view scripts/special-matrix/magic.m @ 30875:5d3faba0342e

doc: Ensure documentation lists output argument when it exists for all m-files. For new users of Octave it is best to show explicit calling forms in the documentation and to show a return argument when it exists. * bp-table.cc, shift.m, accumarray.m, accumdim.m, bincoeff.m, bitcmp.m, bitget.m, bitset.m, blkdiag.m, celldisp.m, cplxpair.m, dblquad.m, flip.m, fliplr.m, flipud.m, idivide.m, int2str.m, interpft.m, logspace.m, num2str.m, polyarea.m, postpad.m, prepad.m, randi.m, repmat.m, rng.m, rot90.m, rotdim.m, structfun.m, triplequad.m, uibuttongroup.m, uicontrol.m, uipanel.m, uipushtool.m, uitoggletool.m, uitoolbar.m, waitforbuttonpress.m, help.m, __additional_help_message__.m, hsv.m, im2double.m, im2frame.m, javachk.m, usejava.m, argnames.m, char.m, formula.m, inline.m, __vectorize__.m, findstr.m, flipdim.m, strmatch.m, vectorize.m, commutation_matrix.m, cond.m, cross.m, duplication_matrix.m, expm.m, orth.m, rank.m, rref.m, trace.m, vech.m, cast.m, compare_versions.m, delete.m, dir.m, fileattrib.m, grabcode.m, gunzip.m, inputname.m, license.m, list_primes.m, ls.m, mexext.m, movefile.m, namelengthmax.m, nargoutchk.m, nthargout.m, substruct.m, swapbytes.m, ver.m, verLessThan.m, what.m, fminunc.m, fsolve.m, fzero.m, optimget.m, __fdjac__.m, matlabroot.m, savepath.m, campos.m, camroll.m, camtarget.m, camup.m, camva.m, camzoom.m, clabel.m, diffuse.m, legend.m, orient.m, rticks.m, specular.m, thetaticks.m, xlim.m, xtickangle.m, xticklabels.m, xticks.m, ylim.m, ytickangle.m, yticklabels.m, yticks.m, zlim.m, ztickangle.m, zticklabels.m, zticks.m, ellipsoid.m, isocolors.m, isonormals.m, stairs.m, surfnorm.m, __actual_axis_position__.m, __pltopt__.m, close.m, graphics_toolkit.m, pan.m, print.m, printd.m, __ghostscript__.m, __gnuplot_print__.m, __opengl_print__.m, rotate3d.m, subplot.m, zoom.m, compan.m, conv.m, poly.m, polyaffine.m, polyder.m, polyint.m, polyout.m, polyreduce.m, polyvalm.m, roots.m, prefdir.m, prefsfile.m, profexplore.m, profexport.m, profshow.m, powerset.m, unique.m, arch_rnd.m, arma_rnd.m, autoreg_matrix.m, bartlett.m, blackman.m, detrend.m, durbinlevinson.m, fftconv.m, fftfilt.m, fftshift.m, fractdiff.m, hamming.m, hanning.m, hurst.m, ifftshift.m, rectangle_lw.m, rectangle_sw.m, triangle_lw.m, sinc.m, sinetone.m, sinewave.m, spectral_adf.m, spectral_xdf.m, spencer.m, ilu.m, __sprand__.m, sprand.m, sprandn.m, sprandsym.m, treelayout.m, beta.m, betainc.m, betaincinv.m, betaln.m, cosint.m, expint.m, factorial.m, gammainc.m, gammaincinv.m, lcm.m, nthroot.m, perms.m, reallog.m, realpow.m, realsqrt.m, sinint.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m, pascal.m, rosser.m, toeplitz.m, vander.m, wilkinson.m, center.m, corr.m, cov.m, discrete_cdf.m, discrete_inv.m, discrete_pdf.m, discrete_rnd.m, empirical_cdf.m, empirical_inv.m, empirical_pdf.m, empirical_rnd.m, kendall.m, kurtosis.m, mad.m, mean.m, meansq.m, median.m, mode.m, moment.m, range.m, ranks.m, run_count.m, skewness.m, spearman.m, statistics.m, std.m, base2dec.m, bin2dec.m, blanks.m, cstrcat.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m, hex2dec.m, index.m, regexptranslate.m, rindex.m, strcat.m, strjust.m, strtrim.m, strtrunc.m, substr.m, untabify.m, __have_feature__.m, __prog_output_assert__.m, __run_test_suite__.m, example.m, fail.m, asctime.m, calendar.m, ctime.m, date.m, etime.m: Add return arguments to @deftypefn macros where they were missing. Rename variables in functions (particularly generic "retval") to match documentation. Rename some return variables for (hopefully) better clarity (e.g., 'ax' to 'hax' to indicate it is a graphics handle to an axes object).
author Rik <rik@octave.org>
date Wed, 30 Mar 2022 20:40:27 -0700
parents 796f54d4ddbf
children 597f3ee61a48
line wrap: on
line source

########################################################################
##
## 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)