Mercurial > octave
view scripts/linear-algebra/null.m @ 30231:c14a536a41cd
null.m: Silence incorrect warning message for row vector inputs (bug #61305)
* null.m: Use diag() to extract column vector from Diagonal Matrix only when
Matrix has more than 1 row. Otherwise, just get the first element with Matrix(1).
Clean up coding of BIST tests. Add BIST tests for input validation.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 07 Oct 2021 09:16:18 -0700 |
parents | eb52033f4e2a |
children | 363fb10055df |
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######################################################################## ## ## Copyright (C) 1994-2021 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## 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 ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {@var{Z} =} null (@var{A}) ## @deftypefnx {} {@var{Z} =} null (@var{A}, @var{tol}) ## Return an orthonormal basis @var{Z} of the null space of @var{A}. ## ## The dimension of the null space @var{Z} is taken as the number of singular ## values of @var{A} not greater than @var{tol}. If the argument @var{tol} ## is missing, it is computed as ## ## @example ## max (size (@var{A})) * max (svd (@var{A}, 0)) * eps ## @end example ## @seealso{orth, svd} ## @end deftypefn function Z = null (A, tol) if (nargin < 1) print_usage (); elseif (nargin == 2 && strcmp (tol, "r")) error ("null: option for rational not yet implemented"); endif [~, S, V] = svd (A, 0); # Use economy-sized svd if possible. if (isempty (A)) ## In case of A = [], zeros (0,X), zeros (X,0) Matlab R2020b seems to ## simply return the nullspace "V" of the svd-decomposition (bug #59630). Z = V; else out_cls = class (V); ## Extract column vector from Diagonal Matrix which depends on size if (rows (S) > 1) s = diag (S); else s = S(1); end if (nargin == 1) tol = max (size (A)) * s(1) * eps (out_cls); endif rank = sum (s > tol); cols = columns (A); if (rank < cols) Z = V(:, rank+1:cols); Z(abs (Z) < eps (out_cls)) = 0; else Z = zeros (cols, 0, out_cls); endif endif endfunction ## Exact tests %!test %! A = { %! [], []; %! zeros(1,0), []; %! zeros(4,0), []; %! zeros(0,1), 1; %! zeros(0,4), eye(4); %! 0, 1; %! 1, zeros(1,0); %! [1 0; 0 1], zeros(2,0); %! [1 0; 1 0], [0 1]'; %! }; %! for i = 1:rows (A) %! assert (null (A{i,1}), A{i,2}); %! assert (null (single (A{i,1})), single (A{i,2})); %! endfor ## Inexact tests %!test %! A = { %! [1 1; 0 0], [-1/sqrt(2) 1/sqrt(2)]'; %! }; %! for i = 1:rows (A) %! assert (null (A{i,1}), A{i,2}, eps); %! assert (null (single (A{i,1})), single (A{i,2}), eps); %! endfor ## Tests with tolerance input %!test %! tol = 1e-4; %! A = { %! @(e) [1 0; 0 tol-e], [0 1]'; %! @(e) [1 0; 0 tol+e], zeros(2,0); %! }; %! for i = 1:rows (A) %! assert (null (A{i,1}(eps ("double")), tol), A{i,2}); %! assert (null (single (A{i,1}(eps ("single"))), tol), single (A{i,2})); %! endfor ## Input corner cases %!assert (null (uint8 ([])), []) ## Test input validation %!error <Invalid call> null () %!error <rational not yet implemented> null (1, 'r')