/*

Copyright (C) 1996-2015 John W. Eaton
Copyright (C) 2008-2009 Jaroslav Hajek

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: A. S. Hodel <scotte@eng.auburn.edu>

#ifdef HAVE_CONFIG_H
#include <config.h>
#endif

#include <string>

#include "CmplxAEPBAL.h"
#include "fCmplxAEPBAL.h"
#include "dbleAEPBAL.h"
#include "floatAEPBAL.h"
#include "CmplxGEPBAL.h"
#include "fCmplxGEPBAL.h"
#include "dbleGEPBAL.h"
#include "floatGEPBAL.h"
#include "quit.h"

#include "defun.h"
#include "error.h"
#include "f77-fcn.h"
#include "errwarn.h"
#include "ovl.h"
#include "utils.h"

DEFUN (balance, args, nargout,
       "-*- texinfo -*-\n\
@deftypefn  {} {@var{AA} =} balance (@var{A})\n\
@deftypefnx {} {@var{AA} =} balance (@var{A}, @var{opt})\n\
@deftypefnx {} {[@var{DD}, @var{AA}] =} balance (@var{A}, @var{opt})\n\
@deftypefnx {} {[@var{D}, @var{P}, @var{AA}] =} balance (@var{A}, @var{opt})\n\
@deftypefnx {} {[@var{CC}, @var{DD}, @var{AA}, @var{BB}] =} balance (@var{A}, @var{B}, @var{opt})\n\
\n\
Balance the matrix @var{A} to reduce numerical errors in future\n\
calculations.\n\
\n\
Compute @code{@var{AA} = @var{DD} \\ @var{A} * @var{DD}} in which @var{AA}\n\
is a matrix whose row and column norms are roughly equal in magnitude, and\n\
@code{@var{DD} = @var{P} * @var{D}}, in which @var{P} is a permutation\n\
matrix and @var{D} is a diagonal matrix of powers of two.  This allows the\n\
equilibration to be computed without round-off.  Results of eigenvalue\n\
calculation are typically improved by balancing first.\n\
\n\
If two output values are requested, @code{balance} returns\n\
the diagonal @var{D} and the permutation @var{P} separately as vectors.\n\
In this case, @code{@var{DD} = eye(n)(:,@var{P}) * diag (@var{D})}, where\n\
@math{n} is the matrix size.\n\
\n\
If four output values are requested, compute @code{@var{AA} =\n\
@var{CC}*@var{A}*@var{DD}} and @code{@var{BB} = @var{CC}*@var{B}*@var{DD}},\n\
in which @var{AA} and @var{BB} have nonzero elements of approximately the\n\
same magnitude and @var{CC} and @var{DD} are permuted diagonal matrices as\n\
in @var{DD} for the algebraic eigenvalue problem.\n\
\n\
The eigenvalue balancing option @var{opt} may be one of:\n\
\n\
@table @asis\n\
@item @qcode{\"noperm\"}, @qcode{\"S\"}\n\
Scale only; do not permute.\n\
\n\
@item @qcode{\"noscal\"}, @qcode{\"P\"}\n\
Permute only; do not scale.\n\
@end table\n\
\n\
Algebraic eigenvalue balancing uses standard @sc{lapack} routines.\n\
\n\
Generalized eigenvalue problem balancing uses Ward's algorithm\n\
(SIAM Journal on Scientific and Statistical Computing, 1981).\n\
@end deftypefn")
{
  int nargin = args.length ();

  if (nargin < 1 || nargin > 3 || nargout < 0)
    print_usage ();

  octave_value_list retval;

  // determine if it's AEP or GEP
  bool AEPcase = nargin == 1 || args(1).is_string ();

  // problem dimension
  octave_idx_type nn = args(0).rows ();

  if (nn != args(0).columns ())
    err_square_matrix_required ("balance");

  bool isfloat = args(0).is_single_type ()
                 || (! AEPcase && args(1).is_single_type ());

  bool complex_case = args(0).is_complex_type ()
                      || (! AEPcase && args(1).is_complex_type ());

  // Extract argument 1 parameter for both AEP and GEP.
  Matrix aa;
  ComplexMatrix caa;
  FloatMatrix faa;
  FloatComplexMatrix fcaa;

  if (isfloat)
    {
      if (complex_case)
        fcaa = args(0).float_complex_matrix_value ();
      else
        faa = args(0).float_matrix_value ();
    }
  else
    {
      if (complex_case)
        caa = args(0).complex_matrix_value ();
      else
        aa = args(0).matrix_value ();
    }

  // Treat AEP/GEP cases.
  if (AEPcase)
    {
      // Algebraic eigenvalue problem.
      bool noperm = false;
      bool noscal = false;
      if (nargin > 1)
        {
          std::string a1s = args(1).string_value ();
          noperm = a1s == "noperm" || a1s == "S";
          noscal = a1s == "noscal" || a1s == "P";
        }

      // balance the AEP
      if (isfloat)
        {
          if (complex_case)
            {
              FloatComplexAEPBALANCE result (fcaa, noperm, noscal);

              if (nargout == 0 || nargout == 1)
                retval = ovl (result.balanced_matrix ());
              else if (nargout == 2)
                retval = ovl (result.balancing_matrix (),
                              result.balanced_matrix ());
              else
                retval = ovl (result.scaling_vector (),
                              result.permuting_vector (),
                              result.balanced_matrix ());
            }
          else
            {
              FloatAEPBALANCE result (faa, noperm, noscal);

              if (nargout == 0 || nargout == 1)
                retval = ovl (result.balanced_matrix ());
              else if (nargout == 2)
                retval = ovl (result.balancing_matrix (),
                              result.balanced_matrix ());
              else
                retval = ovl (result.scaling_vector (),
                              result.permuting_vector (),
                              result.balanced_matrix ());
            }
        }
      else
        {
          if (complex_case)
            {
              ComplexAEPBALANCE result (caa, noperm, noscal);

              if (nargout == 0 || nargout == 1)
                retval = ovl (result.balanced_matrix ());
              else if (nargout == 2)
                retval = ovl (result.balancing_matrix (),
                              result.balanced_matrix ());
              else
                retval = ovl (result.scaling_vector (),
                              result.permuting_vector (),
                              result.balanced_matrix ());
            }
          else
            {
              AEPBALANCE result (aa, noperm, noscal);

              if (nargout == 0 || nargout == 1)
                retval = ovl (result.balanced_matrix ());
              else if (nargout == 2)
                retval = ovl (result.balancing_matrix (),
                              result.balanced_matrix ());
              else
                retval = ovl (result.scaling_vector (),
                              result.permuting_vector (),
                              result.balanced_matrix ());
            }
        }
    }
  else
    {
      std::string bal_job;
      if (nargout == 1)
        warning ("balance: used GEP, should have two output arguments");

      // Generalized eigenvalue problem.
      if (nargin == 2)
        bal_job = "B";
      else
        bal_job = args(2).xstring_value ("balance: OPT argument must be a string");

      if ((nn != args(1).columns ()) || (nn != args(1).rows ()))
        err_nonconformant ();

      Matrix bb;
      ComplexMatrix cbb;
      FloatMatrix fbb;
      FloatComplexMatrix fcbb;

      if (isfloat)
        {
          if (complex_case)
            fcbb = args(1).float_complex_matrix_value ();
          else
            fbb = args(1).float_matrix_value ();
        }
      else
        {
          if (complex_case)
            cbb = args(1).complex_matrix_value ();
          else
            bb = args(1).matrix_value ();
        }

      // balance the GEP
      if (isfloat)
        {
          if (complex_case)
            {
              FloatComplexGEPBALANCE result (fcaa, fcbb, bal_job);

              switch (nargout)
                {
                case 4:
                  retval(3) = result.balanced_matrix2 ();
                  // fall through
                case 3:
                  retval(2) = result.balanced_matrix ();
                  retval(1) = result.balancing_matrix2 ();
                  retval(0) = result.balancing_matrix ();
                  break;
                case 2:
                  retval(1) = result.balancing_matrix2 ();
                  // fall through
                case 1:
                  retval(0) = result.balancing_matrix ();
                  break;
                default:
                  error ("balance: invalid number of output arguments");
                  break;
                }
            }
          else
            {
              FloatGEPBALANCE result (faa, fbb, bal_job);

              switch (nargout)
                {
                case 4:
                  retval(3) = result.balanced_matrix2 ();
                  // fall through
                case 3:
                  retval(2) = result.balanced_matrix ();
                  retval(1) = result.balancing_matrix2 ();
                  retval(0) = result.balancing_matrix ();
                  break;
                case 2:
                  retval(1) = result.balancing_matrix2 ();
                  // fall through
                case 1:
                  retval(0) = result.balancing_matrix ();
                  break;
                default:
                  error ("balance: invalid number of output arguments");
                  break;
                }
            }
        }
      else
        {
          if (complex_case)
            {
              ComplexGEPBALANCE result (caa, cbb, bal_job);

              switch (nargout)
                {
                case 4:
                  retval(3) = result.balanced_matrix2 ();
                  // fall through
                case 3:
                  retval(2) = result.balanced_matrix ();
                  retval(1) = result.balancing_matrix2 ();
                  retval(0) = result.balancing_matrix ();
                  break;
                case 2:
                  retval(1) = result.balancing_matrix2 ();
                  // fall through
                case 1:
                  retval(0) = result.balancing_matrix ();
                  break;
                default:
                  error ("balance: invalid number of output arguments");
                  break;
                }
            }
          else
            {
              GEPBALANCE result (aa, bb, bal_job);

              switch (nargout)
                {
                case 4:
                  retval(3) = result.balanced_matrix2 ();
                  // fall through
                case 3:
                  retval(2) = result.balanced_matrix ();
                  retval(1) = result.balancing_matrix2 ();
                  retval(0) = result.balancing_matrix ();
                  break;
                case 2:
                  retval(1) = result.balancing_matrix2 ();
                  // fall through
                case 1:
                  retval(0) = result.balancing_matrix ();
                  break;
                default:
                  error ("balance: invalid number of output arguments");
                  break;
                }
            }
        }
    }

  return retval;
}