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view main/special-matrix/pascal.m @ 0:6b33357c7561 octave-forge
Initial revision
author | pkienzle |
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date | Wed, 10 Oct 2001 19:54:49 +0000 |
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children | 2ac2777b30bc |
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## Copyright (C) 1999 Peter Ekberg ## ## This program 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 2, or (at your option) ## any later version. ## ## This program 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 this program; see the file COPYING. If not, write to the Free ## Software Foundation, 59 Temple Place - Suite 330, Boston, MA ## 02111-1307, USA. ## usage: pascal (n, t) ## ## Return the Pascal matrix of order n if t=0. ## t defaults to 0. ## Return lower triangular Cholesky factor of the Pascal matrix if t=1. ## Return a transposed and permuted version of pascal(n,1) if t=2. ## ## pascal(n,1)^2 == eye(n) ## pascal(n,2)^3 == eye(n) ## ## See also: hankel, vander, sylvester_matrix, hilb, invhilb, toeplitz ## hadamard, wilkinson, rosser, compan ## Author: peda function retval = pascal (n, t) if (nargin > 2) || (nargin == 0) usage ("pascal (n, t)"); endif if (nargin == 1) t = 0; endif if !is_scalar (n) || !is_scalar (t) error ("pascal expecting scalar arguments, found something else"); endif retval = diag((-1).^[0:n-1]); retval(:,1) = ones(n, 1); for j=2:n-1 for i=j+1:n retval(i,j) = retval(i-1,j) - retval(i-1,j-1); endfor endfor 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