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view scripts/special-matrix/hadamard.m @ 28896:90fea9cc9caa
test: Add expected error message <Invalid call> to BIST tests for nargin.
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asecd.m, asech.m, asind.m, atand.m, cosd.m, cot.m, cotd.m, coth.m, csc.m,
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celldisp.m, common_size.m, deal.m, del2.m, fliplr.m, integral2.m, interp1.m,
isequal.m, isequaln.m, nextpow2.m, pol2cart.m, quad2d.m, quadl.m, quadv.m,
randi.m, rat.m, repelem.m, rescale.m, shiftdim.m, sortrows.m, sph2cart.m,
xor.m, convhull.m, delaunay.m, delaunayn.m, griddata.m, griddatan.m,
inpolygon.m, voronoi.m, voronoin.m, listdlg.m, msgbox.m, questdlg.m,
rmappdata.m, setappdata.m, __gripe_missing_component__.m,
get_first_help_sentence.m, type.m, which.m, cmpermute.m, cmunique.m,
gray2ind.m, imfinfo.m, imshow.m, imwrite.m, ind2rgb.m, movie.m, rgb2ind.m,
importdata.m, bandwidth.m, condeig.m, gls.m, housh.m, linsolve.m, logm.m,
lscov.m, normest.m, normest1.m, ols.m, ordeig.m, planerot.m, qzhess.m, rref.m,
copyfile.m, delete.m, dos.m, fileparts.m, getfield.m, menu.m, mkdir.m,
movefile.m, orderfields.m, publish.m, setfield.m, substruct.m, unix.m,
unpack.m, decic.m, ode23.m, ode23s.m, ode45.m, fminsearch.m, lsqnonneg.m,
pqpnonneg.m, sqp.m, annotation.m, lighting.m, shading.m, area.m, compass.m,
contourc.m, feather.m, fplot.m, hist.m, isocaps.m, isocolors.m, isonormals.m,
isosurface.m, ostreamtube.m, pie.m, pie3.m, reducepatch.m, reducevolume.m,
rose.m, smooth3.m, stairs.m, stem.m, stem3.m, stream2.m, stream3.m,
streamline.m, streamribbon.m, streamtube.m, surfnorm.m, trimesh.m, trisurf.m,
colstyle.m, hgload.m, linkprop.m, meshgrid.m, ndgrid.m, padecoef.m, polyfit.m,
polyval.m, unmkpp.m, profexport.m, ismember.m, unique.m, movfun.m, movslice.m,
periodogram.m, sinc.m, spdiags.m, sprandsym.m, betaincinv.m, ellipke.m,
factor.m, gammainc.m, gammaincinv.m, isprime.m, lcm.m, gallery.m, hadamard.m,
bounds.m, corrcoef.m, discrete_rnd.m, empirical_rnd.m, histc.m, mode.m,
movmad.m, movmax.m, movmean.m, movmedian.m, movmin.m, movprod.m, movstd.m,
movsum.m, movvar.m, ranks.m, runlength.m, zscore.m, str2num.m, strchr.m,
strsplit.m, strtok.m, untabify.m, assert.m, demo.m, example.m, speed.m, test.m,
datenum.m, datevec.m, webread.m, webwrite.m:
Add expected error message <Invalid call> to BIST tests for nargin.
Remove redundant tests for nargin greater than the number of declared inputs
which are now handled by interpreter.
author | Rik <rik@octave.org> |
---|---|
date | Sun, 11 Oct 2020 21:59:35 -0700 |
parents | de5f2f9a64ff |
children | 7854d5752dd2 |
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######################################################################## ## ## Copyright (C) 1993-2020 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/>. ## ######################################################################## ## ## Original version by Paul Kienzle distributed as free software in the ## public domain. ## -*- texinfo -*- ## @deftypefn {} {} hadamard (@var{n}) ## Construct a Hadamard matrix (@nospell{Hn}) of size @var{n}-by-@var{n}. ## ## The size @var{n} must be of the form @math{2^k * p} in which p is one of ## 1, 12, 20 or 28. The returned matrix is normalized, meaning ## @w{@code{Hn(:,1) == 1}} and @w{@code{Hn(1,:) == 1}}. ## ## Some of the properties of Hadamard matrices are: ## ## @itemize @bullet ## @item ## @code{kron (Hm, Hn)} is a Hadamard matrix of size @var{m}-by-@var{n}. ## ## @item ## @code{Hn * Hn' = @var{n} * eye (@var{n})}. ## ## @item ## The rows of @nospell{Hn} are orthogonal. ## ## @item ## @code{det (@var{A}) <= abs (det (Hn))} for all @var{A} with ## @w{@code{abs (@var{A}(i, j)) <= 1}}. ## ## @item ## Multiplying any row or column by -1 and the matrix will remain a Hadamard ## matrix. ## @end itemize ## @seealso{compan, hankel, toeplitz} ## @end deftypefn ## Reference [1] contains a list of Hadamard matrices up to n=256. ## See code for h28 in hadamard.m for an example of how to extend ## this function for additional p. ## ## Reference: ## [1] A Library of Hadamard Matrices, N. J. A. Sloane ## http://www.research.att.com/~njas/hadamard/ function h = hadamard (n) if (nargin < 1) print_usage (); endif ## Find k if n = 2^k*p. k = 0; while (n > 1 && fix (n/2) == n/2) k += 1; n /= 2; endwhile ## Find base hadamard. ## Except for n=2^k, need a multiple of 4. if (n != 1) k -= 2; endif ## Trigger error if not a multiple of 4. if (k < 0) n =- 1; endif switch (n) case 1 h = 1; case 3 h = h12 (); case 5 h = h20 (); case 7 h = h28 (); otherwise error ("hadamard: N must be 2^k*p, for p = 1, 12, 20 or 28"); endswitch ## Build H(2^k*n) from kron(H(2^k),H(n)). h2 = [1,1;1,-1]; while (true) if (fix (k/2) != k/2) h = kron (h2, h); endif k = fix (k/2); if (k == 0) break; endif h2 = kron (h2, h2); endwhile endfunction function h = h12 () tu = [-1,+1,-1,+1,+1,+1,-1,-1,-1,+1,-1]; tl = [-1,-1,+1,-1,-1,-1,+1,+1,+1,-1,+1]; ## Note: assert (tu(2:end), tl(end:-1:2)). h = ones (12); h(2:end,2:end) = toeplitz (tu, tl); endfunction function h = h20 () tu = [+1,-1,-1,+1,+1,+1,+1,-1,+1,-1,+1,-1,-1,-1,-1,+1,+1,-1,-1]; tl = [+1,-1,-1,+1,+1,-1,-1,-1,-1,+1,-1,+1,-1,+1,+1,+1,+1,-1,-1]; ## Note: assert (tu(2:end), tl(end:-1:2)). h = ones (20); h(2:end,2:end) = fliplr (toeplitz (tu, tl)); endfunction function h = h28 () ## Williamson matrix construction from ## http://www.research.att.com/~njas/hadamard/had.28.will.txt ## Normalized so that each row and column starts with +1 h = [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 1 1 1 1 -1 1 1 1 1 -1 1 -1 1 -1 1 -1 1 -1 -1 -1 -1 1 -1 1 1 -1 -1 1 -1 -1 -1 -1 1 1 -1 1 -1 1 1 1 1 1 1 -1 -1 1 -1 -1 -1 1 1 1 1 1 -1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 1 -1 1 1 -1 -1 -1 1 -1 -1 1 1 -1 1 1 1 1 1 -1 -1 -1 1 1 1 -1 1 -1 1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 -1 1 1 1 1 1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 -1 -1 -1 1 -1 1 1 1 -1 1 1 1 1 -1 1 -1 1 -1 1 1 -1 1 1 1 1 -1 -1 1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 1 -1 -1 1 1 1 1 -1 1 -1 -1 1 1 1 1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 -1 1 1 1 1 -1 -1 1 -1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 -1 -1 1 1 1 1 -1 1 1 1 -1 -1 -1 -1 1 -1 1 1 -1 -1 -1 1 1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 1 -1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 1 1 -1 -1 1 -1 -1 1 1 -1 1 -1 -1 -1 1 1 1 -1 -1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 1 1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 1 -1 -1 1 1 1 -1 1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 -1 1 -1 1 1 1 1 -1 -1 1 1 -1 1 -1 1 1 1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 1 1 1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 -1 -1 1 -1 1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 1 -1 1 -1 -1 1 1 -1 -1 -1 -1 1 -1 1 1 1 -1 1 -1 1 1 -1 1 -1 -1 1 1 1 -1 1 -1 -1 -1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 1 1 1 -1 1 -1 1 1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 -1 -1 1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 -1 -1 1 -1 1 1 1 -1 1 -1 -1 1 -1 -1 1 1 1 -1 1 -1 -1 1 1 -1 1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 -1 -1 1 1 1 1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 -1 1 1 1 -1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 -1 1 1 -1 -1 -1 1 -1 1 1 1 -1 1 1 1 -1 -1 1 -1 -1 1 -1 -1 -1 1 1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 -1 -1 1 1 -1 1 1 1 -1 -1 1 1 -1 -1 1 -1]; endfunction %!assert (hadamard (1), 1) %!assert (hadamard (2), [1,1;1,-1]) %!test %! for n = [1,2,4,8,12,24,48,20,28,2^9] %! h = hadamard (n); %! assert (norm (h*h' - n*eye (n)), 0); %! endfor %!error <Invalid call> hadamard () %!error hadamard (1,2) %!error <N must be 2\^k\*p> hadamard (5)