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view scripts/special-matrix/hankel.m @ 27898:4d6d21839dfd
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Files affected: url-transfer.cc, url-transfer.h, acot.m, acoth.m,
acsc.m, acsch.m, asec.m, asech.m, cot.m, coth.m, csc.m, csch.m, sec.m,
sech.m, cart2pol.m, cart2sph.m, deal.m, fliplr.m, flipud.m, int2str.m,
logspace.m, num2str.m, pol2cart.m, rot90.m, sortrows.m, sph2cart.m,
waitbar.m, doc.m, hsv2rgb.m, rgb2hsv.m, beep.m, isstr.m, setstr.m,
strmatch.m, cond.m, rank.m, trace.m, bug_report.m, cast.m, delete.m,
dir.m, list_primes.m, ls.m, ls_command.m, menu.m, pack.m, recycle.m,
substruct.m, version.m, glpk.m, axis.m, box.m, grid.m,
__axis_label__.m, text.m, title.m, view.m, xlabel.m, ylabel.m,
zlabel.m, bar.m, barh.m, comet3.m, hist.m, line.m, loglog.m, mesh.m,
patch.m, plot.m, polar.m, __bar__.m, __line__.m, __plt__.m,
__stem__.m, semilogx.m, semilogy.m, sombrero.m, stairs.m, stem.m,
surface.m, __default_plot_options__.m, __gnuplot_drawnow__.m,
__next_line_color__.m, __plt_get_axis_arg__.m, __pltopt__.m, clf.m,
closereq.m, gca.m, gnuplot_binary.in.m, isfigure.m, meshgrid.m,
__gnuplot_draw_axes__.m, __gnuplot_draw_figure__.m, shg.m, addpref.m,
getpref.m, ispref.m, loadprefs.m, prefsfile.m, saveprefs.m, rmpref.m,
setpref.m, ismember.m, setdiff.m, union.m, hankel.m, hilb.m, vander.m,
median.m, std.m, cstrcat.m, isletter.m, str2num.m, strcat.m,
oruntests.m, rundemos.m, asctime.m, clock.m, ctime.m, date.m, etime.m,
is_leap_year.m.
author | John W. Eaton <jwe@octave.org> |
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date | Thu, 02 Jan 2020 15:43:01 -0500 |
parents | 00f796120a6d |
children | b442ec6dda5c |
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## Copyright (C) 1993-2019 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 ## <https://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 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])