--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/corefcn/hess.cc	Fri Jul 27 15:35:00 2012 -0700
@@ -0,0 +1,189 @@
+/*
+
+Copyright (C) 1996-2012 John W. Eaton
+
+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 "CmplxHESS.h"
+#include "dbleHESS.h"
+#include "fCmplxHESS.h"
+#include "floatHESS.h"
+
+#include "defun.h"
+#include "error.h"
+#include "gripes.h"
+#include "oct-obj.h"
+#include "utils.h"
+
+DEFUN (hess, args, nargout,
+  "-*- texinfo -*-\n\
+@deftypefn  {Built-in Function} {@var{H} =} hess (@var{A})\n\
+@deftypefnx {Built-in Function} {[@var{P}, @var{H}] =} hess (@var{A})\n\
+@cindex Hessenberg decomposition\n\
+Compute the Hessenberg decomposition of the matrix @var{A}.\n\
+\n\
+The Hessenberg decomposition is\n\
+@tex\n\
+$$\n\
+A = PHP^T\n\
+$$\n\
+where $P$ is a square unitary matrix ($P^TP = I$), and $H$\n\
+is upper Hessenberg ($H_{i,j} = 0, \\forall i \\ge j+1$).\n\
+@end tex\n\
+@ifnottex\n\
+@code{@var{P} * @var{H} * @var{P}' = @var{A}} where @var{P} is a square\n\
+unitary matrix (@code{@var{P}' * @var{P} = I}, using complex-conjugate\n\
+transposition) and @var{H} is upper Hessenberg\n\
+(@code{@var{H}(i, j) = 0 forall i >= j+1)}.\n\
+@end ifnottex\n\
+\n\
+The Hessenberg decomposition is usually used as the first step in an\n\
+eigenvalue computation, but has other applications as well (see Golub,\n\
+Nash, and Van Loan, IEEE Transactions on Automatic Control, 1979).\n\
+@end deftypefn")
+{
+  octave_value_list retval;
+
+  int nargin = args.length ();
+
+  if (nargin != 1 || nargout > 2)
+    {
+      print_usage ();
+      return retval;
+    }
+
+  octave_value arg = args(0);
+
+  octave_idx_type nr = arg.rows ();
+  octave_idx_type nc = arg.columns ();
+
+  int arg_is_empty = empty_arg ("hess", nr, nc);
+
+  if (arg_is_empty < 0)
+    return retval;
+  else if (arg_is_empty > 0)
+    return octave_value_list (2, Matrix ());
+
+  if (nr != nc)
+    {
+      gripe_square_matrix_required ("hess");
+      return retval;
+    }
+
+  if (arg.is_single_type ())
+    {
+      if (arg.is_real_type ())
+        {
+         FloatMatrix tmp = arg.float_matrix_value ();
+
+          if (! error_state)
+            {
+              FloatHESS result (tmp);
+
+              if (nargout <= 1)
+                retval(0) = result.hess_matrix ();
+              else
+                {
+                  retval(1) = result.hess_matrix ();
+                  retval(0) = result.unitary_hess_matrix ();
+                }
+            }
+        }
+      else if (arg.is_complex_type ())
+        {
+          FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
+
+          if (! error_state)
+            {
+              FloatComplexHESS result (ctmp);
+
+              if (nargout <= 1)
+                retval(0) = result.hess_matrix ();
+              else
+                {
+                  retval(1) = result.hess_matrix ();
+                  retval(0) = result.unitary_hess_matrix ();
+                }
+            }
+        }
+    }
+  else
+    {
+      if (arg.is_real_type ())
+        {
+          Matrix tmp = arg.matrix_value ();
+
+          if (! error_state)
+            {
+              HESS result (tmp);
+
+              if (nargout <= 1)
+                retval(0) = result.hess_matrix ();
+              else
+                {
+                  retval(1) = result.hess_matrix ();
+                  retval(0) = result.unitary_hess_matrix ();
+                }
+            }
+        }
+      else if (arg.is_complex_type ())
+        {
+          ComplexMatrix ctmp = arg.complex_matrix_value ();
+
+          if (! error_state)
+            {
+              ComplexHESS result (ctmp);
+
+              if (nargout <= 1)
+                retval(0) = result.hess_matrix ();
+              else
+                {
+                  retval(1) = result.hess_matrix ();
+                  retval(0) = result.unitary_hess_matrix ();
+                }
+            }
+        }
+      else
+        {
+          gripe_wrong_type_arg ("hess", arg);
+        }
+    }
+
+  return retval;
+}
+
+/*
+%!test
+%! a = [1, 2, 3; 5, 4, 6; 8, 7, 9];
+%! [p, h] = hess (a);
+%! assert (p * h * p', a, sqrt (eps));
+
+%!test
+%! a = single ([1, 2, 3; 5, 4, 6; 8, 7, 9]);
+%! [p, h] = hess (a);
+%! assert (p * h * p', a, sqrt (eps ("single")));
+
+%!error hess ()
+%!error hess ([1, 2; 3, 4], 2)
+%!error <argument must be a square matrix> hess ([1, 2; 3, 4; 5, 6])
+*/