233 lines
8.8 KiB
C++
233 lines
8.8 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) 2008-2009 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_SOLVETRIANGULAR_H
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#define EIGEN_SOLVETRIANGULAR_H
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namespace Eigen {
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namespace internal {
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// Forward declarations:
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// The following two routines are implemented in the products/TriangularSolver*.h files
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template<typename LhsScalar, typename RhsScalar, typename Index, int Side, int Mode, bool Conjugate, int StorageOrder>
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struct triangular_solve_vector;
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template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder, int OtherStorageOrder>
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struct triangular_solve_matrix;
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// small helper struct extracting some traits on the underlying solver operation
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template<typename Lhs, typename Rhs, int Side>
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class trsolve_traits
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{
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private:
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enum {
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RhsIsVectorAtCompileTime = (Side==OnTheLeft ? Rhs::ColsAtCompileTime : Rhs::RowsAtCompileTime)==1
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};
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public:
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enum {
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Unrolling = (RhsIsVectorAtCompileTime && Rhs::SizeAtCompileTime != Dynamic && Rhs::SizeAtCompileTime <= 8)
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? CompleteUnrolling : NoUnrolling,
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RhsVectors = RhsIsVectorAtCompileTime ? 1 : Dynamic
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};
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};
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template<typename Lhs, typename Rhs,
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int Side, // can be OnTheLeft/OnTheRight
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int Mode, // can be Upper/Lower | UnitDiag
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int Unrolling = trsolve_traits<Lhs,Rhs,Side>::Unrolling,
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int RhsVectors = trsolve_traits<Lhs,Rhs,Side>::RhsVectors
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>
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struct triangular_solver_selector;
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template<typename Lhs, typename Rhs, int Side, int Mode>
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struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,1>
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{
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typedef typename Lhs::Scalar LhsScalar;
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typedef typename Rhs::Scalar RhsScalar;
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typedef blas_traits<Lhs> LhsProductTraits;
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typedef typename LhsProductTraits::ExtractType ActualLhsType;
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typedef Map<Matrix<RhsScalar,Dynamic,1>, Aligned> MappedRhs;
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static void run(const Lhs& lhs, Rhs& rhs)
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{
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ActualLhsType actualLhs = LhsProductTraits::extract(lhs);
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// FIXME find a way to allow an inner stride if packet_traits<Scalar>::size==1
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bool useRhsDirectly = Rhs::InnerStrideAtCompileTime==1 || rhs.innerStride()==1;
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ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhs,rhs.size(),
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(useRhsDirectly ? rhs.data() : 0));
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if(!useRhsDirectly)
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MappedRhs(actualRhs,rhs.size()) = rhs;
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triangular_solve_vector<LhsScalar, RhsScalar, Index, Side, Mode, LhsProductTraits::NeedToConjugate,
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(int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor>
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::run(actualLhs.cols(), actualLhs.data(), actualLhs.outerStride(), actualRhs);
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if(!useRhsDirectly)
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rhs = MappedRhs(actualRhs, rhs.size());
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}
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};
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// the rhs is a matrix
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template<typename Lhs, typename Rhs, int Side, int Mode>
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struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,Dynamic>
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{
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typedef typename Rhs::Scalar Scalar;
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typedef blas_traits<Lhs> LhsProductTraits;
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typedef typename LhsProductTraits::DirectLinearAccessType ActualLhsType;
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static void run(const Lhs& lhs, Rhs& rhs)
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{
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typename internal::add_const_on_value_type<ActualLhsType>::type actualLhs = LhsProductTraits::extract(lhs);
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const Index size = lhs.rows();
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const Index othersize = Side==OnTheLeft? rhs.cols() : rhs.rows();
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typedef internal::gemm_blocking_space<(Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
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Rhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxRowsAtCompileTime,4> BlockingType;
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BlockingType blocking(rhs.rows(), rhs.cols(), size, 1, false);
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triangular_solve_matrix<Scalar,Index,Side,Mode,LhsProductTraits::NeedToConjugate,(int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor,
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(Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor>
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::run(size, othersize, &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &rhs.coeffRef(0,0), rhs.outerStride(), blocking);
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}
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};
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/***************************************************************************
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* meta-unrolling implementation
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***************************************************************************/
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template<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size,
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bool Stop = LoopIndex==Size>
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struct triangular_solver_unroller;
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template<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size>
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struct triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex,Size,false> {
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enum {
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IsLower = ((Mode&Lower)==Lower),
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DiagIndex = IsLower ? LoopIndex : Size - LoopIndex - 1,
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StartIndex = IsLower ? 0 : DiagIndex+1
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};
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static void run(const Lhs& lhs, Rhs& rhs)
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{
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if (LoopIndex>0)
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rhs.coeffRef(DiagIndex) -= lhs.row(DiagIndex).template segment<LoopIndex>(StartIndex).transpose()
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.cwiseProduct(rhs.template segment<LoopIndex>(StartIndex)).sum();
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if(!(Mode & UnitDiag))
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rhs.coeffRef(DiagIndex) /= lhs.coeff(DiagIndex,DiagIndex);
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triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex+1,Size>::run(lhs,rhs);
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}
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};
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template<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size>
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struct triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex,Size,true> {
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static void run(const Lhs&, Rhs&) {}
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};
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template<typename Lhs, typename Rhs, int Mode>
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struct triangular_solver_selector<Lhs,Rhs,OnTheLeft,Mode,CompleteUnrolling,1> {
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static void run(const Lhs& lhs, Rhs& rhs)
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{ triangular_solver_unroller<Lhs,Rhs,Mode,0,Rhs::SizeAtCompileTime>::run(lhs,rhs); }
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};
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template<typename Lhs, typename Rhs, int Mode>
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struct triangular_solver_selector<Lhs,Rhs,OnTheRight,Mode,CompleteUnrolling,1> {
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static void run(const Lhs& lhs, Rhs& rhs)
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{
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Transpose<const Lhs> trLhs(lhs);
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Transpose<Rhs> trRhs(rhs);
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triangular_solver_unroller<Transpose<const Lhs>,Transpose<Rhs>,
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((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),
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0,Rhs::SizeAtCompileTime>::run(trLhs,trRhs);
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}
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};
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} // end namespace internal
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/***************************************************************************
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* TriangularView methods
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***************************************************************************/
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#ifndef EIGEN_PARSED_BY_DOXYGEN
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template<typename MatrixType, unsigned int Mode>
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template<int Side, typename OtherDerived>
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void TriangularViewImpl<MatrixType,Mode,Dense>::solveInPlace(const MatrixBase<OtherDerived>& _other) const
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{
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OtherDerived& other = _other.const_cast_derived();
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eigen_assert( derived().cols() == derived().rows() && ((Side==OnTheLeft && derived().cols() == other.rows()) || (Side==OnTheRight && derived().cols() == other.cols())) );
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eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
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enum { copy = (internal::traits<OtherDerived>::Flags & RowMajorBit) && OtherDerived::IsVectorAtCompileTime && OtherDerived::SizeAtCompileTime!=1};
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typedef typename internal::conditional<copy,
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typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;
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OtherCopy otherCopy(other);
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internal::triangular_solver_selector<MatrixType, typename internal::remove_reference<OtherCopy>::type,
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Side, Mode>::run(derived().nestedExpression(), otherCopy);
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if (copy)
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other = otherCopy;
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}
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template<typename Derived, unsigned int Mode>
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template<int Side, typename Other>
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const internal::triangular_solve_retval<Side,TriangularView<Derived,Mode>,Other>
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TriangularViewImpl<Derived,Mode,Dense>::solve(const MatrixBase<Other>& other) const
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{
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return internal::triangular_solve_retval<Side,TriangularViewType,Other>(derived(), other.derived());
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}
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#endif
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namespace internal {
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template<int Side, typename TriangularType, typename Rhs>
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struct traits<triangular_solve_retval<Side, TriangularType, Rhs> >
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{
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typedef typename internal::plain_matrix_type_column_major<Rhs>::type ReturnType;
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};
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template<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval
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: public ReturnByValue<triangular_solve_retval<Side, TriangularType, Rhs> >
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{
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typedef typename remove_all<typename Rhs::Nested>::type RhsNestedCleaned;
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typedef ReturnByValue<triangular_solve_retval> Base;
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triangular_solve_retval(const TriangularType& tri, const Rhs& rhs)
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: m_triangularMatrix(tri), m_rhs(rhs)
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{}
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inline Index rows() const { return m_rhs.rows(); }
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inline Index cols() const { return m_rhs.cols(); }
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template<typename Dest> inline void evalTo(Dest& dst) const
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{
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if(!is_same_dense(dst,m_rhs))
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dst = m_rhs;
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m_triangularMatrix.template solveInPlace<Side>(dst);
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}
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protected:
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const TriangularType& m_triangularMatrix;
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typename Rhs::Nested m_rhs;
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};
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} // namespace internal
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} // end namespace Eigen
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#endif // EIGEN_SOLVETRIANGULAR_H
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