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
31namespace Eigen {
32namespace 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 */
45template <typename Scalar, typename Index>
46void 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