/*

Copyright (C) 2005-2015 David Bateman
Copyright (C) 1998-2005 Andy Adler

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 "SparseCmplxCHOL.h"
#include "SparsedbleCHOL.h"
#include "oct-spparms.h"
#include "sparse-util.h"
#include "oct-locbuf.h"

#include "ov-re-sparse.h"
#include "ov-cx-sparse.h"
#include "defun-dld.h"
#include "error.h"
#include "errwarn.h"
#include "ovl.h"
#include "utils.h"

DEFUN_DLD (symbfact, args, nargout,
           "-*- texinfo -*-\n\
@deftypefn  {} {[@var{count}, @var{h}, @var{parent}, @var{post}, @var{r}] =} symbfact (@var{S})\n\
@deftypefnx {} {[@dots{}] =} symbfact (@var{S}, @var{typ})\n\
@deftypefnx {} {[@dots{}] =} symbfact (@var{S}, @var{typ}, @var{mode})\n\
\n\
Perform a symbolic factorization analysis on the sparse matrix @var{S}.\n\
\n\
The input variables are\n\
\n\
@table @var\n\
@item S\n\
@var{S} is a complex or real sparse matrix.\n\
\n\
@item typ\n\
Is the type of the factorization and can be one of\n\
\n\
@table @samp\n\
@item sym\n\
Factorize @var{S}.  This is the default.\n\
\n\
@item col\n\
Factorize @code{@var{S}' * @var{S}}.\n\
\n\
@item row\n\
Factorize @tcode{@var{S} * @var{S}'}.\n\
\n\
@item lo\n\
Factorize @tcode{@var{S}'}\n\
@end table\n\
\n\
@item mode\n\
The default is to return the Cholesky@tie{}factorization for @var{r}, and if\n\
@var{mode} is @qcode{'L'}, the conjugate transpose of the\n\
Cholesky@tie{}factorization is returned.  The conjugate transpose version is\n\
faster and uses less memory, but returns the same values for @var{count},\n\
@var{h}, @var{parent} and @var{post} outputs.\n\
@end table\n\
\n\
The output variables are\n\
\n\
@table @var\n\
@item count\n\
The row counts of the Cholesky@tie{}factorization as determined by @var{typ}.\n\
\n\
@item h\n\
The height of the elimination tree.\n\
\n\
@item parent\n\
The elimination tree itself.\n\
\n\
@item post\n\
A sparse boolean matrix whose structure is that of the Cholesky\n\
factorization as determined by @var{typ}.\n\
@end table\n\
@end deftypefn")
{
#ifdef HAVE_CHOLMOD

  int nargin = args.length ();

  if (nargin < 1 || nargin > 3 || nargout > 5)
    print_usage ();

  octave_value_list retval;

  cholmod_common Common;
  cholmod_common *cm = &Common;
  CHOLMOD_NAME(start) (cm);

  double spu = octave_sparse_params::get_key ("spumoni");
  if (spu == 0.)
    {
      cm->print = -1;
      SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, 0);
    }
  else
    {
      cm->print = static_cast<int> (spu) + 2;
      SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, &SparseCholPrint);
    }

  cm->error_handler = &SparseCholError;
  SUITESPARSE_ASSIGN_FPTR2 (divcomplex_func, cm->complex_divide, divcomplex);
  SUITESPARSE_ASSIGN_FPTR2 (hypot_func, cm->hypotenuse, hypot);

  double dummy;
  cholmod_sparse Astore;
  cholmod_sparse *A = &Astore;
  A->packed = true;
  A->sorted = true;
  A->nz = 0;
#ifdef USE_64_BIT_IDX_T
  A->itype = CHOLMOD_LONG;
#else
  A->itype = CHOLMOD_INT;
#endif
  A->dtype = CHOLMOD_DOUBLE;
  A->stype = 1;
  A->x = &dummy;

  if (args(0).is_real_type ())
    {
      const SparseMatrix a = args(0).sparse_matrix_value ();
      A->nrow = a.rows ();
      A->ncol = a.cols ();
      A->p = a.cidx ();
      A->i = a.ridx ();
      A->nzmax = a.nnz ();
      A->xtype = CHOLMOD_REAL;

      if (a.rows () > 0 && a.cols () > 0)
        A->x = a.data ();
    }
  else if (args(0).is_complex_type ())
    {
      const SparseComplexMatrix a = args(0).sparse_complex_matrix_value ();
      A->nrow = a.rows ();
      A->ncol = a.cols ();
      A->p = a.cidx ();
      A->i = a.ridx ();
      A->nzmax = a.nnz ();
      A->xtype = CHOLMOD_COMPLEX;

      if (a.rows () > 0 && a.cols () > 0)
        A->x = a.data ();
    }
  else
    err_wrong_type_arg ("symbfact", args(0));

  octave_idx_type coletree = false;
  octave_idx_type n = A->nrow;

  if (nargin > 1)
    {
      char ch;
      std::string str = args(1).string_value ();
      ch = tolower (str.c_str ()[0]);
      if (ch == 'r')
        A->stype = 0;
      else if (ch == 'c')
        {
          n = A->ncol;
          coletree = true;
          A->stype = 0;
        }
      else if (ch == 's')
        A->stype = 1;
      else if (ch == 's')
        A->stype = -1;
      else
        error ("symbfact: unrecognized TYP in symbolic factorization");
    }

  if (A->stype && A->nrow != A->ncol)
    error ("symbfact: S must be a square matrix");

  OCTAVE_LOCAL_BUFFER (octave_idx_type, Parent, n);
  OCTAVE_LOCAL_BUFFER (octave_idx_type, Post, n);
  OCTAVE_LOCAL_BUFFER (octave_idx_type, ColCount, n);
  OCTAVE_LOCAL_BUFFER (octave_idx_type, First, n);
  OCTAVE_LOCAL_BUFFER (octave_idx_type, Level, n);

  cholmod_sparse *F = CHOLMOD_NAME(transpose) (A, 0, cm);
  cholmod_sparse *Aup, *Alo;

  if (A->stype == 1 || coletree)
    {
      Aup = A ;
      Alo = F ;
    }
  else
    {
      Aup = F ;
      Alo = A ;
    }

  CHOLMOD_NAME(etree) (Aup, Parent, cm);

  if (cm->status < CHOLMOD_OK)
    error ("symbfact: matrix corrupted");

  if (CHOLMOD_NAME(postorder) (Parent, n, 0, Post, cm) != n)
    error ("symbfact: postorder failed");

  CHOLMOD_NAME(rowcolcounts) (Alo, 0, 0, Parent, Post, 0,
                              ColCount, First, Level, cm);

  if (cm->status < CHOLMOD_OK)
    error ("symbfact: matrix corrupted");

  if (nargout > 4)
    {
      cholmod_sparse *A1, *A2;

      if (A->stype == 1)
        {
          A1 = A;
          A2 = 0;
        }
      else if (A->stype == -1)
        {
          A1 = F;
          A2 = 0;
        }
      else if (coletree)
        {
          A1 = F;
          A2 = A;
        }
      else
        {
          A1 = A;
          A2 = F;
        }

      // count the total number of entries in L
      octave_idx_type lnz = 0 ;
      for (octave_idx_type j = 0 ; j < n ; j++)
        lnz += ColCount[j];


      // allocate the output matrix L (pattern-only)
      SparseBoolMatrix L (n, n, lnz);

      // initialize column pointers
      lnz = 0;
      for (octave_idx_type j = 0 ; j < n ; j++)
        {
          L.xcidx(j) = lnz;
          lnz += ColCount[j];
        }
      L.xcidx(n) = lnz;


      // create a copy of the column pointers
      octave_idx_type *W = First;
      for (octave_idx_type j = 0 ; j < n ; j++)
        W[j] = L.xcidx (j);

      // get workspace for computing one row of L
      cholmod_sparse *R
        = CHOLMOD_NAME (allocate_sparse) (n, 1, n, false, true,
                                          0, CHOLMOD_PATTERN, cm);
      octave_idx_type *Rp = static_cast<octave_idx_type *>(R->p);
      octave_idx_type *Ri = static_cast<octave_idx_type *>(R->i);

      // compute L one row at a time
      for (octave_idx_type k = 0 ; k < n ; k++)
        {
          // get the kth row of L and store in the columns of L
          CHOLMOD_NAME (row_subtree) (A1, A2, k, Parent, R, cm) ;
          for (octave_idx_type p = 0 ; p < Rp[1] ; p++)
            L.xridx (W[Ri[p]]++) = k ;

          // add the diagonal entry
          L.xridx (W[k]++) = k ;
        }

      // free workspace
      CHOLMOD_NAME (free_sparse) (&R, cm) ;


      // transpose L to get R, or leave as is
      if (nargin < 3)
        L = L.transpose ();

      // fill numerical values of L with one's
      for (octave_idx_type p = 0 ; p < lnz ; p++)
        L.xdata(p) = true;

      retval(4) = L;
    }

  ColumnVector tmp (n);
  if (nargout > 3)
    {
      for (octave_idx_type i = 0; i < n; i++)
        tmp(i) = Post[i] + 1;
      retval(3) = tmp;
    }

  if (nargout > 2)
    {
      for (octave_idx_type i = 0; i < n; i++)
        tmp(i) = Parent[i] + 1;
      retval(2) = tmp;
    }

  if (nargout > 1)
    {
      // compute the elimination tree height
      octave_idx_type height = 0 ;
      for (int i = 0 ; i < n ; i++)
        height = (height > Level[i] ? height : Level[i]);
      height++ ;
      retval(1) = static_cast<double> (height);
    }

  for (octave_idx_type i = 0; i < n; i++)
    tmp(i) = ColCount[i];
  retval(0) = tmp;

  return retval;

#else
  error ("symbfact: not available in this version of Octave");
#endif
}