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