update packages

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

diff --git a/octave_packages/m/special-matrix/hankel.m b/octave_packages/m/special-matrix/hankel.m
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+## Copyright (C) 1993-2012 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 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} {} hankel (@var{c})
+## @deftypefnx {Function File} {} hankel (@var{c}, @var{r})
+## Return the Hankel matrix constructed from 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, it is assumed to
+## be a vector of zeros with the same size as @var{c}.
+##
+## A Hankel matrix formed from an m-vector @var{c}, and an n-vector
+## @var{r}, has the elements
+## @tex
+## $$
+## H(i, j) = \cases{c_{i+j-1},&$i+j-1\le m$;\cr r_{i+j-m},&otherwise.\cr}
+## $$
+## @end tex
+## @ifnottex
+##
+## @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 ifnottex
+## @seealso{hadamard, toeplitz}
+## @end deftypefn
+
+## Author: jwe
+
+function retval = hankel (c, r)
+
+  if (nargin < 1 || nargin > 2)
+    print_usage ();
+  endif
+
+  if (nargin == 1)
+
+    if (! isvector (c))
+      error ("hankel: C must be a vector");
+    endif
+
+    nr = length (c);
+    nc = nr;
+    data = [c(:) ; zeros(nr, 1)];
+
+  else
+
+    if (! (isvector (c) && isvector (r))) 
+      error ("hankel: C and R must be vectors");
+    elseif (r(1) != c(end))
+      warning ("hankel: column wins anti-diagonal conflict");
+    endif
+
+    nr = length (c);
+    nc = length (r);
+    data = [c(:) ; r(2:end)(:)];
+
+  endif
+   
+  slices = cellslices (data, 1:nc, nr:1:nc+nr-1);
+  retval = horzcat (slices{:});
+
+endfunction
+
+
+%!assert (hankel (1), [1])
+%!assert (hankel ([1, 2]), [1, 2; 2, 0])
+%!assert (hankel ([1, 2], [2; -1; -3]), [1, 2, -1; 2, -1, -3])
+%!assert (hankel (1:3), [1,2,3;2,3,0;3,0,0])
+%!assert (hankel (1:3,3:6), [1,2,3,4;2,3,4,5;3,4,5,6])
+%!assert (hankel (1:3,3:4), [1,2;2,3;3,4])
+%!assert (hankel (1:3,4:6), [1,2,3;2,3,5;3,5,6])
+
+%!error hankel ();
+%!error hankel (1, 2, 3);
+%!error <C must be a vector> hankel ([1, 2; 3, 4])
+%!error <C and R must be vectors> hankel (1:4, [1, 2; 3, 4])
+