# HG changeset patch
# User Jaroslav Hajek <address@hidden>
# Date 1205749585 -3600
# Node ID bc6b66bb8c5c2afb379ff0e5f6aa6d96fcdfb662
# Parent  bf704d1c5e4375253408bbb855f99138cee2bb5c
implement subspace function

diff -r bf704d1c5e43 -r bc6b66bb8c5c scripts/ChangeLog
--- a/scripts/ChangeLog	Fri Mar 14 08:00:50 2008 -0400
+++ b/scripts/ChangeLog	Mon Mar 17 11:26:25 2008 +0100
@@ -1,3 +1,7 @@ 2008-03-14  Kai Habel  <address@hidden
+2008-03-17  Jaroslav Hajek <address@hidden>
+
+	* linear-algebra/subspace.m: New function.
+
 2008-03-14  Kai Habel  <address@hidden>
 
         * plot/__go_draw_axes__.m: Expicitly set gnuplot user
diff -r bf704d1c5e43 -r bc6b66bb8c5c scripts/linear-algebra/Makefile.in
--- a/scripts/linear-algebra/Makefile.in	Fri Mar 14 08:00:50 2008 -0400
+++ b/scripts/linear-algebra/Makefile.in	Mon Mar 17 11:26:25 2008 +0100
@@ -35,7 +35,8 @@ INSTALL_DATA = @INSTALL_DATA@
 
 SOURCES = __norm__.m commutation_matrix.m cond.m condest.m cross.m \
   dmult.m dot.m duplication_matrix.m housh.m krylov.m krylovb.m logm.m \
-  null.m onenormest.m orth.m qzhess.m rank.m rref.m trace.m vec.m vech.m
+  null.m onenormest.m orth.m qzhess.m rank.m rref.m subspace.m trace.m \
+  vec.m vech.m
 
 DISTFILES = $(addprefix $(srcdir)/, Makefile.in $(SOURCES))
 
diff -r bf704d1c5e43 -r bc6b66bb8c5c scripts/linear-algebra/subspace.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/scripts/linear-algebra/subspace.m	Mon Mar 17 11:26:25 2008 +0100
@@ -0,0 +1,54 @@
+## Copyright (C) 2008 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/>.
+##
+## Author: Jaroslav Hajek <address@hidden>
+##
+## 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...
+
+
+## -*- texinfo -*-
+## @deftypefn{Function File} angle = subspace (A, B)
+## determines the largest principal angle between two subspaces 
+## (spanned by columns of matrices @var{A}, @var{B}).
+## @end deftypefn
+
+
+function ang = subspace (A, B)
+
+A = orth (A);
+B = orth (B);
+C = A'*B;
+scos = min (svd (C));
+if (scos^2 > 1/2)
+  if (size (A, 2) >= size (B, 2))
+    C = B - A*C;
+  else
+    C = A - B*C';
+  endif
+  ssin = max (svd (C));
+  ang = asin (min (ssin, 1));
+else
+  ang = acos (scos);
+endif
+