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

annotate scripts/linear-algebra/null.m @ 20815:a260a6acb70f

fix test failures introduced by a22d8a2eb0e5 * scripts/ode/private/integrate_adaptive.m: fix stepping backwards, fix invocation of OutputFcn, fix text of some error messages * scripts/ode/private/integrate_const.m: remove use of option OutputSave * scripts/ode/private/integrate_n_steps.m: remove use of option OutputSave

author	Carlo de Falco <carlo.defalco@polimi.it>
date	Sun, 11 Oct 2015 23:09:01 +0200
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: 6431 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: 6431 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: 6431 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: 6431 diff changeset	17 ## <http://www.gnu.org/licenses/>.
1026 9fc405c8c06c [project @ 1995-01-11 21:17:01 by jwe] jwe parents: 904 diff changeset	18
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 2847 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} {} null (@var{A})
7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	21 ## @deftypefnx {Function File} {} null (@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 null 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 null space is taken as the number of singular values of
03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	25 ## @var{A} not greater than @var{tol}. If the argument @var{tol} is missing,
03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	26 ## it 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: 2847 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: 2847 diff changeset	30 ## @end example
10687 a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	31 ## @seealso{orth}
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 2847 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 = null (A, tol)
557 e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	39
4371 c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	40 if (isempty (A))
c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	41 retval = [];
c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	42 else
c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	43 [U, S, V] = svd (A);
1065 5eeb61cac52e [project @ 1995-01-25 14:04:13 by jwe] jwe parents: 1026 diff changeset	44
4371 c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	45 [rows, cols] = size (A);
c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	46
c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	47 [S_nr, S_nc] = size (S);
557 e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	48
4371 c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	49 if (S_nr == 1 \|\| S_nc == 1)
c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	50 s = S(1);
c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	51 else
c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	52 s = diag (S);
c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	53 endif
557 e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	54
4371 c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	55 if (nargin == 1)
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	56 if (isa (A, "single"))
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 8920 diff changeset	57 tol = max (size (A)) * s (1) * eps ("single");
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	58 else
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 8920 diff changeset	59 tol = max (size (A)) * s (1) * eps;
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	60 endif
4371 c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	61 elseif (nargin != 2)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5428 diff changeset	62 print_usage ();
4371 c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	63 endif
557 e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	64
4371 c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	65 rank = sum (s > tol);
c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	66
c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	67 if (rank < cols)
20038 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	68 retval = V(:, rank+1:cols);
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	69 if (isa (A, "single"))
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	70 retval (abs (retval) < eps ("single")) = 0;
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	71 else
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	72 retval (abs (retval) < eps) = 0;
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	73 endif
4371 c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	74 else
c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	75 retval = zeros (cols, 0);
c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe] jwe parents: 3456 diff changeset	76 endif
557 e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	77 endif
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	78
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe] jwe parents: diff changeset	79 endfunction
12806 a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	80
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	81
20038 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	82 ## FIXME: Need some tests for 'single' variables as well
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	83
12806 a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	84 %!test
a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	85 %! A = 0;
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	86 %! assert (null (A), 1);
12806 a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	87
a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	88 %!test
a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	89 %! A = 1;
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	90 %! assert (null (A), zeros (1,0));
12806 a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	91
a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	92 %!test
a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	93 %! A = [1 0; 0 1];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	94 %! assert (null (A), zeros (2,0));
12806 a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	95
a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	96 %!test
a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	97 %! A = [1 0; 1 0];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	98 %! assert (null (A), [0 1]');
12806 a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	99
a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	100 %!test
a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	101 %! A = [1 1; 0 0];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	102 %! assert (null (A), [-1/sqrt(2) 1/sqrt(2)]', eps);
12806 a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	103
a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	104 %!test
a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	105 %! tol = 1e-4;
a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	106 %! A = [1 0; 0 tol-eps];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	107 %! assert (null (A,tol), [0; 1]);
12806 a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	108
a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	109 %!test
a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	110 %! tol = 1e-4;
a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	111 %! A = [1 0; 0 tol+eps];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	112 %! assert (null (A,tol), zeros (2,0));
12806 a85ddaf8f402 codesprint: Wrote 8 tests for null.m Sean Young <seannz@gmail.com> parents: 12584 diff changeset	113
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	114 %!error null ()
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	115

Mercurial > hg > octave-nkf

annotate scripts/linear-algebra/null.m @ 20815:a260a6acb70f