Mercurial > hg > octave-lyh
annotate scripts/special-matrix/magic.m @ 12639:4d777e05d47c stable
doc: Review and update documentation for "Matrix Manipulation" chapter.
* matrix.txi, arrayfun.m, blkdiag.m, fliplr.m, flipud.m, logspace.m,
postpad.m, prepad.m, randi.m, repmat.m, rot90.m, rotdim.m, shiftdim.m,
sortrows.m, vech.m, xor.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m,
pascal.m, rosser.m, sylvester_matrix.m, toeplitz.m, vander.m, wilkinson.m,
bsxfun.cc, find.cc, lookup.cc, rand.cc, tril.cc, data.cc, arrayfun.m,
blkdiag.m, fliplr.m, flipud.m, logspace.m, postpad.m, prepad.m, randi.m,
repmat.m, rot90.m, rotdim.m, shiftdim.m, sortrows.m, vech.m, xor.m, hadamard.m,
hankel.m, hilb.m, invhilb.m, magic.m, pascal.m, rosser.m, sylvester_matrix.m,
toeplitz.m, vander.m, wilkinson.m, bsxfun.cc (bsxfun), find.cc (find),
lookup.cc (lookup), rand.cc (rand, randn, rande, randg, randp),
tril.cc (triu), data.cc (all, any, horzcat, vertcat, cat, permute, ipermute,
ones, zeros, eye, linspace, resize, reshape, issorted, diff):
Improve docstrings
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Sun, 01 May 2011 08:55:15 -0700 |
| parents | c792872f8942 |
| children | 5180791b8d9e |
| rev | line source |
|---|---|
| 11523 | 1 ## Copyright (C) 1999-2011 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 ## | |
|
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22 ## Create an @var{n}-by-@var{n} magic square. A magic square is an arrangement |
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23 ## of the integers @code{1:n^2} such that the row sums, column sums, and |
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24 ## diagonal sums are all equal to the same value. |
| 5827 | 25 ## |
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Rik <octave@nomad.inbox5.com>
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26 ## Note: @var{n} must be greater than 2 for the magic square to exist. |
| 5827 | 27 ## @end deftypefn |
| 28 | |
| 29 function A = magic(n) | |
| 30 | |
| 31 if (nargin != 1) | |
| 32 print_usage (); | |
| 33 endif | |
| 34 | |
| 35 if (n != floor (n) || n < 0 || n == 2) | |
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36 error ("magic: N must be an positive integer not equal to 2"); |
| 5827 | 37 endif |
| 38 | |
| 39 if (n == 0) | |
| 40 | |
| 41 A = []; | |
| 42 | |
| 43 elseif (mod (n, 2) == 1) | |
| 44 | |
| 45 shift = floor ((0:n*n-1)/n); | |
| 46 c = mod ([1:n*n] - shift + (n-3)/2, n); | |
| 47 r = mod ([n*n:-1:1] + 2*shift, n); | |
| 48 A (c*n+r+1) = 1:n*n; | |
| 49 A = reshape (A, n, n); | |
| 50 | |
| 51 elseif (mod (n, 4) == 0) | |
| 52 | |
| 53 A = reshape (1:n*n, n, n)'; | |
| 54 I = [1:4:n, 4:4:n]; | |
| 55 J = fliplr (I); | |
| 56 A(I,I) = A(J,J); | |
| 57 I = [2:4:n, 3:4:n]; | |
| 58 J = fliplr (I); | |
| 59 A(I,I) = A(J,J); | |
| 60 | |
| 61 elseif (mod (n, 4) == 2) | |
| 62 | |
| 63 m = n/2; | |
| 64 A = magic (m); | |
| 65 A = [A, A+2*m*m; A+3*m*m, A+m*m]; | |
| 66 k = (m-1)/2; | |
| 67 if (k>1) | |
| 68 I = 1:m; | |
| 69 J = [2:k, n-k+2:n]; | |
| 70 A([I,I+m],J) = A([I+m,I],J); | |
| 71 endif | |
| 72 I = [1:k, k+2:m]; | |
| 73 A([I,I+m],1) = A([I+m,I],1); | |
| 74 I = k + 1; | |
| 75 A([I,I+m],I) = A([I+m,I],I); | |
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76 |
| 5827 | 77 endif |
| 78 | |
| 79 endfunction | |
| 80 | |
| 81 %!test | |
| 82 %! for i=3:30 | |
| 83 %! A=magic(i); | |
| 84 %! assert(norm(diff([sum(diag(A)),sum(diag(flipud(A))),sum(A),sum(A')])),0) | |
| 85 %! endfor | |
| 86 %!assert(isempty(magic(0))); | |
| 87 %!assert(magic(1),1); | |
| 88 %!error magic(2) |