update packages

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

diff --git a/octave_packages/m/special-matrix/toeplitz.m b/octave_packages/m/special-matrix/toeplitz.m
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+## Copyright (C) 1993-2012 John W. Eaton
+## Copyright (C) 2009 VZLU Prague
+##
+## 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} {} toeplitz (@var{c})
+## @deftypefnx {Function File} {} toeplitz (@var{c}, @var{r})
+## Return the Toeplitz matrix constructed from the first column @var{c},
+## and (optionally) the first row @var{r}.  If the first element of @var{r}
+## is not the same as the first element of @var{c}, the first element of
+## @var{c} is used.  If the second argument is omitted, the first row is
+## taken to be the same as the first column.
+##
+## A square Toeplitz matrix has the form:
+## @tex
+## $$
+## \left[\matrix{c_0    & r_1     & r_2      & \cdots & r_n\cr
+##               c_1    & c_0     & r_1      & \cdots & r_{n-1}\cr
+##               c_2    & c_1     & c_0      & \cdots & r_{n-2}\cr
+##               \vdots & \vdots  & \vdots   & \ddots & \vdots\cr
+##               c_n    & c_{n-1} & c_{n-2} & \ldots & c_0}\right]
+## $$
+## @end tex
+## @ifnottex
+##
+## @example
+## @group
+## c(0)  r(1)   r(2)  @dots{}  r(n)
+## c(1)  c(0)   r(1)  @dots{} r(n-1)
+## c(2)  c(1)   c(0)  @dots{} r(n-2)
+##  .     .      .   .      .
+##  .     .      .     .    .
+##  .     .      .       .  .
+## c(n) c(n-1) c(n-2) @dots{}  c(0)
+## @end group
+## @end example
+##
+## @end ifnottex
+## @seealso{hankel}
+## @end deftypefn
+
+## Author: jwe && jh
+
+function retval = toeplitz (c, r)
+
+  if (nargin < 1 || nargin > 2)
+    print_usage ();
+  endif
+
+  if (nargin == 1)
+    if (! isvector (c))
+      error ("toeplitz: C must be a vector");
+    endif
+
+    r = c;
+    nr = length (c);
+    nc = nr;
+  else
+    if (! (isvector (c) && isvector (r))) 
+      error ("toeplitz: C and R must be vectors");
+    elseif (r(1) != c(1))
+      warning ("toeplitz: column wins anti-diagonal conflict");
+    endif
+
+    nr = length (c);
+    nc = length (r);
+  endif
+
+  if (nr == 0 || nc == 0)
+    ## Empty matrix.
+    retval = zeros (nr, nc, class (c));
+    return;
+  endif
+
+  ## If we have a single complex argument, we want to return a
+  ## Hermitian-symmetric matrix (actually, this will really only be
+  ## Hermitian-symmetric if the first element of the vector is real).
+  if (nargin == 1 && iscomplex (c))
+    c = conj (c);
+    c(1) = conj (c(1));
+  endif
+
+  if (issparse (c) && issparse (r))
+    c = c(:).';  ## enforce row vector
+    r = r(:).';  ## enforce row vector
+    cidx = find (c);
+    ridx = find (r);
+
+    ## Ignore the first element in r.
+    ridx = ridx(ridx > 1);
+
+    ## Form matrix.
+    retval = spdiags(repmat (c(cidx),nr,1),1-cidx,nr,nc) + ...
+             spdiags(repmat (r(ridx),nr,1),ridx-1,nr,nc);
+  else
+    ## Concatenate data into a single column vector.
+    data = [r(end:-1:2)(:); c(:)];
+
+    ## Get slices.
+    slices = cellslices (data, nc:-1:1, nc+nr-1:-1:nr);
+
+    ## Form matrix.
+    retval = horzcat (slices{:});
+  endif
+
+endfunction
+
+
+%!assert (toeplitz (1), [1])
+%!assert (toeplitz ([1, 2, 3], [1; -3; -5]), [1, -3, -5; 2, 1, -3; 3, 2, 1])
+%!assert (toeplitz ([1, 2, 3], [1; -3i; -5i]), [1, -3i, -5i; 2, 1, -3i; 3, 2, 1])
+
+%% Test input validation
+%!error toeplitz ()
+%!error toeplitz (1, 2, 3)
+%!error <C must be a vector> toeplitz ([1, 2; 3, 4])
+%!error <C and R must be vectors> toeplitz ([1, 2; 3, 4], 1)
+%!error <C and R must be vectors> toeplitz (1, [1, 2; 3, 4])
+