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126 lines
4.1 KiB
126 lines
4.1 KiB
// This file is part of Eigen, a lightweight C++ template library |
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// for linear algebra. |
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// |
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// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr> |
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// |
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// This Source Code Form is subject to the terms of the Mozilla |
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// Public License v. 2.0. If a copy of the MPL was not distributed |
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// with this file, You can obtain one at the mozilla.org home page |
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/* This file is a modified version of heap_relax_snode.c file in SuperLU |
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* -- SuperLU routine (version 3.0) -- |
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* Univ. of California Berkeley, Xerox Palo Alto Research Center, |
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* and Lawrence Berkeley National Lab. |
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* October 15, 2003 |
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* |
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* Copyright (c) 1994 by Xerox Corporation. All rights reserved. |
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* |
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* THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY |
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* EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. |
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* |
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* Permission is hereby granted to use or copy this program for any |
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* purpose, provided the above notices are retained on all copies. |
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* Permission to modify the code and to distribute modified code is |
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* granted, provided the above notices are retained, and a notice that |
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* the code was modified is included with the above copyright notice. |
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*/ |
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#ifndef SPARSELU_HEAP_RELAX_SNODE_H |
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#define SPARSELU_HEAP_RELAX_SNODE_H |
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namespace Eigen { |
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namespace internal { |
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/** |
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* \brief Identify the initial relaxed supernodes |
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* |
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* This routine applied to a symmetric elimination tree. |
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* It assumes that the matrix has been reordered according to the postorder of the etree |
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* \param n The number of columns |
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* \param et elimination tree |
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* \param relax_columns Maximum number of columns allowed in a relaxed snode |
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* \param descendants Number of descendants of each node in the etree |
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* \param relax_end last column in a supernode |
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*/ |
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template <typename Scalar, typename StorageIndex> |
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void SparseLUImpl<Scalar,StorageIndex>::heap_relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end) |
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{ |
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// The etree may not be postordered, but its heap ordered |
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IndexVector post; |
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internal::treePostorder(StorageIndex(n), et, post); // Post order etree |
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IndexVector inv_post(n+1); |
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for (StorageIndex i = 0; i < n+1; ++i) inv_post(post(i)) = i; // inv_post = post.inverse()??? |
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// Renumber etree in postorder |
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IndexVector iwork(n); |
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IndexVector et_save(n+1); |
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for (Index i = 0; i < n; ++i) |
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{ |
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iwork(post(i)) = post(et(i)); |
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} |
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et_save = et; // Save the original etree |
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et = iwork; |
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// compute the number of descendants of each node in the etree |
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relax_end.setConstant(emptyIdxLU); |
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Index j, parent; |
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descendants.setZero(); |
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for (j = 0; j < n; j++) |
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{ |
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parent = et(j); |
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if (parent != n) // not the dummy root |
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descendants(parent) += descendants(j) + 1; |
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} |
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// Identify the relaxed supernodes by postorder traversal of the etree |
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Index snode_start; // beginning of a snode |
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StorageIndex k; |
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Index nsuper_et_post = 0; // Number of relaxed snodes in postordered etree |
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Index nsuper_et = 0; // Number of relaxed snodes in the original etree |
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StorageIndex l; |
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for (j = 0; j < n; ) |
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{ |
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parent = et(j); |
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snode_start = j; |
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while ( parent != n && descendants(parent) < relax_columns ) |
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{ |
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j = parent; |
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parent = et(j); |
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} |
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// Found a supernode in postordered etree, j is the last column |
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++nsuper_et_post; |
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k = StorageIndex(n); |
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for (Index i = snode_start; i <= j; ++i) |
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k = (std::min)(k, inv_post(i)); |
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l = inv_post(j); |
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if ( (l - k) == (j - snode_start) ) // Same number of columns in the snode |
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{ |
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// This is also a supernode in the original etree |
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relax_end(k) = l; // Record last column |
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++nsuper_et; |
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} |
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else |
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{ |
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for (Index i = snode_start; i <= j; ++i) |
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{ |
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l = inv_post(i); |
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if (descendants(i) == 0) |
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{ |
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relax_end(l) = l; |
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++nsuper_et; |
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} |
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} |
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} |
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j++; |
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// Search for a new leaf |
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while (descendants(j) != 0 && j < n) j++; |
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} // End postorder traversal of the etree |
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// Recover the original etree |
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et = et_save; |
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} |
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} // end namespace internal |
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} // end namespace Eigen |
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#endif // SPARSELU_HEAP_RELAX_SNODE_H
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