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

annotate scripts/special-matrix/hankel.m @ 13888:c78ac846fcbc

hankel.m: Recode for 3.5X speedup * hankel.m: Recode for 3.5X speedup

author	Rik <octave@nomad.inbox5.com>
date	Fri, 18 Nov 2011 12:28:20 -0800
parents	4d777e05d47c
children	72c96de7a403

rev	line source
11523 fd0a3ac60b0e update copyright notices John W. Eaton <jwe@octave.org> parents: 10821 diff changeset	1 ## Copyright (C) 1993-2011 John W. Eaton
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	2 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	3 ## This file is part of Octave.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	4 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	5 ## 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	6 ## 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	7 ## 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	8 ## your option) any later version.
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	9 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	10 ## 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	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	12 ## 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	13 ## General Public License for more details.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	14 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	15 ## 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	16 ## 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	17 ## <http://www.gnu.org/licenses/>.
245 16a24e76d6e0 [project @ 1993-12-03 02:00:15 by jwe] jwe parents: 4 diff changeset	18
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	19 ## -- texinfo --
10791 3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation Rik <octave@nomad.inbox5.com> parents: 9211 diff changeset	20 ## @deftypefn {Function File} {} hankel (@var{c})
3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation Rik <octave@nomad.inbox5.com> parents: 9211 diff changeset	21 ## @deftypefnx {Function File} {} hankel (@var{c}, @var{r})
12639 4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	22 ## Return the Hankel matrix constructed from the first column @var{c}, and
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	23 ## (optionally) the last row @var{r}. If the last element of @var{c} is
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	24 ## not the same as the first element of @var{r}, the last element of
4922 cee8d88cf619 [project @ 2004-07-30 19:10:16 by jwe] jwe parents: 3426 diff changeset	25 ## @var{c} is used. If the second argument is omitted, it is assumed to
cee8d88cf619 [project @ 2004-07-30 19:10:16 by jwe] jwe parents: 3426 diff changeset	26 ## be a vector of zeros with the same size as @var{c}.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3408 diff changeset	27 ##
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	28 ## A Hankel matrix formed from an m-vector @var{c}, and an n-vector
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	29 ## @var{r}, has the elements
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	30 ## @tex
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	31 ## $$
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	32 ## H (i, j) = \cases{c_{i+j-1},&$i+j-1\le m$;\cr r_{i+j-m},&otherwise.\cr}
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	33 ## $$
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	34 ## @end tex
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7411 diff changeset	35 ## @ifnottex
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3408 diff changeset	36 ##
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	37 ## @example
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	38 ## @group
4922 cee8d88cf619 [project @ 2004-07-30 19:10:16 by jwe] jwe parents: 3426 diff changeset	39 ## H(i,j) = c(i+j-1), i+j-1 <= m;
cee8d88cf619 [project @ 2004-07-30 19:10:16 by jwe] jwe parents: 3426 diff changeset	40 ## H(i,j) = r(i+j-m), otherwise
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	41 ## @end group
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	42 ## @end example
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10791 diff changeset	43 ##
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7411 diff changeset	44 ## @end ifnottex
12639 4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	45 ## @seealso{hadamard, toeplitz}
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	46 ## @end deftypefn
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	47
2314 949ab8eba8bc [project @ 1996-07-12 03:58:02 by jwe] jwe parents: 2313 diff changeset	48 ## Author: jwe
949ab8eba8bc [project @ 1996-07-12 03:58:02 by jwe] jwe parents: 2313 diff changeset	49
2311 2b5788792cad [project @ 1996-07-11 20:18:38 by jwe] jwe parents: 2303 diff changeset	50 function retval = hankel (c, r)
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	51
13888 c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	52 if (nargin < 1 \|\| nargin > 2)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5731 diff changeset	53 print_usage ();
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	54 endif
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	55
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2314 diff changeset	56 if (nargin == 1)
13888 c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	57
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	58 if (! isvector (c))
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	59 error ("hankel: C must be a vector");
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	60 endif
1396 1ff9a86e2ad5 [project @ 1995-09-14 19:46:14 by jwe] jwe parents: 1315 diff changeset	61
13888 c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	62 nr = length (c);
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	63 nc = nr;
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	64 data = [c(:) ; zeros(nr, 1)];
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	65
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	66 else
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	67
13888 c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	68 if (! (isvector (c) && isvector (r)))
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	69 error ("hankel: C and R must be vectors");
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	70 elseif (r(1) != c(end))
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	71 warning ("hankel: column wins anti-diagonal conflict");
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	72 endif
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	73
13888 c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	74 nr = length (c);
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	75 nc = length (r);
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	76 data = [c(:) ; r(2:end)(:)];
1396 1ff9a86e2ad5 [project @ 1995-09-14 19:46:14 by jwe] jwe parents: 1315 diff changeset	77
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	78 endif
13888 c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	79
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	80 slices = cellslices (data, 1:nc, nr:1:nc+nr-1);
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	81 retval = horzcat (slices{:});
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	82
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	83 endfunction
5731 c7d5a534afa5 [project @ 2006-04-03 19:33:26 by jwe] jwe parents: 5642 diff changeset	84
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	85
13888 c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	86 %!assert (hankel (1), [1])
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	87 %!assert (hankel ([1, 2]), [1, 2; 2, 0])
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	88 %!assert (hankel ([1, 2], [2; -1; -3]), [1, 2, -1; 2, -1, -3])
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	89 %!assert (hankel (1:3), [1,2,3;2,3,0;3,0,0])
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	90 %!assert (hankel (1:3,3:6), [1,2,3,4;2,3,4,5;3,4,5,6])
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	91 %!assert (hankel (1:3,3:4), [1,2;2,3;3,4])
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	92 %!assert (hankel (1:3,4:6), [1,2,3;2,3,5;3,5,6])
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	93
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	94 %!error hankel ();
13888 c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	95 %!error hankel (1, 2, 3);
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	96 %!error <C must be a vector> hankel ([1, 2; 3, 4])
c78ac846fcbc hankel.m: Recode for 3.5X speedup Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	97 %!error <C and R must be vectors> hankel (1:4, [1, 2; 3, 4])
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	98

Mercurial > hg > octave-nkf

annotate scripts/special-matrix/hankel.m @ 13888:c78ac846fcbc