octave-nkf: scripts/linear-algebra/orth.m annotate

annotate scripts/linear-algebra/orth.m @ 20770:c1a6c31ac29a

eliminate more simple uses of error_state * ov-classdef.cc: Eliminate simple uses of error_state.

author	John W. Eaton <jwe@octave.org>
date	Tue, 06 Oct 2015 00:20:02 -0400
parents	03b9d17a2d95
children

rev	line source
19898 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 17744 diff changeset	1 ## Copyright (C) 1994-2015 John W. Eaton
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	2 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	3 ## This file is part of Octave.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	4 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 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: 2312 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: 2312 diff changeset	9 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 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: 2312 diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 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: 2312 diff changeset	13 ## General Public License for more details.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	14 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 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/>.
1026 9fc405c8c06c [project @ 1995-01-11 21:17:01 by jwe] jwe parents: 1022 diff changeset	18
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3141 diff changeset	19 ## -- texinfo --
12584 7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	20 ## @deftypefn {Function File} {} orth (@var{A})
7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	21 ## @deftypefnx {Function File} {} orth (@var{A}, @var{tol})
11470 eb9e0b597d61 Use common names for variables in documentation and code for a few more m-script files. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	22 ## Return an orthonormal basis of the range space of @var{A}.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3372 diff changeset	23 ##
20370 03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	24 ## The dimension of the range space is taken as the number of singular values
03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	25 ## of @var{A} greater than @var{tol}. If the argument @var{tol} is missing, it
03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	26 ## is computed as
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3372 diff changeset	27 ##
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3141 diff changeset	28 ## @example
11470 eb9e0b597d61 Use common names for variables in documentation and code for a few more m-script files. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	29 ## max (size (@var{A})) * max (svd (@var{A})) * eps
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3141 diff changeset	30 ## @end example
10687 a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	31 ## @seealso{null}
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3141 diff changeset	32 ## @end deftypefn
557 e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	33
5428 2a16423e4aa0 [project @ 2005-08-23 18:38:27 by jwe] jwe parents: 5307 diff changeset	34 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
2312 204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	35 ## Created: 24 December 1993.
204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	36 ## Adapted-By: jwe
557 e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	37
2312 204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	38 function retval = orth (A, tol)
557 e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	39
3141 292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	40 if (nargin == 1 \|\| nargin == 2)
557 e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	41
12906 d7a91b3fb7f9 Return empty matrix if the argument to orth is empty (bug #33301) Jordi Gutiérrez Hermoso <jordigh@gmail.com> parents: 12584 diff changeset	42 if (isempty (A))
d7a91b3fb7f9 Return empty matrix if the argument to orth is empty (bug #33301) Jordi Gutiérrez Hermoso <jordigh@gmail.com> parents: 12584 diff changeset	43 retval = [];
d7a91b3fb7f9 Return empty matrix if the argument to orth is empty (bug #33301) Jordi Gutiérrez Hermoso <jordigh@gmail.com> parents: 12584 diff changeset	44 return;
d7a91b3fb7f9 Return empty matrix if the argument to orth is empty (bug #33301) Jordi Gutiérrez Hermoso <jordigh@gmail.com> parents: 12584 diff changeset	45 endif
d7a91b3fb7f9 Return empty matrix if the argument to orth is empty (bug #33301) Jordi Gutiérrez Hermoso <jordigh@gmail.com> parents: 12584 diff changeset	46
3141 292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	47 [U, S, V] = svd (A);
557 e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	48
3141 292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	49 [rows, cols] = size (A);
1065 5eeb61cac52e [project @ 1995-01-25 14:04:13 by jwe] jwe parents: 1026 diff changeset	50
3141 292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	51 [S_nr, S_nc] = size (S);
292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	52
292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	53 if (S_nr == 1 \|\| S_nc == 1)
292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	54 s = S(1);
292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	55 else
292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	56 s = diag (S);
292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	57 endif
557 e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	58
3141 292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	59 if (nargin == 1)
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	60 if (isa (A, "single"))
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 8920 diff changeset	61 tol = max (size (A)) * s (1) * eps ("single");
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	62 else
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 8920 diff changeset	63 tol = max (size (A)) * s (1) * eps;
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	64 endif
3141 292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	65 endif
292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	66
292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	67 rank = sum (s > tol);
557 e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	68
3141 292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	69 if (rank > 0)
20038 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	70 retval = -U(:, 1:rank);
3141 292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	71 else
292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	72 retval = zeros (rows, 0);
292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	73 endif
557 e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	74
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	75 else
3141 292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	76
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5428 diff changeset	77 print_usage ();
3141 292ff0bf484b [project @ 1998-02-03 08:11:07 by jwe] jwe parents: 2847 diff changeset	78
557 e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	79 endif
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	80
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	81 endfunction
13047 69a4609e61e2 codesprint: Add a test to orth.m Carlo de Falco <kingcrimson@tiscali.it> parents: 12906 diff changeset	82
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	83
13047 69a4609e61e2 codesprint: Add a test to orth.m Carlo de Falco <kingcrimson@tiscali.it> parents: 12906 diff changeset	84 %!test
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	85 %! for i = 1:20
13047 69a4609e61e2 codesprint: Add a test to orth.m Carlo de Falco <kingcrimson@tiscali.it> parents: 12906 diff changeset	86 %! A = rand (10, 10);
69a4609e61e2 codesprint: Add a test to orth.m Carlo de Falco <kingcrimson@tiscali.it> parents: 12906 diff changeset	87 %! V = orth (A);
69a4609e61e2 codesprint: Add a test to orth.m Carlo de Falco <kingcrimson@tiscali.it> parents: 12906 diff changeset	88 %! if (det (A) != 0)
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	89 %! assert (V'V, eye (10), 100eps);
13047 69a4609e61e2 codesprint: Add a test to orth.m Carlo de Falco <kingcrimson@tiscali.it> parents: 12906 diff changeset	90 %! endif
69a4609e61e2 codesprint: Add a test to orth.m Carlo de Falco <kingcrimson@tiscali.it> parents: 12906 diff changeset	91 %! endfor
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	92

Mercurial > hg > octave-nkf

annotate scripts/linear-algebra/orth.m @ 20770:c1a6c31ac29a