1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
|
########################################################################
##
## Copyright (C) 1999-2024 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{W} =} wilkinson (@var{n})
## Return the Wilkinson matrix of order @var{n}.
##
## Wilkinson matrices are symmetric and tridiagonal with pairs of nearly, but
## not exactly, equal eigenvalues. They are useful in testing the behavior and
## performance of eigenvalue solvers.
##
## @seealso{rosser, eig}
## @end deftypefn
function W = wilkinson (n)
if (nargin < 1)
print_usage ();
endif
if (! (isscalar (n) && n >= 0 && (n == fix (n))))
error ("wilkinson: N must be a non-negative integer");
endif
side = ones (n-1, 1);
center = abs (-(n-1)/2:(n-1)/2);
W = diag (side, -1) + diag (center) + diag (side, 1);
endfunction
%!assert (wilkinson (0), [])
%!assert (wilkinson (1), 0)
%!assert (wilkinson (2), [0.5,1;1,0.5])
%!assert (wilkinson (3), [1,1,0;1,0,1;0,1,1])
%!assert (wilkinson (4), [1.5,1,0,0;1,0.5,1,0;0,1,0.5,1;0,0,1,1.5])
## Test input validation
%!error <Invalid call> wilkinson ()
%!error <N must be a non-negative integer> wilkinson (ones (2))
%!error <N must be a non-negative integer> wilkinson (-1)
%!error <N must be a non-negative integer> wilkinson (1.5)
|
