X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fm%2Flinear-algebra%2Fsubspace.m;fp=octave_packages%2Fm%2Flinear-algebra%2Fsubspace.m;h=47c986263602be0fbe7764cb112bd11b7765d097;hp=0000000000000000000000000000000000000000;hb=1c0469ada9531828709108a4882a751d2816994a;hpb=63de9f36673d49121015e3695f2c336ea92bc278
diff --git a/octave_packages/m/linear-algebra/subspace.m b/octave_packages/m/linear-algebra/subspace.m
new file mode 100644
index 0000000..47c9862
--- /dev/null
+++ b/octave_packages/m/linear-algebra/subspace.m
@@ -0,0 +1,61 @@
+## Copyright (C) 2008-2012 VZLU Prague, a.s., Czech Republic
+##
+## 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
+## .
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@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
+
+## Author: Jaroslav Hajek
+
+## reference:
+## [1] 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: expecting A and B to 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