 ## Copyright (C) 2009 VZLU Prague
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {} pascal (@var{n})
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22 ## @deftypefnx {Function File} {} pascal (@var{n}, @var{t})
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23 ## Return the Pascal matrix of order @var{n} if @code{@var{t} = 0}.
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24 ##
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25 ## The default value of @var{t} is 0.
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26 ##
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27 ## When @code{@var{t} = 1}, return the pseudo-lower triangular
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28 ## Cholesky@tie{}factor of the Pascal matrix (The sign of some columns may be
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29 ## negative). This matrix is its own inverse, that is
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30 ## @code{pascal (@var{n}, 1) ^ 2 == eye (@var{n})}.
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31 ##
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32 ## If @code{@var{t} = -1}, return the true Cholesky@tie{}factor with strictly
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33 ## positive values on the diagonal.
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34 ##
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35 ## If @code{@var{t} = 2}, return a transposed and permuted version of
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36 ## @code{pascal (@var{n}, 1)}, which is the cube root of the identity matrix.
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37 ## That is, @code{pascal (@var{n}, 2) ^ 3 == eye (@var{n})}.
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38 ##
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39 ## @seealso{chol}
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40 ## @end deftypefn
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41
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42 ## Author: Peter Ekberg
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43 ## (peda)
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44
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45 function retval = pascal (n, t = 0)
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46
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47 if (nargin < 1 || nargin > 2)
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48 print_usage ();
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49 elseif (! (isscalar (n) && isscalar (t)))
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50 error ("pascal: N and T must be scalars");
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51 elseif (! any (t == [-1, 0, 1, 2]))
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52 error ("pascal: expecting T to be -1, 0, 1, or 2, found %d", t);
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53 endif
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54
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55 retval = zeros (n);
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56 if (n > 0)
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57 retval(:,1) = 1;
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58 endif
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59
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60 if (t == -1)
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61 for j = 2:n
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62 retval(j:n,j) = cumsum (retval(j-1:n-1,j-1));
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63 endfor
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64 else
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65 for j = 2:n
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66 retval(j:n,j) = -cumsum (retval(j-1:n-1,j-1));
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67 endfor
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68 endif
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69
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70 if (t == 0)
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71 retval = retval*retval';
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72 elseif (t == 2)
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73 retval = rot90 (retval, 3);
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74 if (rem (n,2) != 1)
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75 retval *= -1;
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76 endif
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77 endif
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78
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79 endfunction
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80
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81
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82 %!assert (pascal (3,-1), [1,0,0;1,1,0;1,2,1])
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83 %!assert (pascal (3,0), [1,1,1;1,2,3;1,3,6])
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84 %!assert (pascal (3,0), pascal (3))
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85 %!assert (pascal (3,1), [1,0,0;1,-1,0;1,-2,1])
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86 %!assert (pascal (3,2), [1,1,1;-2,-1,0;1,0,0])
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87 %!assert (pascal (0,2), [])
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88
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89 ## Test input validation
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90 %!error pascal ()
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91 %!error pascal (1,2,3)
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92 %!error <N and T must be scalars> pascal ([1 2])
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93 %!error <N and T must be scalars> pascal (1, [1 2])
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94 %!error <expecting T to be> pascal (3,-2)
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95 %!error <expecting T to be> pascal (3,4)
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96