Mercurial > octave
view scripts/linear-algebra/subspace.m @ 33577:2506c2d30b32 bytecode-interpreter tip
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author | Arun Giridhar <arungiridhar@gmail.com> |
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date | Sat, 11 May 2024 18:49:01 -0400 |
parents | 2e484f9f1f18 |
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######################################################################## ## ## Copyright (C) 2008-2024 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{angle} =} subspace (@var{A}, @var{B}) ## Determine the largest principal angle between two subspaces ## spanned by the columns of matrices @var{A} and @var{B}. ## @end deftypefn ## Reference: ## Andrew V. Knyazev, Merico E. Argentati: ## Principal Angles between Subspaces in an A-Based Scalar Product: ## Algorithms and Perturbation Estimates. ## SIAM Journal on Scientific Computing, Vol. 23 no. 6, pp. 2008-2040 ## ## other texts are also around... function ang = subspace (A, B) if (nargin != 2) print_usage (); elseif (ndims (A) != 2 || ndims (B) != 2) error ("subspace: A and B must be 2-dimensional arrays"); elseif (rows (A) != rows (B)) error ("subspace: column dimensions of A and B must match"); endif A = orth (A); B = orth (B); c = A'*B; scos = min (svd (c)); if (scos^2 > 1/2) if (columns (A) >= columns (B)) c = B - A*c; else c = A - B*c'; endif ssin = max (svd (c)); ang = asin (min (ssin, 1)); else ang = acos (scos); endif endfunction %!assert (subspace (1, 1), 0) %!assert (subspace ([1, 0]', [1, 1; 0, 1]'), 0, 3*eps) %!assert (subspace ([1, 0, 1]', [1, 1, 0; 1, -1, 0]'), pi/4, 3*eps) %!assert (subspace ([1 5 0 0; -3 2 0 0]', [0 0 4 2; 0 0 4 3]'), pi/2) %!assert (subspace ([1 1 1 1; 1 2 3 4]', [1 -1 -1 1]'), pi/2) %!test %! ## For small angle between subspaces %! theta = pi/200; %! Ry = [cos(theta), 0, sin(theta);0, 1, 0;-sin(theta), 0, cos(theta)]; %! a = Ry*[3*e, 0, 0]'; %! b = [1, 1, 0; 1, -1, 0]'; %! assert (theta, subspace (a, b), eps);