annotate scripts/linear-algebra/null.m @ 14868:5d3a684236b0

maint: Use Octave coding conventions for cuddling parentheses in scripts directory * lin2mu.m, loadaudio.m, wavread.m, accumarray.m, bicubic.m, celldisp.m, colon.m, cplxpair.m, dblquad.m, divergence.m, genvarname.m, gradient.m, int2str.m, interp1.m, interp1q.m, interp2.m, interpn.m, loadobj.m, nthargout.m, __isequal__.m, __splinen__.m, quadgk.m, quadl.m, quadv.m, rat.m, rot90.m, rotdim.m, saveobj.m, subsindex.m, triplequad.m, delaunay3.m, griddata.m, inpolygon.m, tsearchn.m, voronoi.m, get_first_help_sentence.m, which.m, gray2ind.m, pink.m, dlmwrite.m, strread.m, textread.m, textscan.m, housh.m, ishermitian.m, issymmetric.m, krylov.m, logm.m, null.m, rref.m, compare_versions.m, copyfile.m, dump_prefs.m, edit.m, fileparts.m, getappdata.m, isappdata.m, movefile.m, orderfields.m, parseparams.m, __xzip__.m, rmappdata.m, setappdata.m, swapbytes.m, unpack.m, ver.m, fminbnd.m, fminunc.m, fsolve.m, glpk.m, lsqnonneg.m, qp.m, sqp.m, configure_make.m, copy_files.m, describe.m, get_description.m, get_forge_pkg.m, install.m, installed_packages.m, is_architecture_dependent.m, load_package_dirs.m, print_package_description.m, rebuild.m, repackage.m, save_order.m, shell.m, allchild.m, ancestor.m, area.m, axes.m, axis.m, clabel.m, close.m, colorbar.m, comet.m, comet3.m, contour.m, cylinder.m, ezmesh.m, ezsurf.m, findobj.m, fplot.m, hist.m, isocolors.m, isonormals.m, isosurface.m, isprop.m, legend.m, mesh.m, meshz.m, pareto.m, pcolor.m, peaks.m, plot3.m, plotmatrix.m, plotyy.m, polar.m, print.m, __add_datasource__.m, __add_default_menu__.m, __axes_limits__.m, __bar__.m, __clabel__.m, __contour__.m, __errcomm__.m, __errplot__.m, __ezplot__.m, __file_filter__.m, __fltk_print__.m, __ghostscript__.m, __gnuplot_print__.m, __go_draw_axes__.m, __go_draw_figure__.m, __interp_cube__.m, __marching_cube__.m, __patch__.m, __pie__.m, __plt__.m, __print_parse_opts__.m, __quiver__.m, __scatter__.m, __stem__.m, __tight_eps_bbox__.m, __uigetdir_fltk__.m, __uigetfile_fltk__.m, __uiputfile_fltk__.m, quiver.m, quiver3.m, rectangle.m, refreshdata.m, ribbon.m, scatter.m, semilogy.m, shading.m, slice.m, subplot.m, surface.m, surfl.m, surfnorm.m, text.m, uigetfile.m, uiputfile.m, whitebg.m, deconv.m, mkpp.m, pchip.m, polyaffine.m, polyder.m, polygcd.m, polyout.m, polyval.m, ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, splinefit.m, addpref.m, getpref.m, setpref.m, ismember.m, setxor.m, arch_fit.m, arch_rnd.m, arch_test.m, autoreg_matrix.m, diffpara.m, fftconv.m, filter2.m, hanning.m, hurst.m, periodogram.m, triangle_sw.m, sinc.m, spectral_xdf.m, spencer.m, stft.m, synthesis.m, unwrap.m, yulewalker.m, bicgstab.m, gmres.m, pcg.m, pcr.m, __sprand_impl__.m, speye.m, spfun.m, sprandn.m, spstats.m, svds.m, treelayout.m, treeplot.m, bessel.m, factor.m, legendre.m, perms.m, primes.m, magic.m, toeplitz.m, corr.m, cov.m, mean.m, median.m, mode.m, qqplot.m, quantile.m, ranks.m, zscore.m, logistic_regression_likelihood.m, bartlett_test.m, chisquare_test_homogeneity.m, chisquare_test_independence.m, kolmogorov_smirnov_test.m, run_test.m, u_test.m, wilcoxon_test.m, z_test.m, z_test_2.m, bin2dec.m, dec2base.m, mat2str.m, strcat.m, strchr.m, strjust.m, strtok.m, substr.m, untabify.m, assert.m, demo.m, example.m, fail.m, speed.m, test.m, now.m: Use Octave coding conventions for cuddling parentheses in scripts directory.
author Rik <octave@nomad.inbox5.com>
date Tue, 17 Jul 2012 07:08:39 -0700
parents f3d52523cde1
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
14138
72c96de7a403 maint: update copyright notices for 2012
John W. Eaton <jwe@octave.org>
parents: 12890
diff changeset
1 ## Copyright (C) 1994-2012 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 ##
2311
2b5788792cad [project @ 1996-07-11 20:18:38 by jwe]
jwe
parents: 2303
diff changeset
24 ## The dimension of the null space is taken as the number of singular
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
25 ## values of @var{A} not greater than @var{tol}. If the argument @var{tol}
3372
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 2847
diff changeset
26 ## is missing, 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)
c14ec945fabb [project @ 2003-03-26 16:05:59 by jwe]
jwe
parents: 3456
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
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
82 %% FIXME: Need some tests for 'single' variables as well
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