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1 ## Copyright (C) 1999-2001 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 2, or (at your option) |
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8 ## 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, write to the Free |
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17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} magic (@var{n}) |
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22 ## |
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23 ## Create an @var{n}-by-@var{n} magic square. Note that @code{magic |
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24 ## (@var{2})} is undefined since there is no 2-by-2 magic square. |
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25 ## |
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26 ## @end deftypefn |
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27 |
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28 function A = magic(n) |
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29 |
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30 if (nargin != 1) |
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31 print_usage (); |
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32 endif |
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33 |
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34 if (n != floor (n) || n < 0 || n == 2) |
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35 error ("magic: n must be an positive integer not equal to 2"); |
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36 endif |
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37 |
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38 if (n == 0) |
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39 |
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40 A = []; |
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41 |
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42 elseif (mod (n, 2) == 1) |
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43 |
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44 shift = floor ((0:n*n-1)/n); |
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45 c = mod ([1:n*n] - shift + (n-3)/2, n); |
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46 r = mod ([n*n:-1:1] + 2*shift, n); |
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47 A (c*n+r+1) = 1:n*n; |
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48 A = reshape (A, n, n); |
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49 |
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50 elseif (mod (n, 4) == 0) |
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51 |
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52 A = reshape (1:n*n, n, n)'; |
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53 I = [1:4:n, 4:4:n]; |
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54 J = fliplr (I); |
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55 A(I,I) = A(J,J); |
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56 I = [2:4:n, 3:4:n]; |
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57 J = fliplr (I); |
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58 A(I,I) = A(J,J); |
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59 |
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60 elseif (mod (n, 4) == 2) |
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61 |
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62 m = n/2; |
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63 A = magic (m); |
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64 A = [A, A+2*m*m; A+3*m*m, A+m*m]; |
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65 k = (m-1)/2; |
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66 if (k>1) |
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67 I = 1:m; |
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68 J = [2:k, n-k+2:n]; |
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69 A([I,I+m],J) = A([I+m,I],J); |
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70 endif |
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71 I = [1:k, k+2:m]; |
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72 A([I,I+m],1) = A([I+m,I],1); |
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73 I = k + 1; |
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74 A([I,I+m],I) = A([I+m,I],I); |
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75 |
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76 endif |
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77 |
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78 endfunction |
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79 |
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80 %!test |
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81 %! for i=3:30 |
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82 %! A=magic(i); |
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83 %! assert(norm(diff([sum(diag(A)),sum(diag(flipud(A))),sum(A),sum(A')])),0) |
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84 %! endfor |
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85 %!assert(isempty(magic(0))); |
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86 %!assert(magic(1),1); |
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87 %!error magic(2) |
