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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>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, 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 2 of
// the License, or (at your option) any later version.
//
// Eigen 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 Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
/*
* NOTE: This file is the modified version of xpanel_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
/**
* \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
* \param [out]marker
*
*
*/
template <typename MatrixType, typename IndexVector, typename ScalarVector>
void SparseLU::LU_panel_dfs(const int m, const int w, const int jcol, MatrixType& A, IndexVector& perm_r, int& nseg, ScalarVector& dense, IndexVector& panel_lsub, IndexVector& segrep, IndexVector& repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, LU_GlobalLU_t& Glu)
{
int jj; // Index through each column in the panel
int nextl_col; // Next available position in panel_lsub[*,jj]
int krow; // Row index of the current element
int kperm; // permuted row index
int krep; // Supernode representative of the current row
int kmark;
int chperm, chmark, chrep, oldrep, kchild;
int myfnz; // First nonzero element in the current column
int xdfs, maxdfs, kpar;
// Initialize pointers
// IndexVector& marker1 = marker.block(m, m);
VectorBlock<IndexVector> marker1(marker, m, m);
nseg = 0;
IndexVector& xsup = Glu.xsup;
IndexVector& supno = Glu.supno;
IndexVector& lsub = Glu.lsub;
IndexVector& xlsub = Glu.xlsub;
// For each column in the panel
for (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<IndexVector> dense_col(dense,nextl_col, m); // Accumulate a column vector here
// For each nnz in A[*, jj] do depth first search
for (MatrixType::InnerIterator it(A, jj); it; ++it)
{
krow = it.row();
dense_col(krow) = it.val();
kmark = marker(krow);
if (kmark == jj)
continue; // krow visited before, go to the next nonzero
// For each unmarked krow of jj
marker(krow) = jj;
kperm = perm_r(krow);
if (kperm == IND_EMPTY ) {
// krow is in L : place it in structure of L(*, jj)
panel_lsub(nextl_col++) = krow; // krow is indexed into A
}
else
{
// krow is in U : if its supernode-representative krep
// has been explored, update repfnz(*)
krep = xsup(supno(kperm)+1) - 1;
myfnz = repfnz_col(krep);
if (myfnz != IND_EMPTY )
{
// Representative visited before
if (myfnz > kperm ) repfnz_col(krep) = kperm;
}
else
{
// Otherwise, perform dfs starting at krep
oldrep = IND_EMPTY;
parent(krep) = oldrep;
repfnz_col(krep) = kperm;
xdfs = xlsub(krep);
maxdfs = xprune(krep);
do
{
// For each unmarked kchild of krep
while (xdfs < maxdfs)
{
kchild = lsub(xdfs);
xdfs++;
chmark = marker(kchild);
if (chmark != jj )
{
marker(kchild) = jj;
chperm = perm_r(kchild);
if (chperm == IND_EMPTY)
{
// case kchild is in L: place it in L(*, j)
panel_lsub(nextl_col++) = kchild;
}
else
{
// case kchild is in U :
// chrep = its supernode-rep. If its rep has been explored,
// update its repfnz(*)
chrep = xsup(supno(chperm)+1) - 1;
myfnz = repfnz_col(chrep);
if (myfnz != IND_EMPTY)
{ // 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 = 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 (marker1(krep) < jcol )
{
segrep(nseg) = krep;
++nseg;
marker1(krep) = jj;
}
kpar = parent(krep); // Pop recursion, mimic recursion
if (kpar == IND_EMPTY)
break; // dfs done
krep = kpar;
xdfs = xplore(krep);
maxdfs = xprune(krep);
} while (kpar != IND_EMPTY); // Do until empty stack
} // end if (myfnz = -1)
} // end if (kperm == -1)
}// end for nonzeros in column jj
} // end for column jj
}
#endif
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