259 lines
8.6 KiB
C
259 lines
8.6 KiB
C
|
// 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 Index;
|
||
|
|
panel_dfs_traits(Index jcol, Index* marker)
|
||
|
|
: m_jcol(jcol), m_marker(marker)
|
||
|
|
{}
|
||
|
|
bool update_segrep(Index krep, Index 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;
|
||
|
|
Index* m_marker;
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
template <typename Scalar, typename Index>
|
||
|
|
template <typename Traits>
|
||
|
|
void SparseLUImpl<Scalar,Index>::dfs_kernel(const Index 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
|
||
|
|
)
|
||
|
|
{
|
||
|
|
|
||
|
|
Index kmark = marker(krow);
|
||
|
|
|
||
|
|
// For each unmarked krow of jj
|
||
|
|
marker(krow) = jj;
|
||
|
|
Index kperm = perm_r(krow);
|
||
|
|
if (kperm == emptyIdxLU ) {
|
||
|
|
// krow is in L : place it in structure of L(*, jj)
|
||
|
|
panel_lsub(nextl_col++) = 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
|
||
|
|
Index krep = glu.xsup(glu.supno(kperm)+1) - 1;
|
||
|
|
// First nonzero element in the current column:
|
||
|
|
Index myfnz = repfnz_col(krep);
|
||
|
|
|
||
|
|
if (myfnz != emptyIdxLU )
|
||
|
|
{
|
||
|
|
// Representative visited before
|
||
|
|
if (myfnz > kperm ) repfnz_col(krep) = kperm;
|
||
|
|
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// Otherwise, perform dfs starting at krep
|
||
|
|
Index oldrep = emptyIdxLU;
|
||
|
|
parent(krep) = oldrep;
|
||
|
|
repfnz_col(krep) = kperm;
|
||
|
|
Index xdfs = glu.xlsub(krep);
|
||
|
|
Index maxdfs = xprune(krep);
|
||
|
|
|
||
|
|
Index kpar;
|
||
|
|
do
|
||
|
|
{
|
||
|
|
// For each unmarked kchild of krep
|
||
|
|
while (xdfs < maxdfs)
|
||
|
|
{
|
||
|
|
Index kchild = glu.lsub(xdfs);
|
||
|
|
xdfs++;
|
||
|
|
Index chmark = marker(kchild);
|
||
|
|
|
||
|
|
if (chmark != jj )
|
||
|
|
{
|
||
|
|
marker(kchild) = jj;
|
||
|
|
Index 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(*)
|
||
|
|
Index 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 Index>
|
||
|
|
void SparseLUImpl<Scalar,Index>::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 (Index jj = 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();
|
||
|
|
|
||
|
|
Index 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
|