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