Mercurial > octave
view scripts/special-matrix/hadamard.m @ 30920:47cbc69e66cd
eliminate direct access to call stack from evaluator
The call stack is an internal implementation detail of the evaluator.
Direct access to it outside of the evlauator should not be needed.
* pt-eval.h (tree_evaluator::get_call_stack): Delete.
author | John W. Eaton <jwe@octave.org> |
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date | Fri, 08 Apr 2022 15:19:22 -0400 |
parents | 5d3faba0342e |
children | c8ad083a5802 |
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######################################################################## ## ## 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/>. ## ######################################################################## ## ## Original version by Paul Kienzle distributed as free software in the ## public domain. ## -*- texinfo -*- ## @deftypefn {} {@var{h} =} 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)