Mercurial > hg > octave-thorsten
diff scripts/special-matrix/pascal.m @ 5827:1fe78adb91bc
[project @ 2006-05-22 06:25:14 by jwe]
author | jwe |
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date | Mon, 22 May 2006 06:25:14 +0000 |
parents | |
children | 93c65f2a5668 |
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new file mode 100644 --- /dev/null +++ b/scripts/special-matrix/pascal.m @@ -0,0 +1,73 @@ +## Copyright (C) 1999 Peter Ekberg +## +## 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 2, 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, write to the Free +## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA +## 02110-1301, USA. + +## -*- texinfo -*- +## @deftypefn {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 lower triangular Cholesky factor of +## the Pascal matrix if @code{@var{t} = 1}. This matrix is its own +## inverse, that is @code{pascal (@var{n}, 1) ^ 2 == eye (@var{n})}. +## 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{hankel, vander, sylvester_matrix, hilb, invhilb, toeplitz +## hadamard, wilkinson, compan, rosser} +## @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 (! 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