Eigen/src/SparseLU/SparseLU_column_dfs.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

/*

 * NOTE: This file is the modified version of [s,d,c,z]column_dfs.c file in SuperLU

 * -- SuperLU routine (version 2.0) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * November 15, 1997
 *
 * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.
 *
 * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
 * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.
 *
 * Permission is hereby granted to use or copy this program for any
 * purpose, provided the above notices are retained on all copies.
 * Permission to modify the code and to distribute modified code is
 * granted, provided the above notices are retained, and a notice that
 * the code was modified is included with the above copyright notice.
 */
#ifndef SPARSELU_COLUMN_DFS_H
#define SPARSELU_COLUMN_DFS_H

template <typename Scalar, typename StorageIndex>
class SparseLUImpl;
// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

template <typename IndexVector, typename ScalarVector>
struct column_dfs_traits : no_assignment_operator {
  typedef typename ScalarVector::Scalar Scalar;
  typedef typename IndexVector::Scalar StorageIndex;
  column_dfs_traits(Index jcol, Index& jsuper, typename SparseLUImpl<Scalar, StorageIndex>::GlobalLU_t& glu,
                    SparseLUImpl<Scalar, StorageIndex>& luImpl)
      : m_jcol(jcol), m_jsuper_ref(jsuper), m_glu(glu), m_luImpl(luImpl) {}
  bool update_segrep(Index /*krep*/, Index /*jj*/) { return true; }
  void mem_expand(IndexVector& lsub, Index& nextl, Index chmark) {
    if (nextl >= m_glu.nzlmax) m_luImpl.memXpand(lsub, m_glu.nzlmax, nextl, LSUB, m_glu.num_expansions);
    if (chmark != (m_jcol - 1)) m_jsuper_ref = emptyIdxLU;
  }
  enum { ExpandMem = true };

  Index m_jcol;
  Index& m_jsuper_ref;
  typename SparseLUImpl<Scalar, StorageIndex>::GlobalLU_t& m_glu;
  SparseLUImpl<Scalar, StorageIndex>& m_luImpl;
};

/**
 * \brief Performs a symbolic factorization on column jcol and decide the supernode boundary
 *
 * A supernode representative is the last column of a supernode.
 * The nonzeros in U[*,j] are segments that end at supernodes representatives.
 * The routine returns a list of the supernodal representatives
 * in topological order of the dfs that generates them.
 * The location of the first nonzero in each supernodal segment
 * (supernodal entry location) is also returned.
 *
 * \param m number of rows in the matrix
 * \param jcol Current column
 * \param perm_r Row permutation
 * \param maxsuper  Maximum number of column allowed in a supernode
 * \param [in,out] nseg Number of segments in current U[*,j] - new segments appended
 * \param lsub_col defines the rhs vector to start the dfs
 * \param [in,out] segrep Segment representatives - new segments appended
 * \param repfnz  First nonzero location in each row
 * \param xprune
 * \param marker  marker[i] == jj, if i was visited during dfs of current column jj;
 * \param parent
 * \param xplore working array
 * \param glu global LU data
 * \return 0 success
 *         > 0 number of bytes allocated when run out of space
 *
 */
template <typename Scalar, typename StorageIndex>
Index SparseLUImpl<Scalar, StorageIndex>::column_dfs(const Index m, const Index jcol, IndexVector& perm_r,
                                                     Index maxsuper, Index& nseg, BlockIndexVector lsub_col,
                                                     IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune,
                                                     IndexVector& marker, IndexVector& parent, IndexVector& xplore,
                                                     GlobalLU_t& glu) {
  Index jsuper = glu.supno(jcol);
  Index nextl = glu.xlsub(jcol);
  VectorBlock<IndexVector> marker2(marker, 2 * m, m);

  column_dfs_traits<IndexVector, ScalarVector> traits(jcol, jsuper, glu, *this);

  // For each nonzero in A(*,jcol) do dfs
  for (Index k = 0; ((k < m) ? lsub_col[k] != emptyIdxLU : false); k++) {
    Index krow = lsub_col(k);
    lsub_col(k) = emptyIdxLU;
    Index kmark = marker2(krow);

    // krow was visited before, go to the next nonz;
    if (kmark == jcol) continue;

    dfs_kernel(StorageIndex(jcol), perm_r, nseg, glu.lsub, segrep, repfnz, xprune, marker2, parent, xplore, glu, nextl,
               krow, traits);
  }  // for each nonzero ...

  Index fsupc;
  StorageIndex nsuper = glu.supno(jcol);
  StorageIndex jcolp1 = StorageIndex(jcol) + 1;
  Index jcolm1 = jcol - 1;

  // check to see if j belongs in the same supernode as j-1
  if (jcol == 0) {  // Do nothing for column 0
    nsuper = glu.supno(0) = 0;
  } else {
    fsupc = glu.xsup(nsuper);
    StorageIndex jptr = glu.xlsub(jcol);  // Not yet compressed
    StorageIndex jm1ptr = glu.xlsub(jcolm1);

    // Use supernodes of type T2 : see SuperLU paper
    if ((nextl - jptr != jptr - jm1ptr - 1)) jsuper = emptyIdxLU;

    // Make sure the number of columns in a supernode doesn't
    // exceed threshold
    if ((jcol - fsupc) >= maxsuper) jsuper = emptyIdxLU;

    /* If jcol starts a new supernode, reclaim storage space in
     * glu.lsub from previous supernode. Note we only store
     * the subscript set of the first and last columns of
     * a supernode. (first for num values, last for pruning)
     */
    if (jsuper == emptyIdxLU) {    // starts a new supernode
      if ((fsupc < jcolm1 - 1)) {  // >= 3 columns in nsuper
        StorageIndex ito = glu.xlsub(fsupc + 1);
        glu.xlsub(jcolm1) = ito;
        StorageIndex istop = ito + jptr - jm1ptr;
        xprune(jcolm1) = istop;  // initialize xprune(jcol-1)
        glu.xlsub(jcol) = istop;

        for (StorageIndex ifrom = jm1ptr; ifrom < nextl; ++ifrom, ++ito) glu.lsub(ito) = glu.lsub(ifrom);
        nextl = ito;  // = istop + length(jcol)
      }
      nsuper++;
      glu.supno(jcol) = nsuper;
    }  // if a new supernode
  }    // end else:  jcol > 0

  // Tidy up the pointers before exit
  glu.xsup(nsuper + 1) = jcolp1;
  glu.supno(jcolp1) = nsuper;
  xprune(jcol) = StorageIndex(nextl);  // Initialize upper bound for pruning
  glu.xlsub(jcolp1) = StorageIndex(nextl);

  return 0;
}

}  // end namespace internal

}  // end namespace Eigen

#endif