## 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} {} hankel (@var{c}, @var{r})
## Return the Hankel matrix constructed given the first column @var{c}, and
## (optionally) the last row @var{r}.  If the last element of @var{c} is
## not the same as the first element of @var{r}, the last element of
## @var{c} is used.  If the second argument is omitted, the last row is
## taken to be the same as the first column.
##
## A Hankel matrix formed from an m-vector @var{c}, and an n-vector
## @var{r}, has the elements
## @iftex
## @tex
## $$
## H (i, j) = \cases{c_{i+j-1},&$i+j-1\le m$;\cr r_{i+j-m},&otherwise.\cr}
## $$
## @end tex
## @end iftex
## @ifinfo
##
## @example
## @group
## H (i, j) = c (i+j-1),  i+j-1 <= m;
## H (i, j) = r (i+j-m),  otherwise
## @end group
## @end example
## @end ifinfo
## @end deftypefn
## @seealso{vander, sylvester_matrix, hilb, invhilb, and toeplitz}

## Author: jwe
## Paul Kienzle <pkienzle@kienzle.powernet.co.uk>
##    vectorize for speed

function retval = hankel (c, r)

  if (nargin == 1)
    r = zeros (size (c));
  elseif (nargin != 2)
    usage ("hankel (c, r)");
  endif

  [c_nr, c_nc] = size (c);
  [r_nr, r_nc] = size (r);

  if ((c_nr != 1 && c_nc != 1) || (r_nr != 1 && r_nc != 1))
    error ("hankel: expecting vector arguments");
  endif

  if (nargin == 1)
    r (1) = c (length (c));
  endif

  if (c_nc != 1)
    c = c.';
  endif

  if (r_nc != 1)
    r = r.';
  endif

  nc = length (r);
  nr = length (c);

  if (r (1) != c (nr))
    warning ("hankel: column wins anti-diagonal conflict");
  endif

  if (nc > 1)
    c = [ c ; r (2:nc) ];
  endif
  retval = c ( ones (nr, 1) * [1:nc] + [0:nr-1]' * ones (1, nc) );
  retval = reshape (retval, nr, nc);

endfunction