Mercurial > octave

annotate scripts/special-matrix/magic.m @ 27923:bd51beb6205e

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
update formatting of copyright notices * Use <https://octave.org/copyright/> instead of <https://octave.org/COPYRIGHT.html/>. * For consistency with other comments in the Octave sources, use C++-style comments for copyright blocks in C and C++ files. * Use delimiters above and below copyright blocks that are appropriate for the language used in the file. * Eliminate extra spacing inside copyright blocks. * lex.ll (looks_like_copyright): Also allow newlines and carriage returns before the word "Copyright". * scripts/mk-doc.pl (gethelp): Also skip empty comment lines. * bp-table.cc, type.m: Adjust tests.
author John W. Eaton <jwe@octave.org>
date Wed, 08 Jan 2020 11:59:41 -0500
parents 1891570abac8
children d8318c12d903 0a5b15007766
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
27923
bd51beb6205e update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents: 27919
diff changeset
1 ########################################################################
bd51beb6205e update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents: 27919
diff changeset
2 ##
27919
1891570abac8 update Octave Project Developers copyright for the new year
John W. Eaton <jwe@octave.org>
parents: 27918
diff changeset
3 ## Copyright (C) 1999-2020 The Octave Project Developers
27918
b442ec6dda5c use centralized file for copyright info for individual contributors
John W. Eaton <jwe@octave.org>
parents: 26376
diff changeset
4 ##
27923
bd51beb6205e update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents: 27919
diff changeset
5 ## See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents: 27919
diff changeset
6 ## distribution or <https://octave.org/copyright/>.
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
7 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
8 ## This file is part of Octave.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
9 ##
24534
194eb4bd202b maint: Update punctuation for GPL v3 license text.
Rik <rik@octave.org>
parents: 23573
diff changeset
10 ## Octave is free software: you can redistribute it and/or modify it
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
11 ## under the terms of the GNU General Public License as published by
24534
194eb4bd202b maint: Update punctuation for GPL v3 license text.
Rik <rik@octave.org>
parents: 23573
diff changeset
12 ## the Free Software Foundation, either version 3 of the License, or
22755
3a2b891d0b33 maint: Standardize Copyright formatting.
Rik <rik@octave.org>
parents: 22489
diff changeset
13 ## (at your option) any later version.
5827
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 ## 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
16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
22755
3a2b891d0b33 maint: Standardize Copyright formatting.
Rik <rik@octave.org>
parents: 22489
diff changeset
17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3a2b891d0b33 maint: Standardize Copyright formatting.
Rik <rik@octave.org>
parents: 22489
diff changeset
18 ## GNU General Public License for more details.
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
19 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
20 ## 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
21 ## along with Octave; see the file COPYING. If not, see
24534
194eb4bd202b maint: Update punctuation for GPL v3 license text.
Rik <rik@octave.org>
parents: 23573
diff changeset
22 ## <https://www.gnu.org/licenses/>.
27923
bd51beb6205e update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents: 27919
diff changeset
23 ##
bd51beb6205e update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents: 27919
diff changeset
24 ########################################################################
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
25
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
26 ## -*- texinfo -*-
20852
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files.
Rik <rik@octave.org>
parents: 20162
diff changeset
27 ## @deftypefn {} {} magic (@var{n})
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
28 ##
20162
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19833
diff changeset
29 ## 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
30 ##
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19833
diff changeset
31 ## 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
32 ## 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
33 ##
21751
b571fc85953f maint: Use two spaces after period to indicate sentence break.
Rik <rik@octave.org>
parents: 21580
diff changeset
34 ## Note: @var{n} must be a scalar greater than or equal to 3. If you supply
20854
cdf08aacfd86 magic.m: magic(N) accepting all integers (matlab compatibility)
Bernardo Sulzbach <mafagafogigante@gmail.com>
parents: 20852
diff changeset
35 ## @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
36 ## degenerate magic squares 1 and [].
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
37 ## @end deftypefn
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
38
14868
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory
Rik <octave@nomad.inbox5.com>
parents: 14363
diff changeset
39 function A = magic (n)
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
40
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
41 if (nargin != 1)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
42 print_usage ();
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
43 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
44
20881
7234cbd04292 magic.m:Fix failing tests after cset cdf08aacfd86
Andreas Weber <andy.weber.aw@gmail.com>
parents: 20854
diff changeset
45 n = fix (n);
25235
27e6b38571d3 magic.m: Issue an error if input N is negative (bug #53441).
Dildar Sk <dildarsk101010@gmail.com>
parents: 25054
diff changeset
46 if (n < 0)
27e6b38571d3 magic.m: Issue an error if input N is negative (bug #53441).
Dildar Sk <dildarsk101010@gmail.com>
parents: 25054
diff changeset
47 error ("magic: N must be non-negative");
27e6b38571d3 magic.m: Issue an error if input N is negative (bug #53441).
Dildar Sk <dildarsk101010@gmail.com>
parents: 25054
diff changeset
48 elseif (n < 1)
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
49 A = [];
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
50 elseif (mod (n, 2) == 1)
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 shift = floor ((0:n*n-1)/n);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
53 c = mod ([1:n*n] - shift + (n-3)/2, n);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
54 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
55 A(c*n+r+1) = 1:n*n;
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
56 A = reshape (A, n, n);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
57
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
58 elseif (mod (n, 4) == 0)
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 A = reshape (1:n*n, n, n)';
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
61 I = [1:4:n, 4:4:n];
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
62 J = fliplr (I);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
63 A(I,I) = A(J,J);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
64 I = [2:4:n, 3:4:n];
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
65 J = fliplr (I);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
66 A(I,I) = A(J,J);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
67
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
68 elseif (mod (n, 4) == 2)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
69
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
70 m = n/2;
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
71 A = magic (m);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
72 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
73 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
74 if (k > 1)
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
75 I = 1:m;
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
76 J = [2:k, n-k+2:n];
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
77 A([I,I+m],J) = A([I+m,I],J);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
78 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
79 I = [1:k, k+2:m];
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
80 A([I,I+m],1) = A([I+m,I],1);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
81 I = k + 1;
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
82 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
83
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
84 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
85
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
86 endfunction
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
87
13891
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
88
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
89 %!test
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
90 %! 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
91 %! A = magic (i);
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
92 %! 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
93 %! endfor
13891
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
94
22489
93ea313301f9 test: Add bug ids (<#####>) to BIST tests.
Rik <rik@octave.org>
parents: 22323
diff changeset
95 ## Not a magic square but we must return something (bug #46672).
20891
95c0d4c07c56 magic: add tests for magic(2) (bug #46672)
Carnë Draug <carandraug@octave.org>
parents: 20881
diff changeset
96 ## While one day we may change the actual return of magic (2),
95c0d4c07c56 magic: add tests for magic(2) (bug #46672)
Carnë Draug <carandraug@octave.org>
parents: 20881
diff changeset
97 ## this properties still must be true.
23573
1b4f4ec53b4a use new script to tag fixed bugs in tests
John W. Eaton <jwe@octave.org>
parents: 23572
diff changeset
98 %!test <*46672>
20891
95c0d4c07c56 magic: add tests for magic(2) (bug #46672)
Carnë Draug <carandraug@octave.org>
parents: 20881
diff changeset
99 %! m = magic (2);
21580
ecce63c99c3f maint: Add semicolons to terminate code in %! blocks.
Rik <rik@octave.org>
parents: 20891
diff changeset
100 %! assert (size (m), [2 2]);
25235
27e6b38571d3 magic.m: Issue an error if input N is negative (bug #53441).
Dildar Sk <dildarsk101010@gmail.com>
parents: 25054
diff changeset
101 %! assert (m, [4 3; 1 2]);
20891
95c0d4c07c56 magic: add tests for magic(2) (bug #46672)
Carnë Draug <carandraug@octave.org>
parents: 20881
diff changeset
102
13891
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
103 %!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
104 %!assert (magic (1), 1)
20881
7234cbd04292 magic.m:Fix failing tests after cset cdf08aacfd86
Andreas Weber <andy.weber.aw@gmail.com>
parents: 20854
diff changeset
105 %!assert (magic (1.5), 1)
13891
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
106
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
107 ## 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
108 %!error magic ()
5180791b8d9e magic.m: Use Octave spacing convention. Add more input validation tests.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
109 %!error magic (1, 2)
25235
27e6b38571d3 magic.m: Issue an error if input N is negative (bug #53441).
Dildar Sk <dildarsk101010@gmail.com>
parents: 25054
diff changeset
110 %!error <N must be non-negative> magic (-5)