| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. |
| // |
| // Copyright (C) 2008 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_SPARSETRIANGULARSOLVER_H |
| #define EIGEN_SPARSETRIANGULARSOLVER_H |
| |
| #include "./InternalHeaderCheck.h" |
| |
| namespace Eigen { |
| |
| namespace internal { |
| |
| template<typename Lhs, typename Rhs, int Mode, |
| int UpLo = (Mode & Lower) |
| ? Lower |
| : (Mode & Upper) |
| ? Upper |
| : -1, |
| int StorageOrder = int(traits<Lhs>::Flags) & RowMajorBit> |
| struct sparse_solve_triangular_selector; |
| |
| // forward substitution, row-major |
| template<typename Lhs, typename Rhs, int Mode> |
| struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Lower,RowMajor> |
| { |
| typedef typename Rhs::Scalar Scalar; |
| typedef evaluator<Lhs> LhsEval; |
| typedef typename evaluator<Lhs>::InnerIterator LhsIterator; |
| static void run(const Lhs& lhs, Rhs& other) |
| { |
| LhsEval lhsEval(lhs); |
| for(Index col=0 ; col<other.cols() ; ++col) |
| { |
| for(Index i=0; i<lhs.rows(); ++i) |
| { |
| Scalar tmp = other.coeff(i,col); |
| Scalar lastVal(0); |
| Index lastIndex = 0; |
| for(LhsIterator it(lhsEval, i); it; ++it) |
| { |
| lastVal = it.value(); |
| lastIndex = it.index(); |
| if(lastIndex==i) |
| break; |
| tmp -= lastVal * other.coeff(lastIndex,col); |
| } |
| if (Mode & UnitDiag) |
| other.coeffRef(i,col) = tmp; |
| else |
| { |
| eigen_assert(lastIndex==i); |
| other.coeffRef(i,col) = tmp/lastVal; |
| } |
| } |
| } |
| } |
| }; |
| |
| // backward substitution, row-major |
| template<typename Lhs, typename Rhs, int Mode> |
| struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Upper,RowMajor> |
| { |
| typedef typename Rhs::Scalar Scalar; |
| typedef evaluator<Lhs> LhsEval; |
| typedef typename evaluator<Lhs>::InnerIterator LhsIterator; |
| static void run(const Lhs& lhs, Rhs& other) |
| { |
| LhsEval lhsEval(lhs); |
| for(Index col=0 ; col<other.cols() ; ++col) |
| { |
| for(Index i=lhs.rows()-1 ; i>=0 ; --i) |
| { |
| Scalar tmp = other.coeff(i,col); |
| Scalar l_ii(0); |
| LhsIterator it(lhsEval, i); |
| while(it && it.index()<i) |
| ++it; |
| if(!(Mode & UnitDiag)) |
| { |
| eigen_assert(it && it.index()==i); |
| l_ii = it.value(); |
| ++it; |
| } |
| else if (it && it.index() == i) |
| ++it; |
| for(; it; ++it) |
| { |
| tmp -= it.value() * other.coeff(it.index(),col); |
| } |
| |
| if (Mode & UnitDiag) other.coeffRef(i,col) = tmp; |
| else other.coeffRef(i,col) = tmp/l_ii; |
| } |
| } |
| } |
| }; |
| |
| // forward substitution, col-major |
| template<typename Lhs, typename Rhs, int Mode> |
| struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Lower,ColMajor> |
| { |
| typedef typename Rhs::Scalar Scalar; |
| typedef evaluator<Lhs> LhsEval; |
| typedef typename evaluator<Lhs>::InnerIterator LhsIterator; |
| static void run(const Lhs& lhs, Rhs& other) |
| { |
| LhsEval lhsEval(lhs); |
| for(Index col=0 ; col<other.cols() ; ++col) |
| { |
| for(Index i=0; i<lhs.cols(); ++i) |
| { |
| Scalar& tmp = other.coeffRef(i,col); |
| if (!numext::is_exactly_zero(tmp)) // optimization when other is actually sparse |
| { |
| LhsIterator it(lhsEval, i); |
| while(it && it.index()<i) |
| ++it; |
| if(!(Mode & UnitDiag)) |
| { |
| eigen_assert(it && it.index()==i); |
| tmp /= it.value(); |
| } |
| if (it && it.index()==i) |
| ++it; |
| for(; it; ++it) |
| other.coeffRef(it.index(), col) -= tmp * it.value(); |
| } |
| } |
| } |
| } |
| }; |
| |
| // backward substitution, col-major |
| template<typename Lhs, typename Rhs, int Mode> |
| struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Upper,ColMajor> |
| { |
| typedef typename Rhs::Scalar Scalar; |
| typedef evaluator<Lhs> LhsEval; |
| typedef typename evaluator<Lhs>::InnerIterator LhsIterator; |
| static void run(const Lhs& lhs, Rhs& other) |
| { |
| LhsEval lhsEval(lhs); |
| for(Index col=0 ; col<other.cols() ; ++col) |
| { |
| for(Index i=lhs.cols()-1; i>=0; --i) |
| { |
| Scalar& tmp = other.coeffRef(i,col); |
| if (!numext::is_exactly_zero(tmp)) // optimization when other is actually sparse |
| { |
| if(!(Mode & UnitDiag)) |
| { |
| // TODO replace this by a binary search. make sure the binary search is safe for partially sorted elements |
| LhsIterator it(lhsEval, i); |
| while(it && it.index()!=i) |
| ++it; |
| eigen_assert(it && it.index()==i); |
| other.coeffRef(i,col) /= it.value(); |
| } |
| LhsIterator it(lhsEval, i); |
| for(; it && it.index()<i; ++it) |
| other.coeffRef(it.index(), col) -= tmp * it.value(); |
| } |
| } |
| } |
| } |
| }; |
| |
| } // end namespace internal |
| |
| #ifndef EIGEN_PARSED_BY_DOXYGEN |
| |
| template<typename ExpressionType,unsigned int Mode> |
| template<typename OtherDerived> |
| void TriangularViewImpl<ExpressionType,Mode,Sparse>::solveInPlace(MatrixBase<OtherDerived>& other) const |
| { |
| eigen_assert(derived().cols() == derived().rows() && derived().cols() == other.rows()); |
| eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower))); |
| |
| enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit }; |
| |
| typedef typename internal::conditional<copy, |
| typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy; |
| OtherCopy otherCopy(other.derived()); |
| |
| internal::sparse_solve_triangular_selector<ExpressionType, typename internal::remove_reference<OtherCopy>::type, Mode>::run(derived().nestedExpression(), otherCopy); |
| |
| if (copy) |
| other = otherCopy; |
| } |
| #endif |
| |
| // pure sparse path |
| |
| namespace internal { |
| |
| template<typename Lhs, typename Rhs, int Mode, |
| int UpLo = (Mode & Lower) |
| ? Lower |
| : (Mode & Upper) |
| ? Upper |
| : -1, |
| int StorageOrder = int(Lhs::Flags) & (RowMajorBit)> |
| struct sparse_solve_triangular_sparse_selector; |
| |
| // forward substitution, col-major |
| template<typename Lhs, typename Rhs, int Mode, int UpLo> |
| struct sparse_solve_triangular_sparse_selector<Lhs,Rhs,Mode,UpLo,ColMajor> |
| { |
| typedef typename Rhs::Scalar Scalar; |
| typedef typename promote_index_type<typename traits<Lhs>::StorageIndex, |
| typename traits<Rhs>::StorageIndex>::type StorageIndex; |
| static void run(const Lhs& lhs, Rhs& other) |
| { |
| const bool IsLower = (UpLo==Lower); |
| AmbiVector<Scalar,StorageIndex> tempVector(other.rows()*2); |
| tempVector.setBounds(0,other.rows()); |
| |
| Rhs res(other.rows(), other.cols()); |
| res.reserve(other.nonZeros()); |
| |
| for(Index col=0 ; col<other.cols() ; ++col) |
| { |
| // FIXME estimate number of non zeros |
| tempVector.init(.99/*float(other.col(col).nonZeros())/float(other.rows())*/); |
| tempVector.setZero(); |
| tempVector.restart(); |
| for (typename Rhs::InnerIterator rhsIt(other, col); rhsIt; ++rhsIt) |
| { |
| tempVector.coeffRef(rhsIt.index()) = rhsIt.value(); |
| } |
| |
| for(Index i=IsLower?0:lhs.cols()-1; |
| IsLower?i<lhs.cols():i>=0; |
| i+=IsLower?1:-1) |
| { |
| tempVector.restart(); |
| Scalar& ci = tempVector.coeffRef(i); |
| if (!numext::is_exactly_zero(ci)) |
| { |
| // find |
| typename Lhs::InnerIterator it(lhs, i); |
| if(!(Mode & UnitDiag)) |
| { |
| if (IsLower) |
| { |
| eigen_assert(it.index()==i); |
| ci /= it.value(); |
| } |
| else |
| ci /= lhs.coeff(i,i); |
| } |
| tempVector.restart(); |
| if (IsLower) |
| { |
| if (it.index()==i) |
| ++it; |
| for(; it; ++it) |
| tempVector.coeffRef(it.index()) -= ci * it.value(); |
| } |
| else |
| { |
| for(; it && it.index()<i; ++it) |
| tempVector.coeffRef(it.index()) -= ci * it.value(); |
| } |
| } |
| } |
| |
| |
| Index count = 0; |
| // FIXME compute a reference value to filter zeros |
| for (typename AmbiVector<Scalar,StorageIndex>::Iterator it(tempVector/*,1e-12*/); it; ++it) |
| { |
| ++ count; |
| // std::cerr << "fill " << it.index() << ", " << col << "\n"; |
| // std::cout << it.value() << " "; |
| // FIXME use insertBack |
| res.insert(it.index(), col) = it.value(); |
| } |
| // std::cout << "tempVector.nonZeros() == " << int(count) << " / " << (other.rows()) << "\n"; |
| } |
| res.finalize(); |
| other = res.markAsRValue(); |
| } |
| }; |
| |
| } // end namespace internal |
| |
| #ifndef EIGEN_PARSED_BY_DOXYGEN |
| template<typename ExpressionType,unsigned int Mode> |
| template<typename OtherDerived> |
| void TriangularViewImpl<ExpressionType,Mode,Sparse>::solveInPlace(SparseMatrixBase<OtherDerived>& other) const |
| { |
| eigen_assert(derived().cols() == derived().rows() && derived().cols() == other.rows()); |
| eigen_assert( (!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower))); |
| |
| // enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit }; |
| |
| // typedef typename internal::conditional<copy, |
| // typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy; |
| // OtherCopy otherCopy(other.derived()); |
| |
| internal::sparse_solve_triangular_sparse_selector<ExpressionType, OtherDerived, Mode>::run(derived().nestedExpression(), other.derived()); |
| |
| // if (copy) |
| // other = otherCopy; |
| } |
| #endif |
| |
| } // end namespace Eigen |
| |
| #endif // EIGEN_SPARSETRIANGULARSOLVER_H |
