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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 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_SOLVETRIANGULAR_H
+#define EIGEN_SOLVETRIANGULAR_H
+
+namespace Eigen {
+
+namespace internal {
+
+// Forward declarations:
+// The following two routines are implemented in the products/TriangularSolver*.h files
+template<typename LhsScalar, typename RhsScalar, typename Index, int Side, int Mode, bool Conjugate, int StorageOrder>
+struct triangular_solve_vector;
+
+template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder, int OtherStorageOrder, int OtherInnerStride>
+struct triangular_solve_matrix;
+
+// small helper struct extracting some traits on the underlying solver operation
+template<typename Lhs, typename Rhs, int Side>
+class trsolve_traits
+{
+ private:
+ enum {
+ RhsIsVectorAtCompileTime = (Side==OnTheLeft ? Rhs::ColsAtCompileTime : Rhs::RowsAtCompileTime)==1
+ };
+ public:
+ enum {
+ Unrolling = (RhsIsVectorAtCompileTime && Rhs::SizeAtCompileTime != Dynamic && Rhs::SizeAtCompileTime <= 8)
+ ? CompleteUnrolling : NoUnrolling,
+ RhsVectors = RhsIsVectorAtCompileTime ? 1 : Dynamic
+ };
+};
+
+template<typename Lhs, typename Rhs,
+ int Side, // can be OnTheLeft/OnTheRight
+ int Mode, // can be Upper/Lower | UnitDiag
+ int Unrolling = trsolve_traits<Lhs,Rhs,Side>::Unrolling,
+ int RhsVectors = trsolve_traits<Lhs,Rhs,Side>::RhsVectors
+ >
+struct triangular_solver_selector;
+
+template<typename Lhs, typename Rhs, int Side, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,1>
+{
+ typedef typename Lhs::Scalar LhsScalar;
+ typedef typename Rhs::Scalar RhsScalar;
+ typedef blas_traits<Lhs> LhsProductTraits;
+ typedef typename LhsProductTraits::ExtractType ActualLhsType;
+ typedef Map<Matrix<RhsScalar,Dynamic,1>, Aligned> MappedRhs;
+ static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs)
+ {
+ ActualLhsType actualLhs = LhsProductTraits::extract(lhs);
+
+ // FIXME find a way to allow an inner stride if packet_traits<Scalar>::size==1
+
+ bool useRhsDirectly = Rhs::InnerStrideAtCompileTime==1 || rhs.innerStride()==1;
+
+ ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhs,rhs.size(),
+ (useRhsDirectly ? rhs.data() : 0));
+
+ if(!useRhsDirectly)
+ MappedRhs(actualRhs,rhs.size()) = rhs;
+
+ triangular_solve_vector<LhsScalar, RhsScalar, Index, Side, Mode, LhsProductTraits::NeedToConjugate,
+ (int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor>
+ ::run(actualLhs.cols(), actualLhs.data(), actualLhs.outerStride(), actualRhs);
+
+ if(!useRhsDirectly)
+ rhs = MappedRhs(actualRhs, rhs.size());
+ }
+};
+
+// the rhs is a matrix
+template<typename Lhs, typename Rhs, int Side, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,Dynamic>
+{
+ typedef typename Rhs::Scalar Scalar;
+ typedef blas_traits<Lhs> LhsProductTraits;
+ typedef typename LhsProductTraits::DirectLinearAccessType ActualLhsType;
+
+ static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs)
+ {
+ typename internal::add_const_on_value_type<ActualLhsType>::type actualLhs = LhsProductTraits::extract(lhs);
+
+ const Index size = lhs.rows();
+ const Index othersize = Side==OnTheLeft? rhs.cols() : rhs.rows();
+
+ typedef internal::gemm_blocking_space<(Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
+ Rhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxRowsAtCompileTime,4> BlockingType;
+
+ BlockingType blocking(rhs.rows(), rhs.cols(), size, 1, false);
+
+ triangular_solve_matrix<Scalar,Index,Side,Mode,LhsProductTraits::NeedToConjugate,(int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor,
+ (Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor, Rhs::InnerStrideAtCompileTime>
+ ::run(size, othersize, &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &rhs.coeffRef(0,0), rhs.innerStride(), rhs.outerStride(), blocking);
+ }
+};
+
+/***************************************************************************
+* meta-unrolling implementation
+***************************************************************************/
+
+template<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size,
+ bool Stop = LoopIndex==Size>
+struct triangular_solver_unroller;
+
+template<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size>
+struct triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex,Size,false> {
+ enum {
+ IsLower = ((Mode&Lower)==Lower),
+ DiagIndex = IsLower ? LoopIndex : Size - LoopIndex - 1,
+ StartIndex = IsLower ? 0 : DiagIndex+1
+ };
+ static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs)
+ {
+ if (LoopIndex>0)
+ rhs.coeffRef(DiagIndex) -= lhs.row(DiagIndex).template segment<LoopIndex>(StartIndex).transpose()
+ .cwiseProduct(rhs.template segment<LoopIndex>(StartIndex)).sum();
+
+ if(!(Mode & UnitDiag))
+ rhs.coeffRef(DiagIndex) /= lhs.coeff(DiagIndex,DiagIndex);
+
+ triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex+1,Size>::run(lhs,rhs);
+ }
+};
+
+template<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size>
+struct triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex,Size,true> {
+ static EIGEN_DEVICE_FUNC void run(const Lhs&, Rhs&) {}
+};
+
+template<typename Lhs, typename Rhs, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,OnTheLeft,Mode,CompleteUnrolling,1> {
+ static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs)
+ { triangular_solver_unroller<Lhs,Rhs,Mode,0,Rhs::SizeAtCompileTime>::run(lhs,rhs); }
+};
+
+template<typename Lhs, typename Rhs, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,OnTheRight,Mode,CompleteUnrolling,1> {
+ static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs)
+ {
+ Transpose<const Lhs> trLhs(lhs);
+ Transpose<Rhs> trRhs(rhs);
+
+ triangular_solver_unroller<Transpose<const Lhs>,Transpose<Rhs>,
+ ((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),
+ 0,Rhs::SizeAtCompileTime>::run(trLhs,trRhs);
+ }
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* TriangularView methods
+***************************************************************************/
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename MatrixType, unsigned int Mode>
+template<int Side, typename OtherDerived>
+EIGEN_DEVICE_FUNC void TriangularViewImpl<MatrixType,Mode,Dense>::solveInPlace(const MatrixBase<OtherDerived>& _other) const
+{
+ OtherDerived& other = _other.const_cast_derived();
+ eigen_assert( derived().cols() == derived().rows() && ((Side==OnTheLeft && derived().cols() == other.rows()) || (Side==OnTheRight && derived().cols() == other.cols())) );
+ eigen_assert((!(int(Mode) & int(ZeroDiag))) && bool(int(Mode) & (int(Upper) | int(Lower))));
+ // If solving for a 0x0 matrix, nothing to do, simply return.
+ if (derived().cols() == 0)
+ return;
+
+ enum { copy = (internal::traits<OtherDerived>::Flags & RowMajorBit) && OtherDerived::IsVectorAtCompileTime && OtherDerived::SizeAtCompileTime!=1};
+ typedef typename internal::conditional<copy,
+ typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;
+ OtherCopy otherCopy(other);
+
+ internal::triangular_solver_selector<MatrixType, typename internal::remove_reference<OtherCopy>::type,
+ Side, Mode>::run(derived().nestedExpression(), otherCopy);
+
+ if (copy)
+ other = otherCopy;
+}
+
+template<typename Derived, unsigned int Mode>
+template<int Side, typename Other>
+const internal::triangular_solve_retval<Side,TriangularView<Derived,Mode>,Other>
+TriangularViewImpl<Derived,Mode,Dense>::solve(const MatrixBase<Other>& other) const
+{
+ return internal::triangular_solve_retval<Side,TriangularViewType,Other>(derived(), other.derived());
+}
+#endif
+
+namespace internal {
+
+
+template<int Side, typename TriangularType, typename Rhs>
+struct traits<triangular_solve_retval<Side, TriangularType, Rhs> >
+{
+ typedef typename internal::plain_matrix_type_column_major<Rhs>::type ReturnType;
+};
+
+template<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval
+ : public ReturnByValue<triangular_solve_retval<Side, TriangularType, Rhs> >
+{
+ typedef typename remove_all<typename Rhs::Nested>::type RhsNestedCleaned;
+ typedef ReturnByValue<triangular_solve_retval> Base;
+
+ triangular_solve_retval(const TriangularType& tri, const Rhs& rhs)
+ : m_triangularMatrix(tri), m_rhs(rhs)
+ {}
+
+ inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_rhs.rows(); }
+ inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ if(!is_same_dense(dst,m_rhs))
+ dst = m_rhs;
+ m_triangularMatrix.template solveInPlace<Side>(dst);
+ }
+
+ protected:
+ const TriangularType& m_triangularMatrix;
+ typename Rhs::Nested m_rhs;
+};
+
+} // namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SOLVETRIANGULAR_H