## Copyright (C) 1996, 1997 John W. Eaton
##
## 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 2, 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, write to the Free
## Software Foundation, 59 Temple Place - Suite 330, Boston, MA
## 02111-1307, USA.

## -*- texinfo -*-
## @deftypefn {Function File} {} invhilb (@var{n})
## Return the inverse of a Hilbert matrix of order @var{n}.  This is exact.
## Compare with the numerical calculation of @code{inverse (hilb (n))},
## which suffers from the ill-conditioning of the Hilbert matrix, and the
## finite precision of your computer's floating point arithmetic.
## @end deftypefn
## @seealso{hankel, vander, sylvester_matrix, hilb, toeplitz}

## Author: jwe

function retval = invhilb (n)

  if (nargin != 1)
    usage ("invhilb (n)");
  endif

  nmax = length (n);
  if (nmax == 1)
    retval = zeros (n);
    for l = 1:n
      for k = l:n
        tmp = 1;
        for i = 1:n
          tmp = tmp * (i + k - 1);
        endfor
        for i = 1:n
          if (i != k)
            tmp = tmp * (l + i - 1);
          endif
        endfor
        for i = 1:n
          if (i != l)
            tmp = tmp / (i - l);
          endif
        endfor
        for i = 1:n
          if (i != k)
            tmp = tmp / (i - k);
          endif
        endfor
        retval (k, l) = tmp;
        retval (l, k) = tmp;
      endfor
    endfor
  else
    error ("hilb: expecting scalar argument, found something else");
  endif

endfunction