1c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This file is part of Eigen, a lightweight C++ template library 2c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// for linear algebra. 3c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 4c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr> 5c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 6c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This Source Code Form is subject to the terms of the Mozilla 7c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Public License v. 2.0. If a copy of the MPL was not distributed 8c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 10c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#ifndef EIGEN_INCOMPLETE_LUT_H 11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#define EIGEN_INCOMPLETE_LUT_H 12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 137faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathnamespace Eigen { 15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 167faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandeznamespace internal { 177faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 187faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez/** \internal 197faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * Compute a quick-sort split of a vector 207faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * On output, the vector row is permuted such that its elements satisfy 217faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * abs(row(i)) >= abs(row(ncut)) if i<ncut 227faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * abs(row(i)) <= abs(row(ncut)) if i>ncut 237faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * \param row The vector of values 247faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * \param ind The array of index for the elements in @p row 257faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * \param ncut The number of largest elements to keep 267faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez **/ 277faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandeztemplate <typename VectorV, typename VectorI, typename Index> 287faaa9f3f0df9d23790277834d426c3d992ac3baCarlos HernandezIndex QuickSplit(VectorV &row, VectorI &ind, Index ncut) 297faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez{ 307faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez typedef typename VectorV::RealScalar RealScalar; 317faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez using std::swap; 327faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez using std::abs; 337faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index mid; 347faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index n = row.size(); /* length of the vector */ 357faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index first, last ; 367faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 377faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez ncut--; /* to fit the zero-based indices */ 387faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez first = 0; 397faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez last = n-1; 407faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez if (ncut < first || ncut > last ) return 0; 417faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 427faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez do { 437faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez mid = first; 447faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez RealScalar abskey = abs(row(mid)); 457faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez for (Index j = first + 1; j <= last; j++) { 467faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez if ( abs(row(j)) > abskey) { 477faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez ++mid; 487faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez swap(row(mid), row(j)); 497faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez swap(ind(mid), ind(j)); 507faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez } 517faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez } 527faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez /* Interchange for the pivot element */ 537faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez swap(row(mid), row(first)); 547faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez swap(ind(mid), ind(first)); 557faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 567faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez if (mid > ncut) last = mid - 1; 577faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez else if (mid < ncut ) first = mid + 1; 587faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez } while (mid != ncut ); 597faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 607faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez return 0; /* mid is equal to ncut */ 617faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez} 627faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 637faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez}// end namespace internal 647faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 657faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez/** \ingroup IterativeLinearSolvers_Module 667faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * \class IncompleteLUT 677faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * \brief Incomplete LU factorization with dual-threshold strategy 687faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * 697faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * During the numerical factorization, two dropping rules are used : 707faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * 1) any element whose magnitude is less than some tolerance is dropped. 717faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * This tolerance is obtained by multiplying the input tolerance @p droptol 727faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * by the average magnitude of all the original elements in the current row. 737faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * 2) After the elimination of the row, only the @p fill largest elements in 747faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * the L part and the @p fill largest elements in the U part are kept 757faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * (in addition to the diagonal element ). Note that @p fill is computed from 767faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * the input parameter @p fillfactor which is used the ratio to control the fill_in 777faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * relatively to the initial number of nonzero elements. 787faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * 797faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * The two extreme cases are when @p droptol=0 (to keep all the @p fill*2 largest elements) 807faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * and when @p fill=n/2 with @p droptol being different to zero. 817faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * 827faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * References : Yousef Saad, ILUT: A dual threshold incomplete LU factorization, 837faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * Numerical Linear Algebra with Applications, 1(4), pp 387-402, 1994. 847faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * 857faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * NOTE : The following implementation is derived from the ILUT implementation 867faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * in the SPARSKIT package, Copyright (C) 2005, the Regents of the University of Minnesota 877faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * released under the terms of the GNU LGPL: 887faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * http://www-users.cs.umn.edu/~saad/software/SPARSKIT/README 897faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * However, Yousef Saad gave us permission to relicense his ILUT code to MPL2. 907faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * See the Eigen mailing list archive, thread: ILUT, date: July 8, 2012: 917faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * http://listengine.tuxfamily.org/lists.tuxfamily.org/eigen/2012/07/msg00064.html 927faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * alternatively, on GMANE: 937faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * http://comments.gmane.org/gmane.comp.lib.eigen/3302 947faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez */ 95c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename _Scalar> 96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathclass IncompleteLUT : internal::noncopyable 97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 98c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef _Scalar Scalar; 99c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename NumTraits<Scalar>::Real RealScalar; 100c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,Dynamic,1> Vector; 101c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef SparseMatrix<Scalar,RowMajor> FactorType; 102c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef SparseMatrix<Scalar,ColMajor> PermutType; 103c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename FactorType::Index Index; 104c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 105c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath public: 106c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType; 107c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 108c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath IncompleteLUT() 109c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath : m_droptol(NumTraits<Scalar>::dummy_precision()), m_fillfactor(10), 110c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_analysisIsOk(false), m_factorizationIsOk(false), m_isInitialized(false) 111c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath {} 112c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 113c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename MatrixType> 1147faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez IncompleteLUT(const MatrixType& mat, const RealScalar& droptol=NumTraits<Scalar>::dummy_precision(), int fillfactor = 10) 115c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath : m_droptol(droptol),m_fillfactor(fillfactor), 116c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_analysisIsOk(false),m_factorizationIsOk(false),m_isInitialized(false) 117c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 118c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen_assert(fillfactor != 0); 119c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath compute(mat); 120c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 121c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 122c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index rows() const { return m_lu.rows(); } 123c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 124c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index cols() const { return m_lu.cols(); } 125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 126c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief Reports whether previous computation was successful. 127c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 128c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \returns \c Success if computation was succesful, 129c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \c NumericalIssue if the matrix.appears to be negative. 130c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 131c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ComputationInfo info() const 132c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen_assert(m_isInitialized && "IncompleteLUT is not initialized."); 134c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return m_info; 135c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 136c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 137c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename MatrixType> 138c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath void analyzePattern(const MatrixType& amat); 139c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 140c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename MatrixType> 141c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath void factorize(const MatrixType& amat); 142c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 143c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** 144c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Compute an incomplete LU factorization with dual threshold on the matrix mat 145c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * No pivoting is done in this version 146c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 147c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath **/ 148c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename MatrixType> 149c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath IncompleteLUT<Scalar>& compute(const MatrixType& amat) 150c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 151c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath analyzePattern(amat); 152c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath factorize(amat); 1537faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez m_isInitialized = m_factorizationIsOk; 154c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return *this; 155c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 156c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 1577faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez void setDroptol(const RealScalar& droptol); 158c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath void setFillfactor(int fillfactor); 159c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 160c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename Rhs, typename Dest> 161c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath void _solve(const Rhs& b, Dest& x) const 162c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 163c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath x = m_Pinv * b; 164c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath x = m_lu.template triangularView<UnitLower>().solve(x); 165c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath x = m_lu.template triangularView<Upper>().solve(x); 166c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath x = m_P * x; 167c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 168c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 169c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename Rhs> inline const internal::solve_retval<IncompleteLUT, Rhs> 170c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath solve(const MatrixBase<Rhs>& b) const 171c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 172c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen_assert(m_isInitialized && "IncompleteLUT is not initialized."); 173c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen_assert(cols()==b.rows() 174c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath && "IncompleteLUT::solve(): invalid number of rows of the right hand side matrix b"); 175c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return internal::solve_retval<IncompleteLUT, Rhs>(*this, b.derived()); 176c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 177c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 178c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathprotected: 179c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 180c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** keeps off-diagonal entries; drops diagonal entries */ 181c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath struct keep_diag { 182c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline bool operator() (const Index& row, const Index& col, const Scalar&) const 183c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 184c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return row!=col; 185c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 186c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath }; 187c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 188c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathprotected: 189c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 190c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath FactorType m_lu; 191c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath RealScalar m_droptol; 192c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int m_fillfactor; 193c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath bool m_analysisIsOk; 194c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath bool m_factorizationIsOk; 195c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath bool m_isInitialized; 196c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ComputationInfo m_info; 197c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath PermutationMatrix<Dynamic,Dynamic,Index> m_P; // Fill-reducing permutation 198c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath PermutationMatrix<Dynamic,Dynamic,Index> m_Pinv; // Inverse permutation 199c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 200c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 201c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** 202c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Set control parameter droptol 203c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \param droptol Drop any element whose magnitude is less than this tolerance 204c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath **/ 205c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Scalar> 2067faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandezvoid IncompleteLUT<Scalar>::setDroptol(const RealScalar& droptol) 207c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 208c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath this->m_droptol = droptol; 209c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 210c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 211c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** 212c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Set control parameter fillfactor 213c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \param fillfactor This is used to compute the number @p fill_in of largest elements to keep on each row. 214c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath **/ 215c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Scalar> 216c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathvoid IncompleteLUT<Scalar>::setFillfactor(int fillfactor) 217c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 218c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath this->m_fillfactor = fillfactor; 219c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 220c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 221c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename Scalar> 222c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename _MatrixType> 223c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathvoid IncompleteLUT<Scalar>::analyzePattern(const _MatrixType& amat) 224c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 225c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Compute the Fill-reducing permutation 226c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SparseMatrix<Scalar,ColMajor, Index> mat1 = amat; 227c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SparseMatrix<Scalar,ColMajor, Index> mat2 = amat.transpose(); 228c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Symmetrize the pattern 229c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // FIXME for a matrix with nearly symmetric pattern, mat2+mat1 is the appropriate choice. 230c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // on the other hand for a really non-symmetric pattern, mat2*mat1 should be prefered... 231c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SparseMatrix<Scalar,ColMajor, Index> AtA = mat2 + mat1; 232c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AtA.prune(keep_diag()); 233c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath internal::minimum_degree_ordering<Scalar, Index>(AtA, m_P); // Then compute the AMD ordering... 234c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 235c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_Pinv = m_P.inverse(); // ... and the inverse permutation 236c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 237c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_analysisIsOk = true; 238c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 239c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 240c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename Scalar> 241c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename _MatrixType> 242c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathvoid IncompleteLUT<Scalar>::factorize(const _MatrixType& amat) 243c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 244c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath using std::sqrt; 245c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath using std::swap; 246c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath using std::abs; 247c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 248c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen_assert((amat.rows() == amat.cols()) && "The factorization should be done on a square matrix"); 2497faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index n = amat.cols(); // Size of the matrix 250c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_lu.resize(n,n); 251c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Declare Working vectors and variables 252c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector u(n) ; // real values of the row -- maximum size is n -- 253c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VectorXi ju(n); // column position of the values in u -- maximum size is n 254c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VectorXi jr(n); // Indicate the position of the nonzero elements in the vector u -- A zero location is indicated by -1 255c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 256c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Apply the fill-reducing permutation 257c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen_assert(m_analysisIsOk && "You must first call analyzePattern()"); 258c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SparseMatrix<Scalar,RowMajor, Index> mat; 259c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath mat = amat.twistedBy(m_Pinv); 260c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 261c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Initialization 262c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath jr.fill(-1); 263c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ju.fill(0); 264c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath u.fill(0); 265c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 266c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // number of largest elements to keep in each row: 2677faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index fill_in = static_cast<Index> (amat.nonZeros()*m_fillfactor)/n+1; 268c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (fill_in > n) fill_in = n; 269c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 270c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // number of largest nonzero elements to keep in the L and the U part of the current row: 2717faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index nnzL = fill_in/2; 2727faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index nnzU = nnzL; 273c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_lu.reserve(n * (nnzL + nnzU + 1)); 274c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 275c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // global loop over the rows of the sparse matrix 2767faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez for (Index ii = 0; ii < n; ii++) 277c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 278c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // 1 - copy the lower and the upper part of the row i of mat in the working vector u 279c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 2807faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index sizeu = 1; // number of nonzero elements in the upper part of the current row 2817faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index sizel = 0; // number of nonzero elements in the lower part of the current row 282c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ju(ii) = ii; 283c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath u(ii) = 0; 284c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath jr(ii) = ii; 285c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath RealScalar rownorm = 0; 286c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 287c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename FactorType::InnerIterator j_it(mat, ii); // Iterate through the current row ii 288c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for (; j_it; ++j_it) 289c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 2907faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index k = j_it.index(); 291c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (k < ii) 292c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 293c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // copy the lower part 294c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ju(sizel) = k; 295c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath u(sizel) = j_it.value(); 296c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath jr(k) = sizel; 297c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ++sizel; 298c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 299c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath else if (k == ii) 300c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 301c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath u(ii) = j_it.value(); 302c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 303c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath else 304c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 305c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // copy the upper part 3067faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index jpos = ii + sizeu; 307c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ju(jpos) = k; 308c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath u(jpos) = j_it.value(); 309c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath jr(k) = jpos; 310c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ++sizeu; 311c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 3127faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez rownorm += numext::abs2(j_it.value()); 313c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 314c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 315c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // 2 - detect possible zero row 316c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if(rownorm==0) 317c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 318c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_info = NumericalIssue; 319c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return; 320c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 321c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Take the 2-norm of the current row as a relative tolerance 322c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath rownorm = sqrt(rownorm); 323c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 324c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // 3 - eliminate the previous nonzero rows 3257faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index jj = 0; 3267faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index len = 0; 327c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath while (jj < sizel) 328c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 329c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // In order to eliminate in the correct order, 330c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // we must select first the smallest column index among ju(jj:sizel) 3317faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index k; 3327faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index minrow = ju.segment(jj,sizel-jj).minCoeff(&k); // k is relative to the segment 333c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath k += jj; 334c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (minrow != ju(jj)) 335c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 336c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // swap the two locations 3377faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index j = ju(jj); 338c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath swap(ju(jj), ju(k)); 339c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath jr(minrow) = jj; jr(j) = k; 340c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath swap(u(jj), u(k)); 341c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 342c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Reset this location 343c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath jr(minrow) = -1; 344c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 345c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Start elimination 346c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename FactorType::InnerIterator ki_it(m_lu, minrow); 347c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath while (ki_it && ki_it.index() < minrow) ++ki_it; 348c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen_internal_assert(ki_it && ki_it.col()==minrow); 349c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar fact = u(jj) / ki_it.value(); 350c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 351c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // drop too small elements 352c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if(abs(fact) <= m_droptol) 353c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 354c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath jj++; 355c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath continue; 356c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 357c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 358c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // linear combination of the current row ii and the row minrow 359c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ++ki_it; 360c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for (; ki_it; ++ki_it) 361c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 362c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar prod = fact * ki_it.value(); 3637faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index j = ki_it.index(); 3647faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index jpos = jr(j); 365c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (jpos == -1) // fill-in element 366c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 3677faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez Index newpos; 368c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (j >= ii) // dealing with the upper part 369c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 370c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath newpos = ii + sizeu; 371c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath sizeu++; 372c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen_internal_assert(sizeu<=n); 373c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 374c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath else // dealing with the lower part 375c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 376c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath newpos = sizel; 377c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath sizel++; 378c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen_internal_assert(sizel<=ii); 379c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 380c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ju(newpos) = j; 381c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath u(newpos) = -prod; 382c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath jr(j) = newpos; 383c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 384c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath else 385c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath u(jpos) -= prod; 386c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 387c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // store the pivot element 388c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath u(len) = fact; 389c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ju(len) = minrow; 390c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ++len; 391c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 392c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath jj++; 393c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } // end of the elimination on the row ii 394c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 395c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // reset the upper part of the pointer jr to zero 3967faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez for(Index k = 0; k <sizeu; k++) jr(ju(ii+k)) = -1; 397c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 398c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // 4 - partially sort and insert the elements in the m_lu matrix 399c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 400c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // sort the L-part of the row 401c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath sizel = len; 402c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath len = (std::min)(sizel, nnzL); 403c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename Vector::SegmentReturnType ul(u.segment(0, sizel)); 404c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename VectorXi::SegmentReturnType jul(ju.segment(0, sizel)); 4057faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez internal::QuickSplit(ul, jul, len); 406c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 407c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // store the largest m_fill elements of the L part 408c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_lu.startVec(ii); 4097faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez for(Index k = 0; k < len; k++) 410c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_lu.insertBackByOuterInnerUnordered(ii,ju(k)) = u(k); 411c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 412c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // store the diagonal element 413c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // apply a shifting rule to avoid zero pivots (we are doing an incomplete factorization) 414c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (u(ii) == Scalar(0)) 415c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath u(ii) = sqrt(m_droptol) * rownorm; 416c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_lu.insertBackByOuterInnerUnordered(ii, ii) = u(ii); 417c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 418c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // sort the U-part of the row 419c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // apply the dropping rule first 420c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath len = 0; 4217faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez for(Index k = 1; k < sizeu; k++) 422c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 423c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if(abs(u(ii+k)) > m_droptol * rownorm ) 424c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 425c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ++len; 426c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath u(ii + len) = u(ii + k); 427c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ju(ii + len) = ju(ii + k); 428c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 429c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 430c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath sizeu = len + 1; // +1 to take into account the diagonal element 431c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath len = (std::min)(sizeu, nnzU); 432c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename Vector::SegmentReturnType uu(u.segment(ii+1, sizeu-1)); 433c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename VectorXi::SegmentReturnType juu(ju.segment(ii+1, sizeu-1)); 4347faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez internal::QuickSplit(uu, juu, len); 435c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 436c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // store the largest elements of the U part 4377faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez for(Index k = ii + 1; k < ii + len; k++) 438c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_lu.insertBackByOuterInnerUnordered(ii,ju(k)) = u(k); 439c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 440c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 441c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_lu.finalize(); 442c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_lu.makeCompressed(); 443c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 444c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_factorizationIsOk = true; 445c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_info = Success; 446c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 447c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 448c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathnamespace internal { 449c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 450c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename _MatrixType, typename Rhs> 451c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathstruct solve_retval<IncompleteLUT<_MatrixType>, Rhs> 452c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath : solve_retval_base<IncompleteLUT<_MatrixType>, Rhs> 453c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 454c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef IncompleteLUT<_MatrixType> Dec; 455c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs) 456c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 457c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename Dest> void evalTo(Dest& dst) const 458c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 459c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath dec()._solve(rhs(),dst); 460c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 461c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 462c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 463c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} // end namespace internal 464c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 465c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} // end namespace Eigen 466c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 467c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#endif // EIGEN_INCOMPLETE_LUT_H 468