Mercurial > octave
view scripts/special-matrix/pascal.m @ 33570:c978eff7a857 default tip @
maint: Merge stable to default.
author | Markus Mützel <markus.muetzel@gmx.de> |
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date | Sat, 11 May 2024 14:59:27 +0200 |
parents | 2e484f9f1f18 |
children |
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######################################################################## ## ## Copyright (C) 1999-2024 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{P} =} pascal (@var{n}) ## @deftypefnx {} {@var{P} =} pascal (@var{n}, @var{t}) ## Return the Pascal matrix of order @var{n} if @code{@var{t} = 0}. ## ## The default value of @var{t} is 0. ## ## When @code{@var{t} = 1}, return the pseudo-lower triangular ## Cholesky@tie{}factor of the Pascal matrix (The sign of some columns may be ## negative). This matrix is its own inverse, that is ## @code{pascal (@var{n}, 1) ^ 2 == eye (@var{n})}. ## ## If @code{@var{t} = -1}, return the true Cholesky@tie{}factor with strictly ## positive values on the diagonal. ## ## If @code{@var{t} = 2}, return a transposed and permuted version of ## @code{pascal (@var{n}, 1)}, which is the cube root of the identity matrix. ## That is, @code{pascal (@var{n}, 2) ^ 3 == eye (@var{n})}. ## ## @seealso{chol} ## @end deftypefn function P = pascal (n, t = 0) if (nargin < 1) print_usage (); elseif (! (isscalar (n) && isscalar (t))) error ("pascal: N and T must be scalars"); elseif (! any (t == [-1, 0, 1, 2])) error ("pascal: T must be -1, 0, 1, or 2, found %d", t); endif P = zeros (n); if (n > 0) P(:,1) = 1; endif if (t == -1) for j = 2:n P(j:n,j) = cumsum (P(j-1:n-1,j-1)); endfor else for j = 2:n P(j:n,j) = -cumsum (P(j-1:n-1,j-1)); endfor endif if (t == 0) P = P*P'; elseif (t == 2) P = rot90 (P, 3); if (rem (n,2) != 1) P *= -1; endif endif endfunction %!assert (pascal (3,-1), [1,0,0;1,1,0;1,2,1]) %!assert (pascal (3,0), [1,1,1;1,2,3;1,3,6]) %!assert (pascal (3,0), pascal (3)) %!assert (pascal (3,1), [1,0,0;1,-1,0;1,-2,1]) %!assert (pascal (3,2), [1,1,1;-2,-1,0;1,0,0]) %!assert (pascal (0,2), []) ## Test input validation %!error <Invalid call> pascal () %!error <N and T must be scalars> pascal ([1 2]) %!error <N and T must be scalars> pascal (1, [1 2]) %!error <T must be -1> pascal (3,-2) %!error <T must be .* or 2> pascal (3,4)