|
7017
|
1 ## Copyright (C) 1999, 2000, 2001, 2006, 2007 Paul Kienzle |
|
5827
|
2 ## |
|
|
3 ## This file is part of Octave. |
|
|
4 ## |
|
|
5 ## Octave is free software; you can redistribute it and/or modify it |
|
|
6 ## under the terms of the GNU General Public License as published by |
|
7016
|
7 ## the Free Software Foundation; either version 3 of the License, or (at |
|
|
8 ## your option) any later version. |
|
5827
|
9 ## |
|
|
10 ## Octave is distributed in the hope that it will be useful, but |
|
|
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
|
|
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
|
|
13 ## General Public License for more details. |
|
|
14 ## |
|
|
15 ## You should have received a copy of the GNU General Public License |
|
7016
|
16 ## along with Octave; see the file COPYING. If not, see |
|
|
17 ## <http://www.gnu.org/licenses/>. |
|
5827
|
18 |
|
|
19 ## -*- texinfo -*- |
|
|
20 ## @deftypefn {Function File} {} magic (@var{n}) |
|
|
21 ## |
|
|
22 ## Create an @var{n}-by-@var{n} magic square. Note that @code{magic |
|
|
23 ## (@var{2})} is undefined since there is no 2-by-2 magic square. |
|
|
24 ## |
|
|
25 ## @end deftypefn |
|
|
26 |
|
|
27 function A = magic(n) |
|
|
28 |
|
|
29 if (nargin != 1) |
|
|
30 print_usage (); |
|
|
31 endif |
|
|
32 |
|
|
33 if (n != floor (n) || n < 0 || n == 2) |
|
|
34 error ("magic: n must be an positive integer not equal to 2"); |
|
|
35 endif |
|
|
36 |
|
|
37 if (n == 0) |
|
|
38 |
|
|
39 A = []; |
|
|
40 |
|
|
41 elseif (mod (n, 2) == 1) |
|
|
42 |
|
|
43 shift = floor ((0:n*n-1)/n); |
|
|
44 c = mod ([1:n*n] - shift + (n-3)/2, n); |
|
|
45 r = mod ([n*n:-1:1] + 2*shift, n); |
|
|
46 A (c*n+r+1) = 1:n*n; |
|
|
47 A = reshape (A, n, n); |
|
|
48 |
|
|
49 elseif (mod (n, 4) == 0) |
|
|
50 |
|
|
51 A = reshape (1:n*n, n, n)'; |
|
|
52 I = [1:4:n, 4:4:n]; |
|
|
53 J = fliplr (I); |
|
|
54 A(I,I) = A(J,J); |
|
|
55 I = [2:4:n, 3:4:n]; |
|
|
56 J = fliplr (I); |
|
|
57 A(I,I) = A(J,J); |
|
|
58 |
|
|
59 elseif (mod (n, 4) == 2) |
|
|
60 |
|
|
61 m = n/2; |
|
|
62 A = magic (m); |
|
|
63 A = [A, A+2*m*m; A+3*m*m, A+m*m]; |
|
|
64 k = (m-1)/2; |
|
|
65 if (k>1) |
|
|
66 I = 1:m; |
|
|
67 J = [2:k, n-k+2:n]; |
|
|
68 A([I,I+m],J) = A([I+m,I],J); |
|
|
69 endif |
|
|
70 I = [1:k, k+2:m]; |
|
|
71 A([I,I+m],1) = A([I+m,I],1); |
|
|
72 I = k + 1; |
|
|
73 A([I,I+m],I) = A([I+m,I],I); |
|
|
74 |
|
|
75 endif |
|
|
76 |
|
|
77 endfunction |
|
|
78 |
|
|
79 %!test |
|
|
80 %! for i=3:30 |
|
|
81 %! A=magic(i); |
|
|
82 %! assert(norm(diff([sum(diag(A)),sum(diag(flipud(A))),sum(A),sum(A')])),0) |
|
|
83 %! endfor |
|
|
84 %!assert(isempty(magic(0))); |
|
|
85 %!assert(magic(1),1); |
|
|
86 %!error magic(2) |
