17faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez// This file is part of Eigen, a lightweight C++ template library 27faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez// for linear algebra. 37faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez// 47faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr> 57faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez// 67faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez// This Source Code Form is subject to the terms of the Mozilla 77faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez// Public License v. 2.0. If a copy of the MPL was not distributed 87faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 97faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 107faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez/* This file is a modified version of heap_relax_snode.c file in SuperLU 117faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * -- SuperLU routine (version 3.0) -- 127faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * Univ. of California Berkeley, Xerox Palo Alto Research Center, 137faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * and Lawrence Berkeley National Lab. 147faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * October 15, 2003 157faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * 167faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * Copyright (c) 1994 by Xerox Corporation. All rights reserved. 177faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * 187faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY 197faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. 207faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * 217faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * Permission is hereby granted to use or copy this program for any 227faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * purpose, provided the above notices are retained on all copies. 237faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * Permission to modify the code and to distribute modified code is 247faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * granted, provided the above notices are retained, and a notice that 257faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * the code was modified is included with the above copyright notice. 267faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez */ 277faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 287faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez#ifndef SPARSELU_HEAP_RELAX_SNODE_H 297faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez#define SPARSELU_HEAP_RELAX_SNODE_H 307faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 317faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandeznamespace Eigen { 327faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandeznamespace internal { 337faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 347faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez/** 357faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * \brief Identify the initial relaxed supernodes 367faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * 377faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * This routine applied to a symmetric elimination tree. 387faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * It assumes that the matrix has been reordered according to the postorder of the etree 397faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * \param n The number of columns 407faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * \param et elimination tree 417faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * \param relax_columns Maximum number of columns allowed in a relaxed snode 427faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * \param descendants Number of descendants of each node in the etree 437faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * \param relax_end last column in a supernode 447faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez */ 457faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandeztemplate <typename Scalar, typename Index> 467faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandezvoid SparseLUImpl<Scalar,Index>::heap_relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end) 477faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez{ 487faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 497faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez // The etree may not be postordered, but its heap ordered 507faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez IndexVector post; 517faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez internal::treePostorder(n, et, post); // Post order etree 527faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez IndexVector inv_post(n+1); 537faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index i; 547faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez for (i = 0; i < n+1; ++i) inv_post(post(i)) = i; // inv_post = post.inverse()??? 557faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 567faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez // Renumber etree in postorder 577faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez IndexVector iwork(n); 587faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez IndexVector et_save(n+1); 597faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez for (i = 0; i < n; ++i) 607faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez { 617faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez iwork(post(i)) = post(et(i)); 627faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez } 637faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez et_save = et; // Save the original etree 647faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez et = iwork; 657faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 667faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez // compute the number of descendants of each node in the etree 677faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez relax_end.setConstant(emptyIdxLU); 687faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index j, parent; 697faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez descendants.setZero(); 707faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez for (j = 0; j < n; j++) 717faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez { 727faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez parent = et(j); 737faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez if (parent != n) // not the dummy root 747faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez descendants(parent) += descendants(j) + 1; 757faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez } 767faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez // Identify the relaxed supernodes by postorder traversal of the etree 777faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index snode_start; // beginning of a snode 787faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index k; 797faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index nsuper_et_post = 0; // Number of relaxed snodes in postordered etree 807faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index nsuper_et = 0; // Number of relaxed snodes in the original etree 817faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index l; 827faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez for (j = 0; j < n; ) 837faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez { 847faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez parent = et(j); 857faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez snode_start = j; 867faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez while ( parent != n && descendants(parent) < relax_columns ) 877faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez { 887faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez j = parent; 897faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez parent = et(j); 907faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez } 917faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez // Found a supernode in postordered etree, j is the last column 927faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez ++nsuper_et_post; 937faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez k = n; 947faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez for (i = snode_start; i <= j; ++i) 957faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez k = (std::min)(k, inv_post(i)); 967faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez l = inv_post(j); 977faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez if ( (l - k) == (j - snode_start) ) // Same number of columns in the snode 987faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez { 997faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez // This is also a supernode in the original etree 1007faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez relax_end(k) = l; // Record last column 1017faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez ++nsuper_et; 1027faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez } 1037faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez else 1047faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez { 1057faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez for (i = snode_start; i <= j; ++i) 1067faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez { 1077faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez l = inv_post(i); 1087faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez if (descendants(i) == 0) 1097faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez { 1107faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez relax_end(l) = l; 1117faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez ++nsuper_et; 1127faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez } 1137faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez } 1147faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez } 1157faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez j++; 1167faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez // Search for a new leaf 1177faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez while (descendants(j) != 0 && j < n) j++; 1187faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez } // End postorder traversal of the etree 1197faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 1207faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez // Recover the original etree 1217faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez et = et_save; 1227faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez} 1237faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 1247faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez} // end namespace internal 1257faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 1267faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez} // end namespace Eigen 1277faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez#endif // SPARSELU_HEAP_RELAX_SNODE_H 128