octave-nkf: scripts/special-matrix/vander.m annotate

annotate scripts/special-matrix/vander.m @ 14138:72c96de7a403 stable

maint: update copyright notices for 2012

author	John W. Eaton <jwe@octave.org>
date	Mon, 02 Jan 2012 14:25:41 -0500
parents	da929884f51e
children	f3d52523cde1

rev	line source
14138 72c96de7a403 maint: update copyright notices for 2012 John W. Eaton <jwe@octave.org> parents: 13881 diff changeset	1 ## Copyright (C) 1993-2012 John W. Eaton
9104 e0250e2b60ed optimize vander Jaroslav Hajek <highegg@gmail.com> parents: 9041 diff changeset	2 ## Copyright (C) 2009 VZLU Prague
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	3 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	4 ## This file is part of Octave.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	5 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	6 ## Octave is free software; you can redistribute it and/or modify it
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	7 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	8 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	9 ## your option) any later version.
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	10 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	11 ## Octave is distributed in the hope that it will be useful, but
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	14 ## General Public License for more details.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	15 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	16 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	17 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	18 ## <http://www.gnu.org/licenses/>.
245 16a24e76d6e0 [project @ 1993-12-03 02:00:15 by jwe] jwe parents: 4 diff changeset	19
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	20 ## -- texinfo --
10791 3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation Rik <octave@nomad.inbox5.com> parents: 9211 diff changeset	21 ## @deftypefn {Function File} {} vander (@var{c})
3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation Rik <octave@nomad.inbox5.com> parents: 9211 diff changeset	22 ## @deftypefnx {Function File} {} vander (@var{c}, @var{n})
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	23 ## Return the Vandermonde matrix whose next to last column is @var{c}.
9137 eebc7f8e7398 extend vander to allow specified number of columns Jaroslav Hajek <highegg@gmail.com> parents: 9104 diff changeset	24 ## If @var{n} is specified, it determines the number of columns;
eebc7f8e7398 extend vander to allow specified number of columns Jaroslav Hajek <highegg@gmail.com> parents: 9104 diff changeset	25 ## otherwise, @var{n} is taken to be equal to the length of @var{c}.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3408 diff changeset	26 ##
5016 bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe] jwe parents: 4030 diff changeset	27 ## A Vandermonde matrix has the form:
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	28 ## @tex
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	29 ## $$
5016 bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe] jwe parents: 4030 diff changeset	30 ## \left[\matrix{c_1^{n-1} & \cdots & c_1^2 & c_1 & 1 \cr
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe] jwe parents: 4030 diff changeset	31 ## c_2^{n-1} & \cdots & c_2^2 & c_2 & 1 \cr
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe] jwe parents: 4030 diff changeset	32 ## \vdots & \ddots & \vdots & \vdots & \vdots \cr
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe] jwe parents: 4030 diff changeset	33 ## c_n^{n-1} & \cdots & c_n^2 & c_n & 1 }\right]
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	34 ## $$
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	35 ## @end tex
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7411 diff changeset	36 ## @ifnottex
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3408 diff changeset	37 ##
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	38 ## @example
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	39 ## @group
9041 853f96e8008f Cleanup documentation file matrix.texi Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	40 ## c(1)^(n-1) @dots{} c(1)^2 c(1) 1
853f96e8008f Cleanup documentation file matrix.texi Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	41 ## c(2)^(n-1) @dots{} c(2)^2 c(2) 1
5016 bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe] jwe parents: 4030 diff changeset	42 ## . . . . .
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe] jwe parents: 4030 diff changeset	43 ## . . . . .
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe] jwe parents: 4030 diff changeset	44 ## . . . . .
9041 853f96e8008f Cleanup documentation file matrix.texi Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	45 ## c(n)^(n-1) @dots{} c(n)^2 c(n) 1
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	46 ## @end group
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	47 ## @end example
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10791 diff changeset	48 ##
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7411 diff changeset	49 ## @end ifnottex
12639 4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	50 ## @seealso{polyfit}
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	51 ## @end deftypefn
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	52
2314 949ab8eba8bc [project @ 1996-07-12 03:58:02 by jwe] jwe parents: 2313 diff changeset	53 ## Author: jwe
949ab8eba8bc [project @ 1996-07-12 03:58:02 by jwe] jwe parents: 2313 diff changeset	54
9137 eebc7f8e7398 extend vander to allow specified number of columns Jaroslav Hajek <highegg@gmail.com> parents: 9104 diff changeset	55 function retval = vander (c, n)
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	56
9137 eebc7f8e7398 extend vander to allow specified number of columns Jaroslav Hajek <highegg@gmail.com> parents: 9104 diff changeset	57 if (nargin == 1)
eebc7f8e7398 extend vander to allow specified number of columns Jaroslav Hajek <highegg@gmail.com> parents: 9104 diff changeset	58 n = length (c);
eebc7f8e7398 extend vander to allow specified number of columns Jaroslav Hajek <highegg@gmail.com> parents: 9104 diff changeset	59 elseif (nargin != 2)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5642 diff changeset	60 print_usage ();
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	61 endif
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	62
13881 da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	63 if (! isvector (c))
da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	64 error ("vander: polynomial C must be a vector");
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	65 endif
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	66
13881 da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	67 ## avoiding many ^s appears to be faster for n >= 100.
da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	68 retval = zeros (length (c), n, class (c));
da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	69 d = 1;
da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	70 c = c(:);
da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	71 for i = n:-1:1
da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	72 retval(:,i) = d;
da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	73 d .*= c;
da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	74 endfor
da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	75
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	76 endfunction
7387 b429b21abdd4 [project @ 2008-01-15 21:43:11 by jwe] jwe parents: 7017 diff changeset	77
13881 da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	78
7387 b429b21abdd4 [project @ 2008-01-15 21:43:11 by jwe] jwe parents: 7017 diff changeset	79 %!test
b429b21abdd4 [project @ 2008-01-15 21:43:11 by jwe] jwe parents: 7017 diff changeset	80 %! c = [0,1,2,3];
b429b21abdd4 [project @ 2008-01-15 21:43:11 by jwe] jwe parents: 7017 diff changeset	81 %! expect = [0,0,0,1; 1,1,1,1; 8,4,2,1; 27,9,3,1];
13881 da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	82 %! assert(vander (c), expect);
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7387 diff changeset	83
13881 da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	84 %!assert (vander (1), 1)
da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	85 %!assert (vander ([1, 2, 3]), vander ([1; 2; 3]))
da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	86 %!assert (vander ([1, 2, 3]), [1, 1, 1; 4, 2, 1; 9, 3, 1])
da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	87 %!assert (vander ([1, 2, 3]*i), [-1, i, 1; -4, 2i, 1; -9, 3i, 1])
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7387 diff changeset	88
9140 c309e028185e vander.m: update tests John W. Eaton <jwe@octave.org> parents: 9137 diff changeset	89 %!assert(vander (2, 3), [4, 2, 1])
c309e028185e vander.m: update tests John W. Eaton <jwe@octave.org> parents: 9137 diff changeset	90 %!assert(vander ([2, 3], 3), [4, 2, 1; 9, 3, 1])
c309e028185e vander.m: update tests John W. Eaton <jwe@octave.org> parents: 9137 diff changeset	91
13881 da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	92 %!error vander ();
da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	93 %!error vander (1, 2, 3);
da929884f51e vander.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	94 %!error <polynomial C must be a vector> vander ([1, 2; 3, 4]);
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7387 diff changeset	95

Mercurial > octave-nkf

annotate scripts/special-matrix/vander.m @ 14138:72c96de7a403 stable