| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. |
| // |
| // Copyright (C) 2008-2011 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_SUPERLUSUPPORT_H |
| #define EIGEN_SUPERLUSUPPORT_H |
| |
| namespace Eigen { |
| |
| #define DECL_GSSVX(PREFIX,FLOATTYPE,KEYTYPE) \ |
| extern "C" { \ |
| typedef struct { FLOATTYPE for_lu; FLOATTYPE total_needed; int expansions; } PREFIX##mem_usage_t; \ |
| extern void PREFIX##gssvx(superlu_options_t *, SuperMatrix *, int *, int *, int *, \ |
| char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *, \ |
| void *, int, SuperMatrix *, SuperMatrix *, \ |
| FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, \ |
| PREFIX##mem_usage_t *, SuperLUStat_t *, int *); \ |
| } \ |
| inline float SuperLU_gssvx(superlu_options_t *options, SuperMatrix *A, \ |
| int *perm_c, int *perm_r, int *etree, char *equed, \ |
| FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L, \ |
| SuperMatrix *U, void *work, int lwork, \ |
| SuperMatrix *B, SuperMatrix *X, \ |
| FLOATTYPE *recip_pivot_growth, \ |
| FLOATTYPE *rcond, FLOATTYPE *ferr, FLOATTYPE *berr, \ |
| SuperLUStat_t *stats, int *info, KEYTYPE) { \ |
| PREFIX##mem_usage_t mem_usage; \ |
| PREFIX##gssvx(options, A, perm_c, perm_r, etree, equed, R, C, L, \ |
| U, work, lwork, B, X, recip_pivot_growth, rcond, \ |
| ferr, berr, &mem_usage, stats, info); \ |
| return mem_usage.for_lu; /* bytes used by the factor storage */ \ |
| } |
| |
| DECL_GSSVX(s,float,float) |
| DECL_GSSVX(c,float,std::complex<float>) |
| DECL_GSSVX(d,double,double) |
| DECL_GSSVX(z,double,std::complex<double>) |
| |
| #ifdef MILU_ALPHA |
| #define EIGEN_SUPERLU_HAS_ILU |
| #endif |
| |
| #ifdef EIGEN_SUPERLU_HAS_ILU |
| |
| // similarly for the incomplete factorization using gsisx |
| #define DECL_GSISX(PREFIX,FLOATTYPE,KEYTYPE) \ |
| extern "C" { \ |
| extern void PREFIX##gsisx(superlu_options_t *, SuperMatrix *, int *, int *, int *, \ |
| char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *, \ |
| void *, int, SuperMatrix *, SuperMatrix *, FLOATTYPE *, FLOATTYPE *, \ |
| PREFIX##mem_usage_t *, SuperLUStat_t *, int *); \ |
| } \ |
| inline float SuperLU_gsisx(superlu_options_t *options, SuperMatrix *A, \ |
| int *perm_c, int *perm_r, int *etree, char *equed, \ |
| FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L, \ |
| SuperMatrix *U, void *work, int lwork, \ |
| SuperMatrix *B, SuperMatrix *X, \ |
| FLOATTYPE *recip_pivot_growth, \ |
| FLOATTYPE *rcond, \ |
| SuperLUStat_t *stats, int *info, KEYTYPE) { \ |
| PREFIX##mem_usage_t mem_usage; \ |
| PREFIX##gsisx(options, A, perm_c, perm_r, etree, equed, R, C, L, \ |
| U, work, lwork, B, X, recip_pivot_growth, rcond, \ |
| &mem_usage, stats, info); \ |
| return mem_usage.for_lu; /* bytes used by the factor storage */ \ |
| } |
| |
| DECL_GSISX(s,float,float) |
| DECL_GSISX(c,float,std::complex<float>) |
| DECL_GSISX(d,double,double) |
| DECL_GSISX(z,double,std::complex<double>) |
| |
| #endif |
| |
| template<typename MatrixType> |
| struct SluMatrixMapHelper; |
| |
| /** \internal |
| * |
| * A wrapper class for SuperLU matrices. It supports only compressed sparse matrices |
| * and dense matrices. Supernodal and other fancy format are not supported by this wrapper. |
| * |
| * This wrapper class mainly aims to avoids the need of dynamic allocation of the storage structure. |
| */ |
| struct SluMatrix : SuperMatrix |
| { |
| SluMatrix() |
| { |
| Store = &storage; |
| } |
| |
| SluMatrix(const SluMatrix& other) |
| : SuperMatrix(other) |
| { |
| Store = &storage; |
| storage = other.storage; |
| } |
| |
| SluMatrix& operator=(const SluMatrix& other) |
| { |
| SuperMatrix::operator=(static_cast<const SuperMatrix&>(other)); |
| Store = &storage; |
| storage = other.storage; |
| return *this; |
| } |
| |
| struct |
| { |
| union {int nnz;int lda;}; |
| void *values; |
| int *innerInd; |
| int *outerInd; |
| } storage; |
| |
| void setStorageType(Stype_t t) |
| { |
| Stype = t; |
| if (t==SLU_NC || t==SLU_NR || t==SLU_DN) |
| Store = &storage; |
| else |
| { |
| eigen_assert(false && "storage type not supported"); |
| Store = 0; |
| } |
| } |
| |
| template<typename Scalar> |
| void setScalarType() |
| { |
| if (internal::is_same<Scalar,float>::value) |
| Dtype = SLU_S; |
| else if (internal::is_same<Scalar,double>::value) |
| Dtype = SLU_D; |
| else if (internal::is_same<Scalar,std::complex<float> >::value) |
| Dtype = SLU_C; |
| else if (internal::is_same<Scalar,std::complex<double> >::value) |
| Dtype = SLU_Z; |
| else |
| { |
| eigen_assert(false && "Scalar type not supported by SuperLU"); |
| } |
| } |
| |
| template<typename MatrixType> |
| static SluMatrix Map(MatrixBase<MatrixType>& _mat) |
| { |
| MatrixType& mat(_mat.derived()); |
| eigen_assert( ((MatrixType::Flags&RowMajorBit)!=RowMajorBit) && "row-major dense matrices are not supported by SuperLU"); |
| SluMatrix res; |
| res.setStorageType(SLU_DN); |
| res.setScalarType<typename MatrixType::Scalar>(); |
| res.Mtype = SLU_GE; |
| |
| res.nrow = mat.rows(); |
| res.ncol = mat.cols(); |
| |
| res.storage.lda = MatrixType::IsVectorAtCompileTime ? mat.size() : mat.outerStride(); |
| res.storage.values = mat.data(); |
| return res; |
| } |
| |
| template<typename MatrixType> |
| static SluMatrix Map(SparseMatrixBase<MatrixType>& mat) |
| { |
| SluMatrix res; |
| if ((MatrixType::Flags&RowMajorBit)==RowMajorBit) |
| { |
| res.setStorageType(SLU_NR); |
| res.nrow = mat.cols(); |
| res.ncol = mat.rows(); |
| } |
| else |
| { |
| res.setStorageType(SLU_NC); |
| res.nrow = mat.rows(); |
| res.ncol = mat.cols(); |
| } |
| |
| res.Mtype = SLU_GE; |
| |
| res.storage.nnz = mat.nonZeros(); |
| res.storage.values = mat.derived().valuePtr(); |
| res.storage.innerInd = mat.derived().innerIndexPtr(); |
| res.storage.outerInd = mat.derived().outerIndexPtr(); |
| |
| res.setScalarType<typename MatrixType::Scalar>(); |
| |
| // FIXME the following is not very accurate |
| if (MatrixType::Flags & Upper) |
| res.Mtype = SLU_TRU; |
| if (MatrixType::Flags & Lower) |
| res.Mtype = SLU_TRL; |
| |
| eigen_assert(((MatrixType::Flags & SelfAdjoint)==0) && "SelfAdjoint matrix shape not supported by SuperLU"); |
| |
| return res; |
| } |
| }; |
| |
| template<typename Scalar, int Rows, int Cols, int Options, int MRows, int MCols> |
| struct SluMatrixMapHelper<Matrix<Scalar,Rows,Cols,Options,MRows,MCols> > |
| { |
| typedef Matrix<Scalar,Rows,Cols,Options,MRows,MCols> MatrixType; |
| static void run(MatrixType& mat, SluMatrix& res) |
| { |
| eigen_assert( ((Options&RowMajor)!=RowMajor) && "row-major dense matrices is not supported by SuperLU"); |
| res.setStorageType(SLU_DN); |
| res.setScalarType<Scalar>(); |
| res.Mtype = SLU_GE; |
| |
| res.nrow = mat.rows(); |
| res.ncol = mat.cols(); |
| |
| res.storage.lda = mat.outerStride(); |
| res.storage.values = mat.data(); |
| } |
| }; |
| |
| template<typename Derived> |
| struct SluMatrixMapHelper<SparseMatrixBase<Derived> > |
| { |
| typedef Derived MatrixType; |
| static void run(MatrixType& mat, SluMatrix& res) |
| { |
| if ((MatrixType::Flags&RowMajorBit)==RowMajorBit) |
| { |
| res.setStorageType(SLU_NR); |
| res.nrow = mat.cols(); |
| res.ncol = mat.rows(); |
| } |
| else |
| { |
| res.setStorageType(SLU_NC); |
| res.nrow = mat.rows(); |
| res.ncol = mat.cols(); |
| } |
| |
| res.Mtype = SLU_GE; |
| |
| res.storage.nnz = mat.nonZeros(); |
| res.storage.values = mat.valuePtr(); |
| res.storage.innerInd = mat.innerIndexPtr(); |
| res.storage.outerInd = mat.outerIndexPtr(); |
| |
| res.setScalarType<typename MatrixType::Scalar>(); |
| |
| // FIXME the following is not very accurate |
| if (MatrixType::Flags & Upper) |
| res.Mtype = SLU_TRU; |
| if (MatrixType::Flags & Lower) |
| res.Mtype = SLU_TRL; |
| |
| eigen_assert(((MatrixType::Flags & SelfAdjoint)==0) && "SelfAdjoint matrix shape not supported by SuperLU"); |
| } |
| }; |
| |
| namespace internal { |
| |
| template<typename MatrixType> |
| SluMatrix asSluMatrix(MatrixType& mat) |
| { |
| return SluMatrix::Map(mat); |
| } |
| |
| /** View a Super LU matrix as an Eigen expression */ |
| template<typename Scalar, int Flags, typename Index> |
| MappedSparseMatrix<Scalar,Flags,Index> map_superlu(SluMatrix& sluMat) |
| { |
| eigen_assert((Flags&RowMajor)==RowMajor && sluMat.Stype == SLU_NR |
| || (Flags&ColMajor)==ColMajor && sluMat.Stype == SLU_NC); |
| |
| Index outerSize = (Flags&RowMajor)==RowMajor ? sluMat.ncol : sluMat.nrow; |
| |
| return MappedSparseMatrix<Scalar,Flags,Index>( |
| sluMat.nrow, sluMat.ncol, sluMat.storage.outerInd[outerSize], |
| sluMat.storage.outerInd, sluMat.storage.innerInd, reinterpret_cast<Scalar*>(sluMat.storage.values) ); |
| } |
| |
| } // end namespace internal |
| |
| /** \ingroup SuperLUSupport_Module |
| * \class SuperLUBase |
| * \brief The base class for the direct and incomplete LU factorization of SuperLU |
| */ |
| template<typename _MatrixType, typename Derived> |
| class SuperLUBase : internal::noncopyable |
| { |
| public: |
| typedef _MatrixType MatrixType; |
| typedef typename MatrixType::Scalar Scalar; |
| typedef typename MatrixType::RealScalar RealScalar; |
| typedef typename MatrixType::Index Index; |
| typedef Matrix<Scalar,Dynamic,1> Vector; |
| typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType; |
| typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType; |
| typedef SparseMatrix<Scalar> LUMatrixType; |
| |
| public: |
| |
| SuperLUBase() {} |
| |
| ~SuperLUBase() |
| { |
| clearFactors(); |
| } |
| |
| Derived& derived() { return *static_cast<Derived*>(this); } |
| const Derived& derived() const { return *static_cast<const Derived*>(this); } |
| |
| inline Index rows() const { return m_matrix.rows(); } |
| inline Index cols() const { return m_matrix.cols(); } |
| |
| /** \returns a reference to the Super LU option object to configure the Super LU algorithms. */ |
| inline superlu_options_t& options() { return m_sluOptions; } |
| |
| /** \brief Reports whether previous computation was successful. |
| * |
| * \returns \c Success if computation was succesful, |
| * \c NumericalIssue if the matrix.appears to be negative. |
| */ |
| ComputationInfo info() const |
| { |
| eigen_assert(m_isInitialized && "Decomposition is not initialized."); |
| return m_info; |
| } |
| |
| /** Computes the sparse Cholesky decomposition of \a matrix */ |
| void compute(const MatrixType& matrix) |
| { |
| derived().analyzePattern(matrix); |
| derived().factorize(matrix); |
| } |
| |
| /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A. |
| * |
| * \sa compute() |
| */ |
| template<typename Rhs> |
| inline const internal::solve_retval<SuperLUBase, Rhs> solve(const MatrixBase<Rhs>& b) const |
| { |
| eigen_assert(m_isInitialized && "SuperLU is not initialized."); |
| eigen_assert(rows()==b.rows() |
| && "SuperLU::solve(): invalid number of rows of the right hand side matrix b"); |
| return internal::solve_retval<SuperLUBase, Rhs>(*this, b.derived()); |
| } |
| |
| /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A. |
| * |
| * \sa compute() |
| */ |
| // template<typename Rhs> |
| // inline const internal::sparse_solve_retval<SuperLU, Rhs> solve(const SparseMatrixBase<Rhs>& b) const |
| // { |
| // eigen_assert(m_isInitialized && "SuperLU is not initialized."); |
| // eigen_assert(rows()==b.rows() |
| // && "SuperLU::solve(): invalid number of rows of the right hand side matrix b"); |
| // return internal::sparse_solve_retval<SuperLU, Rhs>(*this, b.derived()); |
| // } |
| |
| /** Performs a symbolic decomposition on the sparcity of \a matrix. |
| * |
| * This function is particularly useful when solving for several problems having the same structure. |
| * |
| * \sa factorize() |
| */ |
| void analyzePattern(const MatrixType& /*matrix*/) |
| { |
| m_isInitialized = true; |
| m_info = Success; |
| m_analysisIsOk = true; |
| m_factorizationIsOk = false; |
| } |
| |
| template<typename Stream> |
| void dumpMemory(Stream& s) |
| {} |
| |
| protected: |
| |
| void initFactorization(const MatrixType& a) |
| { |
| set_default_options(&this->m_sluOptions); |
| |
| const int size = a.rows(); |
| m_matrix = a; |
| |
| m_sluA = internal::asSluMatrix(m_matrix); |
| clearFactors(); |
| |
| m_p.resize(size); |
| m_q.resize(size); |
| m_sluRscale.resize(size); |
| m_sluCscale.resize(size); |
| m_sluEtree.resize(size); |
| |
| // set empty B and X |
| m_sluB.setStorageType(SLU_DN); |
| m_sluB.setScalarType<Scalar>(); |
| m_sluB.Mtype = SLU_GE; |
| m_sluB.storage.values = 0; |
| m_sluB.nrow = 0; |
| m_sluB.ncol = 0; |
| m_sluB.storage.lda = size; |
| m_sluX = m_sluB; |
| |
| m_extractedDataAreDirty = true; |
| } |
| |
| void init() |
| { |
| m_info = InvalidInput; |
| m_isInitialized = false; |
| m_sluL.Store = 0; |
| m_sluU.Store = 0; |
| } |
| |
| void extractData() const; |
| |
| void clearFactors() |
| { |
| if(m_sluL.Store) |
| Destroy_SuperNode_Matrix(&m_sluL); |
| if(m_sluU.Store) |
| Destroy_CompCol_Matrix(&m_sluU); |
| |
| m_sluL.Store = 0; |
| m_sluU.Store = 0; |
| |
| memset(&m_sluL,0,sizeof m_sluL); |
| memset(&m_sluU,0,sizeof m_sluU); |
| } |
| |
| // cached data to reduce reallocation, etc. |
| mutable LUMatrixType m_l; |
| mutable LUMatrixType m_u; |
| mutable IntColVectorType m_p; |
| mutable IntRowVectorType m_q; |
| |
| mutable LUMatrixType m_matrix; // copy of the factorized matrix |
| mutable SluMatrix m_sluA; |
| mutable SuperMatrix m_sluL, m_sluU; |
| mutable SluMatrix m_sluB, m_sluX; |
| mutable SuperLUStat_t m_sluStat; |
| mutable superlu_options_t m_sluOptions; |
| mutable std::vector<int> m_sluEtree; |
| mutable Matrix<RealScalar,Dynamic,1> m_sluRscale, m_sluCscale; |
| mutable Matrix<RealScalar,Dynamic,1> m_sluFerr, m_sluBerr; |
| mutable char m_sluEqued; |
| |
| mutable ComputationInfo m_info; |
| bool m_isInitialized; |
| int m_factorizationIsOk; |
| int m_analysisIsOk; |
| mutable bool m_extractedDataAreDirty; |
| |
| private: |
| SuperLUBase(SuperLUBase& ) { } |
| }; |
| |
| |
| /** \ingroup SuperLUSupport_Module |
| * \class SuperLU |
| * \brief A sparse direct LU factorization and solver based on the SuperLU library |
| * |
| * This class allows to solve for A.X = B sparse linear problems via a direct LU factorization |
| * using the SuperLU library. The sparse matrix A must be squared and invertible. The vectors or matrices |
| * X and B can be either dense or sparse. |
| * |
| * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<> |
| * |
| * \sa \ref TutorialSparseDirectSolvers |
| */ |
| template<typename _MatrixType> |
| class SuperLU : public SuperLUBase<_MatrixType,SuperLU<_MatrixType> > |
| { |
| public: |
| typedef SuperLUBase<_MatrixType,SuperLU> Base; |
| typedef _MatrixType MatrixType; |
| typedef typename Base::Scalar Scalar; |
| typedef typename Base::RealScalar RealScalar; |
| typedef typename Base::Index Index; |
| typedef typename Base::IntRowVectorType IntRowVectorType; |
| typedef typename Base::IntColVectorType IntColVectorType; |
| typedef typename Base::LUMatrixType LUMatrixType; |
| typedef TriangularView<LUMatrixType, Lower|UnitDiag> LMatrixType; |
| typedef TriangularView<LUMatrixType, Upper> UMatrixType; |
| |
| public: |
| |
| SuperLU() : Base() { init(); } |
| |
| SuperLU(const MatrixType& matrix) : Base() |
| { |
| Base::init(); |
| compute(matrix); |
| } |
| |
| ~SuperLU() |
| { |
| } |
| |
| /** Performs a symbolic decomposition on the sparcity of \a matrix. |
| * |
| * This function is particularly useful when solving for several problems having the same structure. |
| * |
| * \sa factorize() |
| */ |
| void analyzePattern(const MatrixType& matrix) |
| { |
| m_info = InvalidInput; |
| m_isInitialized = false; |
| Base::analyzePattern(matrix); |
| } |
| |
| /** Performs a numeric decomposition of \a matrix |
| * |
| * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed. |
| * |
| * \sa analyzePattern() |
| */ |
| void factorize(const MatrixType& matrix); |
| |
| #ifndef EIGEN_PARSED_BY_DOXYGEN |
| /** \internal */ |
| template<typename Rhs,typename Dest> |
| void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const; |
| #endif // EIGEN_PARSED_BY_DOXYGEN |
| |
| inline const LMatrixType& matrixL() const |
| { |
| if (m_extractedDataAreDirty) this->extractData(); |
| return m_l; |
| } |
| |
| inline const UMatrixType& matrixU() const |
| { |
| if (m_extractedDataAreDirty) this->extractData(); |
| return m_u; |
| } |
| |
| inline const IntColVectorType& permutationP() const |
| { |
| if (m_extractedDataAreDirty) this->extractData(); |
| return m_p; |
| } |
| |
| inline const IntRowVectorType& permutationQ() const |
| { |
| if (m_extractedDataAreDirty) this->extractData(); |
| return m_q; |
| } |
| |
| Scalar determinant() const; |
| |
| protected: |
| |
| using Base::m_matrix; |
| using Base::m_sluOptions; |
| using Base::m_sluA; |
| using Base::m_sluB; |
| using Base::m_sluX; |
| using Base::m_p; |
| using Base::m_q; |
| using Base::m_sluEtree; |
| using Base::m_sluEqued; |
| using Base::m_sluRscale; |
| using Base::m_sluCscale; |
| using Base::m_sluL; |
| using Base::m_sluU; |
| using Base::m_sluStat; |
| using Base::m_sluFerr; |
| using Base::m_sluBerr; |
| using Base::m_l; |
| using Base::m_u; |
| |
| using Base::m_analysisIsOk; |
| using Base::m_factorizationIsOk; |
| using Base::m_extractedDataAreDirty; |
| using Base::m_isInitialized; |
| using Base::m_info; |
| |
| void init() |
| { |
| Base::init(); |
| |
| set_default_options(&this->m_sluOptions); |
| m_sluOptions.PrintStat = NO; |
| m_sluOptions.ConditionNumber = NO; |
| m_sluOptions.Trans = NOTRANS; |
| m_sluOptions.ColPerm = COLAMD; |
| } |
| |
| |
| private: |
| SuperLU(SuperLU& ) { } |
| }; |
| |
| template<typename MatrixType> |
| void SuperLU<MatrixType>::factorize(const MatrixType& a) |
| { |
| eigen_assert(m_analysisIsOk && "You must first call analyzePattern()"); |
| if(!m_analysisIsOk) |
| { |
| m_info = InvalidInput; |
| return; |
| } |
| |
| this->initFactorization(a); |
| |
| int info = 0; |
| RealScalar recip_pivot_growth, rcond; |
| RealScalar ferr, berr; |
| |
| StatInit(&m_sluStat); |
| SuperLU_gssvx(&m_sluOptions, &m_sluA, m_q.data(), m_p.data(), &m_sluEtree[0], |
| &m_sluEqued, &m_sluRscale[0], &m_sluCscale[0], |
| &m_sluL, &m_sluU, |
| NULL, 0, |
| &m_sluB, &m_sluX, |
| &recip_pivot_growth, &rcond, |
| &ferr, &berr, |
| &m_sluStat, &info, Scalar()); |
| StatFree(&m_sluStat); |
| |
| m_extractedDataAreDirty = true; |
| |
| // FIXME how to better check for errors ??? |
| m_info = info == 0 ? Success : NumericalIssue; |
| m_factorizationIsOk = true; |
| } |
| |
| template<typename MatrixType> |
| template<typename Rhs,typename Dest> |
| void SuperLU<MatrixType>::_solve(const MatrixBase<Rhs> &b, MatrixBase<Dest>& x) const |
| { |
| eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or analyzePattern()/factorize()"); |
| |
| const int size = m_matrix.rows(); |
| const int rhsCols = b.cols(); |
| eigen_assert(size==b.rows()); |
| |
| m_sluOptions.Trans = NOTRANS; |
| m_sluOptions.Fact = FACTORED; |
| m_sluOptions.IterRefine = NOREFINE; |
| |
| |
| m_sluFerr.resize(rhsCols); |
| m_sluBerr.resize(rhsCols); |
| m_sluB = SluMatrix::Map(b.const_cast_derived()); |
| m_sluX = SluMatrix::Map(x.derived()); |
| |
| typename Rhs::PlainObject b_cpy; |
| if(m_sluEqued!='N') |
| { |
| b_cpy = b; |
| m_sluB = SluMatrix::Map(b_cpy.const_cast_derived()); |
| } |
| |
| StatInit(&m_sluStat); |
| int info = 0; |
| RealScalar recip_pivot_growth, rcond; |
| SuperLU_gssvx(&m_sluOptions, &m_sluA, |
| m_q.data(), m_p.data(), |
| &m_sluEtree[0], &m_sluEqued, |
| &m_sluRscale[0], &m_sluCscale[0], |
| &m_sluL, &m_sluU, |
| NULL, 0, |
| &m_sluB, &m_sluX, |
| &recip_pivot_growth, &rcond, |
| &m_sluFerr[0], &m_sluBerr[0], |
| &m_sluStat, &info, Scalar()); |
| StatFree(&m_sluStat); |
| m_info = info==0 ? Success : NumericalIssue; |
| } |
| |
| // the code of this extractData() function has been adapted from the SuperLU's Matlab support code, |
| // |
| // 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. |
| // |
| template<typename MatrixType, typename Derived> |
| void SuperLUBase<MatrixType,Derived>::extractData() const |
| { |
| eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for extracting factors, you must first call either compute() or analyzePattern()/factorize()"); |
| if (m_extractedDataAreDirty) |
| { |
| int upper; |
| int fsupc, istart, nsupr; |
| int lastl = 0, lastu = 0; |
| SCformat *Lstore = static_cast<SCformat*>(m_sluL.Store); |
| NCformat *Ustore = static_cast<NCformat*>(m_sluU.Store); |
| Scalar *SNptr; |
| |
| const int size = m_matrix.rows(); |
| m_l.resize(size,size); |
| m_l.resizeNonZeros(Lstore->nnz); |
| m_u.resize(size,size); |
| m_u.resizeNonZeros(Ustore->nnz); |
| |
| int* Lcol = m_l.outerIndexPtr(); |
| int* Lrow = m_l.innerIndexPtr(); |
| Scalar* Lval = m_l.valuePtr(); |
| |
| int* Ucol = m_u.outerIndexPtr(); |
| int* Urow = m_u.innerIndexPtr(); |
| Scalar* Uval = m_u.valuePtr(); |
| |
| Ucol[0] = 0; |
| Ucol[0] = 0; |
| |
| /* for each supernode */ |
| for (int k = 0; k <= Lstore->nsuper; ++k) |
| { |
| fsupc = L_FST_SUPC(k); |
| istart = L_SUB_START(fsupc); |
| nsupr = L_SUB_START(fsupc+1) - istart; |
| upper = 1; |
| |
| /* for each column in the supernode */ |
| for (int j = fsupc; j < L_FST_SUPC(k+1); ++j) |
| { |
| SNptr = &((Scalar*)Lstore->nzval)[L_NZ_START(j)]; |
| |
| /* Extract U */ |
| for (int i = U_NZ_START(j); i < U_NZ_START(j+1); ++i) |
| { |
| Uval[lastu] = ((Scalar*)Ustore->nzval)[i]; |
| /* Matlab doesn't like explicit zero. */ |
| if (Uval[lastu] != 0.0) |
| Urow[lastu++] = U_SUB(i); |
| } |
| for (int i = 0; i < upper; ++i) |
| { |
| /* upper triangle in the supernode */ |
| Uval[lastu] = SNptr[i]; |
| /* Matlab doesn't like explicit zero. */ |
| if (Uval[lastu] != 0.0) |
| Urow[lastu++] = L_SUB(istart+i); |
| } |
| Ucol[j+1] = lastu; |
| |
| /* Extract L */ |
| Lval[lastl] = 1.0; /* unit diagonal */ |
| Lrow[lastl++] = L_SUB(istart + upper - 1); |
| for (int i = upper; i < nsupr; ++i) |
| { |
| Lval[lastl] = SNptr[i]; |
| /* Matlab doesn't like explicit zero. */ |
| if (Lval[lastl] != 0.0) |
| Lrow[lastl++] = L_SUB(istart+i); |
| } |
| Lcol[j+1] = lastl; |
| |
| ++upper; |
| } /* for j ... */ |
| |
| } /* for k ... */ |
| |
| // squeeze the matrices : |
| m_l.resizeNonZeros(lastl); |
| m_u.resizeNonZeros(lastu); |
| |
| m_extractedDataAreDirty = false; |
| } |
| } |
| |
| template<typename MatrixType> |
| typename SuperLU<MatrixType>::Scalar SuperLU<MatrixType>::determinant() const |
| { |
| eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for computing the determinant, you must first call either compute() or analyzePattern()/factorize()"); |
| |
| if (m_extractedDataAreDirty) |
| this->extractData(); |
| |
| Scalar det = Scalar(1); |
| for (int j=0; j<m_u.cols(); ++j) |
| { |
| if (m_u.outerIndexPtr()[j+1]-m_u.outerIndexPtr()[j] > 0) |
| { |
| int lastId = m_u.outerIndexPtr()[j+1]-1; |
| eigen_assert(m_u.innerIndexPtr()[lastId]<=j); |
| if (m_u.innerIndexPtr()[lastId]==j) |
| det *= m_u.valuePtr()[lastId]; |
| } |
| } |
| if(m_sluEqued!='N') |
| return det/m_sluRscale.prod()/m_sluCscale.prod(); |
| else |
| return det; |
| } |
| |
| #ifdef EIGEN_PARSED_BY_DOXYGEN |
| #define EIGEN_SUPERLU_HAS_ILU |
| #endif |
| |
| #ifdef EIGEN_SUPERLU_HAS_ILU |
| |
| /** \ingroup SuperLUSupport_Module |
| * \class SuperILU |
| * \brief A sparse direct \b incomplete LU factorization and solver based on the SuperLU library |
| * |
| * This class allows to solve for an approximate solution of A.X = B sparse linear problems via an incomplete LU factorization |
| * using the SuperLU library. This class is aimed to be used as a preconditioner of the iterative linear solvers. |
| * |
| * \warning This class requires SuperLU 4 or later. |
| * |
| * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<> |
| * |
| * \sa \ref TutorialSparseDirectSolvers, class ConjugateGradient, class BiCGSTAB |
| */ |
| |
| template<typename _MatrixType> |
| class SuperILU : public SuperLUBase<_MatrixType,SuperILU<_MatrixType> > |
| { |
| public: |
| typedef SuperLUBase<_MatrixType,SuperILU> Base; |
| typedef _MatrixType MatrixType; |
| typedef typename Base::Scalar Scalar; |
| typedef typename Base::RealScalar RealScalar; |
| typedef typename Base::Index Index; |
| |
| public: |
| |
| SuperILU() : Base() { init(); } |
| |
| SuperILU(const MatrixType& matrix) : Base() |
| { |
| init(); |
| compute(matrix); |
| } |
| |
| ~SuperILU() |
| { |
| } |
| |
| /** Performs a symbolic decomposition on the sparcity of \a matrix. |
| * |
| * This function is particularly useful when solving for several problems having the same structure. |
| * |
| * \sa factorize() |
| */ |
| void analyzePattern(const MatrixType& matrix) |
| { |
| Base::analyzePattern(matrix); |
| } |
| |
| /** Performs a numeric decomposition of \a matrix |
| * |
| * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed. |
| * |
| * \sa analyzePattern() |
| */ |
| void factorize(const MatrixType& matrix); |
| |
| #ifndef EIGEN_PARSED_BY_DOXYGEN |
| /** \internal */ |
| template<typename Rhs,typename Dest> |
| void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const; |
| #endif // EIGEN_PARSED_BY_DOXYGEN |
| |
| protected: |
| |
| using Base::m_matrix; |
| using Base::m_sluOptions; |
| using Base::m_sluA; |
| using Base::m_sluB; |
| using Base::m_sluX; |
| using Base::m_p; |
| using Base::m_q; |
| using Base::m_sluEtree; |
| using Base::m_sluEqued; |
| using Base::m_sluRscale; |
| using Base::m_sluCscale; |
| using Base::m_sluL; |
| using Base::m_sluU; |
| using Base::m_sluStat; |
| using Base::m_sluFerr; |
| using Base::m_sluBerr; |
| using Base::m_l; |
| using Base::m_u; |
| |
| using Base::m_analysisIsOk; |
| using Base::m_factorizationIsOk; |
| using Base::m_extractedDataAreDirty; |
| using Base::m_isInitialized; |
| using Base::m_info; |
| |
| void init() |
| { |
| Base::init(); |
| |
| ilu_set_default_options(&m_sluOptions); |
| m_sluOptions.PrintStat = NO; |
| m_sluOptions.ConditionNumber = NO; |
| m_sluOptions.Trans = NOTRANS; |
| m_sluOptions.ColPerm = MMD_AT_PLUS_A; |
| |
| // no attempt to preserve column sum |
| m_sluOptions.ILU_MILU = SILU; |
| // only basic ILU(k) support -- no direct control over memory consumption |
| // better to use ILU_DropRule = DROP_BASIC | DROP_AREA |
| // and set ILU_FillFactor to max memory growth |
| m_sluOptions.ILU_DropRule = DROP_BASIC; |
| m_sluOptions.ILU_DropTol = NumTraits<Scalar>::dummy_precision()*10; |
| } |
| |
| private: |
| SuperILU(SuperILU& ) { } |
| }; |
| |
| template<typename MatrixType> |
| void SuperILU<MatrixType>::factorize(const MatrixType& a) |
| { |
| eigen_assert(m_analysisIsOk && "You must first call analyzePattern()"); |
| if(!m_analysisIsOk) |
| { |
| m_info = InvalidInput; |
| return; |
| } |
| |
| this->initFactorization(a); |
| |
| int info = 0; |
| RealScalar recip_pivot_growth, rcond; |
| |
| StatInit(&m_sluStat); |
| SuperLU_gsisx(&m_sluOptions, &m_sluA, m_q.data(), m_p.data(), &m_sluEtree[0], |
| &m_sluEqued, &m_sluRscale[0], &m_sluCscale[0], |
| &m_sluL, &m_sluU, |
| NULL, 0, |
| &m_sluB, &m_sluX, |
| &recip_pivot_growth, &rcond, |
| &m_sluStat, &info, Scalar()); |
| StatFree(&m_sluStat); |
| |
| // FIXME how to better check for errors ??? |
| m_info = info == 0 ? Success : NumericalIssue; |
| m_factorizationIsOk = true; |
| } |
| |
| template<typename MatrixType> |
| template<typename Rhs,typename Dest> |
| void SuperILU<MatrixType>::_solve(const MatrixBase<Rhs> &b, MatrixBase<Dest>& x) const |
| { |
| eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or analyzePattern()/factorize()"); |
| |
| const int size = m_matrix.rows(); |
| const int rhsCols = b.cols(); |
| eigen_assert(size==b.rows()); |
| |
| m_sluOptions.Trans = NOTRANS; |
| m_sluOptions.Fact = FACTORED; |
| m_sluOptions.IterRefine = NOREFINE; |
| |
| m_sluFerr.resize(rhsCols); |
| m_sluBerr.resize(rhsCols); |
| m_sluB = SluMatrix::Map(b.const_cast_derived()); |
| m_sluX = SluMatrix::Map(x.derived()); |
| |
| typename Rhs::PlainObject b_cpy; |
| if(m_sluEqued!='N') |
| { |
| b_cpy = b; |
| m_sluB = SluMatrix::Map(b_cpy.const_cast_derived()); |
| } |
| |
| int info = 0; |
| RealScalar recip_pivot_growth, rcond; |
| |
| StatInit(&m_sluStat); |
| SuperLU_gsisx(&m_sluOptions, &m_sluA, |
| m_q.data(), m_p.data(), |
| &m_sluEtree[0], &m_sluEqued, |
| &m_sluRscale[0], &m_sluCscale[0], |
| &m_sluL, &m_sluU, |
| NULL, 0, |
| &m_sluB, &m_sluX, |
| &recip_pivot_growth, &rcond, |
| &m_sluStat, &info, Scalar()); |
| StatFree(&m_sluStat); |
| |
| m_info = info==0 ? Success : NumericalIssue; |
| } |
| #endif |
| |
| namespace internal { |
| |
| template<typename _MatrixType, typename Derived, typename Rhs> |
| struct solve_retval<SuperLUBase<_MatrixType,Derived>, Rhs> |
| : solve_retval_base<SuperLUBase<_MatrixType,Derived>, Rhs> |
| { |
| typedef SuperLUBase<_MatrixType,Derived> Dec; |
| EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs) |
| |
| template<typename Dest> void evalTo(Dest& dst) const |
| { |
| dec().derived()._solve(rhs(),dst); |
| } |
| }; |
| |
| template<typename _MatrixType, typename Derived, typename Rhs> |
| struct sparse_solve_retval<SuperLUBase<_MatrixType,Derived>, Rhs> |
| : sparse_solve_retval_base<SuperLUBase<_MatrixType,Derived>, Rhs> |
| { |
| typedef SuperLUBase<_MatrixType,Derived> Dec; |
| EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs) |
| |
| template<typename Dest> void evalTo(Dest& dst) const |
| { |
| dec().derived()._solve(rhs(),dst); |
| } |
| }; |
| |
| } // end namespace internal |
| |
| } // end namespace Eigen |
| |
| #endif // EIGEN_SUPERLUSUPPORT_H |
