Mercurial > octave-nkf
view scripts/special-matrix/pascal.m @ 12747:901d466ee55a stable release-3-4-1
Version 3.4.1 released.
* configure.ac (AC_INIT): Version is now 3.4.1.
(OCTAVE_API_VERSION_NUMBER): Now 45.
(OCTAVE_RELEASE_DATE): Now 2011-06-15.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Wed, 15 Jun 2011 10:35:37 -0400 |
parents | 4d777e05d47c |
children | d4404589498c |
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## Copyright (C) 1999-2011 Peter Ekberg ## Copyright (C) 2009 VZLU Prague ## ## 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 ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {} pascal (@var{n}) ## @deftypefnx {Function File} {} pascal (@var{n}, @var{t}) ## Return the Pascal matrix of order @var{n} if @code{@var{t} = 0}. @var{t} ## defaults to 0. Return the pseudo-lower triangular Cholesky@tie{}factor of ## the Pascal matrix if @code{@var{t} = 1} (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 ## Author: Peter Ekberg ## (peda) function retval = pascal (n, t) if (nargin > 2) || (nargin == 0) print_usage (); endif if (nargin == 1) t = 0; endif if (! isscalar (n) || ! isscalar (t)) error ("pascal: expecting scalar arguments, found something else"); endif if (t < -1 || t > 2) error ("pascal: expecting T to be -1, 0, 1, or 2, found %d", t); endif retval = zeros (n); retval(:,1) = 1; if (t == -1) for j = 2:n retval(j:n,j) = cumsum (retval (j-1:n-1,j-1)); endfor else for j = 2:n retval(j:n,j) = -cumsum (retval (j-1:n-1,j-1)); endfor endif if (t == 0) retval = retval*retval'; elseif (t == 2) retval = retval'; retval = retval(n:-1:1,:); retval(:,n) = -retval(:,n); retval(n,:) = -retval(n,:); if (rem(n,2) != 1) retval = -retval; 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), [0,0,-1;0,-1,2;-1,-1,1]) %!error (pascal(3,4)) %!error (pascal(3,-2)) %!error (pascal()) %!error (pascal(1,2,3))