update packages

[CreaPhase.git] / octave_packages / m / special-matrix / magic.m

diff --git a/octave_packages/m/special-matrix/magic.m b/octave_packages/m/special-matrix/magic.m
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+## Copyright (C) 1999-2012 Paul Kienzle
+##
+## This file is part of Octave.
+##
+## Octave is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or (at
+## your option) any later version.
+##
+## Octave is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+## General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with Octave; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} magic (@var{n})
+##
+## Create an @var{n}-by-@var{n} magic square.  A magic square is an arrangement
+## of the integers @code{1:n^2} such that the row sums, column sums, and
+## diagonal sums are all equal to the same value.
+##
+## Note: @var{n} must be greater than 2 for the magic square to exist.
+## @end deftypefn
+
+function A = magic(n)
+
+  if (nargin != 1)
+    print_usage ();
+  endif
+
+  if (n != fix (n) || n < 0 || n == 2)
+    error ("magic: N must be a positive integer not equal to 2");
+  endif
+
+  if (n == 0)
+
+    A = [];
+
+  elseif (mod (n, 2) == 1)
+
+    shift = floor ((0:n*n-1)/n);
+    c = mod ([1:n*n] - shift + (n-3)/2, n);
+    r = mod ([n*n:-1:1] + 2*shift, n);
+    A(c*n+r+1) = 1:n*n;
+    A = reshape (A, n, n);
+
+  elseif (mod (n, 4) == 0)
+
+    A = reshape (1:n*n, n, n)';
+    I = [1:4:n, 4:4:n];
+    J = fliplr (I);
+    A(I,I) = A(J,J);
+    I = [2:4:n, 3:4:n];
+    J = fliplr (I);
+    A(I,I) = A(J,J);
+
+  elseif (mod (n, 4) == 2)
+
+    m = n/2;
+    A = magic (m);
+    A = [A, A+2*m*m; A+3*m*m, A+m*m];
+    k = (m-1)/2;
+    if (k > 1)
+      I = 1:m;
+      J = [2:k, n-k+2:n];
+      A([I,I+m],J) = A([I+m,I],J);
+    endif
+    I = [1:k, k+2:m];
+    A([I,I+m],1) = A([I+m,I],1);
+    I = k + 1;
+    A([I,I+m],I) = A([I+m,I],I);
+
+  endif
+
+endfunction
+
+
+%!test
+%! for i=3:30
+%!   A = magic (i);
+%!   assert (norm(diff([sum(diag(A)),sum(diag(flipud(A))),sum(A),sum(A')])),0);
+%! endfor
+
+%!assert (isempty (magic (0)))
+%!assert (magic(1), 1)
+
+%% Test input validation
+%!error magic ()
+%!error magic (1, 2)
+%!error <N must be a positive integer not equal to 2> magic (1.5)
+%!error <N must be a positive integer not equal to 2> magic (-1)
+%!error <N must be a positive integer not equal to 2> magic (2)
+