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comparison scripts/special-matrix/pascal.m @ 5827:1fe78adb91bc

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[project @ 2006-05-22 06:25:14 by jwe]
author jwe
date Mon, 22 May 2006 06:25:14 +0000
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children 93c65f2a5668
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5826:6c6ff9b82577 5827:1fe78adb91bc
1 ## Copyright (C) 1999 Peter Ekberg
2 ##
3 ## This file is part of Octave.
4 ##
5 ## Octave is free software; you can redistribute it and/or modify it
6 ## under the terms of the GNU General Public License as published by
7 ## the Free Software Foundation; either version 2, or (at your option)
8 ## any later version.
9 ##
10 ## Octave is distributed in the hope that it will be useful, but
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 ## General Public License for more details.
14 ##
15 ## You should have received a copy of the GNU General Public License
16 ## along with Octave; see the file COPYING. If not, write to the Free
17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
18 ## 02110-1301, USA.
19
20 ## -*- texinfo -*-
21 ## @deftypefn {Function File} {} pascal (@var{n}, @var{t})
22 ##
23 ## Return the Pascal matrix of order @var{n} if @code{@var{t} = 0}.
24 ## @var{t} defaults to 0. Return lower triangular Cholesky factor of
25 ## the Pascal matrix if @code{@var{t} = 1}. This matrix is its own
26 ## inverse, that is @code{pascal (@var{n}, 1) ^ 2 == eye (@var{n})}.
27 ## If @code{@var{t} = 2}, return a transposed and permuted version of
28 ## @code{pascal (@var{n}, 1)}, which is the cube-root of the identity
29 ## matrix. That is @code{pascal (@var{n}, 2) ^ 3 == eye (@var{n})}.
30 ##
31 ## @seealso{hankel, vander, sylvester_matrix, hilb, invhilb, toeplitz
32 ## hadamard, wilkinson, compan, rosser}
33 ## @end deftypefn
34
35 ## Author: Peter Ekberg
36 ## (peda)
37
38 function retval = pascal (n, t)
39
40 if (nargin > 2) || (nargin == 0)
41 print_usage ();
42 endif
43
44 if (nargin == 1)
45 t = 0;
46 endif
47
48 if (! is_scalar (n) || ! is_scalar (t))
49 error ("pascal: expecting scalar arguments, found something else");
50 endif
51
52 retval = diag ((-1).^[0:n-1]);
53 retval(:,1) = ones (n, 1);
54
55 for j = 2:n-1
56 for i = j+1:n
57 retval(i,j) = retval(i-1,j) - retval(i-1,j-1);
58 endfor
59 endfor
60
61 if (t == 0)
62 retval = retval*retval';
63 elseif (t == 2)
64 retval = retval';
65 retval = retval(n:-1:1,:);
66 retval(:,n) = -retval(:,n);
67 retval(n,:) = -retval(n,:);
68 if (rem(n,2) != 1)
69 retval = -retval;
70 endif
71 endif
72
73 endfunction