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25
26## -*- texinfo -*-
27## @deftypefn {} {} wilkinson (@var{n})
28## Return the Wilkinson matrix of order @var{n}.
29##
30## Wilkinson matrices are symmetric and tridiagonal with pairs of nearly, but
31## not exactly, equal eigenvalues.  They are useful in testing the behavior and
32## performance of eigenvalue solvers.
33##
34## @seealso{rosser, eig}
35## @end deftypefn
36
37function retval = wilkinson (n)
38
39  if (nargin != 1)
40    print_usage ();
41  endif
42
43  if (! (isscalar (n) && n >= 0 && (n == fix (n))))
44    error ("wilkinson: N must be a non-negative integer");
45  endif
46
47  side = ones (n-1, 1);
48  center = abs (-(n-1)/2:(n-1)/2);
49  retval = diag (side, -1) + diag (center) + diag (side, 1);
50
51endfunction
52
53
54%!assert (wilkinson (0), [])
55%!assert (wilkinson (1), 0)
56%!assert (wilkinson (2), [0.5,1;1,0.5])
57%!assert (wilkinson (3), [1,1,0;1,0,1;0,1,1])
58%!assert (wilkinson (4), [1.5,1,0,0;1,0.5,1,0;0,1,0.5,1;0,0,1,1.5])
59
60## Test input validation
61%!error wilkinson ()
62%!error wilkinson (1,2)
63%!error <N must be a non-negative integer> wilkinson (ones (2))
64%!error <N must be a non-negative integer> wilkinson (-1)
65%!error <N must be a non-negative integer> wilkinson (1.5)
66