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// 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]panel_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_PANEL_DFS_H
#define SPARSELU_PANEL_DFS_H
namespace Eigen {
namespace internal {
template<typename IndexVector>
struct panel_dfs_traits
{
typedef typename IndexVector::Scalar StorageIndex;
panel_dfs_traits(Index jcol, StorageIndex* marker)
: m_jcol(jcol), m_marker(marker)
{}
bool update_segrep(Index krep, StorageIndex jj)
{
if(m_marker[krep]<m_jcol)
{
m_marker[krep] = jj;
return true;
}
return false;
}
void mem_expand(IndexVector& /*glu.lsub*/, Index /*nextl*/, Index /*chmark*/) {}
enum { ExpandMem = false };
Index m_jcol;
StorageIndex* m_marker;
};
template <typename Scalar, typename StorageIndex>
template <typename Traits>
void SparseLUImpl<Scalar,StorageIndex>::dfs_kernel(const StorageIndex jj, IndexVector& perm_r,
Index& nseg, IndexVector& panel_lsub, IndexVector& segrep,
Ref<IndexVector> repfnz_col, IndexVector& xprune, Ref<IndexVector> marker, IndexVector& parent,
IndexVector& xplore, GlobalLU_t& glu,
Index& nextl_col, Index krow, Traits& traits
)
{
StorageIndex kmark = marker(krow);
// For each unmarked krow of jj
marker(krow) = jj;
StorageIndex kperm = perm_r(krow);
if (kperm == emptyIdxLU ) {
// krow is in L : place it in structure of L(*, jj)
panel_lsub(nextl_col++) = StorageIndex(krow); // krow is indexed into A
traits.mem_expand(panel_lsub, nextl_col, kmark);
}
else
{
// krow is in U : if its supernode-representative krep
// has been explored, update repfnz(*)
// krep = supernode representative of the current row
StorageIndex krep = glu.xsup(glu.supno(kperm)+1) - 1;
// First nonzero element in the current column:
StorageIndex myfnz = repfnz_col(krep);
if (myfnz != emptyIdxLU )
{
// Representative visited before
if (myfnz > kperm ) repfnz_col(krep) = kperm;
}
else
{
// Otherwise, perform dfs starting at krep
StorageIndex oldrep = emptyIdxLU;
parent(krep) = oldrep;
repfnz_col(krep) = kperm;
StorageIndex xdfs = glu.xlsub(krep);
Index maxdfs = xprune(krep);
StorageIndex kpar;
do
{
// For each unmarked kchild of krep
while (xdfs < maxdfs)
{
StorageIndex kchild = glu.lsub(xdfs);
xdfs++;
StorageIndex chmark = marker(kchild);
if (chmark != jj )
{
marker(kchild) = jj;
StorageIndex chperm = perm_r(kchild);
if (chperm == emptyIdxLU)
{
// case kchild is in L: place it in L(*, j)
panel_lsub(nextl_col++) = kchild;
traits.mem_expand(panel_lsub, nextl_col, chmark);
}
else
{
// case kchild is in U :
// chrep = its supernode-rep. If its rep has been explored,
// update its repfnz(*)
StorageIndex chrep = glu.xsup(glu.supno(chperm)+1) - 1;
myfnz = repfnz_col(chrep);
if (myfnz != emptyIdxLU)
{ // Visited before
if (myfnz > chperm)
repfnz_col(chrep) = chperm;
}
else
{ // Cont. dfs at snode-rep of kchild
xplore(krep) = xdfs;
oldrep = krep;
krep = chrep; // Go deeper down G(L)
parent(krep) = oldrep;
repfnz_col(krep) = chperm;
xdfs = glu.xlsub(krep);
maxdfs = xprune(krep);
} // end if myfnz != -1
} // end if chperm == -1
} // end if chmark !=jj
} // end while xdfs < maxdfs
// krow has no more unexplored nbrs :
// Place snode-rep krep in postorder DFS, if this
// segment is seen for the first time. (Note that
// "repfnz(krep)" may change later.)
// Baktrack dfs to its parent
if(traits.update_segrep(krep,jj))
//if (marker1(krep) < jcol )
{
segrep(nseg) = krep;
++nseg;
//marker1(krep) = jj;
}
kpar = parent(krep); // Pop recursion, mimic recursion
if (kpar == emptyIdxLU)
break; // dfs done
krep = kpar;
xdfs = xplore(krep);
maxdfs = xprune(krep);
} while (kpar != emptyIdxLU); // Do until empty stack
} // end if (myfnz = -1)
} // end if (kperm == -1)
}
/**
* \brief Performs a symbolic factorization on a panel of columns [jcol, jcol+w)
*
* 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. This list is
* a superset of the topological order of each individual column within
* the panel.
* The location of the first nonzero in each supernodal segment
* (supernodal entry location) is also returned. Each column has
* a separate list for this purpose.
*
* Two markers arrays are used for dfs :
* marker[i] == jj, if i was visited during dfs of current column jj;
* marker1[i] >= jcol, if i was visited by earlier columns in this panel;
*
* \param[in] m number of rows in the matrix
* \param[in] w Panel size
* \param[in] jcol Starting column of the panel
* \param[in] A Input matrix in column-major storage
* \param[in] perm_r Row permutation
* \param[out] nseg Number of U segments
* \param[out] dense Accumulate the column vectors of the panel
* \param[out] panel_lsub Subscripts of the row in the panel
* \param[out] segrep Segment representative i.e first nonzero row of each segment
* \param[out] repfnz First nonzero location in each row
* \param[out] xprune The pruned elimination tree
* \param[out] marker work vector
* \param parent The elimination tree
* \param xplore work vector
* \param glu The global data structure
*
*/
template <typename Scalar, typename StorageIndex>
void SparseLUImpl<Scalar,StorageIndex>::panel_dfs(const Index m, const Index w, const Index jcol, MatrixType& A, IndexVector& perm_r, Index& nseg, ScalarVector& dense, IndexVector& panel_lsub, IndexVector& segrep, IndexVector& repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu)
{
Index nextl_col; // Next available position in panel_lsub[*,jj]
// Initialize pointers
VectorBlock<IndexVector> marker1(marker, m, m);
nseg = 0;
panel_dfs_traits<IndexVector> traits(jcol, marker1.data());
// For each column in the panel
for (StorageIndex jj = StorageIndex(jcol); jj < jcol + w; jj++)
{
nextl_col = (jj - jcol) * m;
VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero location in each row
VectorBlock<ScalarVector> dense_col(dense,nextl_col, m); // Accumulate a column vector here
// For each nnz in A[*, jj] do depth first search
for (typename MatrixType::InnerIterator it(A, jj); it; ++it)
{
Index krow = it.row();
dense_col(krow) = it.value();
StorageIndex kmark = marker(krow);
if (kmark == jj)
continue; // krow visited before, go to the next nonzero
dfs_kernel(jj, perm_r, nseg, panel_lsub, segrep, repfnz_col, xprune, marker, parent,
xplore, glu, nextl_col, krow, traits);
}// end for nonzeros in column jj
} // end for column jj
}
} // end namespace internal
} // end namespace Eigen
#endif // SPARSELU_PANEL_DFS_H
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