add Eigen as a dependency
This commit is contained in:
Sven Czarnian
773
external/include/eigen3/Eigen/src/SparseLU/SparseLU.h
vendored
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773
external/include/eigen3/Eigen/src/SparseLU/SparseLU.h
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// 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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// Copyright (C) 2012-2014 Gael Guennebaud <gael.guennebaud@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 http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_SPARSE_LU_H
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#define EIGEN_SPARSE_LU_H
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namespace Eigen {
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template <typename _MatrixType, typename _OrderingType = COLAMDOrdering<typename _MatrixType::StorageIndex> > class SparseLU;
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template <typename MappedSparseMatrixType> struct SparseLUMatrixLReturnType;
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template <typename MatrixLType, typename MatrixUType> struct SparseLUMatrixUReturnType;
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/** \ingroup SparseLU_Module
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* \class SparseLU
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*
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* \brief Sparse supernodal LU factorization for general matrices
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*
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* This class implements the supernodal LU factorization for general matrices.
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* It uses the main techniques from the sequential SuperLU package
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* (http://crd-legacy.lbl.gov/~xiaoye/SuperLU/). It handles transparently real
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* and complex arithmetics with single and double precision, depending on the
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* scalar type of your input matrix.
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* The code has been optimized to provide BLAS-3 operations during supernode-panel updates.
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* It benefits directly from the built-in high-performant Eigen BLAS routines.
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* Moreover, when the size of a supernode is very small, the BLAS calls are avoided to
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* enable a better optimization from the compiler. For best performance,
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* you should compile it with NDEBUG flag to avoid the numerous bounds checking on vectors.
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*
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* An important parameter of this class is the ordering method. It is used to reorder the columns
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* (and eventually the rows) of the matrix to reduce the number of new elements that are created during
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* numerical factorization. The cheapest method available is COLAMD.
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* See \link OrderingMethods_Module the OrderingMethods module \endlink for the list of
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* built-in and external ordering methods.
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*
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* Simple example with key steps
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* \code
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* VectorXd x(n), b(n);
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* SparseMatrix<double, ColMajor> A;
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* SparseLU<SparseMatrix<scalar, ColMajor>, COLAMDOrdering<Index> > solver;
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* // fill A and b;
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* // Compute the ordering permutation vector from the structural pattern of A
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* solver.analyzePattern(A);
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* // Compute the numerical factorization
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* solver.factorize(A);
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* //Use the factors to solve the linear system
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* x = solver.solve(b);
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* \endcode
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*
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* \warning The input matrix A should be in a \b compressed and \b column-major form.
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* Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix.
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*
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* \note Unlike the initial SuperLU implementation, there is no step to equilibrate the matrix.
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* For badly scaled matrices, this step can be useful to reduce the pivoting during factorization.
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* If this is the case for your matrices, you can try the basic scaling method at
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* "unsupported/Eigen/src/IterativeSolvers/Scaling.h"
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*
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* \tparam _MatrixType The type of the sparse matrix. It must be a column-major SparseMatrix<>
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* \tparam _OrderingType The ordering method to use, either AMD, COLAMD or METIS. Default is COLMAD
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*
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* \implsparsesolverconcept
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*
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* \sa \ref TutorialSparseSolverConcept
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* \sa \ref OrderingMethods_Module
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*/
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template <typename _MatrixType, typename _OrderingType>
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class SparseLU : public SparseSolverBase<SparseLU<_MatrixType,_OrderingType> >, public internal::SparseLUImpl<typename _MatrixType::Scalar, typename _MatrixType::StorageIndex>
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{
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protected:
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typedef SparseSolverBase<SparseLU<_MatrixType,_OrderingType> > APIBase;
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using APIBase::m_isInitialized;
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public:
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using APIBase::_solve_impl;
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typedef _MatrixType MatrixType;
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typedef _OrderingType OrderingType;
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::RealScalar RealScalar;
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typedef typename MatrixType::StorageIndex StorageIndex;
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typedef SparseMatrix<Scalar,ColMajor,StorageIndex> NCMatrix;
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typedef internal::MappedSuperNodalMatrix<Scalar, StorageIndex> SCMatrix;
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typedef Matrix<Scalar,Dynamic,1> ScalarVector;
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typedef Matrix<StorageIndex,Dynamic,1> IndexVector;
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typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType;
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typedef internal::SparseLUImpl<Scalar, StorageIndex> Base;
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enum {
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ColsAtCompileTime = MatrixType::ColsAtCompileTime,
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MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
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};
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public:
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SparseLU():m_lastError(""),m_Ustore(0,0,0,0,0,0),m_symmetricmode(false),m_diagpivotthresh(1.0),m_detPermR(1)
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{
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initperfvalues();
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}
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explicit SparseLU(const MatrixType& matrix)
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: m_lastError(""),m_Ustore(0,0,0,0,0,0),m_symmetricmode(false),m_diagpivotthresh(1.0),m_detPermR(1)
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{
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initperfvalues();
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compute(matrix);
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}
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~SparseLU()
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{
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// Free all explicit dynamic pointers
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}
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void analyzePattern (const MatrixType& matrix);
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void factorize (const MatrixType& matrix);
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void simplicialfactorize(const MatrixType& matrix);
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/**
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* Compute the symbolic and numeric factorization of the input sparse matrix.
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* The input matrix should be in column-major storage.
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*/
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void compute (const MatrixType& matrix)
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{
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// Analyze
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analyzePattern(matrix);
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//Factorize
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factorize(matrix);
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}
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inline Index rows() const { return m_mat.rows(); }
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inline Index cols() const { return m_mat.cols(); }
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/** Indicate that the pattern of the input matrix is symmetric */
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void isSymmetric(bool sym)
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{
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m_symmetricmode = sym;
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}
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/** \returns an expression of the matrix L, internally stored as supernodes
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* The only operation available with this expression is the triangular solve
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* \code
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* y = b; matrixL().solveInPlace(y);
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* \endcode
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*/
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SparseLUMatrixLReturnType<SCMatrix> matrixL() const
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{
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return SparseLUMatrixLReturnType<SCMatrix>(m_Lstore);
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}
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/** \returns an expression of the matrix U,
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* The only operation available with this expression is the triangular solve
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* \code
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* y = b; matrixU().solveInPlace(y);
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* \endcode
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*/
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SparseLUMatrixUReturnType<SCMatrix,MappedSparseMatrix<Scalar,ColMajor,StorageIndex> > matrixU() const
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{
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return SparseLUMatrixUReturnType<SCMatrix, MappedSparseMatrix<Scalar,ColMajor,StorageIndex> >(m_Lstore, m_Ustore);
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}
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/**
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* \returns a reference to the row matrix permutation \f$ P_r \f$ such that \f$P_r A P_c^T = L U\f$
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* \sa colsPermutation()
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*/
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inline const PermutationType& rowsPermutation() const
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{
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return m_perm_r;
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}
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/**
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* \returns a reference to the column matrix permutation\f$ P_c^T \f$ such that \f$P_r A P_c^T = L U\f$
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* \sa rowsPermutation()
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*/
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inline const PermutationType& colsPermutation() const
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{
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return m_perm_c;
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}
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/** Set the threshold used for a diagonal entry to be an acceptable pivot. */
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void setPivotThreshold(const RealScalar& thresh)
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{
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m_diagpivotthresh = thresh;
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}
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#ifdef EIGEN_PARSED_BY_DOXYGEN
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/** \returns the solution X of \f$ A X = B \f$ using the current decomposition of A.
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*
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* \warning the destination matrix X in X = this->solve(B) must be colmun-major.
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*
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* \sa compute()
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*/
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template<typename Rhs>
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inline const Solve<SparseLU, Rhs> solve(const MatrixBase<Rhs>& B) const;
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#endif // EIGEN_PARSED_BY_DOXYGEN
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/** \brief Reports whether previous computation was successful.
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*
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* \returns \c Success if computation was succesful,
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* \c NumericalIssue if the LU factorization reports a problem, zero diagonal for instance
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* \c InvalidInput if the input matrix is invalid
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*
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* \sa iparm()
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*/
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ComputationInfo info() const
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{
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eigen_assert(m_isInitialized && "Decomposition is not initialized.");
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return m_info;
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}
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/**
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* \returns A string describing the type of error
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*/
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std::string lastErrorMessage() const
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{
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return m_lastError;
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}
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template<typename Rhs, typename Dest>
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bool _solve_impl(const MatrixBase<Rhs> &B, MatrixBase<Dest> &X_base) const
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{
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Dest& X(X_base.derived());
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eigen_assert(m_factorizationIsOk && "The matrix should be factorized first");
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EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0,
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THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
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// Permute the right hand side to form X = Pr*B
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// on return, X is overwritten by the computed solution
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X.resize(B.rows(),B.cols());
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// this ugly const_cast_derived() helps to detect aliasing when applying the permutations
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for(Index j = 0; j < B.cols(); ++j)
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X.col(j) = rowsPermutation() * B.const_cast_derived().col(j);
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//Forward substitution with L
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this->matrixL().solveInPlace(X);
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this->matrixU().solveInPlace(X);
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// Permute back the solution
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for (Index j = 0; j < B.cols(); ++j)
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X.col(j) = colsPermutation().inverse() * X.col(j);
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return true;
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}
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/**
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* \returns the absolute value of the determinant of the matrix of which
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* *this is the QR decomposition.
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*
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* \warning a determinant can be very big or small, so for matrices
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* of large enough dimension, there is a risk of overflow/underflow.
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* One way to work around that is to use logAbsDeterminant() instead.
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*
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* \sa logAbsDeterminant(), signDeterminant()
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*/
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Scalar absDeterminant()
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{
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using std::abs;
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eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
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// Initialize with the determinant of the row matrix
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Scalar det = Scalar(1.);
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// Note that the diagonal blocks of U are stored in supernodes,
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// which are available in the L part :)
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for (Index j = 0; j < this->cols(); ++j)
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{
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for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
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{
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if(it.index() == j)
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{
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det *= abs(it.value());
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break;
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}
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}
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}
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return det;
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}
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/** \returns the natural log of the absolute value of the determinant of the matrix
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* of which **this is the QR decomposition
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*
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* \note This method is useful to work around the risk of overflow/underflow that's
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* inherent to the determinant computation.
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*
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* \sa absDeterminant(), signDeterminant()
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*/
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Scalar logAbsDeterminant() const
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{
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using std::log;
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using std::abs;
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eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
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Scalar det = Scalar(0.);
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for (Index j = 0; j < this->cols(); ++j)
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{
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for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
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{
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if(it.row() < j) continue;
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if(it.row() == j)
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{
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det += log(abs(it.value()));
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break;
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}
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}
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}
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return det;
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}
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/** \returns A number representing the sign of the determinant
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*
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* \sa absDeterminant(), logAbsDeterminant()
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*/
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Scalar signDeterminant()
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{
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eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
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// Initialize with the determinant of the row matrix
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Index det = 1;
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// Note that the diagonal blocks of U are stored in supernodes,
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// which are available in the L part :)
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for (Index j = 0; j < this->cols(); ++j)
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{
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for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
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{
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if(it.index() == j)
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{
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if(it.value()<0)
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det = -det;
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else if(it.value()==0)
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return 0;
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break;
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}
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}
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}
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return det * m_detPermR * m_detPermC;
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}
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/** \returns The determinant of the matrix.
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*
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* \sa absDeterminant(), logAbsDeterminant()
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*/
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Scalar determinant()
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{
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eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
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// Initialize with the determinant of the row matrix
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Scalar det = Scalar(1.);
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// Note that the diagonal blocks of U are stored in supernodes,
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// which are available in the L part :)
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for (Index j = 0; j < this->cols(); ++j)
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{
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for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
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{
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if(it.index() == j)
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{
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det *= it.value();
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break;
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}
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}
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}
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return (m_detPermR * m_detPermC) > 0 ? det : -det;
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}
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protected:
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// Functions
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void initperfvalues()
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{
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m_perfv.panel_size = 16;
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m_perfv.relax = 1;
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m_perfv.maxsuper = 128;
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m_perfv.rowblk = 16;
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m_perfv.colblk = 8;
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m_perfv.fillfactor = 20;
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}
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// Variables
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mutable ComputationInfo m_info;
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bool m_factorizationIsOk;
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bool m_analysisIsOk;
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std::string m_lastError;
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NCMatrix m_mat; // The input (permuted ) matrix
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SCMatrix m_Lstore; // The lower triangular matrix (supernodal)
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MappedSparseMatrix<Scalar,ColMajor,StorageIndex> m_Ustore; // The upper triangular matrix
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PermutationType m_perm_c; // Column permutation
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PermutationType m_perm_r ; // Row permutation
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IndexVector m_etree; // Column elimination tree
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typename Base::GlobalLU_t m_glu;
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// SparseLU options
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bool m_symmetricmode;
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// values for performance
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internal::perfvalues m_perfv;
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RealScalar m_diagpivotthresh; // Specifies the threshold used for a diagonal entry to be an acceptable pivot
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Index m_nnzL, m_nnzU; // Nonzeros in L and U factors
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Index m_detPermR, m_detPermC; // Determinants of the permutation matrices
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private:
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// Disable copy constructor
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SparseLU (const SparseLU& );
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}; // End class SparseLU
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// Functions needed by the anaysis phase
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/**
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* Compute the column permutation to minimize the fill-in
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*
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* - Apply this permutation to the input matrix -
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*
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* - Compute the column elimination tree on the permuted matrix
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*
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* - Postorder the elimination tree and the column permutation
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*
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*/
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template <typename MatrixType, typename OrderingType>
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void SparseLU<MatrixType, OrderingType>::analyzePattern(const MatrixType& mat)
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{
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//TODO It is possible as in SuperLU to compute row and columns scaling vectors to equilibrate the matrix mat.
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// Firstly, copy the whole input matrix.
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m_mat = mat;
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// Compute fill-in ordering
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OrderingType ord;
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ord(m_mat,m_perm_c);
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// Apply the permutation to the column of the input matrix
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if (m_perm_c.size())
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{
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m_mat.uncompress(); //NOTE: The effect of this command is only to create the InnerNonzeros pointers. FIXME : This vector is filled but not subsequently used.
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// Then, permute only the column pointers
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ei_declare_aligned_stack_constructed_variable(StorageIndex,outerIndexPtr,mat.cols()+1,mat.isCompressed()?const_cast<StorageIndex*>(mat.outerIndexPtr()):0);
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// If the input matrix 'mat' is uncompressed, then the outer-indices do not match the ones of m_mat, and a copy is thus needed.
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if(!mat.isCompressed())
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IndexVector::Map(outerIndexPtr, mat.cols()+1) = IndexVector::Map(m_mat.outerIndexPtr(),mat.cols()+1);
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// Apply the permutation and compute the nnz per column.
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for (Index i = 0; i < mat.cols(); i++)
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{
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m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i];
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m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i+1] - outerIndexPtr[i];
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}
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}
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// Compute the column elimination tree of the permuted matrix
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IndexVector firstRowElt;
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internal::coletree(m_mat, m_etree,firstRowElt);
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// In symmetric mode, do not do postorder here
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if (!m_symmetricmode) {
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IndexVector post, iwork;
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// Post order etree
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internal::treePostorder(StorageIndex(m_mat.cols()), m_etree, post);
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// Renumber etree in postorder
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Index m = m_mat.cols();
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iwork.resize(m+1);
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for (Index i = 0; i < m; ++i) iwork(post(i)) = post(m_etree(i));
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m_etree = iwork;
|
||||
|
||||
// Postmultiply A*Pc by post, i.e reorder the matrix according to the postorder of the etree
|
||||
PermutationType post_perm(m);
|
||||
for (Index i = 0; i < m; i++)
|
||||
post_perm.indices()(i) = post(i);
|
||||
|
||||
// Combine the two permutations : postorder the permutation for future use
|
||||
if(m_perm_c.size()) {
|
||||
m_perm_c = post_perm * m_perm_c;
|
||||
}
|
||||
|
||||
} // end postordering
|
||||
|
||||
m_analysisIsOk = true;
|
||||
}
|
||||
|
||||
// Functions needed by the numerical factorization phase
|
||||
|
||||
|
||||
/**
|
||||
* - Numerical factorization
|
||||
* - Interleaved with the symbolic factorization
|
||||
* On exit, info is
|
||||
*
|
||||
* = 0: successful factorization
|
||||
*
|
||||
* > 0: if info = i, and i is
|
||||
*
|
||||
* <= A->ncol: U(i,i) is exactly zero. The factorization has
|
||||
* been completed, but the factor U is exactly singular,
|
||||
* and division by zero will occur if it is used to solve a
|
||||
* system of equations.
|
||||
*
|
||||
* > A->ncol: number of bytes allocated when memory allocation
|
||||
* failure occurred, plus A->ncol. If lwork = -1, it is
|
||||
* the estimated amount of space needed, plus A->ncol.
|
||||
*/
|
||||
template <typename MatrixType, typename OrderingType>
|
||||
void SparseLU<MatrixType, OrderingType>::factorize(const MatrixType& matrix)
|
||||
{
|
||||
using internal::emptyIdxLU;
|
||||
eigen_assert(m_analysisIsOk && "analyzePattern() should be called first");
|
||||
eigen_assert((matrix.rows() == matrix.cols()) && "Only for squared matrices");
|
||||
|
||||
m_isInitialized = true;
|
||||
|
||||
|
||||
// Apply the column permutation computed in analyzepattern()
|
||||
// m_mat = matrix * m_perm_c.inverse();
|
||||
m_mat = matrix;
|
||||
if (m_perm_c.size())
|
||||
{
|
||||
m_mat.uncompress(); //NOTE: The effect of this command is only to create the InnerNonzeros pointers.
|
||||
//Then, permute only the column pointers
|
||||
const StorageIndex * outerIndexPtr;
|
||||
if (matrix.isCompressed()) outerIndexPtr = matrix.outerIndexPtr();
|
||||
else
|
||||
{
|
||||
StorageIndex* outerIndexPtr_t = new StorageIndex[matrix.cols()+1];
|
||||
for(Index i = 0; i <= matrix.cols(); i++) outerIndexPtr_t[i] = m_mat.outerIndexPtr()[i];
|
||||
outerIndexPtr = outerIndexPtr_t;
|
||||
}
|
||||
for (Index i = 0; i < matrix.cols(); i++)
|
||||
{
|
||||
m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i];
|
||||
m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i+1] - outerIndexPtr[i];
|
||||
}
|
||||
if(!matrix.isCompressed()) delete[] outerIndexPtr;
|
||||
}
|
||||
else
|
||||
{ //FIXME This should not be needed if the empty permutation is handled transparently
|
||||
m_perm_c.resize(matrix.cols());
|
||||
for(StorageIndex i = 0; i < matrix.cols(); ++i) m_perm_c.indices()(i) = i;
|
||||
}
|
||||
|
||||
Index m = m_mat.rows();
|
||||
Index n = m_mat.cols();
|
||||
Index nnz = m_mat.nonZeros();
|
||||
Index maxpanel = m_perfv.panel_size * m;
|
||||
// Allocate working storage common to the factor routines
|
||||
Index lwork = 0;
|
||||
Index info = Base::memInit(m, n, nnz, lwork, m_perfv.fillfactor, m_perfv.panel_size, m_glu);
|
||||
if (info)
|
||||
{
|
||||
m_lastError = "UNABLE TO ALLOCATE WORKING MEMORY\n\n" ;
|
||||
m_factorizationIsOk = false;
|
||||
return ;
|
||||
}
|
||||
|
||||
// Set up pointers for integer working arrays
|
||||
IndexVector segrep(m); segrep.setZero();
|
||||
IndexVector parent(m); parent.setZero();
|
||||
IndexVector xplore(m); xplore.setZero();
|
||||
IndexVector repfnz(maxpanel);
|
||||
IndexVector panel_lsub(maxpanel);
|
||||
IndexVector xprune(n); xprune.setZero();
|
||||
IndexVector marker(m*internal::LUNoMarker); marker.setZero();
|
||||
|
||||
repfnz.setConstant(-1);
|
||||
panel_lsub.setConstant(-1);
|
||||
|
||||
// Set up pointers for scalar working arrays
|
||||
ScalarVector dense;
|
||||
dense.setZero(maxpanel);
|
||||
ScalarVector tempv;
|
||||
tempv.setZero(internal::LUnumTempV(m, m_perfv.panel_size, m_perfv.maxsuper, /*m_perfv.rowblk*/m) );
|
||||
|
||||
// Compute the inverse of perm_c
|
||||
PermutationType iperm_c(m_perm_c.inverse());
|
||||
|
||||
// Identify initial relaxed snodes
|
||||
IndexVector relax_end(n);
|
||||
if ( m_symmetricmode == true )
|
||||
Base::heap_relax_snode(n, m_etree, m_perfv.relax, marker, relax_end);
|
||||
else
|
||||
Base::relax_snode(n, m_etree, m_perfv.relax, marker, relax_end);
|
||||
|
||||
|
||||
m_perm_r.resize(m);
|
||||
m_perm_r.indices().setConstant(-1);
|
||||
marker.setConstant(-1);
|
||||
m_detPermR = 1; // Record the determinant of the row permutation
|
||||
|
||||
m_glu.supno(0) = emptyIdxLU; m_glu.xsup.setConstant(0);
|
||||
m_glu.xsup(0) = m_glu.xlsub(0) = m_glu.xusub(0) = m_glu.xlusup(0) = Index(0);
|
||||
|
||||
// Work on one 'panel' at a time. A panel is one of the following :
|
||||
// (a) a relaxed supernode at the bottom of the etree, or
|
||||
// (b) panel_size contiguous columns, <panel_size> defined by the user
|
||||
Index jcol;
|
||||
IndexVector panel_histo(n);
|
||||
Index pivrow; // Pivotal row number in the original row matrix
|
||||
Index nseg1; // Number of segments in U-column above panel row jcol
|
||||
Index nseg; // Number of segments in each U-column
|
||||
Index irep;
|
||||
Index i, k, jj;
|
||||
for (jcol = 0; jcol < n; )
|
||||
{
|
||||
// Adjust panel size so that a panel won't overlap with the next relaxed snode.
|
||||
Index panel_size = m_perfv.panel_size; // upper bound on panel width
|
||||
for (k = jcol + 1; k < (std::min)(jcol+panel_size, n); k++)
|
||||
{
|
||||
if (relax_end(k) != emptyIdxLU)
|
||||
{
|
||||
panel_size = k - jcol;
|
||||
break;
|
||||
}
|
||||
}
|
||||
if (k == n)
|
||||
panel_size = n - jcol;
|
||||
|
||||
// Symbolic outer factorization on a panel of columns
|
||||
Base::panel_dfs(m, panel_size, jcol, m_mat, m_perm_r.indices(), nseg1, dense, panel_lsub, segrep, repfnz, xprune, marker, parent, xplore, m_glu);
|
||||
|
||||
// Numeric sup-panel updates in topological order
|
||||
Base::panel_bmod(m, panel_size, jcol, nseg1, dense, tempv, segrep, repfnz, m_glu);
|
||||
|
||||
// Sparse LU within the panel, and below the panel diagonal
|
||||
for ( jj = jcol; jj< jcol + panel_size; jj++)
|
||||
{
|
||||
k = (jj - jcol) * m; // Column index for w-wide arrays
|
||||
|
||||
nseg = nseg1; // begin after all the panel segments
|
||||
//Depth-first-search for the current column
|
||||
VectorBlock<IndexVector> panel_lsubk(panel_lsub, k, m);
|
||||
VectorBlock<IndexVector> repfnz_k(repfnz, k, m);
|
||||
info = Base::column_dfs(m, jj, m_perm_r.indices(), m_perfv.maxsuper, nseg, panel_lsubk, segrep, repfnz_k, xprune, marker, parent, xplore, m_glu);
|
||||
if ( info )
|
||||
{
|
||||
m_lastError = "UNABLE TO EXPAND MEMORY IN COLUMN_DFS() ";
|
||||
m_info = NumericalIssue;
|
||||
m_factorizationIsOk = false;
|
||||
return;
|
||||
}
|
||||
// Numeric updates to this column
|
||||
VectorBlock<ScalarVector> dense_k(dense, k, m);
|
||||
VectorBlock<IndexVector> segrep_k(segrep, nseg1, m-nseg1);
|
||||
info = Base::column_bmod(jj, (nseg - nseg1), dense_k, tempv, segrep_k, repfnz_k, jcol, m_glu);
|
||||
if ( info )
|
||||
{
|
||||
m_lastError = "UNABLE TO EXPAND MEMORY IN COLUMN_BMOD() ";
|
||||
m_info = NumericalIssue;
|
||||
m_factorizationIsOk = false;
|
||||
return;
|
||||
}
|
||||
|
||||
// Copy the U-segments to ucol(*)
|
||||
info = Base::copy_to_ucol(jj, nseg, segrep, repfnz_k ,m_perm_r.indices(), dense_k, m_glu);
|
||||
if ( info )
|
||||
{
|
||||
m_lastError = "UNABLE TO EXPAND MEMORY IN COPY_TO_UCOL() ";
|
||||
m_info = NumericalIssue;
|
||||
m_factorizationIsOk = false;
|
||||
return;
|
||||
}
|
||||
|
||||
// Form the L-segment
|
||||
info = Base::pivotL(jj, m_diagpivotthresh, m_perm_r.indices(), iperm_c.indices(), pivrow, m_glu);
|
||||
if ( info )
|
||||
{
|
||||
m_lastError = "THE MATRIX IS STRUCTURALLY SINGULAR ... ZERO COLUMN AT ";
|
||||
std::ostringstream returnInfo;
|
||||
returnInfo << info;
|
||||
m_lastError += returnInfo.str();
|
||||
m_info = NumericalIssue;
|
||||
m_factorizationIsOk = false;
|
||||
return;
|
||||
}
|
||||
|
||||
// Update the determinant of the row permutation matrix
|
||||
// FIXME: the following test is not correct, we should probably take iperm_c into account and pivrow is not directly the row pivot.
|
||||
if (pivrow != jj) m_detPermR = -m_detPermR;
|
||||
|
||||
// Prune columns (0:jj-1) using column jj
|
||||
Base::pruneL(jj, m_perm_r.indices(), pivrow, nseg, segrep, repfnz_k, xprune, m_glu);
|
||||
|
||||
// Reset repfnz for this column
|
||||
for (i = 0; i < nseg; i++)
|
||||
{
|
||||
irep = segrep(i);
|
||||
repfnz_k(irep) = emptyIdxLU;
|
||||
}
|
||||
} // end SparseLU within the panel
|
||||
jcol += panel_size; // Move to the next panel
|
||||
} // end for -- end elimination
|
||||
|
||||
m_detPermR = m_perm_r.determinant();
|
||||
m_detPermC = m_perm_c.determinant();
|
||||
|
||||
// Count the number of nonzeros in factors
|
||||
Base::countnz(n, m_nnzL, m_nnzU, m_glu);
|
||||
// Apply permutation to the L subscripts
|
||||
Base::fixupL(n, m_perm_r.indices(), m_glu);
|
||||
|
||||
// Create supernode matrix L
|
||||
m_Lstore.setInfos(m, n, m_glu.lusup, m_glu.xlusup, m_glu.lsub, m_glu.xlsub, m_glu.supno, m_glu.xsup);
|
||||
// Create the column major upper sparse matrix U;
|
||||
new (&m_Ustore) MappedSparseMatrix<Scalar, ColMajor, StorageIndex> ( m, n, m_nnzU, m_glu.xusub.data(), m_glu.usub.data(), m_glu.ucol.data() );
|
||||
|
||||
m_info = Success;
|
||||
m_factorizationIsOk = true;
|
||||
}
|
||||
|
||||
template<typename MappedSupernodalType>
|
||||
struct SparseLUMatrixLReturnType : internal::no_assignment_operator
|
||||
{
|
||||
typedef typename MappedSupernodalType::Scalar Scalar;
|
||||
explicit SparseLUMatrixLReturnType(const MappedSupernodalType& mapL) : m_mapL(mapL)
|
||||
{ }
|
||||
Index rows() { return m_mapL.rows(); }
|
||||
Index cols() { return m_mapL.cols(); }
|
||||
template<typename Dest>
|
||||
void solveInPlace( MatrixBase<Dest> &X) const
|
||||
{
|
||||
m_mapL.solveInPlace(X);
|
||||
}
|
||||
const MappedSupernodalType& m_mapL;
|
||||
};
|
||||
|
||||
template<typename MatrixLType, typename MatrixUType>
|
||||
struct SparseLUMatrixUReturnType : internal::no_assignment_operator
|
||||
{
|
||||
typedef typename MatrixLType::Scalar Scalar;
|
||||
SparseLUMatrixUReturnType(const MatrixLType& mapL, const MatrixUType& mapU)
|
||||
: m_mapL(mapL),m_mapU(mapU)
|
||||
{ }
|
||||
Index rows() { return m_mapL.rows(); }
|
||||
Index cols() { return m_mapL.cols(); }
|
||||
|
||||
template<typename Dest> void solveInPlace(MatrixBase<Dest> &X) const
|
||||
{
|
||||
Index nrhs = X.cols();
|
||||
Index n = X.rows();
|
||||
// Backward solve with U
|
||||
for (Index k = m_mapL.nsuper(); k >= 0; k--)
|
||||
{
|
||||
Index fsupc = m_mapL.supToCol()[k];
|
||||
Index lda = m_mapL.colIndexPtr()[fsupc+1] - m_mapL.colIndexPtr()[fsupc]; // leading dimension
|
||||
Index nsupc = m_mapL.supToCol()[k+1] - fsupc;
|
||||
Index luptr = m_mapL.colIndexPtr()[fsupc];
|
||||
|
||||
if (nsupc == 1)
|
||||
{
|
||||
for (Index j = 0; j < nrhs; j++)
|
||||
{
|
||||
X(fsupc, j) /= m_mapL.valuePtr()[luptr];
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > A( &(m_mapL.valuePtr()[luptr]), nsupc, nsupc, OuterStride<>(lda) );
|
||||
Map< Matrix<Scalar,Dynamic,Dest::ColsAtCompileTime, ColMajor>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) );
|
||||
U = A.template triangularView<Upper>().solve(U);
|
||||
}
|
||||
|
||||
for (Index j = 0; j < nrhs; ++j)
|
||||
{
|
||||
for (Index jcol = fsupc; jcol < fsupc + nsupc; jcol++)
|
||||
{
|
||||
typename MatrixUType::InnerIterator it(m_mapU, jcol);
|
||||
for ( ; it; ++it)
|
||||
{
|
||||
Index irow = it.index();
|
||||
X(irow, j) -= X(jcol, j) * it.value();
|
||||
}
|
||||
}
|
||||
}
|
||||
} // End For U-solve
|
||||
}
|
||||
const MatrixLType& m_mapL;
|
||||
const MatrixUType& m_mapU;
|
||||
};
|
||||
|
||||
} // End namespace Eigen
|
||||
|
||||
#endif
|
||||
66
external/include/eigen3/Eigen/src/SparseLU/SparseLUImpl.h
vendored
Normal file
66
external/include/eigen3/Eigen/src/SparseLU/SparseLUImpl.h
vendored
Normal file
@@ -0,0 +1,66 @@
|
||||
// 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/.
|
||||
#ifndef SPARSELU_IMPL_H
|
||||
#define SPARSELU_IMPL_H
|
||||
|
||||
namespace Eigen {
|
||||
namespace internal {
|
||||
|
||||
/** \ingroup SparseLU_Module
|
||||
* \class SparseLUImpl
|
||||
* Base class for sparseLU
|
||||
*/
|
||||
template <typename Scalar, typename StorageIndex>
|
||||
class SparseLUImpl
|
||||
{
|
||||
public:
|
||||
typedef Matrix<Scalar,Dynamic,1> ScalarVector;
|
||||
typedef Matrix<StorageIndex,Dynamic,1> IndexVector;
|
||||
typedef Matrix<Scalar,Dynamic,Dynamic,ColMajor> ScalarMatrix;
|
||||
typedef Map<ScalarMatrix, 0, OuterStride<> > MappedMatrixBlock;
|
||||
typedef typename ScalarVector::RealScalar RealScalar;
|
||||
typedef Ref<Matrix<Scalar,Dynamic,1> > BlockScalarVector;
|
||||
typedef Ref<Matrix<StorageIndex,Dynamic,1> > BlockIndexVector;
|
||||
typedef LU_GlobalLU_t<IndexVector, ScalarVector> GlobalLU_t;
|
||||
typedef SparseMatrix<Scalar,ColMajor,StorageIndex> MatrixType;
|
||||
|
||||
protected:
|
||||
template <typename VectorType>
|
||||
Index expand(VectorType& vec, Index& length, Index nbElts, Index keep_prev, Index& num_expansions);
|
||||
Index memInit(Index m, Index n, Index annz, Index lwork, Index fillratio, Index panel_size, GlobalLU_t& glu);
|
||||
template <typename VectorType>
|
||||
Index memXpand(VectorType& vec, Index& maxlen, Index nbElts, MemType memtype, Index& num_expansions);
|
||||
void heap_relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end);
|
||||
void relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end);
|
||||
Index snode_dfs(const Index jcol, const Index kcol,const MatrixType& mat, IndexVector& xprune, IndexVector& marker, GlobalLU_t& glu);
|
||||
Index snode_bmod (const Index jcol, const Index fsupc, ScalarVector& dense, GlobalLU_t& glu);
|
||||
Index pivotL(const Index jcol, const RealScalar& diagpivotthresh, IndexVector& perm_r, IndexVector& iperm_c, Index& pivrow, GlobalLU_t& glu);
|
||||
template <typename Traits>
|
||||
void dfs_kernel(const StorageIndex jj, IndexVector& perm_r,
|
||||
Index& nseg, IndexVector& panel_lsub, IndexVector& segrep,
|
||||
Ref<IndexVector> repfnz_col, IndexVector& xprune, Ref<IndexVector> marker, IndexVector& parent,
|
||||
IndexVector& xplore, GlobalLU_t& glu, Index& nextl_col, Index krow, Traits& traits);
|
||||
void panel_dfs(const Index m, const Index w, const Index jcol, MatrixType& A, IndexVector& perm_r, Index& nseg, ScalarVector& dense, IndexVector& panel_lsub, IndexVector& segrep, IndexVector& repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu);
|
||||
|
||||
void panel_bmod(const Index m, const Index w, const Index jcol, const Index nseg, ScalarVector& dense, ScalarVector& tempv, IndexVector& segrep, IndexVector& repfnz, GlobalLU_t& glu);
|
||||
Index column_dfs(const Index m, const Index jcol, IndexVector& perm_r, Index maxsuper, Index& nseg, BlockIndexVector lsub_col, IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu);
|
||||
Index column_bmod(const Index jcol, const Index nseg, BlockScalarVector dense, ScalarVector& tempv, BlockIndexVector segrep, BlockIndexVector repfnz, Index fpanelc, GlobalLU_t& glu);
|
||||
Index copy_to_ucol(const Index jcol, const Index nseg, IndexVector& segrep, BlockIndexVector repfnz ,IndexVector& perm_r, BlockScalarVector dense, GlobalLU_t& glu);
|
||||
void pruneL(const Index jcol, const IndexVector& perm_r, const Index pivrow, const Index nseg, const IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune, GlobalLU_t& glu);
|
||||
void countnz(const Index n, Index& nnzL, Index& nnzU, GlobalLU_t& glu);
|
||||
void fixupL(const Index n, const IndexVector& perm_r, GlobalLU_t& glu);
|
||||
|
||||
template<typename , typename >
|
||||
friend struct column_dfs_traits;
|
||||
};
|
||||
|
||||
} // end namespace internal
|
||||
} // namespace Eigen
|
||||
|
||||
#endif
|
||||
226
external/include/eigen3/Eigen/src/SparseLU/SparseLU_Memory.h
vendored
Normal file
226
external/include/eigen3/Eigen/src/SparseLU/SparseLU_Memory.h
vendored
Normal file
@@ -0,0 +1,226 @@
|
||||
// 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/.
|
||||
|
||||
/*
|
||||
|
||||
* NOTE: This file is the modified version of [s,d,c,z]memory.c files in SuperLU
|
||||
|
||||
* -- SuperLU routine (version 3.1) --
|
||||
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
|
||||
* and Lawrence Berkeley National Lab.
|
||||
* August 1, 2008
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
|
||||
#ifndef EIGEN_SPARSELU_MEMORY
|
||||
#define EIGEN_SPARSELU_MEMORY
|
||||
|
||||
namespace Eigen {
|
||||
namespace internal {
|
||||
|
||||
enum { LUNoMarker = 3 };
|
||||
enum {emptyIdxLU = -1};
|
||||
inline Index LUnumTempV(Index& m, Index& w, Index& t, Index& b)
|
||||
{
|
||||
return (std::max)(m, (t+b)*w);
|
||||
}
|
||||
|
||||
template< typename Scalar>
|
||||
inline Index LUTempSpace(Index&m, Index& w)
|
||||
{
|
||||
return (2*w + 4 + LUNoMarker) * m * sizeof(Index) + (w + 1) * m * sizeof(Scalar);
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
/**
|
||||
* Expand the existing storage to accomodate more fill-ins
|
||||
* \param vec Valid pointer to the vector to allocate or expand
|
||||
* \param[in,out] length At input, contain the current length of the vector that is to be increased. At output, length of the newly allocated vector
|
||||
* \param[in] nbElts Current number of elements in the factors
|
||||
* \param keep_prev 1: use length and do not expand the vector; 0: compute new_len and expand
|
||||
* \param[in,out] num_expansions Number of times the memory has been expanded
|
||||
*/
|
||||
template <typename Scalar, typename StorageIndex>
|
||||
template <typename VectorType>
|
||||
Index SparseLUImpl<Scalar,StorageIndex>::expand(VectorType& vec, Index& length, Index nbElts, Index keep_prev, Index& num_expansions)
|
||||
{
|
||||
|
||||
float alpha = 1.5; // Ratio of the memory increase
|
||||
Index new_len; // New size of the allocated memory
|
||||
|
||||
if(num_expansions == 0 || keep_prev)
|
||||
new_len = length ; // First time allocate requested
|
||||
else
|
||||
new_len = (std::max)(length+1,Index(alpha * length));
|
||||
|
||||
VectorType old_vec; // Temporary vector to hold the previous values
|
||||
if (nbElts > 0 )
|
||||
old_vec = vec.segment(0,nbElts);
|
||||
|
||||
//Allocate or expand the current vector
|
||||
#ifdef EIGEN_EXCEPTIONS
|
||||
try
|
||||
#endif
|
||||
{
|
||||
vec.resize(new_len);
|
||||
}
|
||||
#ifdef EIGEN_EXCEPTIONS
|
||||
catch(std::bad_alloc& )
|
||||
#else
|
||||
if(!vec.size())
|
||||
#endif
|
||||
{
|
||||
if (!num_expansions)
|
||||
{
|
||||
// First time to allocate from LUMemInit()
|
||||
// Let LUMemInit() deals with it.
|
||||
return -1;
|
||||
}
|
||||
if (keep_prev)
|
||||
{
|
||||
// In this case, the memory length should not not be reduced
|
||||
return new_len;
|
||||
}
|
||||
else
|
||||
{
|
||||
// Reduce the size and increase again
|
||||
Index tries = 0; // Number of attempts
|
||||
do
|
||||
{
|
||||
alpha = (alpha + 1)/2;
|
||||
new_len = (std::max)(length+1,Index(alpha * length));
|
||||
#ifdef EIGEN_EXCEPTIONS
|
||||
try
|
||||
#endif
|
||||
{
|
||||
vec.resize(new_len);
|
||||
}
|
||||
#ifdef EIGEN_EXCEPTIONS
|
||||
catch(std::bad_alloc& )
|
||||
#else
|
||||
if (!vec.size())
|
||||
#endif
|
||||
{
|
||||
tries += 1;
|
||||
if ( tries > 10) return new_len;
|
||||
}
|
||||
} while (!vec.size());
|
||||
}
|
||||
}
|
||||
//Copy the previous values to the newly allocated space
|
||||
if (nbElts > 0)
|
||||
vec.segment(0, nbElts) = old_vec;
|
||||
|
||||
|
||||
length = new_len;
|
||||
if(num_expansions) ++num_expansions;
|
||||
return 0;
|
||||
}
|
||||
|
||||
/**
|
||||
* \brief Allocate various working space for the numerical factorization phase.
|
||||
* \param m number of rows of the input matrix
|
||||
* \param n number of columns
|
||||
* \param annz number of initial nonzeros in the matrix
|
||||
* \param lwork if lwork=-1, this routine returns an estimated size of the required memory
|
||||
* \param glu persistent data to facilitate multiple factors : will be deleted later ??
|
||||
* \param fillratio estimated ratio of fill in the factors
|
||||
* \param panel_size Size of a panel
|
||||
* \return an estimated size of the required memory if lwork = -1; otherwise, return the size of actually allocated memory when allocation failed, and 0 on success
|
||||
* \note Unlike SuperLU, this routine does not support successive factorization with the same pattern and the same row permutation
|
||||
*/
|
||||
template <typename Scalar, typename StorageIndex>
|
||||
Index SparseLUImpl<Scalar,StorageIndex>::memInit(Index m, Index n, Index annz, Index lwork, Index fillratio, Index panel_size, GlobalLU_t& glu)
|
||||
{
|
||||
Index& num_expansions = glu.num_expansions; //No memory expansions so far
|
||||
num_expansions = 0;
|
||||
glu.nzumax = glu.nzlumax = (std::min)(fillratio * (annz+1) / n, m) * n; // estimated number of nonzeros in U
|
||||
glu.nzlmax = (std::max)(Index(4), fillratio) * (annz+1) / 4; // estimated nnz in L factor
|
||||
// Return the estimated size to the user if necessary
|
||||
Index tempSpace;
|
||||
tempSpace = (2*panel_size + 4 + LUNoMarker) * m * sizeof(Index) + (panel_size + 1) * m * sizeof(Scalar);
|
||||
if (lwork == emptyIdxLU)
|
||||
{
|
||||
Index estimated_size;
|
||||
estimated_size = (5 * n + 5) * sizeof(Index) + tempSpace
|
||||
+ (glu.nzlmax + glu.nzumax) * sizeof(Index) + (glu.nzlumax+glu.nzumax) * sizeof(Scalar) + n;
|
||||
return estimated_size;
|
||||
}
|
||||
|
||||
// Setup the required space
|
||||
|
||||
// First allocate Integer pointers for L\U factors
|
||||
glu.xsup.resize(n+1);
|
||||
glu.supno.resize(n+1);
|
||||
glu.xlsub.resize(n+1);
|
||||
glu.xlusup.resize(n+1);
|
||||
glu.xusub.resize(n+1);
|
||||
|
||||
// Reserve memory for L/U factors
|
||||
do
|
||||
{
|
||||
if( (expand<ScalarVector>(glu.lusup, glu.nzlumax, 0, 0, num_expansions)<0)
|
||||
|| (expand<ScalarVector>(glu.ucol, glu.nzumax, 0, 0, num_expansions)<0)
|
||||
|| (expand<IndexVector> (glu.lsub, glu.nzlmax, 0, 0, num_expansions)<0)
|
||||
|| (expand<IndexVector> (glu.usub, glu.nzumax, 0, 1, num_expansions)<0) )
|
||||
{
|
||||
//Reduce the estimated size and retry
|
||||
glu.nzlumax /= 2;
|
||||
glu.nzumax /= 2;
|
||||
glu.nzlmax /= 2;
|
||||
if (glu.nzlumax < annz ) return glu.nzlumax;
|
||||
}
|
||||
} while (!glu.lusup.size() || !glu.ucol.size() || !glu.lsub.size() || !glu.usub.size());
|
||||
|
||||
++num_expansions;
|
||||
return 0;
|
||||
|
||||
} // end LuMemInit
|
||||
|
||||
/**
|
||||
* \brief Expand the existing storage
|
||||
* \param vec vector to expand
|
||||
* \param[in,out] maxlen On input, previous size of vec (Number of elements to copy ). on output, new size
|
||||
* \param nbElts current number of elements in the vector.
|
||||
* \param memtype Type of the element to expand
|
||||
* \param num_expansions Number of expansions
|
||||
* \return 0 on success, > 0 size of the memory allocated so far
|
||||
*/
|
||||
template <typename Scalar, typename StorageIndex>
|
||||
template <typename VectorType>
|
||||
Index SparseLUImpl<Scalar,StorageIndex>::memXpand(VectorType& vec, Index& maxlen, Index nbElts, MemType memtype, Index& num_expansions)
|
||||
{
|
||||
Index failed_size;
|
||||
if (memtype == USUB)
|
||||
failed_size = this->expand<VectorType>(vec, maxlen, nbElts, 1, num_expansions);
|
||||
else
|
||||
failed_size = this->expand<VectorType>(vec, maxlen, nbElts, 0, num_expansions);
|
||||
|
||||
if (failed_size)
|
||||
return failed_size;
|
||||
|
||||
return 0 ;
|
||||
}
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
} // end namespace Eigen
|
||||
#endif // EIGEN_SPARSELU_MEMORY
|
||||
110
external/include/eigen3/Eigen/src/SparseLU/SparseLU_Structs.h
vendored
Normal file
110
external/include/eigen3/Eigen/src/SparseLU/SparseLU_Structs.h
vendored
Normal file
@@ -0,0 +1,110 @@
|
||||
// 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/.
|
||||
|
||||
/*
|
||||
* NOTE: This file comes from a partly modified version of files slu_[s,d,c,z]defs.h
|
||||
* -- SuperLU routine (version 4.1) --
|
||||
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
|
||||
* and Lawrence Berkeley National Lab.
|
||||
* November, 2010
|
||||
*
|
||||
* Global data structures used in LU factorization -
|
||||
*
|
||||
* nsuper: #supernodes = nsuper + 1, numbered [0, nsuper].
|
||||
* (xsup,supno): supno[i] is the supernode no to which i belongs;
|
||||
* xsup(s) points to the beginning of the s-th supernode.
|
||||
* e.g. supno 0 1 2 2 3 3 3 4 4 4 4 4 (n=12)
|
||||
* xsup 0 1 2 4 7 12
|
||||
* Note: dfs will be performed on supernode rep. relative to the new
|
||||
* row pivoting ordering
|
||||
*
|
||||
* (xlsub,lsub): lsub[*] contains the compressed subscript of
|
||||
* rectangular supernodes; xlsub[j] points to the starting
|
||||
* location of the j-th column in lsub[*]. Note that xlsub
|
||||
* is indexed by column.
|
||||
* Storage: original row subscripts
|
||||
*
|
||||
* During the course of sparse LU factorization, we also use
|
||||
* (xlsub,lsub) for the purpose of symmetric pruning. For each
|
||||
* supernode {s,s+1,...,t=s+r} with first column s and last
|
||||
* column t, the subscript set
|
||||
* lsub[j], j=xlsub[s], .., xlsub[s+1]-1
|
||||
* is the structure of column s (i.e. structure of this supernode).
|
||||
* It is used for the storage of numerical values.
|
||||
* Furthermore,
|
||||
* lsub[j], j=xlsub[t], .., xlsub[t+1]-1
|
||||
* is the structure of the last column t of this supernode.
|
||||
* It is for the purpose of symmetric pruning. Therefore, the
|
||||
* structural subscripts can be rearranged without making physical
|
||||
* interchanges among the numerical values.
|
||||
*
|
||||
* However, if the supernode has only one column, then we
|
||||
* only keep one set of subscripts. For any subscript interchange
|
||||
* performed, similar interchange must be done on the numerical
|
||||
* values.
|
||||
*
|
||||
* The last column structures (for pruning) will be removed
|
||||
* after the numercial LU factorization phase.
|
||||
*
|
||||
* (xlusup,lusup): lusup[*] contains the numerical values of the
|
||||
* rectangular supernodes; xlusup[j] points to the starting
|
||||
* location of the j-th column in storage vector lusup[*]
|
||||
* Note: xlusup is indexed by column.
|
||||
* Each rectangular supernode is stored by column-major
|
||||
* scheme, consistent with Fortran 2-dim array storage.
|
||||
*
|
||||
* (xusub,ucol,usub): ucol[*] stores the numerical values of
|
||||
* U-columns outside the rectangular supernodes. The row
|
||||
* subscript of nonzero ucol[k] is stored in usub[k].
|
||||
* xusub[i] points to the starting location of column i in ucol.
|
||||
* Storage: new row subscripts; that is subscripts of PA.
|
||||
*/
|
||||
|
||||
#ifndef EIGEN_LU_STRUCTS
|
||||
#define EIGEN_LU_STRUCTS
|
||||
namespace Eigen {
|
||||
namespace internal {
|
||||
|
||||
typedef enum {LUSUP, UCOL, LSUB, USUB, LLVL, ULVL} MemType;
|
||||
|
||||
template <typename IndexVector, typename ScalarVector>
|
||||
struct LU_GlobalLU_t {
|
||||
typedef typename IndexVector::Scalar StorageIndex;
|
||||
IndexVector xsup; //First supernode column ... xsup(s) points to the beginning of the s-th supernode
|
||||
IndexVector supno; // Supernode number corresponding to this column (column to supernode mapping)
|
||||
ScalarVector lusup; // nonzero values of L ordered by columns
|
||||
IndexVector lsub; // Compressed row indices of L rectangular supernodes.
|
||||
IndexVector xlusup; // pointers to the beginning of each column in lusup
|
||||
IndexVector xlsub; // pointers to the beginning of each column in lsub
|
||||
Index nzlmax; // Current max size of lsub
|
||||
Index nzlumax; // Current max size of lusup
|
||||
ScalarVector ucol; // nonzero values of U ordered by columns
|
||||
IndexVector usub; // row indices of U columns in ucol
|
||||
IndexVector xusub; // Pointers to the beginning of each column of U in ucol
|
||||
Index nzumax; // Current max size of ucol
|
||||
Index n; // Number of columns in the matrix
|
||||
Index num_expansions;
|
||||
};
|
||||
|
||||
// Values to set for performance
|
||||
struct perfvalues {
|
||||
Index panel_size; // a panel consists of at most <panel_size> consecutive columns
|
||||
Index relax; // To control degree of relaxing supernodes. If the number of nodes (columns)
|
||||
// in a subtree of the elimination tree is less than relax, this subtree is considered
|
||||
// as one supernode regardless of the row structures of those columns
|
||||
Index maxsuper; // The maximum size for a supernode in complete LU
|
||||
Index rowblk; // The minimum row dimension for 2-D blocking to be used;
|
||||
Index colblk; // The minimum column dimension for 2-D blocking to be used;
|
||||
Index fillfactor; // The estimated fills factors for L and U, compared with A
|
||||
};
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
} // end namespace Eigen
|
||||
#endif // EIGEN_LU_STRUCTS
|
||||
301
external/include/eigen3/Eigen/src/SparseLU/SparseLU_SupernodalMatrix.h
vendored
Normal file
301
external/include/eigen3/Eigen/src/SparseLU/SparseLU_SupernodalMatrix.h
vendored
Normal file
@@ -0,0 +1,301 @@
|
||||
// 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>
|
||||
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@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/.
|
||||
|
||||
#ifndef EIGEN_SPARSELU_SUPERNODAL_MATRIX_H
|
||||
#define EIGEN_SPARSELU_SUPERNODAL_MATRIX_H
|
||||
|
||||
namespace Eigen {
|
||||
namespace internal {
|
||||
|
||||
/** \ingroup SparseLU_Module
|
||||
* \brief a class to manipulate the L supernodal factor from the SparseLU factorization
|
||||
*
|
||||
* This class contain the data to easily store
|
||||
* and manipulate the supernodes during the factorization and solution phase of Sparse LU.
|
||||
* Only the lower triangular matrix has supernodes.
|
||||
*
|
||||
* NOTE : This class corresponds to the SCformat structure in SuperLU
|
||||
*
|
||||
*/
|
||||
/* TODO
|
||||
* InnerIterator as for sparsematrix
|
||||
* SuperInnerIterator to iterate through all supernodes
|
||||
* Function for triangular solve
|
||||
*/
|
||||
template <typename _Scalar, typename _StorageIndex>
|
||||
class MappedSuperNodalMatrix
|
||||
{
|
||||
public:
|
||||
typedef _Scalar Scalar;
|
||||
typedef _StorageIndex StorageIndex;
|
||||
typedef Matrix<StorageIndex,Dynamic,1> IndexVector;
|
||||
typedef Matrix<Scalar,Dynamic,1> ScalarVector;
|
||||
public:
|
||||
MappedSuperNodalMatrix()
|
||||
{
|
||||
|
||||
}
|
||||
MappedSuperNodalMatrix(Index m, Index n, ScalarVector& nzval, IndexVector& nzval_colptr, IndexVector& rowind,
|
||||
IndexVector& rowind_colptr, IndexVector& col_to_sup, IndexVector& sup_to_col )
|
||||
{
|
||||
setInfos(m, n, nzval, nzval_colptr, rowind, rowind_colptr, col_to_sup, sup_to_col);
|
||||
}
|
||||
|
||||
~MappedSuperNodalMatrix()
|
||||
{
|
||||
|
||||
}
|
||||
/**
|
||||
* Set appropriate pointers for the lower triangular supernodal matrix
|
||||
* These infos are available at the end of the numerical factorization
|
||||
* FIXME This class will be modified such that it can be use in the course
|
||||
* of the factorization.
|
||||
*/
|
||||
void setInfos(Index m, Index n, ScalarVector& nzval, IndexVector& nzval_colptr, IndexVector& rowind,
|
||||
IndexVector& rowind_colptr, IndexVector& col_to_sup, IndexVector& sup_to_col )
|
||||
{
|
||||
m_row = m;
|
||||
m_col = n;
|
||||
m_nzval = nzval.data();
|
||||
m_nzval_colptr = nzval_colptr.data();
|
||||
m_rowind = rowind.data();
|
||||
m_rowind_colptr = rowind_colptr.data();
|
||||
m_nsuper = col_to_sup(n);
|
||||
m_col_to_sup = col_to_sup.data();
|
||||
m_sup_to_col = sup_to_col.data();
|
||||
}
|
||||
|
||||
/**
|
||||
* Number of rows
|
||||
*/
|
||||
Index rows() { return m_row; }
|
||||
|
||||
/**
|
||||
* Number of columns
|
||||
*/
|
||||
Index cols() { return m_col; }
|
||||
|
||||
/**
|
||||
* Return the array of nonzero values packed by column
|
||||
*
|
||||
* The size is nnz
|
||||
*/
|
||||
Scalar* valuePtr() { return m_nzval; }
|
||||
|
||||
const Scalar* valuePtr() const
|
||||
{
|
||||
return m_nzval;
|
||||
}
|
||||
/**
|
||||
* Return the pointers to the beginning of each column in \ref valuePtr()
|
||||
*/
|
||||
StorageIndex* colIndexPtr()
|
||||
{
|
||||
return m_nzval_colptr;
|
||||
}
|
||||
|
||||
const StorageIndex* colIndexPtr() const
|
||||
{
|
||||
return m_nzval_colptr;
|
||||
}
|
||||
|
||||
/**
|
||||
* Return the array of compressed row indices of all supernodes
|
||||
*/
|
||||
StorageIndex* rowIndex() { return m_rowind; }
|
||||
|
||||
const StorageIndex* rowIndex() const
|
||||
{
|
||||
return m_rowind;
|
||||
}
|
||||
|
||||
/**
|
||||
* Return the location in \em rowvaluePtr() which starts each column
|
||||
*/
|
||||
StorageIndex* rowIndexPtr() { return m_rowind_colptr; }
|
||||
|
||||
const StorageIndex* rowIndexPtr() const
|
||||
{
|
||||
return m_rowind_colptr;
|
||||
}
|
||||
|
||||
/**
|
||||
* Return the array of column-to-supernode mapping
|
||||
*/
|
||||
StorageIndex* colToSup() { return m_col_to_sup; }
|
||||
|
||||
const StorageIndex* colToSup() const
|
||||
{
|
||||
return m_col_to_sup;
|
||||
}
|
||||
/**
|
||||
* Return the array of supernode-to-column mapping
|
||||
*/
|
||||
StorageIndex* supToCol() { return m_sup_to_col; }
|
||||
|
||||
const StorageIndex* supToCol() const
|
||||
{
|
||||
return m_sup_to_col;
|
||||
}
|
||||
|
||||
/**
|
||||
* Return the number of supernodes
|
||||
*/
|
||||
Index nsuper() const
|
||||
{
|
||||
return m_nsuper;
|
||||
}
|
||||
|
||||
class InnerIterator;
|
||||
template<typename Dest>
|
||||
void solveInPlace( MatrixBase<Dest>&X) const;
|
||||
|
||||
|
||||
|
||||
|
||||
protected:
|
||||
Index m_row; // Number of rows
|
||||
Index m_col; // Number of columns
|
||||
Index m_nsuper; // Number of supernodes
|
||||
Scalar* m_nzval; //array of nonzero values packed by column
|
||||
StorageIndex* m_nzval_colptr; //nzval_colptr[j] Stores the location in nzval[] which starts column j
|
||||
StorageIndex* m_rowind; // Array of compressed row indices of rectangular supernodes
|
||||
StorageIndex* m_rowind_colptr; //rowind_colptr[j] stores the location in rowind[] which starts column j
|
||||
StorageIndex* m_col_to_sup; // col_to_sup[j] is the supernode number to which column j belongs
|
||||
StorageIndex* m_sup_to_col; //sup_to_col[s] points to the starting column of the s-th supernode
|
||||
|
||||
private :
|
||||
};
|
||||
|
||||
/**
|
||||
* \brief InnerIterator class to iterate over nonzero values of the current column in the supernodal matrix L
|
||||
*
|
||||
*/
|
||||
template<typename Scalar, typename StorageIndex>
|
||||
class MappedSuperNodalMatrix<Scalar,StorageIndex>::InnerIterator
|
||||
{
|
||||
public:
|
||||
InnerIterator(const MappedSuperNodalMatrix& mat, Index outer)
|
||||
: m_matrix(mat),
|
||||
m_outer(outer),
|
||||
m_supno(mat.colToSup()[outer]),
|
||||
m_idval(mat.colIndexPtr()[outer]),
|
||||
m_startidval(m_idval),
|
||||
m_endidval(mat.colIndexPtr()[outer+1]),
|
||||
m_idrow(mat.rowIndexPtr()[mat.supToCol()[mat.colToSup()[outer]]]),
|
||||
m_endidrow(mat.rowIndexPtr()[mat.supToCol()[mat.colToSup()[outer]]+1])
|
||||
{}
|
||||
inline InnerIterator& operator++()
|
||||
{
|
||||
m_idval++;
|
||||
m_idrow++;
|
||||
return *this;
|
||||
}
|
||||
inline Scalar value() const { return m_matrix.valuePtr()[m_idval]; }
|
||||
|
||||
inline Scalar& valueRef() { return const_cast<Scalar&>(m_matrix.valuePtr()[m_idval]); }
|
||||
|
||||
inline Index index() const { return m_matrix.rowIndex()[m_idrow]; }
|
||||
inline Index row() const { return index(); }
|
||||
inline Index col() const { return m_outer; }
|
||||
|
||||
inline Index supIndex() const { return m_supno; }
|
||||
|
||||
inline operator bool() const
|
||||
{
|
||||
return ( (m_idval < m_endidval) && (m_idval >= m_startidval)
|
||||
&& (m_idrow < m_endidrow) );
|
||||
}
|
||||
|
||||
protected:
|
||||
const MappedSuperNodalMatrix& m_matrix; // Supernodal lower triangular matrix
|
||||
const Index m_outer; // Current column
|
||||
const Index m_supno; // Current SuperNode number
|
||||
Index m_idval; // Index to browse the values in the current column
|
||||
const Index m_startidval; // Start of the column value
|
||||
const Index m_endidval; // End of the column value
|
||||
Index m_idrow; // Index to browse the row indices
|
||||
Index m_endidrow; // End index of row indices of the current column
|
||||
};
|
||||
|
||||
/**
|
||||
* \brief Solve with the supernode triangular matrix
|
||||
*
|
||||
*/
|
||||
template<typename Scalar, typename Index_>
|
||||
template<typename Dest>
|
||||
void MappedSuperNodalMatrix<Scalar,Index_>::solveInPlace( MatrixBase<Dest>&X) const
|
||||
{
|
||||
/* Explicit type conversion as the Index type of MatrixBase<Dest> may be wider than Index */
|
||||
// eigen_assert(X.rows() <= NumTraits<Index>::highest());
|
||||
// eigen_assert(X.cols() <= NumTraits<Index>::highest());
|
||||
Index n = int(X.rows());
|
||||
Index nrhs = Index(X.cols());
|
||||
const Scalar * Lval = valuePtr(); // Nonzero values
|
||||
Matrix<Scalar,Dynamic,Dest::ColsAtCompileTime, ColMajor> work(n, nrhs); // working vector
|
||||
work.setZero();
|
||||
for (Index k = 0; k <= nsuper(); k ++)
|
||||
{
|
||||
Index fsupc = supToCol()[k]; // First column of the current supernode
|
||||
Index istart = rowIndexPtr()[fsupc]; // Pointer index to the subscript of the current column
|
||||
Index nsupr = rowIndexPtr()[fsupc+1] - istart; // Number of rows in the current supernode
|
||||
Index nsupc = supToCol()[k+1] - fsupc; // Number of columns in the current supernode
|
||||
Index nrow = nsupr - nsupc; // Number of rows in the non-diagonal part of the supernode
|
||||
Index irow; //Current index row
|
||||
|
||||
if (nsupc == 1 )
|
||||
{
|
||||
for (Index j = 0; j < nrhs; j++)
|
||||
{
|
||||
InnerIterator it(*this, fsupc);
|
||||
++it; // Skip the diagonal element
|
||||
for (; it; ++it)
|
||||
{
|
||||
irow = it.row();
|
||||
X(irow, j) -= X(fsupc, j) * it.value();
|
||||
}
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
// The supernode has more than one column
|
||||
Index luptr = colIndexPtr()[fsupc];
|
||||
Index lda = colIndexPtr()[fsupc+1] - luptr;
|
||||
|
||||
// Triangular solve
|
||||
Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > A( &(Lval[luptr]), nsupc, nsupc, OuterStride<>(lda) );
|
||||
Map< Matrix<Scalar,Dynamic,Dest::ColsAtCompileTime, ColMajor>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) );
|
||||
U = A.template triangularView<UnitLower>().solve(U);
|
||||
|
||||
// Matrix-vector product
|
||||
new (&A) Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > ( &(Lval[luptr+nsupc]), nrow, nsupc, OuterStride<>(lda) );
|
||||
work.topRows(nrow).noalias() = A * U;
|
||||
|
||||
//Begin Scatter
|
||||
for (Index j = 0; j < nrhs; j++)
|
||||
{
|
||||
Index iptr = istart + nsupc;
|
||||
for (Index i = 0; i < nrow; i++)
|
||||
{
|
||||
irow = rowIndex()[iptr];
|
||||
X(irow, j) -= work(i, j); // Scatter operation
|
||||
work(i, j) = Scalar(0);
|
||||
iptr++;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_SPARSELU_MATRIX_H
|
||||
80
external/include/eigen3/Eigen/src/SparseLU/SparseLU_Utils.h
vendored
Normal file
80
external/include/eigen3/Eigen/src/SparseLU/SparseLU_Utils.h
vendored
Normal file
@@ -0,0 +1,80 @@
|
||||
// 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/.
|
||||
|
||||
|
||||
#ifndef EIGEN_SPARSELU_UTILS_H
|
||||
#define EIGEN_SPARSELU_UTILS_H
|
||||
|
||||
namespace Eigen {
|
||||
namespace internal {
|
||||
|
||||
/**
|
||||
* \brief Count Nonzero elements in the factors
|
||||
*/
|
||||
template <typename Scalar, typename StorageIndex>
|
||||
void SparseLUImpl<Scalar,StorageIndex>::countnz(const Index n, Index& nnzL, Index& nnzU, GlobalLU_t& glu)
|
||||
{
|
||||
nnzL = 0;
|
||||
nnzU = (glu.xusub)(n);
|
||||
Index nsuper = (glu.supno)(n);
|
||||
Index jlen;
|
||||
Index i, j, fsupc;
|
||||
if (n <= 0 ) return;
|
||||
// For each supernode
|
||||
for (i = 0; i <= nsuper; i++)
|
||||
{
|
||||
fsupc = glu.xsup(i);
|
||||
jlen = glu.xlsub(fsupc+1) - glu.xlsub(fsupc);
|
||||
|
||||
for (j = fsupc; j < glu.xsup(i+1); j++)
|
||||
{
|
||||
nnzL += jlen;
|
||||
nnzU += j - fsupc + 1;
|
||||
jlen--;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* \brief Fix up the data storage lsub for L-subscripts.
|
||||
*
|
||||
* It removes the subscripts sets for structural pruning,
|
||||
* and applies permutation to the remaining subscripts
|
||||
*
|
||||
*/
|
||||
template <typename Scalar, typename StorageIndex>
|
||||
void SparseLUImpl<Scalar,StorageIndex>::fixupL(const Index n, const IndexVector& perm_r, GlobalLU_t& glu)
|
||||
{
|
||||
Index fsupc, i, j, k, jstart;
|
||||
|
||||
StorageIndex nextl = 0;
|
||||
Index nsuper = (glu.supno)(n);
|
||||
|
||||
// For each supernode
|
||||
for (i = 0; i <= nsuper; i++)
|
||||
{
|
||||
fsupc = glu.xsup(i);
|
||||
jstart = glu.xlsub(fsupc);
|
||||
glu.xlsub(fsupc) = nextl;
|
||||
for (j = jstart; j < glu.xlsub(fsupc + 1); j++)
|
||||
{
|
||||
glu.lsub(nextl) = perm_r(glu.lsub(j)); // Now indexed into P*A
|
||||
nextl++;
|
||||
}
|
||||
for (k = fsupc+1; k < glu.xsup(i+1); k++)
|
||||
glu.xlsub(k) = nextl; // other columns in supernode i
|
||||
}
|
||||
|
||||
glu.xlsub(n) = nextl;
|
||||
}
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
} // end namespace Eigen
|
||||
#endif // EIGEN_SPARSELU_UTILS_H
|
||||
181
external/include/eigen3/Eigen/src/SparseLU/SparseLU_column_bmod.h
vendored
Normal file
181
external/include/eigen3/Eigen/src/SparseLU/SparseLU_column_bmod.h
vendored
Normal file
@@ -0,0 +1,181 @@
|
||||
// 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>
|
||||
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@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/.
|
||||
|
||||
/*
|
||||
|
||||
* NOTE: This file is the modified version of xcolumn_bmod.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.
|
||||
*/
|
||||
#ifndef SPARSELU_COLUMN_BMOD_H
|
||||
#define SPARSELU_COLUMN_BMOD_H
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
namespace internal {
|
||||
/**
|
||||
* \brief Performs numeric block updates (sup-col) in topological order
|
||||
*
|
||||
* \param jcol current column to update
|
||||
* \param nseg Number of segments in the U part
|
||||
* \param dense Store the full representation of the column
|
||||
* \param tempv working array
|
||||
* \param segrep segment representative ...
|
||||
* \param repfnz ??? First nonzero column in each row ??? ...
|
||||
* \param fpanelc First column in the current panel
|
||||
* \param glu Global LU data.
|
||||
* \return 0 - successful return
|
||||
* > 0 - number of bytes allocated when run out of space
|
||||
*
|
||||
*/
|
||||
template <typename Scalar, typename StorageIndex>
|
||||
Index SparseLUImpl<Scalar,StorageIndex>::column_bmod(const Index jcol, const Index nseg, BlockScalarVector dense, ScalarVector& tempv,
|
||||
BlockIndexVector segrep, BlockIndexVector repfnz, Index fpanelc, GlobalLU_t& glu)
|
||||
{
|
||||
Index jsupno, k, ksub, krep, ksupno;
|
||||
Index lptr, nrow, isub, irow, nextlu, new_next, ufirst;
|
||||
Index fsupc, nsupc, nsupr, luptr, kfnz, no_zeros;
|
||||
/* krep = representative of current k-th supernode
|
||||
* fsupc = first supernodal column
|
||||
* nsupc = number of columns in a supernode
|
||||
* nsupr = number of rows in a supernode
|
||||
* luptr = location of supernodal LU-block in storage
|
||||
* kfnz = first nonz in the k-th supernodal segment
|
||||
* no_zeros = no lf leading zeros in a supernodal U-segment
|
||||
*/
|
||||
|
||||
jsupno = glu.supno(jcol);
|
||||
// For each nonzero supernode segment of U[*,j] in topological order
|
||||
k = nseg - 1;
|
||||
Index d_fsupc; // distance between the first column of the current panel and the
|
||||
// first column of the current snode
|
||||
Index fst_col; // First column within small LU update
|
||||
Index segsize;
|
||||
for (ksub = 0; ksub < nseg; ksub++)
|
||||
{
|
||||
krep = segrep(k); k--;
|
||||
ksupno = glu.supno(krep);
|
||||
if (jsupno != ksupno )
|
||||
{
|
||||
// outside the rectangular supernode
|
||||
fsupc = glu.xsup(ksupno);
|
||||
fst_col = (std::max)(fsupc, fpanelc);
|
||||
|
||||
// Distance from the current supernode to the current panel;
|
||||
// d_fsupc = 0 if fsupc > fpanelc
|
||||
d_fsupc = fst_col - fsupc;
|
||||
|
||||
luptr = glu.xlusup(fst_col) + d_fsupc;
|
||||
lptr = glu.xlsub(fsupc) + d_fsupc;
|
||||
|
||||
kfnz = repfnz(krep);
|
||||
kfnz = (std::max)(kfnz, fpanelc);
|
||||
|
||||
segsize = krep - kfnz + 1;
|
||||
nsupc = krep - fst_col + 1;
|
||||
nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc);
|
||||
nrow = nsupr - d_fsupc - nsupc;
|
||||
Index lda = glu.xlusup(fst_col+1) - glu.xlusup(fst_col);
|
||||
|
||||
|
||||
// Perform a triangular solver and block update,
|
||||
// then scatter the result of sup-col update to dense
|
||||
no_zeros = kfnz - fst_col;
|
||||
if(segsize==1)
|
||||
LU_kernel_bmod<1>::run(segsize, dense, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
|
||||
else
|
||||
LU_kernel_bmod<Dynamic>::run(segsize, dense, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
|
||||
} // end if jsupno
|
||||
} // end for each segment
|
||||
|
||||
// Process the supernodal portion of L\U[*,j]
|
||||
nextlu = glu.xlusup(jcol);
|
||||
fsupc = glu.xsup(jsupno);
|
||||
|
||||
// copy the SPA dense into L\U[*,j]
|
||||
Index mem;
|
||||
new_next = nextlu + glu.xlsub(fsupc + 1) - glu.xlsub(fsupc);
|
||||
Index offset = internal::first_multiple<Index>(new_next, internal::packet_traits<Scalar>::size) - new_next;
|
||||
if(offset)
|
||||
new_next += offset;
|
||||
while (new_next > glu.nzlumax )
|
||||
{
|
||||
mem = memXpand<ScalarVector>(glu.lusup, glu.nzlumax, nextlu, LUSUP, glu.num_expansions);
|
||||
if (mem) return mem;
|
||||
}
|
||||
|
||||
for (isub = glu.xlsub(fsupc); isub < glu.xlsub(fsupc+1); isub++)
|
||||
{
|
||||
irow = glu.lsub(isub);
|
||||
glu.lusup(nextlu) = dense(irow);
|
||||
dense(irow) = Scalar(0.0);
|
||||
++nextlu;
|
||||
}
|
||||
|
||||
if(offset)
|
||||
{
|
||||
glu.lusup.segment(nextlu,offset).setZero();
|
||||
nextlu += offset;
|
||||
}
|
||||
glu.xlusup(jcol + 1) = StorageIndex(nextlu); // close L\U(*,jcol);
|
||||
|
||||
/* For more updates within the panel (also within the current supernode),
|
||||
* should start from the first column of the panel, or the first column
|
||||
* of the supernode, whichever is bigger. There are two cases:
|
||||
* 1) fsupc < fpanelc, then fst_col <-- fpanelc
|
||||
* 2) fsupc >= fpanelc, then fst_col <-- fsupc
|
||||
*/
|
||||
fst_col = (std::max)(fsupc, fpanelc);
|
||||
|
||||
if (fst_col < jcol)
|
||||
{
|
||||
// Distance between the current supernode and the current panel
|
||||
// d_fsupc = 0 if fsupc >= fpanelc
|
||||
d_fsupc = fst_col - fsupc;
|
||||
|
||||
lptr = glu.xlsub(fsupc) + d_fsupc;
|
||||
luptr = glu.xlusup(fst_col) + d_fsupc;
|
||||
nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc); // leading dimension
|
||||
nsupc = jcol - fst_col; // excluding jcol
|
||||
nrow = nsupr - d_fsupc - nsupc;
|
||||
|
||||
// points to the beginning of jcol in snode L\U(jsupno)
|
||||
ufirst = glu.xlusup(jcol) + d_fsupc;
|
||||
Index lda = glu.xlusup(jcol+1) - glu.xlusup(jcol);
|
||||
MappedMatrixBlock A( &(glu.lusup.data()[luptr]), nsupc, nsupc, OuterStride<>(lda) );
|
||||
VectorBlock<ScalarVector> u(glu.lusup, ufirst, nsupc);
|
||||
u = A.template triangularView<UnitLower>().solve(u);
|
||||
|
||||
new (&A) MappedMatrixBlock ( &(glu.lusup.data()[luptr+nsupc]), nrow, nsupc, OuterStride<>(lda) );
|
||||
VectorBlock<ScalarVector> l(glu.lusup, ufirst+nsupc, nrow);
|
||||
l.noalias() -= A * u;
|
||||
|
||||
} // End if fst_col
|
||||
return 0;
|
||||
}
|
||||
|
||||
} // end namespace internal
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // SPARSELU_COLUMN_BMOD_H
|
||||
179
external/include/eigen3/Eigen/src/SparseLU/SparseLU_column_dfs.h
vendored
Normal file
179
external/include/eigen3/Eigen/src/SparseLU/SparseLU_column_dfs.h
vendored
Normal file
@@ -0,0 +1,179 @@
|
||||
// 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/.
|
||||
|
||||
/*
|
||||
|
||||
* NOTE: This file is the modified version of [s,d,c,z]column_dfs.c file in SuperLU
|
||||
|
||||
* -- SuperLU routine (version 2.0) --
|
||||
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
|
||||
* and Lawrence Berkeley National Lab.
|
||||
* November 15, 1997
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
#ifndef SPARSELU_COLUMN_DFS_H
|
||||
#define SPARSELU_COLUMN_DFS_H
|
||||
|
||||
template <typename Scalar, typename StorageIndex> class SparseLUImpl;
|
||||
namespace Eigen {
|
||||
|
||||
namespace internal {
|
||||
|
||||
template<typename IndexVector, typename ScalarVector>
|
||||
struct column_dfs_traits : no_assignment_operator
|
||||
{
|
||||
typedef typename ScalarVector::Scalar Scalar;
|
||||
typedef typename IndexVector::Scalar StorageIndex;
|
||||
column_dfs_traits(Index jcol, Index& jsuper, typename SparseLUImpl<Scalar, StorageIndex>::GlobalLU_t& glu, SparseLUImpl<Scalar, StorageIndex>& luImpl)
|
||||
: m_jcol(jcol), m_jsuper_ref(jsuper), m_glu(glu), m_luImpl(luImpl)
|
||||
{}
|
||||
bool update_segrep(Index /*krep*/, Index /*jj*/)
|
||||
{
|
||||
return true;
|
||||
}
|
||||
void mem_expand(IndexVector& lsub, Index& nextl, Index chmark)
|
||||
{
|
||||
if (nextl >= m_glu.nzlmax)
|
||||
m_luImpl.memXpand(lsub, m_glu.nzlmax, nextl, LSUB, m_glu.num_expansions);
|
||||
if (chmark != (m_jcol-1)) m_jsuper_ref = emptyIdxLU;
|
||||
}
|
||||
enum { ExpandMem = true };
|
||||
|
||||
Index m_jcol;
|
||||
Index& m_jsuper_ref;
|
||||
typename SparseLUImpl<Scalar, StorageIndex>::GlobalLU_t& m_glu;
|
||||
SparseLUImpl<Scalar, StorageIndex>& m_luImpl;
|
||||
};
|
||||
|
||||
|
||||
/**
|
||||
* \brief Performs a symbolic factorization on column jcol and decide the supernode boundary
|
||||
*
|
||||
* A supernode representative is the last column of a supernode.
|
||||
* The nonzeros in U[*,j] are segments that end at supernodes representatives.
|
||||
* The routine returns a list of the supernodal representatives
|
||||
* in topological order of the dfs that generates them.
|
||||
* The location of the first nonzero in each supernodal segment
|
||||
* (supernodal entry location) is also returned.
|
||||
*
|
||||
* \param m number of rows in the matrix
|
||||
* \param jcol Current column
|
||||
* \param perm_r Row permutation
|
||||
* \param maxsuper Maximum number of column allowed in a supernode
|
||||
* \param [in,out] nseg Number of segments in current U[*,j] - new segments appended
|
||||
* \param lsub_col defines the rhs vector to start the dfs
|
||||
* \param [in,out] segrep Segment representatives - new segments appended
|
||||
* \param repfnz First nonzero location in each row
|
||||
* \param xprune
|
||||
* \param marker marker[i] == jj, if i was visited during dfs of current column jj;
|
||||
* \param parent
|
||||
* \param xplore working array
|
||||
* \param glu global LU data
|
||||
* \return 0 success
|
||||
* > 0 number of bytes allocated when run out of space
|
||||
*
|
||||
*/
|
||||
template <typename Scalar, typename StorageIndex>
|
||||
Index SparseLUImpl<Scalar,StorageIndex>::column_dfs(const Index m, const Index jcol, IndexVector& perm_r, Index maxsuper, Index& nseg,
|
||||
BlockIndexVector lsub_col, IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune,
|
||||
IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu)
|
||||
{
|
||||
|
||||
Index jsuper = glu.supno(jcol);
|
||||
Index nextl = glu.xlsub(jcol);
|
||||
VectorBlock<IndexVector> marker2(marker, 2*m, m);
|
||||
|
||||
|
||||
column_dfs_traits<IndexVector, ScalarVector> traits(jcol, jsuper, glu, *this);
|
||||
|
||||
// For each nonzero in A(*,jcol) do dfs
|
||||
for (Index k = 0; ((k < m) ? lsub_col[k] != emptyIdxLU : false) ; k++)
|
||||
{
|
||||
Index krow = lsub_col(k);
|
||||
lsub_col(k) = emptyIdxLU;
|
||||
Index kmark = marker2(krow);
|
||||
|
||||
// krow was visited before, go to the next nonz;
|
||||
if (kmark == jcol) continue;
|
||||
|
||||
dfs_kernel(StorageIndex(jcol), perm_r, nseg, glu.lsub, segrep, repfnz, xprune, marker2, parent,
|
||||
xplore, glu, nextl, krow, traits);
|
||||
} // for each nonzero ...
|
||||
|
||||
Index fsupc;
|
||||
StorageIndex nsuper = glu.supno(jcol);
|
||||
StorageIndex jcolp1 = StorageIndex(jcol) + 1;
|
||||
Index jcolm1 = jcol - 1;
|
||||
|
||||
// check to see if j belongs in the same supernode as j-1
|
||||
if ( jcol == 0 )
|
||||
{ // Do nothing for column 0
|
||||
nsuper = glu.supno(0) = 0 ;
|
||||
}
|
||||
else
|
||||
{
|
||||
fsupc = glu.xsup(nsuper);
|
||||
StorageIndex jptr = glu.xlsub(jcol); // Not yet compressed
|
||||
StorageIndex jm1ptr = glu.xlsub(jcolm1);
|
||||
|
||||
// Use supernodes of type T2 : see SuperLU paper
|
||||
if ( (nextl-jptr != jptr-jm1ptr-1) ) jsuper = emptyIdxLU;
|
||||
|
||||
// Make sure the number of columns in a supernode doesn't
|
||||
// exceed threshold
|
||||
if ( (jcol - fsupc) >= maxsuper) jsuper = emptyIdxLU;
|
||||
|
||||
/* If jcol starts a new supernode, reclaim storage space in
|
||||
* glu.lsub from previous supernode. Note we only store
|
||||
* the subscript set of the first and last columns of
|
||||
* a supernode. (first for num values, last for pruning)
|
||||
*/
|
||||
if (jsuper == emptyIdxLU)
|
||||
{ // starts a new supernode
|
||||
if ( (fsupc < jcolm1-1) )
|
||||
{ // >= 3 columns in nsuper
|
||||
StorageIndex ito = glu.xlsub(fsupc+1);
|
||||
glu.xlsub(jcolm1) = ito;
|
||||
StorageIndex istop = ito + jptr - jm1ptr;
|
||||
xprune(jcolm1) = istop; // intialize xprune(jcol-1)
|
||||
glu.xlsub(jcol) = istop;
|
||||
|
||||
for (StorageIndex ifrom = jm1ptr; ifrom < nextl; ++ifrom, ++ito)
|
||||
glu.lsub(ito) = glu.lsub(ifrom);
|
||||
nextl = ito; // = istop + length(jcol)
|
||||
}
|
||||
nsuper++;
|
||||
glu.supno(jcol) = nsuper;
|
||||
} // if a new supernode
|
||||
} // end else: jcol > 0
|
||||
|
||||
// Tidy up the pointers before exit
|
||||
glu.xsup(nsuper+1) = jcolp1;
|
||||
glu.supno(jcolp1) = nsuper;
|
||||
xprune(jcol) = StorageIndex(nextl); // Intialize upper bound for pruning
|
||||
glu.xlsub(jcolp1) = StorageIndex(nextl);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif
|
||||
107
external/include/eigen3/Eigen/src/SparseLU/SparseLU_copy_to_ucol.h
vendored
Normal file
107
external/include/eigen3/Eigen/src/SparseLU/SparseLU_copy_to_ucol.h
vendored
Normal file
@@ -0,0 +1,107 @@
|
||||
// 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/.
|
||||
/*
|
||||
|
||||
* NOTE: This file is the modified version of [s,d,c,z]copy_to_ucol.c file in SuperLU
|
||||
|
||||
* -- SuperLU routine (version 2.0) --
|
||||
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
|
||||
* and Lawrence Berkeley National Lab.
|
||||
* November 15, 1997
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
#ifndef SPARSELU_COPY_TO_UCOL_H
|
||||
#define SPARSELU_COPY_TO_UCOL_H
|
||||
|
||||
namespace Eigen {
|
||||
namespace internal {
|
||||
|
||||
/**
|
||||
* \brief Performs numeric block updates (sup-col) in topological order
|
||||
*
|
||||
* \param jcol current column to update
|
||||
* \param nseg Number of segments in the U part
|
||||
* \param segrep segment representative ...
|
||||
* \param repfnz First nonzero column in each row ...
|
||||
* \param perm_r Row permutation
|
||||
* \param dense Store the full representation of the column
|
||||
* \param glu Global LU data.
|
||||
* \return 0 - successful return
|
||||
* > 0 - number of bytes allocated when run out of space
|
||||
*
|
||||
*/
|
||||
template <typename Scalar, typename StorageIndex>
|
||||
Index SparseLUImpl<Scalar,StorageIndex>::copy_to_ucol(const Index jcol, const Index nseg, IndexVector& segrep,
|
||||
BlockIndexVector repfnz ,IndexVector& perm_r, BlockScalarVector dense, GlobalLU_t& glu)
|
||||
{
|
||||
Index ksub, krep, ksupno;
|
||||
|
||||
Index jsupno = glu.supno(jcol);
|
||||
|
||||
// For each nonzero supernode segment of U[*,j] in topological order
|
||||
Index k = nseg - 1, i;
|
||||
StorageIndex nextu = glu.xusub(jcol);
|
||||
Index kfnz, isub, segsize;
|
||||
Index new_next,irow;
|
||||
Index fsupc, mem;
|
||||
for (ksub = 0; ksub < nseg; ksub++)
|
||||
{
|
||||
krep = segrep(k); k--;
|
||||
ksupno = glu.supno(krep);
|
||||
if (jsupno != ksupno ) // should go into ucol();
|
||||
{
|
||||
kfnz = repfnz(krep);
|
||||
if (kfnz != emptyIdxLU)
|
||||
{ // Nonzero U-segment
|
||||
fsupc = glu.xsup(ksupno);
|
||||
isub = glu.xlsub(fsupc) + kfnz - fsupc;
|
||||
segsize = krep - kfnz + 1;
|
||||
new_next = nextu + segsize;
|
||||
while (new_next > glu.nzumax)
|
||||
{
|
||||
mem = memXpand<ScalarVector>(glu.ucol, glu.nzumax, nextu, UCOL, glu.num_expansions);
|
||||
if (mem) return mem;
|
||||
mem = memXpand<IndexVector>(glu.usub, glu.nzumax, nextu, USUB, glu.num_expansions);
|
||||
if (mem) return mem;
|
||||
|
||||
}
|
||||
|
||||
for (i = 0; i < segsize; i++)
|
||||
{
|
||||
irow = glu.lsub(isub);
|
||||
glu.usub(nextu) = perm_r(irow); // Unlike the L part, the U part is stored in its final order
|
||||
glu.ucol(nextu) = dense(irow);
|
||||
dense(irow) = Scalar(0.0);
|
||||
nextu++;
|
||||
isub++;
|
||||
}
|
||||
|
||||
} // end nonzero U-segment
|
||||
|
||||
} // end if jsupno
|
||||
|
||||
} // end for each segment
|
||||
glu.xusub(jcol + 1) = nextu; // close U(*,jcol)
|
||||
return 0;
|
||||
}
|
||||
|
||||
} // namespace internal
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // SPARSELU_COPY_TO_UCOL_H
|
||||
280
external/include/eigen3/Eigen/src/SparseLU/SparseLU_gemm_kernel.h
vendored
Normal file
280
external/include/eigen3/Eigen/src/SparseLU/SparseLU_gemm_kernel.h
vendored
Normal file
@@ -0,0 +1,280 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@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/.
|
||||
|
||||
#ifndef EIGEN_SPARSELU_GEMM_KERNEL_H
|
||||
#define EIGEN_SPARSELU_GEMM_KERNEL_H
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
namespace internal {
|
||||
|
||||
|
||||
/** \internal
|
||||
* A general matrix-matrix product kernel optimized for the SparseLU factorization.
|
||||
* - A, B, and C must be column major
|
||||
* - lda and ldc must be multiples of the respective packet size
|
||||
* - C must have the same alignment as A
|
||||
*/
|
||||
template<typename Scalar>
|
||||
EIGEN_DONT_INLINE
|
||||
void sparselu_gemm(Index m, Index n, Index d, const Scalar* A, Index lda, const Scalar* B, Index ldb, Scalar* C, Index ldc)
|
||||
{
|
||||
using namespace Eigen::internal;
|
||||
|
||||
typedef typename packet_traits<Scalar>::type Packet;
|
||||
enum {
|
||||
NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
|
||||
PacketSize = packet_traits<Scalar>::size,
|
||||
PM = 8, // peeling in M
|
||||
RN = 2, // register blocking
|
||||
RK = NumberOfRegisters>=16 ? 4 : 2, // register blocking
|
||||
BM = 4096/sizeof(Scalar), // number of rows of A-C per chunk
|
||||
SM = PM*PacketSize // step along M
|
||||
};
|
||||
Index d_end = (d/RK)*RK; // number of columns of A (rows of B) suitable for full register blocking
|
||||
Index n_end = (n/RN)*RN; // number of columns of B-C suitable for processing RN columns at once
|
||||
Index i0 = internal::first_default_aligned(A,m);
|
||||
|
||||
eigen_internal_assert(((lda%PacketSize)==0) && ((ldc%PacketSize)==0) && (i0==internal::first_default_aligned(C,m)));
|
||||
|
||||
// handle the non aligned rows of A and C without any optimization:
|
||||
for(Index i=0; i<i0; ++i)
|
||||
{
|
||||
for(Index j=0; j<n; ++j)
|
||||
{
|
||||
Scalar c = C[i+j*ldc];
|
||||
for(Index k=0; k<d; ++k)
|
||||
c += B[k+j*ldb] * A[i+k*lda];
|
||||
C[i+j*ldc] = c;
|
||||
}
|
||||
}
|
||||
// process the remaining rows per chunk of BM rows
|
||||
for(Index ib=i0; ib<m; ib+=BM)
|
||||
{
|
||||
Index actual_b = std::min<Index>(BM, m-ib); // actual number of rows
|
||||
Index actual_b_end1 = (actual_b/SM)*SM; // actual number of rows suitable for peeling
|
||||
Index actual_b_end2 = (actual_b/PacketSize)*PacketSize; // actual number of rows suitable for vectorization
|
||||
|
||||
// Let's process two columns of B-C at once
|
||||
for(Index j=0; j<n_end; j+=RN)
|
||||
{
|
||||
const Scalar* Bc0 = B+(j+0)*ldb;
|
||||
const Scalar* Bc1 = B+(j+1)*ldb;
|
||||
|
||||
for(Index k=0; k<d_end; k+=RK)
|
||||
{
|
||||
|
||||
// load and expand a RN x RK block of B
|
||||
Packet b00, b10, b20, b30, b01, b11, b21, b31;
|
||||
{ b00 = pset1<Packet>(Bc0[0]); }
|
||||
{ b10 = pset1<Packet>(Bc0[1]); }
|
||||
if(RK==4) { b20 = pset1<Packet>(Bc0[2]); }
|
||||
if(RK==4) { b30 = pset1<Packet>(Bc0[3]); }
|
||||
{ b01 = pset1<Packet>(Bc1[0]); }
|
||||
{ b11 = pset1<Packet>(Bc1[1]); }
|
||||
if(RK==4) { b21 = pset1<Packet>(Bc1[2]); }
|
||||
if(RK==4) { b31 = pset1<Packet>(Bc1[3]); }
|
||||
|
||||
Packet a0, a1, a2, a3, c0, c1, t0, t1;
|
||||
|
||||
const Scalar* A0 = A+ib+(k+0)*lda;
|
||||
const Scalar* A1 = A+ib+(k+1)*lda;
|
||||
const Scalar* A2 = A+ib+(k+2)*lda;
|
||||
const Scalar* A3 = A+ib+(k+3)*lda;
|
||||
|
||||
Scalar* C0 = C+ib+(j+0)*ldc;
|
||||
Scalar* C1 = C+ib+(j+1)*ldc;
|
||||
|
||||
a0 = pload<Packet>(A0);
|
||||
a1 = pload<Packet>(A1);
|
||||
if(RK==4)
|
||||
{
|
||||
a2 = pload<Packet>(A2);
|
||||
a3 = pload<Packet>(A3);
|
||||
}
|
||||
else
|
||||
{
|
||||
// workaround "may be used uninitialized in this function" warning
|
||||
a2 = a3 = a0;
|
||||
}
|
||||
|
||||
#define KMADD(c, a, b, tmp) {tmp = b; tmp = pmul(a,tmp); c = padd(c,tmp);}
|
||||
#define WORK(I) \
|
||||
c0 = pload<Packet>(C0+i+(I)*PacketSize); \
|
||||
c1 = pload<Packet>(C1+i+(I)*PacketSize); \
|
||||
KMADD(c0, a0, b00, t0) \
|
||||
KMADD(c1, a0, b01, t1) \
|
||||
a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \
|
||||
KMADD(c0, a1, b10, t0) \
|
||||
KMADD(c1, a1, b11, t1) \
|
||||
a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \
|
||||
if(RK==4){ KMADD(c0, a2, b20, t0) }\
|
||||
if(RK==4){ KMADD(c1, a2, b21, t1) }\
|
||||
if(RK==4){ a2 = pload<Packet>(A2+i+(I+1)*PacketSize); }\
|
||||
if(RK==4){ KMADD(c0, a3, b30, t0) }\
|
||||
if(RK==4){ KMADD(c1, a3, b31, t1) }\
|
||||
if(RK==4){ a3 = pload<Packet>(A3+i+(I+1)*PacketSize); }\
|
||||
pstore(C0+i+(I)*PacketSize, c0); \
|
||||
pstore(C1+i+(I)*PacketSize, c1)
|
||||
|
||||
// process rows of A' - C' with aggressive vectorization and peeling
|
||||
for(Index i=0; i<actual_b_end1; i+=PacketSize*8)
|
||||
{
|
||||
EIGEN_ASM_COMMENT("SPARSELU_GEMML_KERNEL1");
|
||||
prefetch((A0+i+(5)*PacketSize));
|
||||
prefetch((A1+i+(5)*PacketSize));
|
||||
if(RK==4) prefetch((A2+i+(5)*PacketSize));
|
||||
if(RK==4) prefetch((A3+i+(5)*PacketSize));
|
||||
|
||||
WORK(0);
|
||||
WORK(1);
|
||||
WORK(2);
|
||||
WORK(3);
|
||||
WORK(4);
|
||||
WORK(5);
|
||||
WORK(6);
|
||||
WORK(7);
|
||||
}
|
||||
// process the remaining rows with vectorization only
|
||||
for(Index i=actual_b_end1; i<actual_b_end2; i+=PacketSize)
|
||||
{
|
||||
WORK(0);
|
||||
}
|
||||
#undef WORK
|
||||
// process the remaining rows without vectorization
|
||||
for(Index i=actual_b_end2; i<actual_b; ++i)
|
||||
{
|
||||
if(RK==4)
|
||||
{
|
||||
C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3];
|
||||
C1[i] += A0[i]*Bc1[0]+A1[i]*Bc1[1]+A2[i]*Bc1[2]+A3[i]*Bc1[3];
|
||||
}
|
||||
else
|
||||
{
|
||||
C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1];
|
||||
C1[i] += A0[i]*Bc1[0]+A1[i]*Bc1[1];
|
||||
}
|
||||
}
|
||||
|
||||
Bc0 += RK;
|
||||
Bc1 += RK;
|
||||
} // peeled loop on k
|
||||
} // peeled loop on the columns j
|
||||
// process the last column (we now perform a matrix-vector product)
|
||||
if((n-n_end)>0)
|
||||
{
|
||||
const Scalar* Bc0 = B+(n-1)*ldb;
|
||||
|
||||
for(Index k=0; k<d_end; k+=RK)
|
||||
{
|
||||
|
||||
// load and expand a 1 x RK block of B
|
||||
Packet b00, b10, b20, b30;
|
||||
b00 = pset1<Packet>(Bc0[0]);
|
||||
b10 = pset1<Packet>(Bc0[1]);
|
||||
if(RK==4) b20 = pset1<Packet>(Bc0[2]);
|
||||
if(RK==4) b30 = pset1<Packet>(Bc0[3]);
|
||||
|
||||
Packet a0, a1, a2, a3, c0, t0/*, t1*/;
|
||||
|
||||
const Scalar* A0 = A+ib+(k+0)*lda;
|
||||
const Scalar* A1 = A+ib+(k+1)*lda;
|
||||
const Scalar* A2 = A+ib+(k+2)*lda;
|
||||
const Scalar* A3 = A+ib+(k+3)*lda;
|
||||
|
||||
Scalar* C0 = C+ib+(n_end)*ldc;
|
||||
|
||||
a0 = pload<Packet>(A0);
|
||||
a1 = pload<Packet>(A1);
|
||||
if(RK==4)
|
||||
{
|
||||
a2 = pload<Packet>(A2);
|
||||
a3 = pload<Packet>(A3);
|
||||
}
|
||||
else
|
||||
{
|
||||
// workaround "may be used uninitialized in this function" warning
|
||||
a2 = a3 = a0;
|
||||
}
|
||||
|
||||
#define WORK(I) \
|
||||
c0 = pload<Packet>(C0+i+(I)*PacketSize); \
|
||||
KMADD(c0, a0, b00, t0) \
|
||||
a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \
|
||||
KMADD(c0, a1, b10, t0) \
|
||||
a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \
|
||||
if(RK==4){ KMADD(c0, a2, b20, t0) }\
|
||||
if(RK==4){ a2 = pload<Packet>(A2+i+(I+1)*PacketSize); }\
|
||||
if(RK==4){ KMADD(c0, a3, b30, t0) }\
|
||||
if(RK==4){ a3 = pload<Packet>(A3+i+(I+1)*PacketSize); }\
|
||||
pstore(C0+i+(I)*PacketSize, c0);
|
||||
|
||||
// agressive vectorization and peeling
|
||||
for(Index i=0; i<actual_b_end1; i+=PacketSize*8)
|
||||
{
|
||||
EIGEN_ASM_COMMENT("SPARSELU_GEMML_KERNEL2");
|
||||
WORK(0);
|
||||
WORK(1);
|
||||
WORK(2);
|
||||
WORK(3);
|
||||
WORK(4);
|
||||
WORK(5);
|
||||
WORK(6);
|
||||
WORK(7);
|
||||
}
|
||||
// vectorization only
|
||||
for(Index i=actual_b_end1; i<actual_b_end2; i+=PacketSize)
|
||||
{
|
||||
WORK(0);
|
||||
}
|
||||
// remaining scalars
|
||||
for(Index i=actual_b_end2; i<actual_b; ++i)
|
||||
{
|
||||
if(RK==4)
|
||||
C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3];
|
||||
else
|
||||
C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1];
|
||||
}
|
||||
|
||||
Bc0 += RK;
|
||||
#undef WORK
|
||||
}
|
||||
}
|
||||
|
||||
// process the last columns of A, corresponding to the last rows of B
|
||||
Index rd = d-d_end;
|
||||
if(rd>0)
|
||||
{
|
||||
for(Index j=0; j<n; ++j)
|
||||
{
|
||||
enum {
|
||||
Alignment = PacketSize>1 ? Aligned : 0
|
||||
};
|
||||
typedef Map<Matrix<Scalar,Dynamic,1>, Alignment > MapVector;
|
||||
typedef Map<const Matrix<Scalar,Dynamic,1>, Alignment > ConstMapVector;
|
||||
if(rd==1) MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b);
|
||||
|
||||
else if(rd==2) MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b)
|
||||
+ B[1+d_end+j*ldb] * ConstMapVector(A+(d_end+1)*lda+ib, actual_b);
|
||||
|
||||
else MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b)
|
||||
+ B[1+d_end+j*ldb] * ConstMapVector(A+(d_end+1)*lda+ib, actual_b)
|
||||
+ B[2+d_end+j*ldb] * ConstMapVector(A+(d_end+2)*lda+ib, actual_b);
|
||||
}
|
||||
}
|
||||
|
||||
} // blocking on the rows of A and C
|
||||
}
|
||||
#undef KMADD
|
||||
|
||||
} // namespace internal
|
||||
|
||||
} // namespace Eigen
|
||||
|
||||
#endif // EIGEN_SPARSELU_GEMM_KERNEL_H
|
||||
126
external/include/eigen3/Eigen/src/SparseLU/SparseLU_heap_relax_snode.h
vendored
Normal file
126
external/include/eigen3/Eigen/src/SparseLU/SparseLU_heap_relax_snode.h
vendored
Normal file
@@ -0,0 +1,126 @@
|
||||
// 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.
|
||||
*/
|
||||
|
||||
#ifndef SPARSELU_HEAP_RELAX_SNODE_H
|
||||
#define SPARSELU_HEAP_RELAX_SNODE_H
|
||||
|
||||
namespace Eigen {
|
||||
namespace internal {
|
||||
|
||||
/**
|
||||
* \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
|
||||
130
external/include/eigen3/Eigen/src/SparseLU/SparseLU_kernel_bmod.h
vendored
Normal file
130
external/include/eigen3/Eigen/src/SparseLU/SparseLU_kernel_bmod.h
vendored
Normal file
@@ -0,0 +1,130 @@
|
||||
// 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>
|
||||
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@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/.
|
||||
|
||||
#ifndef SPARSELU_KERNEL_BMOD_H
|
||||
#define SPARSELU_KERNEL_BMOD_H
|
||||
|
||||
namespace Eigen {
|
||||
namespace internal {
|
||||
|
||||
template <int SegSizeAtCompileTime> struct LU_kernel_bmod
|
||||
{
|
||||
/** \internal
|
||||
* \brief Performs numeric block updates from a given supernode to a single column
|
||||
*
|
||||
* \param segsize Size of the segment (and blocks ) to use for updates
|
||||
* \param[in,out] dense Packed values of the original matrix
|
||||
* \param tempv temporary vector to use for updates
|
||||
* \param lusup array containing the supernodes
|
||||
* \param lda Leading dimension in the supernode
|
||||
* \param nrow Number of rows in the rectangular part of the supernode
|
||||
* \param lsub compressed row subscripts of supernodes
|
||||
* \param lptr pointer to the first column of the current supernode in lsub
|
||||
* \param no_zeros Number of nonzeros elements before the diagonal part of the supernode
|
||||
*/
|
||||
template <typename BlockScalarVector, typename ScalarVector, typename IndexVector>
|
||||
static EIGEN_DONT_INLINE void run(const Index segsize, BlockScalarVector& dense, ScalarVector& tempv, ScalarVector& lusup, Index& luptr, const Index lda,
|
||||
const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros);
|
||||
};
|
||||
|
||||
template <int SegSizeAtCompileTime>
|
||||
template <typename BlockScalarVector, typename ScalarVector, typename IndexVector>
|
||||
EIGEN_DONT_INLINE void LU_kernel_bmod<SegSizeAtCompileTime>::run(const Index segsize, BlockScalarVector& dense, ScalarVector& tempv, ScalarVector& lusup, Index& luptr, const Index lda,
|
||||
const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros)
|
||||
{
|
||||
typedef typename ScalarVector::Scalar Scalar;
|
||||
// First, copy U[*,j] segment from dense(*) to tempv(*)
|
||||
// The result of triangular solve is in tempv[*];
|
||||
// The result of matric-vector update is in dense[*]
|
||||
Index isub = lptr + no_zeros;
|
||||
Index i;
|
||||
Index irow;
|
||||
for (i = 0; i < ((SegSizeAtCompileTime==Dynamic)?segsize:SegSizeAtCompileTime); i++)
|
||||
{
|
||||
irow = lsub(isub);
|
||||
tempv(i) = dense(irow);
|
||||
++isub;
|
||||
}
|
||||
// Dense triangular solve -- start effective triangle
|
||||
luptr += lda * no_zeros + no_zeros;
|
||||
// Form Eigen matrix and vector
|
||||
Map<Matrix<Scalar,SegSizeAtCompileTime,SegSizeAtCompileTime, ColMajor>, 0, OuterStride<> > A( &(lusup.data()[luptr]), segsize, segsize, OuterStride<>(lda) );
|
||||
Map<Matrix<Scalar,SegSizeAtCompileTime,1> > u(tempv.data(), segsize);
|
||||
|
||||
u = A.template triangularView<UnitLower>().solve(u);
|
||||
|
||||
// Dense matrix-vector product y <-- B*x
|
||||
luptr += segsize;
|
||||
const Index PacketSize = internal::packet_traits<Scalar>::size;
|
||||
Index ldl = internal::first_multiple(nrow, PacketSize);
|
||||
Map<Matrix<Scalar,Dynamic,SegSizeAtCompileTime, ColMajor>, 0, OuterStride<> > B( &(lusup.data()[luptr]), nrow, segsize, OuterStride<>(lda) );
|
||||
Index aligned_offset = internal::first_default_aligned(tempv.data()+segsize, PacketSize);
|
||||
Index aligned_with_B_offset = (PacketSize-internal::first_default_aligned(B.data(), PacketSize))%PacketSize;
|
||||
Map<Matrix<Scalar,Dynamic,1>, 0, OuterStride<> > l(tempv.data()+segsize+aligned_offset+aligned_with_B_offset, nrow, OuterStride<>(ldl) );
|
||||
|
||||
l.setZero();
|
||||
internal::sparselu_gemm<Scalar>(l.rows(), l.cols(), B.cols(), B.data(), B.outerStride(), u.data(), u.outerStride(), l.data(), l.outerStride());
|
||||
|
||||
// Scatter tempv[] into SPA dense[] as a temporary storage
|
||||
isub = lptr + no_zeros;
|
||||
for (i = 0; i < ((SegSizeAtCompileTime==Dynamic)?segsize:SegSizeAtCompileTime); i++)
|
||||
{
|
||||
irow = lsub(isub++);
|
||||
dense(irow) = tempv(i);
|
||||
}
|
||||
|
||||
// Scatter l into SPA dense[]
|
||||
for (i = 0; i < nrow; i++)
|
||||
{
|
||||
irow = lsub(isub++);
|
||||
dense(irow) -= l(i);
|
||||
}
|
||||
}
|
||||
|
||||
template <> struct LU_kernel_bmod<1>
|
||||
{
|
||||
template <typename BlockScalarVector, typename ScalarVector, typename IndexVector>
|
||||
static EIGEN_DONT_INLINE void run(const Index /*segsize*/, BlockScalarVector& dense, ScalarVector& /*tempv*/, ScalarVector& lusup, Index& luptr,
|
||||
const Index lda, const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros);
|
||||
};
|
||||
|
||||
|
||||
template <typename BlockScalarVector, typename ScalarVector, typename IndexVector>
|
||||
EIGEN_DONT_INLINE void LU_kernel_bmod<1>::run(const Index /*segsize*/, BlockScalarVector& dense, ScalarVector& /*tempv*/, ScalarVector& lusup, Index& luptr,
|
||||
const Index lda, const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros)
|
||||
{
|
||||
typedef typename ScalarVector::Scalar Scalar;
|
||||
typedef typename IndexVector::Scalar StorageIndex;
|
||||
Scalar f = dense(lsub(lptr + no_zeros));
|
||||
luptr += lda * no_zeros + no_zeros + 1;
|
||||
const Scalar* a(lusup.data() + luptr);
|
||||
const StorageIndex* irow(lsub.data()+lptr + no_zeros + 1);
|
||||
Index i = 0;
|
||||
for (; i+1 < nrow; i+=2)
|
||||
{
|
||||
Index i0 = *(irow++);
|
||||
Index i1 = *(irow++);
|
||||
Scalar a0 = *(a++);
|
||||
Scalar a1 = *(a++);
|
||||
Scalar d0 = dense.coeff(i0);
|
||||
Scalar d1 = dense.coeff(i1);
|
||||
d0 -= f*a0;
|
||||
d1 -= f*a1;
|
||||
dense.coeffRef(i0) = d0;
|
||||
dense.coeffRef(i1) = d1;
|
||||
}
|
||||
if(i<nrow)
|
||||
dense.coeffRef(*(irow++)) -= f * *(a++);
|
||||
}
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
} // end namespace Eigen
|
||||
#endif // SPARSELU_KERNEL_BMOD_H
|
||||
223
external/include/eigen3/Eigen/src/SparseLU/SparseLU_panel_bmod.h
vendored
Normal file
223
external/include/eigen3/Eigen/src/SparseLU/SparseLU_panel_bmod.h
vendored
Normal file
@@ -0,0 +1,223 @@
|
||||
// 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>
|
||||
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@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/.
|
||||
|
||||
/*
|
||||
|
||||
* NOTE: This file is the modified version of [s,d,c,z]panel_bmod.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.
|
||||
*/
|
||||
#ifndef SPARSELU_PANEL_BMOD_H
|
||||
#define SPARSELU_PANEL_BMOD_H
|
||||
|
||||
namespace Eigen {
|
||||
namespace internal {
|
||||
|
||||
/**
|
||||
* \brief Performs numeric block updates (sup-panel) in topological order.
|
||||
*
|
||||
* Before entering this routine, the original nonzeros in the panel
|
||||
* were already copied i nto the spa[m,w]
|
||||
*
|
||||
* \param m number of rows in the matrix
|
||||
* \param w Panel size
|
||||
* \param jcol Starting column of the panel
|
||||
* \param nseg Number of segments in the U part
|
||||
* \param dense Store the full representation of the panel
|
||||
* \param tempv working array
|
||||
* \param segrep segment representative... first row in the segment
|
||||
* \param repfnz First nonzero rows
|
||||
* \param glu Global LU data.
|
||||
*
|
||||
*
|
||||
*/
|
||||
template <typename Scalar, typename StorageIndex>
|
||||
void SparseLUImpl<Scalar,StorageIndex>::panel_bmod(const Index m, const Index w, const Index jcol,
|
||||
const Index nseg, ScalarVector& dense, ScalarVector& tempv,
|
||||
IndexVector& segrep, IndexVector& repfnz, GlobalLU_t& glu)
|
||||
{
|
||||
|
||||
Index ksub,jj,nextl_col;
|
||||
Index fsupc, nsupc, nsupr, nrow;
|
||||
Index krep, kfnz;
|
||||
Index lptr; // points to the row subscripts of a supernode
|
||||
Index luptr; // ...
|
||||
Index segsize,no_zeros ;
|
||||
// For each nonz supernode segment of U[*,j] in topological order
|
||||
Index k = nseg - 1;
|
||||
const Index PacketSize = internal::packet_traits<Scalar>::size;
|
||||
|
||||
for (ksub = 0; ksub < nseg; ksub++)
|
||||
{ // For each updating supernode
|
||||
/* krep = representative of current k-th supernode
|
||||
* fsupc = first supernodal column
|
||||
* nsupc = number of columns in a supernode
|
||||
* nsupr = number of rows in a supernode
|
||||
*/
|
||||
krep = segrep(k); k--;
|
||||
fsupc = glu.xsup(glu.supno(krep));
|
||||
nsupc = krep - fsupc + 1;
|
||||
nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc);
|
||||
nrow = nsupr - nsupc;
|
||||
lptr = glu.xlsub(fsupc);
|
||||
|
||||
// loop over the panel columns to detect the actual number of columns and rows
|
||||
Index u_rows = 0;
|
||||
Index u_cols = 0;
|
||||
for (jj = jcol; jj < jcol + w; jj++)
|
||||
{
|
||||
nextl_col = (jj-jcol) * m;
|
||||
VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
|
||||
|
||||
kfnz = repfnz_col(krep);
|
||||
if ( kfnz == emptyIdxLU )
|
||||
continue; // skip any zero segment
|
||||
|
||||
segsize = krep - kfnz + 1;
|
||||
u_cols++;
|
||||
u_rows = (std::max)(segsize,u_rows);
|
||||
}
|
||||
|
||||
if(nsupc >= 2)
|
||||
{
|
||||
Index ldu = internal::first_multiple<Index>(u_rows, PacketSize);
|
||||
Map<ScalarMatrix, Aligned, OuterStride<> > U(tempv.data(), u_rows, u_cols, OuterStride<>(ldu));
|
||||
|
||||
// gather U
|
||||
Index u_col = 0;
|
||||
for (jj = jcol; jj < jcol + w; jj++)
|
||||
{
|
||||
nextl_col = (jj-jcol) * m;
|
||||
VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
|
||||
VectorBlock<ScalarVector> dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here
|
||||
|
||||
kfnz = repfnz_col(krep);
|
||||
if ( kfnz == emptyIdxLU )
|
||||
continue; // skip any zero segment
|
||||
|
||||
segsize = krep - kfnz + 1;
|
||||
luptr = glu.xlusup(fsupc);
|
||||
no_zeros = kfnz - fsupc;
|
||||
|
||||
Index isub = lptr + no_zeros;
|
||||
Index off = u_rows-segsize;
|
||||
for (Index i = 0; i < off; i++) U(i,u_col) = 0;
|
||||
for (Index i = 0; i < segsize; i++)
|
||||
{
|
||||
Index irow = glu.lsub(isub);
|
||||
U(i+off,u_col) = dense_col(irow);
|
||||
++isub;
|
||||
}
|
||||
u_col++;
|
||||
}
|
||||
// solve U = A^-1 U
|
||||
luptr = glu.xlusup(fsupc);
|
||||
Index lda = glu.xlusup(fsupc+1) - glu.xlusup(fsupc);
|
||||
no_zeros = (krep - u_rows + 1) - fsupc;
|
||||
luptr += lda * no_zeros + no_zeros;
|
||||
MappedMatrixBlock A(glu.lusup.data()+luptr, u_rows, u_rows, OuterStride<>(lda) );
|
||||
U = A.template triangularView<UnitLower>().solve(U);
|
||||
|
||||
// update
|
||||
luptr += u_rows;
|
||||
MappedMatrixBlock B(glu.lusup.data()+luptr, nrow, u_rows, OuterStride<>(lda) );
|
||||
eigen_assert(tempv.size()>w*ldu + nrow*w + 1);
|
||||
|
||||
Index ldl = internal::first_multiple<Index>(nrow, PacketSize);
|
||||
Index offset = (PacketSize-internal::first_default_aligned(B.data(), PacketSize)) % PacketSize;
|
||||
MappedMatrixBlock L(tempv.data()+w*ldu+offset, nrow, u_cols, OuterStride<>(ldl));
|
||||
|
||||
L.setZero();
|
||||
internal::sparselu_gemm<Scalar>(L.rows(), L.cols(), B.cols(), B.data(), B.outerStride(), U.data(), U.outerStride(), L.data(), L.outerStride());
|
||||
|
||||
// scatter U and L
|
||||
u_col = 0;
|
||||
for (jj = jcol; jj < jcol + w; jj++)
|
||||
{
|
||||
nextl_col = (jj-jcol) * m;
|
||||
VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
|
||||
VectorBlock<ScalarVector> dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here
|
||||
|
||||
kfnz = repfnz_col(krep);
|
||||
if ( kfnz == emptyIdxLU )
|
||||
continue; // skip any zero segment
|
||||
|
||||
segsize = krep - kfnz + 1;
|
||||
no_zeros = kfnz - fsupc;
|
||||
Index isub = lptr + no_zeros;
|
||||
|
||||
Index off = u_rows-segsize;
|
||||
for (Index i = 0; i < segsize; i++)
|
||||
{
|
||||
Index irow = glu.lsub(isub++);
|
||||
dense_col(irow) = U.coeff(i+off,u_col);
|
||||
U.coeffRef(i+off,u_col) = 0;
|
||||
}
|
||||
|
||||
// Scatter l into SPA dense[]
|
||||
for (Index i = 0; i < nrow; i++)
|
||||
{
|
||||
Index irow = glu.lsub(isub++);
|
||||
dense_col(irow) -= L.coeff(i,u_col);
|
||||
L.coeffRef(i,u_col) = 0;
|
||||
}
|
||||
u_col++;
|
||||
}
|
||||
}
|
||||
else // level 2 only
|
||||
{
|
||||
// Sequence through each column in the panel
|
||||
for (jj = jcol; jj < jcol + w; jj++)
|
||||
{
|
||||
nextl_col = (jj-jcol) * m;
|
||||
VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
|
||||
VectorBlock<ScalarVector> dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here
|
||||
|
||||
kfnz = repfnz_col(krep);
|
||||
if ( kfnz == emptyIdxLU )
|
||||
continue; // skip any zero segment
|
||||
|
||||
segsize = krep - kfnz + 1;
|
||||
luptr = glu.xlusup(fsupc);
|
||||
|
||||
Index lda = glu.xlusup(fsupc+1)-glu.xlusup(fsupc);// nsupr
|
||||
|
||||
// Perform a trianglar solve and block update,
|
||||
// then scatter the result of sup-col update to dense[]
|
||||
no_zeros = kfnz - fsupc;
|
||||
if(segsize==1) LU_kernel_bmod<1>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
|
||||
else if(segsize==2) LU_kernel_bmod<2>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
|
||||
else if(segsize==3) LU_kernel_bmod<3>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
|
||||
else LU_kernel_bmod<Dynamic>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
|
||||
} // End for each column in the panel
|
||||
}
|
||||
|
||||
} // End for each updating supernode
|
||||
} // end panel bmod
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // SPARSELU_PANEL_BMOD_H
|
||||
258
external/include/eigen3/Eigen/src/SparseLU/SparseLU_panel_dfs.h
vendored
Normal file
258
external/include/eigen3/Eigen/src/SparseLU/SparseLU_panel_dfs.h
vendored
Normal file
@@ -0,0 +1,258 @@
|
||||
// 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/.
|
||||
|
||||
/*
|
||||
|
||||
* NOTE: This file is the modified version of [s,d,c,z]panel_dfs.c file in SuperLU
|
||||
|
||||
* -- SuperLU routine (version 2.0) --
|
||||
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
|
||||
* and Lawrence Berkeley National Lab.
|
||||
* November 15, 1997
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
#ifndef SPARSELU_PANEL_DFS_H
|
||||
#define SPARSELU_PANEL_DFS_H
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
namespace internal {
|
||||
|
||||
template<typename IndexVector>
|
||||
struct panel_dfs_traits
|
||||
{
|
||||
typedef typename IndexVector::Scalar StorageIndex;
|
||||
panel_dfs_traits(Index jcol, StorageIndex* marker)
|
||||
: m_jcol(jcol), m_marker(marker)
|
||||
{}
|
||||
bool update_segrep(Index krep, StorageIndex jj)
|
||||
{
|
||||
if(m_marker[krep]<m_jcol)
|
||||
{
|
||||
m_marker[krep] = jj;
|
||||
return true;
|
||||
}
|
||||
return false;
|
||||
}
|
||||
void mem_expand(IndexVector& /*glu.lsub*/, Index /*nextl*/, Index /*chmark*/) {}
|
||||
enum { ExpandMem = false };
|
||||
Index m_jcol;
|
||||
StorageIndex* m_marker;
|
||||
};
|
||||
|
||||
|
||||
template <typename Scalar, typename StorageIndex>
|
||||
template <typename Traits>
|
||||
void SparseLUImpl<Scalar,StorageIndex>::dfs_kernel(const StorageIndex jj, IndexVector& perm_r,
|
||||
Index& nseg, IndexVector& panel_lsub, IndexVector& segrep,
|
||||
Ref<IndexVector> repfnz_col, IndexVector& xprune, Ref<IndexVector> marker, IndexVector& parent,
|
||||
IndexVector& xplore, GlobalLU_t& glu,
|
||||
Index& nextl_col, Index krow, Traits& traits
|
||||
)
|
||||
{
|
||||
|
||||
StorageIndex kmark = marker(krow);
|
||||
|
||||
// For each unmarked krow of jj
|
||||
marker(krow) = jj;
|
||||
StorageIndex kperm = perm_r(krow);
|
||||
if (kperm == emptyIdxLU ) {
|
||||
// krow is in L : place it in structure of L(*, jj)
|
||||
panel_lsub(nextl_col++) = StorageIndex(krow); // krow is indexed into A
|
||||
|
||||
traits.mem_expand(panel_lsub, nextl_col, kmark);
|
||||
}
|
||||
else
|
||||
{
|
||||
// krow is in U : if its supernode-representative krep
|
||||
// has been explored, update repfnz(*)
|
||||
// krep = supernode representative of the current row
|
||||
StorageIndex krep = glu.xsup(glu.supno(kperm)+1) - 1;
|
||||
// First nonzero element in the current column:
|
||||
StorageIndex myfnz = repfnz_col(krep);
|
||||
|
||||
if (myfnz != emptyIdxLU )
|
||||
{
|
||||
// Representative visited before
|
||||
if (myfnz > kperm ) repfnz_col(krep) = kperm;
|
||||
|
||||
}
|
||||
else
|
||||
{
|
||||
// Otherwise, perform dfs starting at krep
|
||||
StorageIndex oldrep = emptyIdxLU;
|
||||
parent(krep) = oldrep;
|
||||
repfnz_col(krep) = kperm;
|
||||
StorageIndex xdfs = glu.xlsub(krep);
|
||||
Index maxdfs = xprune(krep);
|
||||
|
||||
StorageIndex kpar;
|
||||
do
|
||||
{
|
||||
// For each unmarked kchild of krep
|
||||
while (xdfs < maxdfs)
|
||||
{
|
||||
StorageIndex kchild = glu.lsub(xdfs);
|
||||
xdfs++;
|
||||
StorageIndex chmark = marker(kchild);
|
||||
|
||||
if (chmark != jj )
|
||||
{
|
||||
marker(kchild) = jj;
|
||||
StorageIndex chperm = perm_r(kchild);
|
||||
|
||||
if (chperm == emptyIdxLU)
|
||||
{
|
||||
// case kchild is in L: place it in L(*, j)
|
||||
panel_lsub(nextl_col++) = kchild;
|
||||
traits.mem_expand(panel_lsub, nextl_col, chmark);
|
||||
}
|
||||
else
|
||||
{
|
||||
// case kchild is in U :
|
||||
// chrep = its supernode-rep. If its rep has been explored,
|
||||
// update its repfnz(*)
|
||||
StorageIndex chrep = glu.xsup(glu.supno(chperm)+1) - 1;
|
||||
myfnz = repfnz_col(chrep);
|
||||
|
||||
if (myfnz != emptyIdxLU)
|
||||
{ // Visited before
|
||||
if (myfnz > chperm)
|
||||
repfnz_col(chrep) = chperm;
|
||||
}
|
||||
else
|
||||
{ // Cont. dfs at snode-rep of kchild
|
||||
xplore(krep) = xdfs;
|
||||
oldrep = krep;
|
||||
krep = chrep; // Go deeper down G(L)
|
||||
parent(krep) = oldrep;
|
||||
repfnz_col(krep) = chperm;
|
||||
xdfs = glu.xlsub(krep);
|
||||
maxdfs = xprune(krep);
|
||||
|
||||
} // end if myfnz != -1
|
||||
} // end if chperm == -1
|
||||
|
||||
} // end if chmark !=jj
|
||||
} // end while xdfs < maxdfs
|
||||
|
||||
// krow has no more unexplored nbrs :
|
||||
// Place snode-rep krep in postorder DFS, if this
|
||||
// segment is seen for the first time. (Note that
|
||||
// "repfnz(krep)" may change later.)
|
||||
// Baktrack dfs to its parent
|
||||
if(traits.update_segrep(krep,jj))
|
||||
//if (marker1(krep) < jcol )
|
||||
{
|
||||
segrep(nseg) = krep;
|
||||
++nseg;
|
||||
//marker1(krep) = jj;
|
||||
}
|
||||
|
||||
kpar = parent(krep); // Pop recursion, mimic recursion
|
||||
if (kpar == emptyIdxLU)
|
||||
break; // dfs done
|
||||
krep = kpar;
|
||||
xdfs = xplore(krep);
|
||||
maxdfs = xprune(krep);
|
||||
|
||||
} while (kpar != emptyIdxLU); // Do until empty stack
|
||||
|
||||
} // end if (myfnz = -1)
|
||||
|
||||
} // end if (kperm == -1)
|
||||
}
|
||||
|
||||
/**
|
||||
* \brief Performs a symbolic factorization on a panel of columns [jcol, jcol+w)
|
||||
*
|
||||
* A supernode representative is the last column of a supernode.
|
||||
* The nonzeros in U[*,j] are segments that end at supernodes representatives
|
||||
*
|
||||
* The routine returns a list of the supernodal representatives
|
||||
* in topological order of the dfs that generates them. This list is
|
||||
* a superset of the topological order of each individual column within
|
||||
* the panel.
|
||||
* The location of the first nonzero in each supernodal segment
|
||||
* (supernodal entry location) is also returned. Each column has
|
||||
* a separate list for this purpose.
|
||||
*
|
||||
* Two markers arrays are used for dfs :
|
||||
* marker[i] == jj, if i was visited during dfs of current column jj;
|
||||
* marker1[i] >= jcol, if i was visited by earlier columns in this panel;
|
||||
*
|
||||
* \param[in] m number of rows in the matrix
|
||||
* \param[in] w Panel size
|
||||
* \param[in] jcol Starting column of the panel
|
||||
* \param[in] A Input matrix in column-major storage
|
||||
* \param[in] perm_r Row permutation
|
||||
* \param[out] nseg Number of U segments
|
||||
* \param[out] dense Accumulate the column vectors of the panel
|
||||
* \param[out] panel_lsub Subscripts of the row in the panel
|
||||
* \param[out] segrep Segment representative i.e first nonzero row of each segment
|
||||
* \param[out] repfnz First nonzero location in each row
|
||||
* \param[out] xprune The pruned elimination tree
|
||||
* \param[out] marker work vector
|
||||
* \param parent The elimination tree
|
||||
* \param xplore work vector
|
||||
* \param glu The global data structure
|
||||
*
|
||||
*/
|
||||
|
||||
template <typename Scalar, typename StorageIndex>
|
||||
void SparseLUImpl<Scalar,StorageIndex>::panel_dfs(const Index m, const Index w, const Index jcol, MatrixType& A, IndexVector& perm_r, Index& nseg, ScalarVector& dense, IndexVector& panel_lsub, IndexVector& segrep, IndexVector& repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu)
|
||||
{
|
||||
Index nextl_col; // Next available position in panel_lsub[*,jj]
|
||||
|
||||
// Initialize pointers
|
||||
VectorBlock<IndexVector> marker1(marker, m, m);
|
||||
nseg = 0;
|
||||
|
||||
panel_dfs_traits<IndexVector> traits(jcol, marker1.data());
|
||||
|
||||
// For each column in the panel
|
||||
for (StorageIndex jj = StorageIndex(jcol); jj < jcol + w; jj++)
|
||||
{
|
||||
nextl_col = (jj - jcol) * m;
|
||||
|
||||
VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero location in each row
|
||||
VectorBlock<ScalarVector> dense_col(dense,nextl_col, m); // Accumulate a column vector here
|
||||
|
||||
|
||||
// For each nnz in A[*, jj] do depth first search
|
||||
for (typename MatrixType::InnerIterator it(A, jj); it; ++it)
|
||||
{
|
||||
Index krow = it.row();
|
||||
dense_col(krow) = it.value();
|
||||
|
||||
StorageIndex kmark = marker(krow);
|
||||
if (kmark == jj)
|
||||
continue; // krow visited before, go to the next nonzero
|
||||
|
||||
dfs_kernel(jj, perm_r, nseg, panel_lsub, segrep, repfnz_col, xprune, marker, parent,
|
||||
xplore, glu, nextl_col, krow, traits);
|
||||
}// end for nonzeros in column jj
|
||||
|
||||
} // end for column jj
|
||||
}
|
||||
|
||||
} // end namespace internal
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // SPARSELU_PANEL_DFS_H
|
||||
137
external/include/eigen3/Eigen/src/SparseLU/SparseLU_pivotL.h
vendored
Normal file
137
external/include/eigen3/Eigen/src/SparseLU/SparseLU_pivotL.h
vendored
Normal file
@@ -0,0 +1,137 @@
|
||||
// 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/.
|
||||
|
||||
/*
|
||||
|
||||
* NOTE: This file is the modified version of xpivotL.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.
|
||||
*/
|
||||
#ifndef SPARSELU_PIVOTL_H
|
||||
#define SPARSELU_PIVOTL_H
|
||||
|
||||
namespace Eigen {
|
||||
namespace internal {
|
||||
|
||||
/**
|
||||
* \brief Performs the numerical pivotin on the current column of L, and the CDIV operation.
|
||||
*
|
||||
* Pivot policy :
|
||||
* (1) Compute thresh = u * max_(i>=j) abs(A_ij);
|
||||
* (2) IF user specifies pivot row k and abs(A_kj) >= thresh THEN
|
||||
* pivot row = k;
|
||||
* ELSE IF abs(A_jj) >= thresh THEN
|
||||
* pivot row = j;
|
||||
* ELSE
|
||||
* pivot row = m;
|
||||
*
|
||||
* Note: If you absolutely want to use a given pivot order, then set u=0.0.
|
||||
*
|
||||
* \param jcol The current column of L
|
||||
* \param diagpivotthresh diagonal pivoting threshold
|
||||
* \param[in,out] perm_r Row permutation (threshold pivoting)
|
||||
* \param[in] iperm_c column permutation - used to finf diagonal of Pc*A*Pc'
|
||||
* \param[out] pivrow The pivot row
|
||||
* \param glu Global LU data
|
||||
* \return 0 if success, i > 0 if U(i,i) is exactly zero
|
||||
*
|
||||
*/
|
||||
template <typename Scalar, typename StorageIndex>
|
||||
Index SparseLUImpl<Scalar,StorageIndex>::pivotL(const Index jcol, const RealScalar& diagpivotthresh, IndexVector& perm_r, IndexVector& iperm_c, Index& pivrow, GlobalLU_t& glu)
|
||||
{
|
||||
|
||||
Index fsupc = (glu.xsup)((glu.supno)(jcol)); // First column in the supernode containing the column jcol
|
||||
Index nsupc = jcol - fsupc; // Number of columns in the supernode portion, excluding jcol; nsupc >=0
|
||||
Index lptr = glu.xlsub(fsupc); // pointer to the starting location of the row subscripts for this supernode portion
|
||||
Index nsupr = glu.xlsub(fsupc+1) - lptr; // Number of rows in the supernode
|
||||
Index lda = glu.xlusup(fsupc+1) - glu.xlusup(fsupc); // leading dimension
|
||||
Scalar* lu_sup_ptr = &(glu.lusup.data()[glu.xlusup(fsupc)]); // Start of the current supernode
|
||||
Scalar* lu_col_ptr = &(glu.lusup.data()[glu.xlusup(jcol)]); // Start of jcol in the supernode
|
||||
StorageIndex* lsub_ptr = &(glu.lsub.data()[lptr]); // Start of row indices of the supernode
|
||||
|
||||
// Determine the largest abs numerical value for partial pivoting
|
||||
Index diagind = iperm_c(jcol); // diagonal index
|
||||
RealScalar pivmax(-1.0);
|
||||
Index pivptr = nsupc;
|
||||
Index diag = emptyIdxLU;
|
||||
RealScalar rtemp;
|
||||
Index isub, icol, itemp, k;
|
||||
for (isub = nsupc; isub < nsupr; ++isub) {
|
||||
using std::abs;
|
||||
rtemp = abs(lu_col_ptr[isub]);
|
||||
if (rtemp > pivmax) {
|
||||
pivmax = rtemp;
|
||||
pivptr = isub;
|
||||
}
|
||||
if (lsub_ptr[isub] == diagind) diag = isub;
|
||||
}
|
||||
|
||||
// Test for singularity
|
||||
if ( pivmax <= RealScalar(0.0) ) {
|
||||
// if pivmax == -1, the column is structurally empty, otherwise it is only numerically zero
|
||||
pivrow = pivmax < RealScalar(0.0) ? diagind : lsub_ptr[pivptr];
|
||||
perm_r(pivrow) = StorageIndex(jcol);
|
||||
return (jcol+1);
|
||||
}
|
||||
|
||||
RealScalar thresh = diagpivotthresh * pivmax;
|
||||
|
||||
// Choose appropriate pivotal element
|
||||
|
||||
{
|
||||
// Test if the diagonal element can be used as a pivot (given the threshold value)
|
||||
if (diag >= 0 )
|
||||
{
|
||||
// Diagonal element exists
|
||||
using std::abs;
|
||||
rtemp = abs(lu_col_ptr[diag]);
|
||||
if (rtemp != RealScalar(0.0) && rtemp >= thresh) pivptr = diag;
|
||||
}
|
||||
pivrow = lsub_ptr[pivptr];
|
||||
}
|
||||
|
||||
// Record pivot row
|
||||
perm_r(pivrow) = StorageIndex(jcol);
|
||||
// Interchange row subscripts
|
||||
if (pivptr != nsupc )
|
||||
{
|
||||
std::swap( lsub_ptr[pivptr], lsub_ptr[nsupc] );
|
||||
// Interchange numerical values as well, for the two rows in the whole snode
|
||||
// such that L is indexed the same way as A
|
||||
for (icol = 0; icol <= nsupc; icol++)
|
||||
{
|
||||
itemp = pivptr + icol * lda;
|
||||
std::swap(lu_sup_ptr[itemp], lu_sup_ptr[nsupc + icol * lda]);
|
||||
}
|
||||
}
|
||||
// cdiv operations
|
||||
Scalar temp = Scalar(1.0) / lu_col_ptr[nsupc];
|
||||
for (k = nsupc+1; k < nsupr; k++)
|
||||
lu_col_ptr[k] *= temp;
|
||||
return 0;
|
||||
}
|
||||
|
||||
} // end namespace internal
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // SPARSELU_PIVOTL_H
|
||||
136
external/include/eigen3/Eigen/src/SparseLU/SparseLU_pruneL.h
vendored
Normal file
136
external/include/eigen3/Eigen/src/SparseLU/SparseLU_pruneL.h
vendored
Normal file
@@ -0,0 +1,136 @@
|
||||
// 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/.
|
||||
|
||||
/*
|
||||
|
||||
* NOTE: This file is the modified version of [s,d,c,z]pruneL.c file in SuperLU
|
||||
|
||||
* -- SuperLU routine (version 2.0) --
|
||||
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
|
||||
* and Lawrence Berkeley National Lab.
|
||||
* November 15, 1997
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
#ifndef SPARSELU_PRUNEL_H
|
||||
#define SPARSELU_PRUNEL_H
|
||||
|
||||
namespace Eigen {
|
||||
namespace internal {
|
||||
|
||||
/**
|
||||
* \brief Prunes the L-structure.
|
||||
*
|
||||
* It prunes the L-structure of supernodes whose L-structure contains the current pivot row "pivrow"
|
||||
*
|
||||
*
|
||||
* \param jcol The current column of L
|
||||
* \param[in] perm_r Row permutation
|
||||
* \param[out] pivrow The pivot row
|
||||
* \param nseg Number of segments
|
||||
* \param segrep
|
||||
* \param repfnz
|
||||
* \param[out] xprune
|
||||
* \param glu Global LU data
|
||||
*
|
||||
*/
|
||||
template <typename Scalar, typename StorageIndex>
|
||||
void SparseLUImpl<Scalar,StorageIndex>::pruneL(const Index jcol, const IndexVector& perm_r, const Index pivrow, const Index nseg,
|
||||
const IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune, GlobalLU_t& glu)
|
||||
{
|
||||
// For each supernode-rep irep in U(*,j]
|
||||
Index jsupno = glu.supno(jcol);
|
||||
Index i,irep,irep1;
|
||||
bool movnum, do_prune = false;
|
||||
Index kmin = 0, kmax = 0, minloc, maxloc,krow;
|
||||
for (i = 0; i < nseg; i++)
|
||||
{
|
||||
irep = segrep(i);
|
||||
irep1 = irep + 1;
|
||||
do_prune = false;
|
||||
|
||||
// Don't prune with a zero U-segment
|
||||
if (repfnz(irep) == emptyIdxLU) continue;
|
||||
|
||||
// If a snode overlaps with the next panel, then the U-segment
|
||||
// is fragmented into two parts -- irep and irep1. We should let
|
||||
// pruning occur at the rep-column in irep1s snode.
|
||||
if (glu.supno(irep) == glu.supno(irep1) ) continue; // don't prune
|
||||
|
||||
// If it has not been pruned & it has a nonz in row L(pivrow,i)
|
||||
if (glu.supno(irep) != jsupno )
|
||||
{
|
||||
if ( xprune (irep) >= glu.xlsub(irep1) )
|
||||
{
|
||||
kmin = glu.xlsub(irep);
|
||||
kmax = glu.xlsub(irep1) - 1;
|
||||
for (krow = kmin; krow <= kmax; krow++)
|
||||
{
|
||||
if (glu.lsub(krow) == pivrow)
|
||||
{
|
||||
do_prune = true;
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
if (do_prune)
|
||||
{
|
||||
// do a quicksort-type partition
|
||||
// movnum=true means that the num values have to be exchanged
|
||||
movnum = false;
|
||||
if (irep == glu.xsup(glu.supno(irep)) ) // Snode of size 1
|
||||
movnum = true;
|
||||
|
||||
while (kmin <= kmax)
|
||||
{
|
||||
if (perm_r(glu.lsub(kmax)) == emptyIdxLU)
|
||||
kmax--;
|
||||
else if ( perm_r(glu.lsub(kmin)) != emptyIdxLU)
|
||||
kmin++;
|
||||
else
|
||||
{
|
||||
// kmin below pivrow (not yet pivoted), and kmax
|
||||
// above pivrow: interchange the two suscripts
|
||||
std::swap(glu.lsub(kmin), glu.lsub(kmax));
|
||||
|
||||
// If the supernode has only one column, then we
|
||||
// only keep one set of subscripts. For any subscript
|
||||
// intercnahge performed, similar interchange must be
|
||||
// done on the numerical values.
|
||||
if (movnum)
|
||||
{
|
||||
minloc = glu.xlusup(irep) + ( kmin - glu.xlsub(irep) );
|
||||
maxloc = glu.xlusup(irep) + ( kmax - glu.xlsub(irep) );
|
||||
std::swap(glu.lusup(minloc), glu.lusup(maxloc));
|
||||
}
|
||||
kmin++;
|
||||
kmax--;
|
||||
}
|
||||
} // end while
|
||||
|
||||
xprune(irep) = StorageIndex(kmin); //Pruning
|
||||
} // end if do_prune
|
||||
} // end pruning
|
||||
} // End for each U-segment
|
||||
}
|
||||
|
||||
} // end namespace internal
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // SPARSELU_PRUNEL_H
|
||||
83
external/include/eigen3/Eigen/src/SparseLU/SparseLU_relax_snode.h
vendored
Normal file
83
external/include/eigen3/Eigen/src/SparseLU/SparseLU_relax_snode.h
vendored
Normal file
@@ -0,0 +1,83 @@
|
||||
// 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.
|
||||
*/
|
||||
|
||||
#ifndef SPARSELU_RELAX_SNODE_H
|
||||
#define SPARSELU_RELAX_SNODE_H
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
namespace internal {
|
||||
|
||||
/**
|
||||
* \brief Identify the initial relaxed supernodes
|
||||
*
|
||||
* This routine is applied to a column 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>::relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end)
|
||||
{
|
||||
|
||||
// compute the number of descendants of each node in the etree
|
||||
Index parent;
|
||||
relax_end.setConstant(emptyIdxLU);
|
||||
descendants.setZero();
|
||||
for (Index 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
|
||||
for (Index 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
|
||||
relax_end(snode_start) = StorageIndex(j); // Record last column
|
||||
j++;
|
||||
// Search for a new leaf
|
||||
while (descendants(j) != 0 && j < n) j++;
|
||||
} // End postorder traversal of the etree
|
||||
|
||||
}
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
} // end namespace Eigen
|
||||
#endif
|
||||
Reference in New Issue
Block a user