hess.cc

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/*

Copyright (C) 1996-2013 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\
@seealso{eig, chol, lu, qr, qz, schur, svd}\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])
*/