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 /* This file is a modified version of heap_relax_snode.c file in SuperLU
11 * -- SuperLU routine (version 3.0) --
12 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
13 * and Lawrence Berkeley National Lab.
14 * October 15, 2003
15 *
16 * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
17 *
18 * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
19 * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
20 *
21 * Permission is hereby granted to use or copy this program for any
22 * purpose, provided the above notices are retained on all copies.
23 * Permission to modify the code and to distribute modified code is
24 * granted, provided the above notices are retained, and a notice that
25 * the code was modified is included with the above copyright notice.
26 */
27
28 #ifndef SPARSELU_HEAP_RELAX_SNODE_H
29 #define SPARSELU_HEAP_RELAX_SNODE_H
30
31 namespace Eigen {
32 namespace internal {
33
34 /**
35 * \brief Identify the initial relaxed supernodes
36 *
37 * This routine applied to a symmetric elimination tree.
38 * It assumes that the matrix has been reordered according to the postorder of the etree
39 * \param n The number of columns
40 * \param et elimination tree
41 * \param relax_columns Maximum number of columns allowed in a relaxed snode
42 * \param descendants Number of descendants of each node in the etree
43 * \param relax_end last column in a supernode
44 */
45 template <typename Scalar, typename Index>
heap_relax_snode(const Index n,IndexVector & et,const Index relax_columns,IndexVector & descendants,IndexVector & relax_end)46 void SparseLUImpl<Scalar,Index>::heap_relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end)
47 {
48
49 // The etree may not be postordered, but its heap ordered
50 IndexVector post;
51 internal::treePostorder(n, et, post); // Post order etree
52 IndexVector inv_post(n+1);
53 Index i;
54 for (i = 0; i < n+1; ++i) inv_post(post(i)) = i; // inv_post = post.inverse()???
55
56 // Renumber etree in postorder
57 IndexVector iwork(n);
58 IndexVector et_save(n+1);
59 for (i = 0; i < n; ++i)
60 {
61 iwork(post(i)) = post(et(i));
62 }
63 et_save = et; // Save the original etree
64 et = iwork;
65
66 // compute the number of descendants of each node in the etree
67 relax_end.setConstant(emptyIdxLU);
68 Index j, parent;
69 descendants.setZero();
70 for (j = 0; j < n; j++)
71 {
72 parent = et(j);
73 if (parent != n) // not the dummy root
74 descendants(parent) += descendants(j) + 1;
75 }
76 // Identify the relaxed supernodes by postorder traversal of the etree
77 Index snode_start; // beginning of a snode
78 Index k;
79 Index nsuper_et_post = 0; // Number of relaxed snodes in postordered etree
80 Index nsuper_et = 0; // Number of relaxed snodes in the original etree
81 Index l;
82 for (j = 0; j < n; )
83 {
84 parent = et(j);
85 snode_start = j;
86 while ( parent != n && descendants(parent) < relax_columns )
87 {
88 j = parent;
89 parent = et(j);
90 }
91 // Found a supernode in postordered etree, j is the last column
92 ++nsuper_et_post;
93 k = n;
94 for (i = snode_start; i <= j; ++i)
95 k = (std::min)(k, inv_post(i));
96 l = inv_post(j);
97 if ( (l - k) == (j - snode_start) ) // Same number of columns in the snode
98 {
99 // This is also a supernode in the original etree
100 relax_end(k) = l; // Record last column
101 ++nsuper_et;
102 }
103 else
104 {
105 for (i = snode_start; i <= j; ++i)
106 {
107 l = inv_post(i);
108 if (descendants(i) == 0)
109 {
110 relax_end(l) = l;
111 ++nsuper_et;
112 }
113 }
114 }
115 j++;
116 // Search for a new leaf
117 while (descendants(j) != 0 && j < n) j++;
118 } // End postorder traversal of the etree
119
120 // Recover the original etree
121 et = et_save;
122 }
123
124 } // end namespace internal
125
126 } // end namespace Eigen
127 #endif // SPARSELU_HEAP_RELAX_SNODE_H
128