--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/DLD-FUNCTIONS/mgorth.cc	Wed Mar 16 13:36:27 2011 -0700
@@ -0,0 +1,154 @@
+/*
+
+Copyright (C) 2009-2011 Carlo de Falco
+Copyright (C) 2010 VZLU Prague
+
+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/>.
+
+*/
+
+#ifdef HAVE_CONFIG_H
+#include <config.h>
+#endif
+
+#include "oct-norm.h"
+#include "defun-dld.h"
+#include "error.h"
+#include "gripes.h"
+
+template <class ColumnVector, class Matrix, class RowVector>
+static void 
+do_mgorth (ColumnVector& x, const Matrix& V, RowVector& h) 
+{
+  octave_idx_type Vc = V.columns ();
+  h = RowVector (Vc + 1);
+  for (octave_idx_type j = 0; j < Vc; j++)
+    {
+      ColumnVector Vcj = V.column (j);
+      h(j) = RowVector (Vcj.hermitian ()) * x;
+      x -= h(j) * Vcj;
+    }
+
+  h(Vc) = xnorm (x);
+  if (real (h(Vc)) > 0)
+    x = x / h(Vc);
+}
+
+DEFUN_DLD (mgorth, args, nargout,
+  "-*- texinfo -*-\n\
+@deftypefn {Loadable Function} {[@var{y}, @var{h}] =} mgorth (@var{x}, @var{v})\n\
+Orthogonalize a given column vector @var{x} with respect to a given\n\
+orthonormal basis @var{v} using a modified Gram-Schmidt orthogonalization.  \n\
+On exit, @var{y} is a unit vector such that:\n\
+\n\
+@example\n\
+@group\n\
+  norm (@var{y}) = 1\n\
+  @var{v}' * @var{y} = 0\n\
+  @var{x} = @var{h}*[@var{v}, @var{y}]\n\
+@end group\n\
+@end example\n\
+\n\
+@end deftypefn")
+{
+  octave_value_list retval;
+
+  int nargin = args.length();
+
+  if (nargin != 2 || nargout > 2)
+  {
+    print_usage (); 
+    return retval;
+  }
+
+  octave_value arg_x = args(0);
+  octave_value arg_v = args(1);
+
+  if (arg_v.ndims () != 2 || arg_x.ndims () != 2 || arg_x.columns () != 1
+      || arg_v.rows () != arg_x.rows ())
+    {
+      error ("mgorth: V should me a matrix, and X a column vector with"
+             " the same number of rows as V.");
+      return retval;
+    }
+
+  if (! arg_x.is_numeric_type () && ! arg_v.is_numeric_type ())
+    {
+      error ("mgorth: X and V must be numeric");
+    }
+ 
+  bool iscomplex = (arg_x.is_complex_type () || arg_v.is_complex_type ());
+  if (arg_x.is_single_type () || arg_v.is_single_type ())
+    {
+      if (iscomplex)
+        {
+          FloatComplexColumnVector x = arg_x.float_complex_column_vector_value ();
+          FloatComplexMatrix V = arg_v.float_complex_matrix_value ();
+          FloatComplexRowVector h;
+          do_mgorth (x, V, h);
+          retval(1) = h;
+          retval(0) = x;
+        }
+      else
+        {
+          FloatColumnVector x = arg_x.float_column_vector_value ();
+          FloatMatrix V = arg_v.float_matrix_value ();
+          FloatRowVector h;
+          do_mgorth (x, V, h);
+          retval(1) = h;
+          retval(0) = x;
+        }
+    }
+  else
+    {
+      if (iscomplex)
+        {
+          ComplexColumnVector x = arg_x.complex_column_vector_value ();
+          ComplexMatrix V = arg_v.complex_matrix_value ();
+          ComplexRowVector h;
+          do_mgorth (x, V, h);
+          retval(1) = h;
+          retval(0) = x;
+        }
+      else
+        {
+          ColumnVector x = arg_x.column_vector_value ();
+          Matrix V = arg_v.matrix_value ();
+          RowVector h;
+          do_mgorth (x, V, h);
+          retval(1) = h;
+          retval(0) = x;
+        }
+    }
+
+  return retval;
+}
+
+/*
+  
+%!test
+%! for ii=1:100; assert (abs (mgorth (randn (5, 1), eye (5, 4))), [0 0 0 0 1]', eps); endfor
+
+%!test
+%! a = hilb (5);
+%! a(:, 1) /= norm (a(:, 1));
+%! for ii = 1:5
+%!   a(:, ii) = mgorth (a(:, ii), a(:, 1:ii-1));
+%! endfor
+%! assert (a' * a, eye (5), 1e10);
+
+*/