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annotate scripts/special-matrix/magic.m @ 19022:5eca3080c7cd

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maint: Merge Stefan's changesets onto default after verification.
author Rik <rik@octave.org>
date Sat, 14 Jun 2014 13:24:46 -0700
parents d63878346099
children 4197fc428c7d
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rev   line source
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d63878346099 maint: Update copyright notices for release.
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1 ## Copyright (C) 1999-2013 Paul Kienzle
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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} {} magic (@var{n})
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21 ##
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22 ## Create an @var{n}-by-@var{n} magic square. A magic square is an arrangement
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23 ## of the integers @code{1:n^2} such that the row sums, column sums, and
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24 ## diagonal sums are all equal to the same value.
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25 ##
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26 ## Note: @var{n} must be greater than 2 for the magic square to exist.
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27 ## @end deftypefn
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28
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29 function A = magic (n)
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30
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31 if (nargin != 1)
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32 print_usage ();
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33 endif
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34
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35 if (n != fix (n) || n < 0 || n == 2)
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36 error ("magic: N must be a positive integer not equal to 2");
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37 endif
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38
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39 if (n == 0)
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40
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41 A = [];
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42
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43 elseif (mod (n, 2) == 1)
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44
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45 shift = floor ((0:n*n-1)/n);
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46 c = mod ([1:n*n] - shift + (n-3)/2, n);
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47 r = mod ([n*n:-1:1] + 2*shift, n);
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48 A(c*n+r+1) = 1:n*n;
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49 A = reshape (A, n, n);
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50
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51 elseif (mod (n, 4) == 0)
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52
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53 A = reshape (1:n*n, n, n)';
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54 I = [1:4:n, 4:4:n];
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55 J = fliplr (I);
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56 A(I,I) = A(J,J);
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57 I = [2:4:n, 3:4:n];
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58 J = fliplr (I);
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59 A(I,I) = A(J,J);
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60
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61 elseif (mod (n, 4) == 2)
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62
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63 m = n/2;
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64 A = magic (m);
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65 A = [A, A+2*m*m; A+3*m*m, A+m*m];
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66 k = (m-1)/2;
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67 if (k > 1)
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68 I = 1:m;
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69 J = [2:k, n-k+2:n];
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70 A([I,I+m],J) = A([I+m,I],J);
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71 endif
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72 I = [1:k, k+2:m];
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73 A([I,I+m],1) = A([I+m,I],1);
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74 I = k + 1;
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75 A([I,I+m],I) = A([I+m,I],I);
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76
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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 %!test
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83 %! for i = 3:30
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84 %! A = magic (i);
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85 %! assert (norm(diff([sum(diag(A)),sum(diag(flipud(A))),sum(A),sum(A')])),0);
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86 %! endfor
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87
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88 %!assert (isempty (magic (0)))
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89 %!assert (magic (1), 1)
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90
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91 %% Test input validation
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92 %!error magic ()
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93 %!error magic (1, 2)
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94 %!error <N must be a positive integer not equal to 2> magic (1.5)
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95 %!error <N must be a positive integer not equal to 2> magic (-1)
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96 %!error <N must be a positive integer not equal to 2> magic (2)
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97