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// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2012 Désiré Nuentsa-Wakam // // 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 // IWYU pragma: private #include "./InternalHeaderCheck.h" namespace Eigen { namespace internal { template 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 template void SparseLUImpl::dfs_kernel(const StorageIndex jj, IndexVector& perm_r, Index& nseg, IndexVector& panel_lsub, IndexVector& segrep, Ref repfnz_col, IndexVector& xprune, Ref 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 void SparseLUImpl::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 marker1(marker, m, m); nseg = 0; panel_dfs_traits 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 repfnz_col(repfnz, nextl_col, m); // First nonzero location in each row VectorBlock 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