Mercurial > octave
view scripts/special-matrix/toeplitz.m @ 30875:5d3faba0342e
doc: Ensure documentation lists output argument when it exists for all m-files.
For new users of Octave it is best to show explicit calling forms
in the documentation and to show a return argument when it exists.
* bp-table.cc, shift.m, accumarray.m, accumdim.m, bincoeff.m, bitcmp.m,
bitget.m, bitset.m, blkdiag.m, celldisp.m, cplxpair.m, dblquad.m, flip.m,
fliplr.m, flipud.m, idivide.m, int2str.m, interpft.m, logspace.m, num2str.m,
polyarea.m, postpad.m, prepad.m, randi.m, repmat.m, rng.m, rot90.m, rotdim.m,
structfun.m, triplequad.m, uibuttongroup.m, uicontrol.m, uipanel.m,
uipushtool.m, uitoggletool.m, uitoolbar.m, waitforbuttonpress.m, help.m,
__additional_help_message__.m, hsv.m, im2double.m, im2frame.m, javachk.m,
usejava.m, argnames.m, char.m, formula.m, inline.m, __vectorize__.m, findstr.m,
flipdim.m, strmatch.m, vectorize.m, commutation_matrix.m, cond.m, cross.m,
duplication_matrix.m, expm.m, orth.m, rank.m, rref.m, trace.m, vech.m, cast.m,
compare_versions.m, delete.m, dir.m, fileattrib.m, grabcode.m, gunzip.m,
inputname.m, license.m, list_primes.m, ls.m, mexext.m, movefile.m,
namelengthmax.m, nargoutchk.m, nthargout.m, substruct.m, swapbytes.m, ver.m,
verLessThan.m, what.m, fminunc.m, fsolve.m, fzero.m, optimget.m, __fdjac__.m,
matlabroot.m, savepath.m, campos.m, camroll.m, camtarget.m, camup.m, camva.m,
camzoom.m, clabel.m, diffuse.m, legend.m, orient.m, rticks.m, specular.m,
thetaticks.m, xlim.m, xtickangle.m, xticklabels.m, xticks.m, ylim.m,
ytickangle.m, yticklabels.m, yticks.m, zlim.m, ztickangle.m, zticklabels.m,
zticks.m, ellipsoid.m, isocolors.m, isonormals.m, stairs.m, surfnorm.m,
__actual_axis_position__.m, __pltopt__.m, close.m, graphics_toolkit.m, pan.m,
print.m, printd.m, __ghostscript__.m, __gnuplot_print__.m, __opengl_print__.m,
rotate3d.m, subplot.m, zoom.m, compan.m, conv.m, poly.m, polyaffine.m,
polyder.m, polyint.m, polyout.m, polyreduce.m, polyvalm.m, roots.m, prefdir.m,
prefsfile.m, profexplore.m, profexport.m, profshow.m, powerset.m, unique.m,
arch_rnd.m, arma_rnd.m, autoreg_matrix.m, bartlett.m, blackman.m, detrend.m,
durbinlevinson.m, fftconv.m, fftfilt.m, fftshift.m, fractdiff.m, hamming.m,
hanning.m, hurst.m, ifftshift.m, rectangle_lw.m, rectangle_sw.m, triangle_lw.m,
sinc.m, sinetone.m, sinewave.m, spectral_adf.m, spectral_xdf.m, spencer.m,
ilu.m, __sprand__.m, sprand.m, sprandn.m, sprandsym.m, treelayout.m, beta.m,
betainc.m, betaincinv.m, betaln.m, cosint.m, expint.m, factorial.m, gammainc.m,
gammaincinv.m, lcm.m, nthroot.m, perms.m, reallog.m, realpow.m, realsqrt.m,
sinint.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m, pascal.m, rosser.m,
toeplitz.m, vander.m, wilkinson.m, center.m, corr.m, cov.m, discrete_cdf.m,
discrete_inv.m, discrete_pdf.m, discrete_rnd.m, empirical_cdf.m,
empirical_inv.m, empirical_pdf.m, empirical_rnd.m, kendall.m, kurtosis.m,
mad.m, mean.m, meansq.m, median.m, mode.m, moment.m, range.m, ranks.m,
run_count.m, skewness.m, spearman.m, statistics.m, std.m, base2dec.m,
bin2dec.m, blanks.m, cstrcat.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m,
hex2dec.m, index.m, regexptranslate.m, rindex.m, strcat.m, strjust.m,
strtrim.m, strtrunc.m, substr.m, untabify.m, __have_feature__.m,
__prog_output_assert__.m, __run_test_suite__.m, example.m, fail.m, asctime.m,
calendar.m, ctime.m, date.m, etime.m:
Add return arguments to @deftypefn macros where they were missing. Rename
variables in functions (particularly generic "retval") to match documentation.
Rename some return variables for (hopefully) better clarity (e.g., 'ax' to 'hax'
to indicate it is a graphics handle to an axes object).
author | Rik <rik@octave.org> |
---|---|
date | Wed, 30 Mar 2022 20:40:27 -0700 |
parents | 796f54d4ddbf |
children | 597f3ee61a48 |
line wrap: on
line source
######################################################################## ## ## Copyright (C) 1993-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## 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 {} {@var{T} =} toeplitz (@var{c}) ## @deftypefnx {} {@var{T} =} 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 second argument is omitted, the first row is taken to be the ## same as the first column. 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. ## ## A Toeplitz, or diagonal-constant, matrix has the same value along each ## diagonal. Although it need not be square, it often is. An @nospell{MxN} ## Toeplitz matrix has the form: ## @tex ## $$ ## \left[\matrix{c_1 & r_2 & r_3 & \cdots & r_n\cr ## c_2 & c_1 & r_2 & \cdots & r_{n-1}\cr ## c_3 & c_2 & c_1 & \cdots & r_{n-2}\cr ## \vdots & \vdots & \vdots & \ddots & \vdots\cr ## c_m & c_{m-1} & c_{m-2} & \ldots & c{m-n+1}}\right] ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## c(1) r(2) r(3) @dots{} r(n) ## c(2) c(1) r(2) @dots{} r(n-1) ## c(3) c(2) c(1) @dots{} r(n-2) ## . . . . . ## . . . . . ## . . . . . ## c(m) c(m-1) c(m-2) @dots{} c(m-n+1) ## @end group ## @end example ## ## @end ifnottex ## @seealso{hankel} ## @end deftypefn function T = toeplitz (c, r) if (nargin < 1) 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 diagonal conflict"); endif nr = length (c); nc = length (r); endif if (nr == 0 || nc == 0) ## Empty matrix. T = 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. T = 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. T = 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 <Invalid call> toeplitz () %!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])