X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fm%2Fspecial-matrix%2Fhankel.m;fp=octave_packages%2Fm%2Fspecial-matrix%2Fhankel.m;h=473d27c46270eb639b8b230e169d3772a86b8b68;hp=0000000000000000000000000000000000000000;hb=1c0469ada9531828709108a4882a751d2816994a;hpb=63de9f36673d49121015e3695f2c336ea92bc278 diff --git a/octave_packages/m/special-matrix/hankel.m b/octave_packages/m/special-matrix/hankel.m new file mode 100644 index 0000000..473d27c --- /dev/null +++ b/octave_packages/m/special-matrix/hankel.m @@ -0,0 +1,98 @@ +## 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 +## . + +## -*- 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 hankel ([1, 2; 3, 4]) +%!error hankel (1:4, [1, 2; 3, 4]) +