update packages

[CreaPhase.git] / octave_packages / m / special-matrix / wilkinson.m

diff --git a/octave_packages/m/special-matrix/wilkinson.m b/octave_packages/m/special-matrix/wilkinson.m
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+## Copyright (C) 1999-2012 Peter Ekberg
+##
+## 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} 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
+
+## Author: Peter Ekberg
+##         (peda)
+
+function retval = 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);
+  retval = 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 wilkinson ()
+%!error wilkinson (1,2)
+%!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)
+