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