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[CreaPhase.git] / octave_packages / m / linear-algebra / subspace.m

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+## 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- 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 <highegg@gmail.com>
+
+## 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