/*

Copyright (C) 2005-2013 David Bateman

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 "defun.h"
#include "error.h"
#include "gripes.h"
#include "oct-obj.h"
#include "utils.h"
#include "oct-map.h"

#include "MatrixType.h"
#include "SparseCmplxLU.h"
#include "SparsedbleLU.h"
#include "ov-re-sparse.h"
#include "ov-cx-sparse.h"

DEFUN (luinc, args, nargout,
       "-*- texinfo -*-\n\
@deftypefn  {Built-in Function} {[@var{L}, @var{U}, @var{P}, @var{Q}] =} luinc (@var{A}, '0')\n\
@deftypefnx {Built-in Function} {[@var{L}, @var{U}, @var{P}, @var{Q}] =} luinc (@var{A}, @var{droptol})\n\
@deftypefnx {Built-in Function} {[@var{L}, @var{U}, @var{P}, @var{Q}] =} luinc (@var{A}, @var{opts})\n\
@cindex LU decomposition\n\
Produce the incomplete LU@tie{}factorization of the sparse matrix @var{A}.\n\
Two types of incomplete factorization are possible, and the type\n\
is determined by the second argument to @code{luinc}.\n\
\n\
Called with a second argument of @qcode{'0'}, the zero-level incomplete\n\
LU@tie{}factorization is produced.  This creates a factorization of @var{A}\n\
where the position of the nonzero arguments correspond to the same\n\
positions as in the matrix @var{A}.\n\
\n\
Alternatively, the fill-in of the incomplete LU@tie{}factorization can\n\
be controlled through the variable @var{droptol} or the structure\n\
@var{opts}.  The @sc{umfpack} multifrontal factorization code by Tim A.\n\
Davis is used for the incomplete LU@tie{}factorization, (availability\n\
@url{http://www.cise.ufl.edu/research/sparse/umfpack/})\n\
\n\
@var{droptol} determines the values below which the values in the\n\
LU@tie{} factorization are dropped and replaced by zero.  It must be a\n\
positive scalar, and any values in the factorization whose absolute value\n\
are less than this value are dropped, expect if leaving them increase the\n\
sparsity of the matrix.  Setting @var{droptol} to zero results in a complete\n\
LU@tie{}factorization which is the default.\n\
\n\
@var{opts} is a structure containing one or more of the fields\n\
\n\
@table @code\n\
@item droptol\n\
The drop tolerance as above.  If @var{opts} only contains @code{droptol}\n\
then this is equivalent to using the variable @var{droptol}.\n\
\n\
@item milu\n\
A logical variable flagging whether to use the modified incomplete\n\
LU@tie{} factorization.  In the case that @code{milu} is true, the dropped\n\
values are subtracted from the diagonal of the matrix @var{U} of the\n\
factorization.  The default is @code{false}.\n\
\n\
@item udiag\n\
A logical variable that flags whether zero elements on the diagonal of\n\
@var{U} should be replaced with @var{droptol} to attempt to avoid singular\n\
factors.  The default is @code{false}.\n\
\n\
@item thresh\n\
Defines the pivot threshold in the interval [0,1].  Values outside that\n\
range are ignored.\n\
@end table\n\
\n\
All other fields in @var{opts} are ignored.  The outputs from @code{luinc}\n\
are the same as for @code{lu}.\n\
\n\
Given the string argument @qcode{\"vector\"}, @code{luinc} returns the\n\
values of @var{p} @var{q} as vector values.\n\
@seealso{sparse, lu}\n\
@end deftypefn")
{
  int nargin = args.length ();
  octave_value_list retval;

  if (nargin == 0)
    print_usage ();
  else if (nargin < 2 || nargin > 3)
    error ("luinc: incorrect number of arguments");
  else
    {
      bool zero_level = false;
      bool milu = false;
      bool udiag = false;
      Matrix thresh;
      double droptol = -1.;
      bool vecout = false;

      if (args(1).is_string ())
        {
          if (args(1).string_value () == "0")
            zero_level = true;
          else
            error ("luinc: unrecognized string argument");
        }
      else if (args(1).is_map ())
        {
          octave_scalar_map map = args(1).scalar_map_value ();

          if (! error_state)
            {
              octave_value tmp;

              tmp = map.getfield ("droptol");
              if (tmp.is_defined ())
                droptol = tmp.double_value ();

              tmp = map.getfield ("milu");
              if (tmp.is_defined ())
                {
                  double val = tmp.double_value ();

                  milu = (val == 0. ? false : true);
                }

              tmp = map.getfield ("udiag");
              if (tmp.is_defined ())
                {
                  double val = tmp.double_value ();

                  udiag = (val == 0. ? false : true);
                }

              tmp = map.getfield ("thresh");
              if (tmp.is_defined ())
                {
                  thresh = tmp.matrix_value ();

                  if (thresh.nelem () == 1)
                    {
                      thresh.resize (1,2);
                      thresh(1) = thresh(0);
                    }
                  else if (thresh.nelem () != 2)
                    {
                      error ("luinc: expecting 2-element vector for thresh");
                      return retval;
                    }
                }
            }
          else
            {
              error ("luinc: OPTS must be a scalar structure");
              return retval;
            }
        }
      else
        droptol = args(1).double_value ();

      if (nargin == 3)
        {
          std::string tmp = args(2).string_value ();

          if (! error_state)
            {
              if (tmp.compare ("vector") == 0)
                vecout = true;
              else
                error ("luinc: unrecognized string argument");
            }
        }

      // FIXME: Add code for zero-level factorization
      if (zero_level)
        error ("luinc: zero-level factorization not implemented");

      if (!error_state)
        {
          if (args(0).type_name () == "sparse matrix")
            {
              SparseMatrix sm = args(0).sparse_matrix_value ();
              octave_idx_type sm_nr = sm.rows ();
              octave_idx_type sm_nc = sm.cols ();
              ColumnVector Qinit (sm_nc);

              for (octave_idx_type i = 0; i < sm_nc; i++)
                Qinit (i) = i;

              if (! error_state)
                {
                  switch (nargout)
                    {
                    case 0:
                    case 1:
                    case 2:
                      {
                        SparseLU fact (sm, Qinit, thresh, false, true, droptol,
                                       milu, udiag);

                        if (! error_state)
                          {
                            SparseMatrix P = fact.Pr ();
                            SparseMatrix L = P.transpose () * fact.L ();
                            retval(1)
                              = octave_value (fact.U (),
                                              MatrixType (MatrixType::Upper));
                            retval(0)
                              = octave_value (L, MatrixType
                                                   (MatrixType::Permuted_Lower,
                                                    sm_nr, fact.row_perm ()));
                          }
                      }
                      break;

                    case 3:
                      {
                        SparseLU fact (sm, Qinit, thresh, false, true, droptol,
                                       milu, udiag);

                        if (! error_state)
                          {
                            if (vecout)
                              retval(2) = fact.Pr_vec ();
                            else
                              retval(2) = fact.Pr_mat ();
                            retval(1)
                              = octave_value (fact.U (),
                                              MatrixType (MatrixType::Upper));
                            retval(0)
                              = octave_value (fact.L (),
                                              MatrixType (MatrixType::Lower));
                          }
                      }
                      break;

                    case 4:
                    default:
                      {
                        SparseLU fact (sm, Qinit, thresh, false, false, droptol,
                                       milu, udiag);

                        if (! error_state)
                          {
                            if (vecout)
                              {
                                retval(3) = fact.Pc_vec ();
                                retval(2) = fact.Pr_vec ();
                              }
                            else
                              {
                                retval(3) = fact.Pc_mat ();
                                retval(2) = fact.Pr_mat ();
                              }
                            retval(1)
                              = octave_value (fact.U (),
                                              MatrixType (MatrixType::Upper));
                            retval(0)
                              = octave_value (fact.L (),
                                              MatrixType (MatrixType::Lower));
                          }
                      }
                      break;
                    }
                }
            }
          else if (args(0).type_name () == "sparse complex matrix")
            {
              SparseComplexMatrix sm =
                args(0).sparse_complex_matrix_value ();
              octave_idx_type sm_nr = sm.rows ();
              octave_idx_type sm_nc = sm.cols ();
              ColumnVector Qinit (sm_nc);

              for (octave_idx_type i = 0; i < sm_nc; i++)
                Qinit (i) = i;

              if (! error_state)
                {
                  switch (nargout)
                    {
                    case 0:
                    case 1:
                    case 2:
                      {
                        SparseComplexLU fact (sm, Qinit, thresh, false, true,
                                              droptol, milu, udiag);


                        if (! error_state)
                          {
                            SparseMatrix P = fact.Pr ();
                            SparseComplexMatrix L = P.transpose () * fact.L ();
                            retval(1)
                              = octave_value (fact.U (),
                                              MatrixType (MatrixType::Upper));
                            retval(0)
                              = octave_value (L, MatrixType
                                                  (MatrixType::Permuted_Lower,
                                                   sm_nr, fact.row_perm ()));
                          }
                      }
                      break;

                    case 3:
                      {
                        SparseComplexLU fact (sm, Qinit, thresh, false, true,
                                              droptol, milu, udiag);

                        if (! error_state)
                          {
                            if (vecout)
                              retval(2) = fact.Pr_vec ();
                            else
                              retval(2) = fact.Pr_mat ();
                            retval(1)
                              = octave_value (fact.U (),
                                              MatrixType (MatrixType::Upper));
                            retval(0)
                              = octave_value (fact.L (),
                                              MatrixType (MatrixType::Lower));
                          }
                      }
                      break;

                    case 4:
                    default:
                      {
                        SparseComplexLU fact (sm, Qinit, thresh, false, false,
                                              droptol, milu, udiag);

                        if (! error_state)
                          {
                            if (vecout)
                              {
                                retval(3) = fact.Pc_vec ();
                                retval(2) = fact.Pr_vec ();
                              }
                            else
                              {
                                retval(3) = fact.Pc_mat ();
                                retval(2) = fact.Pr_mat ();
                              }
                            retval(1)
                              = octave_value (fact.U (),
                                              MatrixType (MatrixType::Upper));
                            retval(0)
                              = octave_value (fact.L (),
                                              MatrixType (MatrixType::Lower));
                          }
                      }
                      break;
                    }
                }
            }
          else
            error ("luinc: matrix A must be sparse");
        }
    }

  return retval;
}

/*
%!testif HAVE_UMFPACK
%! a = sparse ([1,2,0,0;0,1,2,0;1e-14,0,3,0;0,0,0,1]);
%! [l,u] = luinc (a, 1e-10);
%! assert (l*u, sparse ([1,2,0,0;0,1,2,0;0,0,3,0;0,0,0,1]), 1e-10);
%! opts.droptol = 1e-10;
%! [l,u] = luinc (a, opts);
%! assert (l*u, sparse ([1,2,0,0;0,1,2,0;0,0,3,0;0,0,0,1]), 1e-10);

%!testif HAVE_UMFPACK
%! a = sparse ([1i,2,0,0;0,1,2,0;1e-14,0,3,0;0,0,0,1]);
%! [l,u] = luinc (a, 1e-10);
%! assert (l*u, sparse ([1i,2,0,0;0,1,2,0;0,0,3,0;0,0,0,1]), 1e-10);
%! opts.droptol = 1e-10;
%! [l,u] = luinc (a, opts);
%! assert (l*u, sparse ([1i,2,0,0;0,1,2,0;0,0,3,0;0,0,0,1]), 1e-10);
*/