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259 lines
8.8 KiB
259 lines
8.8 KiB
6 years ago
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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/*
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* NOTE: This file is the modified version of [s,d,c,z]panel_dfs.c file in SuperLU
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* -- SuperLU routine (version 2.0) --
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* Univ. of California Berkeley, Xerox Palo Alto Research Center,
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* and Lawrence Berkeley National Lab.
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* November 15, 1997
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*
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* Copyright (c) 1994 by Xerox Corporation. All rights reserved.
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*
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* THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
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* EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
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*
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* Permission is hereby granted to use or copy this program for any
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* purpose, provided the above notices are retained on all copies.
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* Permission to modify the code and to distribute modified code is
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* granted, provided the above notices are retained, and a notice that
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* the code was modified is included with the above copyright notice.
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*/
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#ifndef SPARSELU_PANEL_DFS_H
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#define SPARSELU_PANEL_DFS_H
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namespace Eigen {
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namespace internal {
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template<typename IndexVector>
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struct panel_dfs_traits
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{
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typedef typename IndexVector::Scalar StorageIndex;
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panel_dfs_traits(Index jcol, StorageIndex* marker)
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: m_jcol(jcol), m_marker(marker)
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{}
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bool update_segrep(Index krep, StorageIndex jj)
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{
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if(m_marker[krep]<m_jcol)
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{
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m_marker[krep] = jj;
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return true;
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}
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return false;
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}
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void mem_expand(IndexVector& /*glu.lsub*/, Index /*nextl*/, Index /*chmark*/) {}
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enum { ExpandMem = false };
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Index m_jcol;
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StorageIndex* m_marker;
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};
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template <typename Scalar, typename StorageIndex>
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template <typename Traits>
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void SparseLUImpl<Scalar,StorageIndex>::dfs_kernel(const StorageIndex jj, IndexVector& perm_r,
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Index& nseg, IndexVector& panel_lsub, IndexVector& segrep,
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Ref<IndexVector> repfnz_col, IndexVector& xprune, Ref<IndexVector> marker, IndexVector& parent,
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IndexVector& xplore, GlobalLU_t& glu,
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Index& nextl_col, Index krow, Traits& traits
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)
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{
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StorageIndex kmark = marker(krow);
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// For each unmarked krow of jj
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marker(krow) = jj;
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StorageIndex kperm = perm_r(krow);
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if (kperm == emptyIdxLU ) {
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// krow is in L : place it in structure of L(*, jj)
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panel_lsub(nextl_col++) = StorageIndex(krow); // krow is indexed into A
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traits.mem_expand(panel_lsub, nextl_col, kmark);
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}
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else
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{
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// krow is in U : if its supernode-representative krep
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// has been explored, update repfnz(*)
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// krep = supernode representative of the current row
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StorageIndex krep = glu.xsup(glu.supno(kperm)+1) - 1;
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// First nonzero element in the current column:
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StorageIndex myfnz = repfnz_col(krep);
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if (myfnz != emptyIdxLU )
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{
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// Representative visited before
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if (myfnz > kperm ) repfnz_col(krep) = kperm;
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}
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else
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{
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// Otherwise, perform dfs starting at krep
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StorageIndex oldrep = emptyIdxLU;
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parent(krep) = oldrep;
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repfnz_col(krep) = kperm;
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StorageIndex xdfs = glu.xlsub(krep);
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Index maxdfs = xprune(krep);
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StorageIndex kpar;
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do
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{
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// For each unmarked kchild of krep
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while (xdfs < maxdfs)
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{
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StorageIndex kchild = glu.lsub(xdfs);
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xdfs++;
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StorageIndex chmark = marker(kchild);
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if (chmark != jj )
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{
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marker(kchild) = jj;
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StorageIndex chperm = perm_r(kchild);
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if (chperm == emptyIdxLU)
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{
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// case kchild is in L: place it in L(*, j)
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panel_lsub(nextl_col++) = kchild;
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traits.mem_expand(panel_lsub, nextl_col, chmark);
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}
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else
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{
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// case kchild is in U :
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// chrep = its supernode-rep. If its rep has been explored,
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// update its repfnz(*)
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StorageIndex chrep = glu.xsup(glu.supno(chperm)+1) - 1;
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myfnz = repfnz_col(chrep);
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if (myfnz != emptyIdxLU)
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{ // Visited before
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if (myfnz > chperm)
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repfnz_col(chrep) = chperm;
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}
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else
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{ // Cont. dfs at snode-rep of kchild
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xplore(krep) = xdfs;
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oldrep = krep;
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krep = chrep; // Go deeper down G(L)
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parent(krep) = oldrep;
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repfnz_col(krep) = chperm;
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xdfs = glu.xlsub(krep);
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maxdfs = xprune(krep);
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} // end if myfnz != -1
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} // end if chperm == -1
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} // end if chmark !=jj
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} // end while xdfs < maxdfs
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// krow has no more unexplored nbrs :
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// Place snode-rep krep in postorder DFS, if this
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// segment is seen for the first time. (Note that
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// "repfnz(krep)" may change later.)
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// Baktrack dfs to its parent
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if(traits.update_segrep(krep,jj))
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//if (marker1(krep) < jcol )
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{
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segrep(nseg) = krep;
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++nseg;
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//marker1(krep) = jj;
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}
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kpar = parent(krep); // Pop recursion, mimic recursion
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if (kpar == emptyIdxLU)
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break; // dfs done
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krep = kpar;
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xdfs = xplore(krep);
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maxdfs = xprune(krep);
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} while (kpar != emptyIdxLU); // Do until empty stack
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} // end if (myfnz = -1)
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} // end if (kperm == -1)
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}
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/**
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* \brief Performs a symbolic factorization on a panel of columns [jcol, jcol+w)
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*
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* A supernode representative is the last column of a supernode.
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* The nonzeros in U[*,j] are segments that end at supernodes representatives
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*
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* The routine returns a list of the supernodal representatives
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* in topological order of the dfs that generates them. This list is
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* a superset of the topological order of each individual column within
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* the panel.
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* The location of the first nonzero in each supernodal segment
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* (supernodal entry location) is also returned. Each column has
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* a separate list for this purpose.
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*
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* Two markers arrays are used for dfs :
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* marker[i] == jj, if i was visited during dfs of current column jj;
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* marker1[i] >= jcol, if i was visited by earlier columns in this panel;
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*
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* \param[in] m number of rows in the matrix
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* \param[in] w Panel size
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* \param[in] jcol Starting column of the panel
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* \param[in] A Input matrix in column-major storage
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* \param[in] perm_r Row permutation
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* \param[out] nseg Number of U segments
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* \param[out] dense Accumulate the column vectors of the panel
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* \param[out] panel_lsub Subscripts of the row in the panel
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* \param[out] segrep Segment representative i.e first nonzero row of each segment
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* \param[out] repfnz First nonzero location in each row
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* \param[out] xprune The pruned elimination tree
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* \param[out] marker work vector
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* \param parent The elimination tree
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* \param xplore work vector
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* \param glu The global data structure
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*
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*/
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template <typename Scalar, typename StorageIndex>
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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)
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{
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Index nextl_col; // Next available position in panel_lsub[*,jj]
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// Initialize pointers
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VectorBlock<IndexVector> marker1(marker, m, m);
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nseg = 0;
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panel_dfs_traits<IndexVector> traits(jcol, marker1.data());
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// For each column in the panel
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for (StorageIndex jj = StorageIndex(jcol); jj < jcol + w; jj++)
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{
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nextl_col = (jj - jcol) * m;
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VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero location in each row
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VectorBlock<ScalarVector> dense_col(dense,nextl_col, m); // Accumulate a column vector here
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// For each nnz in A[*, jj] do depth first search
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for (typename MatrixType::InnerIterator it(A, jj); it; ++it)
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{
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Index krow = it.row();
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dense_col(krow) = it.value();
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StorageIndex kmark = marker(krow);
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if (kmark == jj)
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continue; // krow visited before, go to the next nonzero
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dfs_kernel(jj, perm_r, nseg, panel_lsub, segrep, repfnz_col, xprune, marker, parent,
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xplore, glu, nextl_col, krow, traits);
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}// end for nonzeros in column jj
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} // end for column jj
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}
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} // end namespace internal
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} // end namespace Eigen
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#endif // SPARSELU_PANEL_DFS_H
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