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// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2008-2009 Gael Guennebaud // // 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 // IWYU pragma: private #include "./InternalHeaderCheck.h" namespace Eigen { namespace internal { // Forward declarations: // The following two routines are implemented in the products/TriangularSolver*.h files template struct triangular_solve_vector; template struct triangular_solve_matrix; // small helper struct extracting some traits on the underlying solver operation template 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 ::Unrolling, int RhsVectors = trsolve_traits::RhsVectors> struct triangular_solver_selector; template struct triangular_solver_selector { typedef typename Lhs::Scalar LhsScalar; typedef typename Rhs::Scalar RhsScalar; typedef blas_traits LhsProductTraits; typedef typename LhsProductTraits::ExtractType ActualLhsType; typedef Map, 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::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::run(actualLhs.cols(), actualLhs.data(), actualLhs.outerStride(), actualRhs); if (!useRhsDirectly) rhs = MappedRhs(actualRhs, rhs.size()); } }; // the rhs is a matrix template struct triangular_solver_selector { typedef typename Rhs::Scalar Scalar; typedef blas_traits LhsProductTraits; typedef typename LhsProductTraits::DirectLinearAccessType ActualLhsType; static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs) { add_const_on_value_type_t 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; // Nothing to solve. if (actualLhs.size() == 0 || rhs.size() == 0) { return; } BlockingType blocking(rhs.rows(), rhs.cols(), size, 1, false); triangular_solve_matrix::run(size, othersize, &actualLhs.coeffRef(0, 0), actualLhs.outerStride(), &rhs.coeffRef(0, 0), rhs.innerStride(), rhs.outerStride(), blocking); } }; /*************************************************************************** * meta-unrolling implementation ***************************************************************************/ template struct triangular_solver_unroller; template struct triangular_solver_unroller { 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(StartIndex) .transpose() .cwiseProduct(rhs.template segment(StartIndex)) .sum(); if (!(Mode & UnitDiag)) rhs.coeffRef(DiagIndex) /= lhs.coeff(DiagIndex, DiagIndex); triangular_solver_unroller::run(lhs, rhs); } }; template struct triangular_solver_unroller { static EIGEN_DEVICE_FUNC void run(const Lhs&, Rhs&) {} }; template struct triangular_solver_selector { static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs) { triangular_solver_unroller::run(lhs, rhs); } }; template struct triangular_solver_selector { static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs) { Transpose trLhs(lhs); Transpose trRhs(rhs); triangular_solver_unroller, Transpose, ((Mode & Upper) == Upper ? Lower : Upper) | (Mode & UnitDiag), 0, Rhs::SizeAtCompileTime>::run(trLhs, trRhs); } }; } // end namespace internal /*************************************************************************** * TriangularView methods ***************************************************************************/ #ifndef EIGEN_PARSED_BY_DOXYGEN template template EIGEN_DEVICE_FUNC void TriangularViewImpl::solveInPlace( const MatrixBase& _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::Flags & RowMajorBit) && OtherDerived::IsVectorAtCompileTime && OtherDerived::SizeAtCompileTime != 1 }; typedef std::conditional_t::type, OtherDerived&> OtherCopy; OtherCopy otherCopy(other); internal::triangular_solver_selector, Side, Mode>::run( derived().nestedExpression(), otherCopy); if (copy) other = otherCopy; } template template const internal::triangular_solve_retval, Other> TriangularViewImpl::solve(const MatrixBase& other) const { return internal::triangular_solve_retval(derived(), other.derived()); } #endif namespace internal { template struct traits > { typedef typename internal::plain_matrix_type_column_major::type ReturnType; }; template struct triangular_solve_retval : public ReturnByValue > { typedef remove_all_t RhsNestedCleaned; typedef ReturnByValue Base; triangular_solve_retval(const TriangularType& tri, const Rhs& rhs) : m_triangularMatrix(tri), m_rhs(rhs) {} constexpr Index rows() const noexcept { return m_rhs.rows(); } constexpr Index cols() const noexcept { return m_rhs.cols(); } template inline void evalTo(Dest& dst) const { if (!is_same_dense(dst, m_rhs)) dst = m_rhs; m_triangularMatrix.template solveInPlace(dst); } protected: const TriangularType& m_triangularMatrix; typename Rhs::Nested m_rhs; }; } // namespace internal } // end namespace Eigen #endif // EIGEN_SOLVETRIANGULAR_H