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comparison FIXES/vander.m @ 0:6b33357c7561 octave-forge

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author pkienzle
date Wed, 10 Oct 2001 19:54:49 +0000
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-1:000000000000 0:6b33357c7561
1 ## Copyright (C) 1996, 1997 John W. Eaton
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, 59 Temple Place - Suite 330, Boston, MA
18 ## 02111-1307, USA.
19
20 ## -*- texinfo -*-
21 ## @deftypefn {Function File} {} vander (@var{c})
22 ## Return the Vandermonde matrix whose next to last column is @var{c}.
23 ##
24 ## A Vandermonde matrix has the form
25 ## @iftex
26 ## @tex
27 ## $$
28 ## \left[\matrix{c_0^n & \ldots & c_0^2 & c_0 & 1\cr
29 ## c_1^n & \ldots & c_1^2 & c_1 & 1\cr
30 ## \vdots & & \vdots & \vdots & \vdots\cr
31 ## c_n^n & \ldots & c_n^2 & c_n & 1}\right].
32 ## $$
33 ## @end tex
34 ## @end iftex
35 ## @ifinfo
36 ##
37 ## @example
38 ## @group
39 ## c(0)^n ... c(0)^2 c(0) 1
40 ## c(1)^n ... c(1)^2 c(1) 1
41 ## . . . .
42 ## . . . .
43 ## . . . .
44 ##
45 ## c(n)^n ... c(n)^2 c(n) 1
46 ## @end group
47 ## @end example
48 ## @end ifinfo
49 ## @end deftypefn
50 ## @seealso{hankel, sylvester_matrix, hilb, invhilb, and toeplitz}
51
52 ## Author: jwe
53 ## Paul Kienzle <pkienzle@kienzle.powernet.co.uk>
54 ## vectorized for speed
55
56 function retval = vander (c)
57
58 if (nargin != 1)
59 usage ("vander (c)");
60 endif
61
62 if (!is_vector (c))
63 error ("vander: argument must be a vector");
64 endif
65
66 n = length (c);
67 retval = c ([1:n]' * ones (1, n));
68 retval = reshape (retval, n, n);
69 retval = retval .^ (ones (n, 1) * [n-1:-1:0]);
70
71 endfunction