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view scripts/special-matrix/hankel.m @ 21546:f7f97d7e9294
doc: Wrap m-file docstrings to 79 characters + newline (80 total).
* isrecording.m, soundsc.m, delaunay3.m, cell2mat.m, cumtrapz.m, del2.m,
inputParser.m, interp1.m, interp3.m, narginchk.m, profile.m,
validateattributes.m, delaunayn.m, tsearchn.m, voronoin.m, brighten.m,
cmunique.m, colorcube.m, imfinfo.m, imshow.m, edit.m, orderfields.m, run.m,
warning_ids.m, ode23.m, ode45.m, odeget.m, integrate_adaptive.m, kahan.m,
ode_struct_value_check.m, runge_kutta_23.m, fminunc.m, fsolve.m, fzero.m,
pkg.m, build.m, specular.m, view.m, bar.m, barh.m, contour3.m, isosurface.m,
line.m, pie.m, pie3.m, quiver3.m, scatter.m, scatter3.m, stem3.m, stemleaf.m,
surfl.m, tetramesh.m, isfigure.m, mkpp.m, pchip.m, residue.m, splinefit.m,
rmpref.m, unique.m, eigs.m, ilu.m, factor.m, factorial.m, gallery.m, hankel.m,
histc.m, ols.m, finv.m, fpdf.m, kruskal_wallis_test.m, weekday.m:
Wrap m-file docstrings to 79 characters + newline (80 total).
author | Rik <rik@octave.org> |
---|---|
date | Sun, 27 Mar 2016 15:50:01 -0700 |
parents | acd6e203031d |
children | bac0d6f07a3e |
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## Copyright (C) 1993-2015 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 {} {} hankel (@var{c}) ## @deftypefnx {} {} 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]) %!warning <column wins anti-diagonal conflict> %! 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])