1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10 /*
11
12 * NOTE: This file is the modified version of [s,d,c,z]column_dfs.c file in SuperLU
13
14 * -- SuperLU routine (version 2.0) --
15 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
16 * and Lawrence Berkeley National Lab.
17 * November 15, 1997
18 *
19 * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
20 *
21 * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
22 * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
23 *
24 * Permission is hereby granted to use or copy this program for any
25 * purpose, provided the above notices are retained on all copies.
26 * Permission to modify the code and to distribute modified code is
27 * granted, provided the above notices are retained, and a notice that
28 * the code was modified is included with the above copyright notice.
29 */
30 #ifndef SPARSELU_COLUMN_DFS_H
31 #define SPARSELU_COLUMN_DFS_H
32
33 template <typename Scalar, typename StorageIndex> class SparseLUImpl;
34 namespace Eigen {
35
36 namespace internal {
37
38 template<typename IndexVector, typename ScalarVector>
39 struct column_dfs_traits : no_assignment_operator
40 {
41 typedef typename ScalarVector::Scalar Scalar;
42 typedef typename IndexVector::Scalar StorageIndex;
column_dfs_traitscolumn_dfs_traits43 column_dfs_traits(Index jcol, Index& jsuper, typename SparseLUImpl<Scalar, StorageIndex>::GlobalLU_t& glu, SparseLUImpl<Scalar, StorageIndex>& luImpl)
44 : m_jcol(jcol), m_jsuper_ref(jsuper), m_glu(glu), m_luImpl(luImpl)
45 {}
update_segrepcolumn_dfs_traits46 bool update_segrep(Index /*krep*/, Index /*jj*/)
47 {
48 return true;
49 }
mem_expandcolumn_dfs_traits50 void mem_expand(IndexVector& lsub, Index& nextl, Index chmark)
51 {
52 if (nextl >= m_glu.nzlmax)
53 m_luImpl.memXpand(lsub, m_glu.nzlmax, nextl, LSUB, m_glu.num_expansions);
54 if (chmark != (m_jcol-1)) m_jsuper_ref = emptyIdxLU;
55 }
56 enum { ExpandMem = true };
57
58 Index m_jcol;
59 Index& m_jsuper_ref;
60 typename SparseLUImpl<Scalar, StorageIndex>::GlobalLU_t& m_glu;
61 SparseLUImpl<Scalar, StorageIndex>& m_luImpl;
62 };
63
64
65 /**
66 * \brief Performs a symbolic factorization on column jcol and decide the supernode boundary
67 *
68 * A supernode representative is the last column of a supernode.
69 * The nonzeros in U[*,j] are segments that end at supernodes representatives.
70 * The routine returns a list of the supernodal representatives
71 * in topological order of the dfs that generates them.
72 * The location of the first nonzero in each supernodal segment
73 * (supernodal entry location) is also returned.
74 *
75 * \param m number of rows in the matrix
76 * \param jcol Current column
77 * \param perm_r Row permutation
78 * \param maxsuper Maximum number of column allowed in a supernode
79 * \param [in,out] nseg Number of segments in current U[*,j] - new segments appended
80 * \param lsub_col defines the rhs vector to start the dfs
81 * \param [in,out] segrep Segment representatives - new segments appended
82 * \param repfnz First nonzero location in each row
83 * \param xprune
84 * \param marker marker[i] == jj, if i was visited during dfs of current column jj;
85 * \param parent
86 * \param xplore working array
87 * \param glu global LU data
88 * \return 0 success
89 * > 0 number of bytes allocated when run out of space
90 *
91 */
92 template <typename Scalar, typename StorageIndex>
column_dfs(const Index m,const Index jcol,IndexVector & perm_r,Index maxsuper,Index & nseg,BlockIndexVector lsub_col,IndexVector & segrep,BlockIndexVector repfnz,IndexVector & xprune,IndexVector & marker,IndexVector & parent,IndexVector & xplore,GlobalLU_t & glu)93 Index SparseLUImpl<Scalar,StorageIndex>::column_dfs(const Index m, const Index jcol, IndexVector& perm_r, Index maxsuper, Index& nseg,
94 BlockIndexVector lsub_col, IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune,
95 IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu)
96 {
97
98 Index jsuper = glu.supno(jcol);
99 Index nextl = glu.xlsub(jcol);
100 VectorBlock<IndexVector> marker2(marker, 2*m, m);
101
102
103 column_dfs_traits<IndexVector, ScalarVector> traits(jcol, jsuper, glu, *this);
104
105 // For each nonzero in A(*,jcol) do dfs
106 for (Index k = 0; ((k < m) ? lsub_col[k] != emptyIdxLU : false) ; k++)
107 {
108 Index krow = lsub_col(k);
109 lsub_col(k) = emptyIdxLU;
110 Index kmark = marker2(krow);
111
112 // krow was visited before, go to the next nonz;
113 if (kmark == jcol) continue;
114
115 dfs_kernel(StorageIndex(jcol), perm_r, nseg, glu.lsub, segrep, repfnz, xprune, marker2, parent,
116 xplore, glu, nextl, krow, traits);
117 } // for each nonzero ...
118
119 Index fsupc;
120 StorageIndex nsuper = glu.supno(jcol);
121 StorageIndex jcolp1 = StorageIndex(jcol) + 1;
122 Index jcolm1 = jcol - 1;
123
124 // check to see if j belongs in the same supernode as j-1
125 if ( jcol == 0 )
126 { // Do nothing for column 0
127 nsuper = glu.supno(0) = 0 ;
128 }
129 else
130 {
131 fsupc = glu.xsup(nsuper);
132 StorageIndex jptr = glu.xlsub(jcol); // Not yet compressed
133 StorageIndex jm1ptr = glu.xlsub(jcolm1);
134
135 // Use supernodes of type T2 : see SuperLU paper
136 if ( (nextl-jptr != jptr-jm1ptr-1) ) jsuper = emptyIdxLU;
137
138 // Make sure the number of columns in a supernode doesn't
139 // exceed threshold
140 if ( (jcol - fsupc) >= maxsuper) jsuper = emptyIdxLU;
141
142 /* If jcol starts a new supernode, reclaim storage space in
143 * glu.lsub from previous supernode. Note we only store
144 * the subscript set of the first and last columns of
145 * a supernode. (first for num values, last for pruning)
146 */
147 if (jsuper == emptyIdxLU)
148 { // starts a new supernode
149 if ( (fsupc < jcolm1-1) )
150 { // >= 3 columns in nsuper
151 StorageIndex ito = glu.xlsub(fsupc+1);
152 glu.xlsub(jcolm1) = ito;
153 StorageIndex istop = ito + jptr - jm1ptr;
154 xprune(jcolm1) = istop; // intialize xprune(jcol-1)
155 glu.xlsub(jcol) = istop;
156
157 for (StorageIndex ifrom = jm1ptr; ifrom < nextl; ++ifrom, ++ito)
158 glu.lsub(ito) = glu.lsub(ifrom);
159 nextl = ito; // = istop + length(jcol)
160 }
161 nsuper++;
162 glu.supno(jcol) = nsuper;
163 } // if a new supernode
164 } // end else: jcol > 0
165
166 // Tidy up the pointers before exit
167 glu.xsup(nsuper+1) = jcolp1;
168 glu.supno(jcolp1) = nsuper;
169 xprune(jcol) = StorageIndex(nextl); // Intialize upper bound for pruning
170 glu.xlsub(jcolp1) = StorageIndex(nextl);
171
172 return 0;
173 }
174
175 } // end namespace internal
176
177 } // end namespace Eigen
178
179 #endif
180