Mercurial > octave

annotate scripts/special-matrix/magic.m @ 20854:cdf08aacfd86

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
magic.m: magic(N) accepting all integers (matlab compatibility)
author Bernardo Sulzbach <mafagafogigante@gmail.com>
date Sat, 12 Dec 2015 13:01:52 -0200
parents 516bb87ea72e
children 7234cbd04292
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
19697
4197fc428c7d maint: Update copyright notices for 2015.
John W. Eaton <jwe@octave.org>
parents: 17744
diff changeset
1 ## Copyright (C) 1999-2015 Paul Kienzle
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
2 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
3 ## This file is part of Octave.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
4 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
5 ## Octave is free software; you can redistribute it and/or modify it
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
6 ## under the terms of the GNU General Public License as published by
7016
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 5827
diff changeset
7 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 5827
diff changeset
8 ## your option) any later version.
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
9 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
10 ## Octave is distributed in the hope that it will be useful, but
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
13 ## General Public License for more details.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
14 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
15 ## You should have received a copy of the GNU General Public License
7016
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 5827
diff changeset
16 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 5827
diff changeset
17 ## <http://www.gnu.org/licenses/>.
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
18
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
19 ## -*- texinfo -*-
20852
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files.
Rik <rik@octave.org>
parents: 20162
diff changeset
20 ## @deftypefn {} {} magic (@var{n})
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
21 ##
20162
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19833
diff changeset
22 ## Create an @var{n}-by-@var{n} magic square.
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19833
diff changeset
23 ##
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19833
diff changeset
24 ## A magic square is an arrangement of the integers @code{1:n^2} such that the
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19833
diff changeset
25 ## row sums, column sums, and diagonal sums are all equal to the same value.
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
26 ##
20854
cdf08aacfd86 magic.m: magic(N) accepting all integers (matlab compatibility)
Bernardo Sulzbach <mafagafogigante@gmail.com>
parents: 20852
diff changeset
27 ## Note: @var{n} must be a scalar greater than or equal to 3. If you supply
cdf08aacfd86 magic.m: magic(N) accepting all integers (matlab compatibility)
Bernardo Sulzbach <mafagafogigante@gmail.com>
parents: 20852
diff changeset
28 ## @var{n} less than 3, magic returns either a nonmagic square, or else the
cdf08aacfd86 magic.m: magic(N) accepting all integers (matlab compatibility)
Bernardo Sulzbach <mafagafogigante@gmail.com>
parents: 20852
diff changeset
29 ## degenerate magic squares 1 and [].
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
30 ## @end deftypefn
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
31
14868
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory
Rik <octave@nomad.inbox5.com>
parents: 14363
diff changeset
32 function A = magic (n)
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
33
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
34 if (nargin != 1)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
35 print_usage ();
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
36 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
37
20854
cdf08aacfd86 magic.m: magic(N) accepting all integers (matlab compatibility)
Bernardo Sulzbach <mafagafogigante@gmail.com>
parents: 20852
diff changeset
38 if (n < 1)
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
39
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
40 A = [];
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
41
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
42 elseif (mod (n, 2) == 1)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
43
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
44 shift = floor ((0:n*n-1)/n);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
45 c = mod ([1:n*n] - shift + (n-3)/2, n);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
46 r = mod ([n*n:-1:1] + 2*shift, n);
13891
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
47 A(c*n+r+1) = 1:n*n;
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
48 A = reshape (A, n, n);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
49
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
50 elseif (mod (n, 4) == 0)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
51
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
52 A = reshape (1:n*n, n, n)';
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
53 I = [1:4:n, 4:4:n];
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
54 J = fliplr (I);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
55 A(I,I) = A(J,J);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
56 I = [2:4:n, 3:4:n];
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
57 J = fliplr (I);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
58 A(I,I) = A(J,J);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
59
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
60 elseif (mod (n, 4) == 2)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
61
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
62 m = n/2;
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
63 A = magic (m);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
64 A = [A, A+2*m*m; A+3*m*m, A+m*m];
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
65 k = (m-1)/2;
13891
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
66 if (k > 1)
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
67 I = 1:m;
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
68 J = [2:k, n-k+2:n];
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
69 A([I,I+m],J) = A([I+m,I],J);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
70 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
71 I = [1:k, k+2:m];
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
72 A([I,I+m],1) = A([I+m,I],1);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
73 I = k + 1;
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
74 A([I,I+m],I) = A([I+m,I],I);
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
75
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
76 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
77
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
78 endfunction
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
79
13891
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
80
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
81 %!test
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
82 %! for i = 3:30
13891
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
83 %! A = magic (i);
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
84 %! assert (norm(diff([sum(diag(A)),sum(diag(flipud(A))),sum(A),sum(A')])),0);
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
85 %! endfor
13891
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
86
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
87 %!assert (isempty (magic (0)))
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
88 %!assert (magic (1), 1)
13891
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
89
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
90 ## Test input validation
13891
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
91 %!error magic ()
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
92 %!error magic (1, 2)
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
93 %!error <N must be a positive integer not equal to 2> magic (1.5)
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
94 %!error <N must be a positive integer not equal to 2> magic (-1)
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
95 %!error <N must be a positive integer not equal to 2> magic (2)
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
96