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gallery.m: clean and vectorize part of qmult. * scripts/special-matrix/gallery.m: make qmult() follow Octave guidelines, vectorize last for loop in qmult().
author Antonio Pino Robles <data.script93@gmail.com>
date Thu, 28 May 2015 18:32:47 +0200
parents 9fc020886ae9
children 03b9d17a2d95
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4197fc428c7d maint: Update copyright notices for 2015.
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1 ## Copyright (C) 2010-2015 Jaroslav Hajek
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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} {} powerset (@var{a})
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21 ## @deftypefnx {Function File} {} powerset (@var{a}, "rows")
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22 ## Compute the powerset (all subsets) of the set @var{a}.
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23 ##
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24 ## The set @var{a} must be a numerical matrix or a cell array of strings. The
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25 ## output will always be a cell array of either vectors or strings.
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26 ##
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27 ## With the optional second argument @qcode{"rows"}, each row of the set @var{a}
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28 ## is considered one element of the set. The input must be a 2-D numeric
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29 ## matrix to use this argument.
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30 ##
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31 ## @seealso{unique, union, intersect, setdiff, setxor, ismember}
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32 ## @end deftypefn
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33
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34 function p = powerset (a, byrows_arg)
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35
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36 if (nargin < 1 || nargin > 2)
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37 print_usage ();
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38 endif
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39
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40 byrows = false;
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41 if (nargin == 2)
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42 if (! strcmpi (byrows_arg, "rows"))
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43 error ('powerset: expecting second argument to be "rows"');
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44 elseif (iscell (a))
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45 error ('powerset: "rows" not valid for cell arrays');
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46 else
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47 byrows = true;
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48 endif
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49 endif
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50
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51 if (iscell (a) && ! iscellstr (a))
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52 error ("powerset: cell arrays can only be used for character strings");
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53 endif
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54
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55 if (byrows)
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56 a = unique (a, "rows");
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57 n = rows (a);
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58 else
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59 a = unique (a);
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60 n = numel (a);
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61 endif
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62
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63 if (n == 0)
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64 p = {};
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65 else
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66 if (n > 32)
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67 error ("powerset: not implemented for more than 32 elements");
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68 endif
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69
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70 ## Logical rep
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71 b = reshape (bitunpack (uint32 (0:2^n-1)), 32, 2^n)(1:n,:);
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72 ## Convert to indices and lengths.
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73 [i, k] = find (b);
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74 k = sum (b, 1);
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75
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76 ## Index and split.
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77 if (byrows)
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78 p = mat2cell (a(i,:), k, columns (a));
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79 else
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80 if (rows (a) == 1)
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81 p = mat2cell (a(i), 1, k);
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82 else
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83 p = mat2cell (a(i), k, 1);
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84 endif
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85 endif
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86 endif
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87
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88 endfunction
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90
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91 %!test
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92 %! c = sort (cellstr ({[], [1], [2], [3], [1, 2], [1, 3], [2, 3], [1, 2, 3]}));
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93 %! p = sort (cellstr (powerset ([1, 2, 3])));
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94 %! assert (p, c);
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95
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96 %!test
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97 %! c = sort (cellstr ({ [], [1:3], [2:4], [3:5], [1:3; 2:4], [1:3; 3:5], [2:4; 3:5], [1:3; 2:4; 3:5]}));
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98 %! p = sort (cellstr (powerset ([1:3;2:4;3:5], "rows")));
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99 %! assert (p,c);
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100
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101 %!assert (powerset([]), {}); # always return a cell array
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102
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103 ## Test input validation
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104 %!error powerset ()
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105 %!error powerset (1,2,3)
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106 %!error <expecting second argument to be "rows"> powerset (1, "cols")
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107 %!error <"rows" not valid for cell arrays> powerset ({1}, "rows")
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108 %!error <cell arrays can only be used for character> powerset ({1})
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109 %!error <not implemented for more than 32 elements> powerset (1:33)
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110