Mercurial > octave-antonio
view scripts/linear-algebra/orth.m @ 20160:03b9d17a2d95 stable
doc: Update more docstrings to have one sentence summary as first line.
Reviewed io, java, linear-algebra, prefs, and set script directories.
* scripts/io/beep.m, scripts/io/dlmwrite.m, scripts/io/importdata.m,
scripts/io/strread.m, scripts/io/textread.m, scripts/java/javaArray.m,
scripts/java/java_get.m, scripts/java/java_set.m, scripts/java/javaaddpath.m,
scripts/java/javachk.m, scripts/java/javaclasspath.m, scripts/java/javamem.m,
scripts/java/javarmpath.m, scripts/linear-algebra/bandwidth.m,
scripts/linear-algebra/commutation_matrix.m, scripts/linear-algebra/cond.m,
scripts/linear-algebra/condest.m, scripts/linear-algebra/cross.m,
scripts/linear-algebra/duplication_matrix.m, scripts/linear-algebra/expm.m,
scripts/linear-algebra/housh.m, scripts/linear-algebra/isdefinite.m,
scripts/linear-algebra/ishermitian.m, scripts/linear-algebra/issymmetric.m,
scripts/linear-algebra/istril.m, scripts/linear-algebra/istriu.m,
scripts/linear-algebra/krylov.m, scripts/linear-algebra/logm.m,
scripts/linear-algebra/normest.m, scripts/linear-algebra/null.m,
scripts/linear-algebra/onenormest.m, scripts/linear-algebra/orth.m,
scripts/linear-algebra/qzhess.m, scripts/linear-algebra/rank.m,
scripts/linear-algebra/rref.m, scripts/linear-algebra/vech.m,
scripts/path/matlabroot.m, scripts/prefs/addpref.m, scripts/prefs/getpref.m,
scripts/prefs/ispref.m, scripts/prefs/rmpref.m, scripts/prefs/setpref.m,
scripts/set/powerset.m, scripts/set/setdiff.m:
Update more docstrings to have one sentence summary as first line.
author | Rik <rik@octave.org> |
---|---|
date | Sun, 03 May 2015 15:36:23 -0700 |
parents | 9fc020886ae9 |
children |
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## Copyright (C) 1994-2015 John W. Eaton ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {} orth (@var{A}) ## @deftypefnx {Function File} {} orth (@var{A}, @var{tol}) ## Return an orthonormal basis of the range space of @var{A}. ## ## The dimension of the range space is taken as the number of singular values ## of @var{A} greater than @var{tol}. If the argument @var{tol} is missing, it ## is computed as ## ## @example ## max (size (@var{A})) * max (svd (@var{A})) * eps ## @end example ## @seealso{null} ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Created: 24 December 1993. ## Adapted-By: jwe function retval = orth (A, tol) if (nargin == 1 || nargin == 2) if (isempty (A)) retval = []; return; endif [U, S, V] = svd (A); [rows, cols] = size (A); [S_nr, S_nc] = size (S); if (S_nr == 1 || S_nc == 1) s = S(1); else s = diag (S); endif if (nargin == 1) if (isa (A, "single")) tol = max (size (A)) * s (1) * eps ("single"); else tol = max (size (A)) * s (1) * eps; endif endif rank = sum (s > tol); if (rank > 0) retval = -U(:, 1:rank); else retval = zeros (rows, 0); endif else print_usage (); endif endfunction %!test %! for i = 1:20 %! A = rand (10, 10); %! V = orth (A); %! if (det (A) != 0) %! assert (V'*V, eye (10), 100*eps); %! endif %! endfor