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annotate scripts/special-matrix/magic.m @ 25235:27e6b38571d3

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magic.m: Issue an error if input N is negative (bug #53441). * magic.m: Check for negative N and call error() if found. Add BIST test to check new code.
author Dildar Sk <dildarsk101010@gmail.com>
date Fri, 23 Mar 2018 19:03:45 -0400
parents 6652d3823428
children 00f796120a6d
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 ## Copyright (C) 1999-2018 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
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8 ## (at 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
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13 ## GNU 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 ## <https://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {} {} magic (@var{n})
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21 ##
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22 ## Create an @var{n}-by-@var{n} magic square.
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23 ##
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24 ## A magic square is an arrangement of the integers @code{1:n^2} such that the
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25 ## row sums, column sums, and diagonal sums are all equal to the same value.
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26 ##
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27 ## Note: @var{n} must be a scalar greater than or equal to 3. If you supply
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28 ## @var{n} less than 3, magic returns either a nonmagic square, or else the
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29 ## degenerate magic squares 1 and [].
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30 ## @end deftypefn
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31
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32 function A = magic (n)
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33
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34 if (nargin != 1)
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35 print_usage ();
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36 endif
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37
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38 n = fix (n);
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39 if (n < 0)
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40 error ("magic: N must be non-negative");
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41 elseif (n < 1)
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42 A = [];
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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 ## Not a magic square but we must return something (bug #46672).
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89 ## While one day we may change the actual return of magic (2),
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90 ## this properties still must be true.
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91 %!test <*46672>
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92 %! m = magic (2);
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93 %! assert (size (m), [2 2]);
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94 %! assert (m, [4 3; 1 2]);
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95
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96 %!assert (isempty (magic (0)))
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97 %!assert (magic (1), 1)
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98 %!assert (magic (1.5), 1)
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99
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100 ## Test input validation
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101 %!error magic ()
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102 %!error magic (1, 2)
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103 %!error <N must be non-negative> magic (-5)