683 lines
25 KiB
C++
683 lines
25 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> struct cholmod_configure_matrix;
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template<> struct cholmod_configure_matrix<double> {
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template<typename CholmodType>
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static void run(CholmodType& mat) {
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mat.xtype = CHOLMOD_REAL;
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mat.dtype = CHOLMOD_DOUBLE;
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}
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};
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template<> struct cholmod_configure_matrix<std::complex<double> > {
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template<typename CholmodType>
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static void run(CholmodType& mat) {
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mat.xtype = CHOLMOD_COMPLEX;
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mat.dtype = CHOLMOD_DOUBLE;
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}
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};
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// Other scalar types are not yet supported by Cholmod
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// template<> struct cholmod_configure_matrix<float> {
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// template<typename CholmodType>
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// static void run(CholmodType& mat) {
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// mat.xtype = CHOLMOD_REAL;
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// mat.dtype = CHOLMOD_SINGLE;
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// }
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// };
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//
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// template<> struct cholmod_configure_matrix<std::complex<float> > {
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// template<typename CholmodType>
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// static void run(CholmodType& mat) {
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// mat.xtype = CHOLMOD_COMPLEX;
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// mat.dtype = CHOLMOD_SINGLE;
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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 _StorageIndex>
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cholmod_sparse viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_StorageIndex> > 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<_StorageIndex,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<_StorageIndex,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>::run(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(Ref<SparseMatrix<_Scalar,_Options,_Index> >(mat.const_cast_derived()));
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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 SparseVector<_Scalar,_Options,_Index>& mat)
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{
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cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_Index> >(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<const SparseMatrix<_Scalar,_Options,_Index>, UpLo>& mat)
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{
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cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_Index> >(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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// swap stype for rowmajor matrices (only works for real matrices)
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EIGEN_STATIC_ASSERT((_Options & RowMajorBit) == 0 || NumTraits<_Scalar>::IsComplex == 0, THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
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if(_Options & RowMajorBit) 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>::run(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 StorageIndex>
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MappedSparseMatrix<Scalar,Flags,StorageIndex> viewAsEigen(cholmod_sparse& cm)
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{
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return MappedSparseMatrix<Scalar,Flags,StorageIndex>
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(cm.nrow, cm.ncol, static_cast<StorageIndex*>(cm.p)[cm.ncol],
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static_cast<StorageIndex*>(cm.p), static_cast<StorageIndex*>(cm.i),static_cast<Scalar*>(cm.x) );
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}
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namespace internal {
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// template specializations for int and long that call the correct cholmod method
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#define EIGEN_CHOLMOD_SPECIALIZE0(ret, name) \
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template<typename _StorageIndex> inline ret cm_ ## name (cholmod_common &Common) { return cholmod_ ## name (&Common); } \
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template<> inline ret cm_ ## name<SuiteSparse_long> (cholmod_common &Common) { return cholmod_l_ ## name (&Common); }
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#define EIGEN_CHOLMOD_SPECIALIZE1(ret, name, t1, a1) \
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template<typename _StorageIndex> inline ret cm_ ## name (t1& a1, cholmod_common &Common) { return cholmod_ ## name (&a1, &Common); } \
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template<> inline ret cm_ ## name<SuiteSparse_long> (t1& a1, cholmod_common &Common) { return cholmod_l_ ## name (&a1, &Common); }
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EIGEN_CHOLMOD_SPECIALIZE0(int, start)
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EIGEN_CHOLMOD_SPECIALIZE0(int, finish)
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EIGEN_CHOLMOD_SPECIALIZE1(int, free_factor, cholmod_factor*, L)
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EIGEN_CHOLMOD_SPECIALIZE1(int, free_dense, cholmod_dense*, X)
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EIGEN_CHOLMOD_SPECIALIZE1(int, free_sparse, cholmod_sparse*, A)
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EIGEN_CHOLMOD_SPECIALIZE1(cholmod_factor*, analyze, cholmod_sparse, A)
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template<typename _StorageIndex> inline cholmod_dense* cm_solve (int sys, cholmod_factor& L, cholmod_dense& B, cholmod_common &Common) { return cholmod_solve (sys, &L, &B, &Common); }
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template<> inline cholmod_dense* cm_solve<SuiteSparse_long> (int sys, cholmod_factor& L, cholmod_dense& B, cholmod_common &Common) { return cholmod_l_solve (sys, &L, &B, &Common); }
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template<typename _StorageIndex> inline cholmod_sparse* cm_spsolve (int sys, cholmod_factor& L, cholmod_sparse& B, cholmod_common &Common) { return cholmod_spsolve (sys, &L, &B, &Common); }
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template<> inline cholmod_sparse* cm_spsolve<SuiteSparse_long> (int sys, cholmod_factor& L, cholmod_sparse& B, cholmod_common &Common) { return cholmod_l_spsolve (sys, &L, &B, &Common); }
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template<typename _StorageIndex>
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inline int cm_factorize_p (cholmod_sparse* A, double beta[2], _StorageIndex* fset, std::size_t fsize, cholmod_factor* L, cholmod_common &Common) { return cholmod_factorize_p (A, beta, fset, fsize, L, &Common); }
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template<>
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inline int cm_factorize_p<SuiteSparse_long> (cholmod_sparse* A, double beta[2], SuiteSparse_long* fset, std::size_t fsize, cholmod_factor* L, cholmod_common &Common) { return cholmod_l_factorize_p (A, beta, fset, fsize, L, &Common); }
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#undef EIGEN_CHOLMOD_SPECIALIZE0
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#undef EIGEN_CHOLMOD_SPECIALIZE1
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} // namespace internal
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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 : public SparseSolverBase<Derived>
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{
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protected:
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typedef SparseSolverBase<Derived> Base;
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using Base::derived;
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using Base::m_isInitialized;
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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::StorageIndex StorageIndex;
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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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CholmodBase()
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: m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false)
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{
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EIGEN_STATIC_ASSERT((internal::is_same<double,RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);
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m_shiftOffset[0] = m_shiftOffset[1] = 0.0;
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internal::cm_start<StorageIndex>(m_cholmod);
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}
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explicit CholmodBase(const MatrixType& matrix)
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: m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false)
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{
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EIGEN_STATIC_ASSERT((internal::is_same<double,RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);
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m_shiftOffset[0] = m_shiftOffset[1] = 0.0;
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internal::cm_start<StorageIndex>(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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internal::cm_free_factor<StorageIndex>(m_cholmodFactor, m_cholmod);
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internal::cm_finish<StorageIndex>(m_cholmod);
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}
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inline StorageIndex cols() const { return internal::convert_index<StorageIndex, Index>(m_cholmodFactor->n); }
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inline StorageIndex rows() const { return internal::convert_index<StorageIndex, Index>(m_cholmodFactor->n); }
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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 successful,
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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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/** 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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internal::cm_free_factor<StorageIndex>(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 = internal::cm_analyze<StorageIndex>(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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internal::cm_factorize_p<StorageIndex>(&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_impl(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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// Cholmod needs column-major storage without inner-stride, which corresponds to the default behavior of Ref.
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Ref<const Matrix<typename Rhs::Scalar,Dynamic,Dynamic,ColMajor> > b_ref(b.derived());
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cholmod_dense b_cd = viewAsCholmod(b_ref);
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cholmod_dense* x_cd = internal::cm_solve<StorageIndex>(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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return;
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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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// NOTE Actually, the copy can be avoided by calling cholmod_solve2 instead of cholmod_solve
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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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internal::cm_free_dense<StorageIndex>(x_cd, m_cholmod);
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}
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/** \internal */
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template<typename RhsDerived, typename DestDerived>
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void _solve_impl(const SparseMatrixBase<RhsDerived> &b, SparseMatrixBase<DestDerived> &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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Ref<SparseMatrix<typename RhsDerived::Scalar,ColMajor,typename RhsDerived::StorageIndex> > b_ref(b.const_cast_derived());
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cholmod_sparse b_cs = viewAsCholmod(b_ref);
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cholmod_sparse* x_cs = internal::cm_spsolve<StorageIndex>(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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return;
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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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// NOTE cholmod_spsolve in fact just calls the dense solver for blocks of 4 columns at a time (similar to Eigen's sparse solver)
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dest.derived() = viewAsEigen<typename DestDerived::Scalar,ColMajor,typename DestDerived::StorageIndex>(*x_cs);
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internal::cm_free_sparse<StorageIndex>(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] = double(offset);
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return derived();
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}
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/** \returns the determinant of the underlying matrix from the current factorization */
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Scalar determinant() const
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{
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using std::exp;
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return exp(logDeterminant());
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}
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/** \returns the log determinant of the underlying matrix from the current factorization */
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Scalar logDeterminant() const
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{
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using std::log;
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using numext::real;
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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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RealScalar logDet = 0;
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Scalar *x = static_cast<Scalar*>(m_cholmodFactor->x);
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if (m_cholmodFactor->is_super)
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{
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// Supernodal factorization stored as a packed list of dense column-major blocs,
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// as described by the following structure:
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// super[k] == index of the first column of the j-th super node
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StorageIndex *super = static_cast<StorageIndex*>(m_cholmodFactor->super);
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// pi[k] == offset to the description of row indices
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StorageIndex *pi = static_cast<StorageIndex*>(m_cholmodFactor->pi);
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// px[k] == offset to the respective dense block
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StorageIndex *px = static_cast<StorageIndex*>(m_cholmodFactor->px);
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Index nb_super_nodes = m_cholmodFactor->nsuper;
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for (Index k=0; k < nb_super_nodes; ++k)
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{
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StorageIndex ncols = super[k + 1] - super[k];
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StorageIndex nrows = pi[k + 1] - pi[k];
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Map<const Array<Scalar,1,Dynamic>, 0, InnerStride<> > sk(x + px[k], ncols, InnerStride<>(nrows+1));
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logDet += sk.real().log().sum();
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}
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}
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else
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{
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// Simplicial factorization stored as standard CSC matrix.
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StorageIndex *p = static_cast<StorageIndex*>(m_cholmodFactor->p);
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Index size = m_cholmodFactor->n;
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for (Index k=0; k<size; ++k)
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logDet += log(real( x[p[k]] ));
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}
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if (m_cholmodFactor->is_ll)
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logDet *= 2.0;
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return logDet;
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};
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template<typename Stream>
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void dumpMemory(Stream& /*s*/)
|
|
{}
|
|
|
|
protected:
|
|
mutable cholmod_common m_cholmod;
|
|
cholmod_factor* m_cholmodFactor;
|
|
double m_shiftOffset[2];
|
|
mutable ComputationInfo m_info;
|
|
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.
|
|
*
|
|
* \implsparsesolverconcept
|
|
*
|
|
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
|
|
*
|
|
* \warning Only double precision real and complex scalar types are supported by Cholmod.
|
|
*
|
|
* \sa \ref TutorialSparseSolverConcept, 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();
|
|
this->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.
|
|
*
|
|
* \implsparsesolverconcept
|
|
*
|
|
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
|
|
*
|
|
* \warning Only double precision real and complex scalar types are supported by Cholmod.
|
|
*
|
|
* \sa \ref TutorialSparseSolverConcept, 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();
|
|
this->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.
|
|
*
|
|
* \implsparsesolverconcept
|
|
*
|
|
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
|
|
*
|
|
* \warning Only double precision real and complex scalar types are supported by Cholmod.
|
|
*
|
|
* \sa \ref TutorialSparseSolverConcept
|
|
*/
|
|
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();
|
|
this->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.
|
|
*
|
|
* \implsparsesolverconcept
|
|
*
|
|
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
|
|
*
|
|
* \warning Only double precision real and complex scalar types are supported by Cholmod.
|
|
*
|
|
* \sa \ref TutorialSparseSolverConcept
|
|
*/
|
|
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();
|
|
this->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;
|
|
}
|
|
};
|
|
|
|
} // end namespace Eigen
|
|
|
|
#endif // EIGEN_CHOLMODSUPPORT_H
|