Mercurial > octave
view scripts/special-matrix/magic.m @ 31201:a8b0acc018a2
maint: merge stable to default
author | Rik <rik@octave.org> |
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date | Wed, 24 Aug 2022 08:55:39 -0700 |
parents | 5d3faba0342e |
children | 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 1999-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## 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 ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {@var{M} =} 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 a scalar greater than or equal to 3. If you supply ## @var{n} less than 3, magic returns either a nonmagic square, or else the ## degenerate magic squares 1 and []. ## @end deftypefn function M = magic (n) if (nargin < 1) print_usage (); endif n = fix (n); if (n < 0) error ("magic: N must be non-negative"); elseif (n < 1) M = []; 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); M(c*n+r+1) = 1:n*n; M = reshape (M, n, n); elseif (mod (n, 4) == 0) M = reshape (1:n*n, n, n)'; I = [1:4:n, 4:4:n]; J = fliplr (I); M(I,I) = M(J,J); I = [2:4:n, 3:4:n]; J = fliplr (I); M(I,I) = M(J,J); elseif (mod (n, 4) == 2) m = n/2; M = magic (m); M = [M, M+2*m*m; M+3*m*m, M+m*m]; k = (m-1)/2; if (k > 1) I = 1:m; J = [2:k, n-k+2:n]; M([I,I+m],J) = M([I+m,I],J); endif I = [1:k, k+2:m]; M([I,I+m],1) = M([I+m,I],1); I = k + 1; M([I,I+m],I) = M([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 ## Not a magic square but we must return something (bug #46672). ## While one day we may change the actual return of magic (2), ## this properties still must be true. %!test <*46672> %! m = magic (2); %! assert (size (m), [2 2]); %! assert (m, [4 3; 1 2]); %!assert (isempty (magic (0))) %!assert (magic (1), 1) %!assert (magic (1.5), 1) ## Test input validation %!error <Invalid call> magic () %!error <N must be non-negative> magic (-5)