| 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>
|
|---|
| 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
|
|---|
