// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2008-2010 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_CHOLMODSUPPORT_H #define EIGEN_CHOLMODSUPPORT_H namespace Eigen { namespace internal { template<typename Scalar, typename CholmodType> void cholmod_configure_matrix(CholmodType& mat) { if (internal::is_same<Scalar,float>::value) { mat.xtype = CHOLMOD_REAL; mat.dtype = CHOLMOD_SINGLE; } else if (internal::is_same<Scalar,double>::value) { mat.xtype = CHOLMOD_REAL; mat.dtype = CHOLMOD_DOUBLE; } else if (internal::is_same<Scalar,std::complex<float> >::value) { mat.xtype = CHOLMOD_COMPLEX; mat.dtype = CHOLMOD_SINGLE; } else if (internal::is_same<Scalar,std::complex<double> >::value) { mat.xtype = CHOLMOD_COMPLEX; mat.dtype = CHOLMOD_DOUBLE; } else { eigen_assert(false && "Scalar type not supported by CHOLMOD"); } } } // namespace internal /** Wraps the Eigen sparse matrix \a mat into a Cholmod sparse matrix object. * Note that the data are shared. */ template<typename _Scalar, int _Options, typename _Index> cholmod_sparse viewAsCholmod(SparseMatrix<_Scalar,_Options,_Index>& mat) { cholmod_sparse res; res.nzmax = mat.nonZeros(); res.nrow = mat.rows();; res.ncol = mat.cols(); res.p = mat.outerIndexPtr(); res.i = mat.innerIndexPtr(); res.x = mat.valuePtr(); res.z = 0; res.sorted = 1; if(mat.isCompressed()) { res.packed = 1; res.nz = 0; } else { res.packed = 0; res.nz = mat.innerNonZeroPtr(); } res.dtype = 0; res.stype = -1; if (internal::is_same<_Index,int>::value) { res.itype = CHOLMOD_INT; } else if (internal::is_same<_Index,UF_long>::value) { res.itype = CHOLMOD_LONG; } else { eigen_assert(false && "Index type not supported yet"); } // setup res.xtype internal::cholmod_configure_matrix<_Scalar>(res); res.stype = 0; return res; } template<typename _Scalar, int _Options, typename _Index> const cholmod_sparse viewAsCholmod(const SparseMatrix<_Scalar,_Options,_Index>& mat) { cholmod_sparse res = viewAsCholmod(mat.const_cast_derived()); return res; } /** Returns a view of the Eigen sparse matrix \a mat as Cholmod sparse matrix. * The data are not copied but shared. */ template<typename _Scalar, int _Options, typename _Index, unsigned int UpLo> cholmod_sparse viewAsCholmod(const SparseSelfAdjointView<SparseMatrix<_Scalar,_Options,_Index>, UpLo>& mat) { cholmod_sparse res = viewAsCholmod(mat.matrix().const_cast_derived()); if(UpLo==Upper) res.stype = 1; if(UpLo==Lower) res.stype = -1; return res; } /** Returns a view of the Eigen \b dense matrix \a mat as Cholmod dense matrix. * The data are not copied but shared. */ template<typename Derived> cholmod_dense viewAsCholmod(MatrixBase<Derived>& mat) { EIGEN_STATIC_ASSERT((internal::traits<Derived>::Flags&RowMajorBit)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES); typedef typename Derived::Scalar Scalar; cholmod_dense res; res.nrow = mat.rows(); res.ncol = mat.cols(); res.nzmax = res.nrow * res.ncol; res.d = Derived::IsVectorAtCompileTime ? mat.derived().size() : mat.derived().outerStride(); res.x = (void*)(mat.derived().data()); res.z = 0; internal::cholmod_configure_matrix<Scalar>(res); return res; } /** Returns a view of the Cholmod sparse matrix \a cm as an Eigen sparse matrix. * The data are not copied but shared. */ template<typename Scalar, int Flags, typename Index> MappedSparseMatrix<Scalar,Flags,Index> viewAsEigen(cholmod_sparse& cm) { return MappedSparseMatrix<Scalar,Flags,Index> (cm.nrow, cm.ncol, static_cast<Index*>(cm.p)[cm.ncol], static_cast<Index*>(cm.p), static_cast<Index*>(cm.i),static_cast<Scalar*>(cm.x) ); } enum CholmodMode { CholmodAuto, CholmodSimplicialLLt, CholmodSupernodalLLt, CholmodLDLt }; /** \ingroup CholmodSupport_Module * \class CholmodBase * \brief The base class for the direct Cholesky factorization of Cholmod * \sa class CholmodSupernodalLLT, class CholmodSimplicialLDLT, class CholmodSimplicialLLT */ template<typename _MatrixType, int _UpLo, typename Derived> class CholmodBase : internal::noncopyable { public: typedef _MatrixType MatrixType; enum { UpLo = _UpLo }; typedef typename MatrixType::Scalar Scalar; typedef typename MatrixType::RealScalar RealScalar; typedef MatrixType CholMatrixType; typedef typename MatrixType::Index Index; public: CholmodBase() : m_cholmodFactor(0), m_info(Success), m_isInitialized(false) { m_shiftOffset[0] = m_shiftOffset[1] = RealScalar(0.0); cholmod_start(&m_cholmod); } CholmodBase(const MatrixType& matrix) : m_cholmodFactor(0), m_info(Success), m_isInitialized(false) { m_shiftOffset[0] = m_shiftOffset[1] = RealScalar(0.0); cholmod_start(&m_cholmod); compute(matrix); } ~CholmodBase() { if(m_cholmodFactor) cholmod_free_factor(&m_cholmodFactor, &m_cholmod); cholmod_finish(&m_cholmod); } inline Index cols() const { return m_cholmodFactor->n; } inline Index rows() const { return m_cholmodFactor->n; } Derived& derived() { return *static_cast<Derived*>(this); } const Derived& derived() const { return *static_cast<const Derived*>(this); } /** \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 */ Derived& compute(const MatrixType& matrix) { analyzePattern(matrix); factorize(matrix); return 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::solve_retval<CholmodBase, Rhs> solve(const MatrixBase<Rhs>& b) const { eigen_assert(m_isInitialized && "LLT is not initialized."); eigen_assert(rows()==b.rows() && "CholmodDecomposition::solve(): invalid number of rows of the right hand side matrix b"); return internal::solve_retval<CholmodBase, 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<CholmodBase, Rhs> solve(const SparseMatrixBase<Rhs>& b) const { eigen_assert(m_isInitialized && "LLT is not initialized."); eigen_assert(rows()==b.rows() && "CholmodDecomposition::solve(): invalid number of rows of the right hand side matrix b"); return internal::sparse_solve_retval<CholmodBase, Rhs>(*this, b.derived()); } /** Performs a symbolic decomposition on the sparsity pattern of \a matrix. * * This function is particularly useful when solving for several problems having the same structure. * * \sa factorize() */ void analyzePattern(const MatrixType& matrix) { if(m_cholmodFactor) { cholmod_free_factor(&m_cholmodFactor, &m_cholmod); m_cholmodFactor = 0; } cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>()); m_cholmodFactor = cholmod_analyze(&A, &m_cholmod); this->m_isInitialized = true; this->m_info = Success; m_analysisIsOk = true; m_factorizationIsOk = false; } /** Performs a numeric decomposition of \a matrix * * The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been performed. * * \sa analyzePattern() */ void factorize(const MatrixType& matrix) { eigen_assert(m_analysisIsOk && "You must first call analyzePattern()"); cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>()); cholmod_factorize_p(&A, m_shiftOffset, 0, 0, m_cholmodFactor, &m_cholmod); // If the factorization failed, minor is the column at which it did. On success minor == n. this->m_info = (m_cholmodFactor->minor == m_cholmodFactor->n ? Success : NumericalIssue); m_factorizationIsOk = true; } /** Returns a reference to the Cholmod's configuration structure to get a full control over the performed operations. * See the Cholmod user guide for details. */ cholmod_common& cholmod() { return m_cholmod; } #ifndef EIGEN_PARSED_BY_DOXYGEN /** \internal */ template<typename Rhs,typename Dest> void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const { eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()"); const Index size = m_cholmodFactor->n; EIGEN_UNUSED_VARIABLE(size); eigen_assert(size==b.rows()); // note: cd stands for Cholmod Dense Rhs& b_ref(b.const_cast_derived()); cholmod_dense b_cd = viewAsCholmod(b_ref); cholmod_dense* x_cd = cholmod_solve(CHOLMOD_A, m_cholmodFactor, &b_cd, &m_cholmod); if(!x_cd) { this->m_info = NumericalIssue; } // TODO optimize this copy by swapping when possible (be careful with alignment, etc.) dest = Matrix<Scalar,Dest::RowsAtCompileTime,Dest::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x),b.rows(),b.cols()); cholmod_free_dense(&x_cd, &m_cholmod); } /** \internal */ template<typename RhsScalar, int RhsOptions, typename RhsIndex, typename DestScalar, int DestOptions, typename DestIndex> void _solve(const SparseMatrix<RhsScalar,RhsOptions,RhsIndex> &b, SparseMatrix<DestScalar,DestOptions,DestIndex> &dest) const { eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()"); const Index size = m_cholmodFactor->n; EIGEN_UNUSED_VARIABLE(size); eigen_assert(size==b.rows()); // note: cs stands for Cholmod Sparse cholmod_sparse b_cs = viewAsCholmod(b); cholmod_sparse* x_cs = cholmod_spsolve(CHOLMOD_A, m_cholmodFactor, &b_cs, &m_cholmod); if(!x_cs) { this->m_info = NumericalIssue; } // TODO optimize this copy by swapping when possible (be careful with alignment, etc.) dest = viewAsEigen<DestScalar,DestOptions,DestIndex>(*x_cs); cholmod_free_sparse(&x_cs, &m_cholmod); } #endif // EIGEN_PARSED_BY_DOXYGEN /** Sets the shift parameter that will be used to adjust the diagonal coefficients during the numerical factorization. * * During the numerical factorization, an offset term is added to the diagonal coefficients:\n * \c d_ii = \a offset + \c d_ii * * The default is \a offset=0. * * \returns a reference to \c *this. */ Derived& setShift(const RealScalar& offset) { m_shiftOffset[0] = offset; return derived(); } template<typename Stream> void dumpMemory(Stream& /*s*/) {} protected: mutable cholmod_common m_cholmod; cholmod_factor* m_cholmodFactor; RealScalar m_shiftOffset[2]; mutable ComputationInfo m_info; bool m_isInitialized; int m_factorizationIsOk; int m_analysisIsOk; }; /** \ingroup CholmodSupport_Module * \class CholmodSimplicialLLT * \brief A simplicial direct Cholesky (LLT) factorization and solver based on Cholmod * * This class allows to solve for A.X = B sparse linear problems via a simplicial LL^T Cholesky factorization * using the Cholmod library. * This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Therefore, it has little practical interest. * The sparse matrix A must be selfadjoint and positive definite. 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<> * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower * or Upper. Default is Lower. * * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed. * * \sa \ref TutorialSparseDirectSolvers, class CholmodSupernodalLLT, class SimplicialLLT */ template<typename _MatrixType, int _UpLo = Lower> class CholmodSimplicialLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT<_MatrixType, _UpLo> > { typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT> Base; using Base::m_cholmod; public: typedef _MatrixType MatrixType; CholmodSimplicialLLT() : Base() { init(); } CholmodSimplicialLLT(const MatrixType& matrix) : Base() { init(); compute(matrix); } ~CholmodSimplicialLLT() {} protected: void init() { m_cholmod.final_asis = 0; m_cholmod.supernodal = CHOLMOD_SIMPLICIAL; m_cholmod.final_ll = 1; } }; /** \ingroup CholmodSupport_Module * \class CholmodSimplicialLDLT * \brief A simplicial direct Cholesky (LDLT) factorization and solver based on Cholmod * * This class allows to solve for A.X = B sparse linear problems via a simplicial LDL^T Cholesky factorization * using the Cholmod library. * This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Therefore, it has little practical interest. * The sparse matrix A must be selfadjoint and positive definite. 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<> * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower * or Upper. Default is Lower. * * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed. * * \sa \ref TutorialSparseDirectSolvers, class CholmodSupernodalLLT, class SimplicialLDLT */ template<typename _MatrixType, int _UpLo = Lower> class CholmodSimplicialLDLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT<_MatrixType, _UpLo> > { typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT> Base; using Base::m_cholmod; public: typedef _MatrixType MatrixType; CholmodSimplicialLDLT() : Base() { init(); } CholmodSimplicialLDLT(const MatrixType& matrix) : Base() { init(); compute(matrix); } ~CholmodSimplicialLDLT() {} protected: void init() { m_cholmod.final_asis = 1; m_cholmod.supernodal = CHOLMOD_SIMPLICIAL; } }; /** \ingroup CholmodSupport_Module * \class CholmodSupernodalLLT * \brief A supernodal Cholesky (LLT) factorization and solver based on Cholmod * * This class allows to solve for A.X = B sparse linear problems via a supernodal LL^T Cholesky factorization * using the Cholmod library. * This supernodal variant performs best on dense enough problems, e.g., 3D FEM, or very high order 2D FEM. * The sparse matrix A must be selfadjoint and positive definite. 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<> * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower * or Upper. Default is Lower. * * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed. * * \sa \ref TutorialSparseDirectSolvers */ template<typename _MatrixType, int _UpLo = Lower> class CholmodSupernodalLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT<_MatrixType, _UpLo> > { typedef CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT> Base; using Base::m_cholmod; public: typedef _MatrixType MatrixType; CholmodSupernodalLLT() : Base() { init(); } CholmodSupernodalLLT(const MatrixType& matrix) : Base() { init(); compute(matrix); } ~CholmodSupernodalLLT() {} protected: void init() { m_cholmod.final_asis = 1; m_cholmod.supernodal = CHOLMOD_SUPERNODAL; } }; /** \ingroup CholmodSupport_Module * \class CholmodDecomposition * \brief A general Cholesky factorization and solver based on Cholmod * * This class allows to solve for A.X = B sparse linear problems via a LL^T or LDL^T Cholesky factorization * using the Cholmod library. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices * X and B can be either dense or sparse. * * This variant permits to change the underlying Cholesky method at runtime. * On the other hand, it does not provide access to the result of the factorization. * The default is to let Cholmod automatically choose between a simplicial and supernodal factorization. * * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<> * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower * or Upper. Default is Lower. * * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed. * * \sa \ref TutorialSparseDirectSolvers */ template<typename _MatrixType, int _UpLo = Lower> class CholmodDecomposition : public CholmodBase<_MatrixType, _UpLo, CholmodDecomposition<_MatrixType, _UpLo> > { typedef CholmodBase<_MatrixType, _UpLo, CholmodDecomposition> Base; using Base::m_cholmod; public: typedef _MatrixType MatrixType; CholmodDecomposition() : Base() { init(); } CholmodDecomposition(const MatrixType& matrix) : Base() { init(); compute(matrix); } ~CholmodDecomposition() {} void setMode(CholmodMode mode) { switch(mode) { case CholmodAuto: m_cholmod.final_asis = 1; m_cholmod.supernodal = CHOLMOD_AUTO; break; case CholmodSimplicialLLt: m_cholmod.final_asis = 0; m_cholmod.supernodal = CHOLMOD_SIMPLICIAL; m_cholmod.final_ll = 1; break; case CholmodSupernodalLLt: m_cholmod.final_asis = 1; m_cholmod.supernodal = CHOLMOD_SUPERNODAL; break; case CholmodLDLt: m_cholmod.final_asis = 1; m_cholmod.supernodal = CHOLMOD_SIMPLICIAL; break; default: break; } } protected: void init() { m_cholmod.final_asis = 1; m_cholmod.supernodal = CHOLMOD_AUTO; } }; namespace internal { template<typename _MatrixType, int _UpLo, typename Derived, typename Rhs> struct solve_retval<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs> : solve_retval_base<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs> { typedef CholmodBase<_MatrixType,_UpLo,Derived> Dec; EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs) template<typename Dest> void evalTo(Dest& dst) const { dec()._solve(rhs(),dst); } }; template<typename _MatrixType, int _UpLo, typename Derived, typename Rhs> struct sparse_solve_retval<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs> : sparse_solve_retval_base<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs> { typedef CholmodBase<_MatrixType,_UpLo,Derived> Dec; EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs) template<typename Dest> void evalTo(Dest& dst) const { dec()._solve(rhs(),dst); } }; } // end namespace internal } // end namespace Eigen #endif // EIGEN_CHOLMODSUPPORT_H