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Diffstat (limited to 'extern/Eigen3/Eigen/src/Core/SolveTriangular.h')
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1 files changed, 263 insertions, 0 deletions
diff --git a/extern/Eigen3/Eigen/src/Core/SolveTriangular.h b/extern/Eigen3/Eigen/src/Core/SolveTriangular.h new file mode 100644 index 00000000000..71e129c7f12 --- /dev/null +++ b/extern/Eigen3/Eigen/src/Core/SolveTriangular.h @@ -0,0 +1,263 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// Eigen is free software; you can redistribute it and/or +// modify it under the terms of the GNU Lesser General Public +// License as published by the Free Software Foundation; either +// version 3 of the License, or (at your option) any later version. +// +// Alternatively, you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of +// the License, or (at your option) any later version. +// +// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY +// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU Lesser General Public +// License and a copy of the GNU General Public License along with +// Eigen. If not, see <http://www.gnu.org/licenses/>. + +#ifndef EIGEN_SOLVETRIANGULAR_H +#define EIGEN_SOLVETRIANGULAR_H + +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> +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 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, typename Lhs::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 typename Rhs::Index Index; + typedef blas_traits<Lhs> LhsProductTraits; + typedef typename LhsProductTraits::DirectLinearAccessType ActualLhsType; + static void run(const Lhs& lhs, Rhs& rhs) + { + const ActualLhsType actualLhs = LhsProductTraits::extract(lhs); + triangular_solve_matrix<Scalar,Index,Side,Mode,LhsProductTraits::NeedToConjugate,(int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor, + (Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor> + ::run(lhs.rows(), Side==OnTheLeft? rhs.cols() : rhs.rows(), &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &rhs.coeffRef(0,0), rhs.outerStride()); + } +}; + +/*************************************************************************** +* meta-unrolling implementation +***************************************************************************/ + +template<typename Lhs, typename Rhs, int Mode, int Index, int Size, + bool Stop = Index==Size> +struct triangular_solver_unroller; + +template<typename Lhs, typename Rhs, int Mode, int Index, int Size> +struct triangular_solver_unroller<Lhs,Rhs,Mode,Index,Size,false> { + enum { + IsLower = ((Mode&Lower)==Lower), + I = IsLower ? Index : Size - Index - 1, + S = IsLower ? 0 : I+1 + }; + static void run(const Lhs& lhs, Rhs& rhs) + { + if (Index>0) + rhs.coeffRef(I) -= lhs.row(I).template segment<Index>(S).transpose() + .cwiseProduct(rhs.template segment<Index>(S)).sum(); + + if(!(Mode & UnitDiag)) + rhs.coeffRef(I) /= lhs.coeff(I,I); + + triangular_solver_unroller<Lhs,Rhs,Mode,Index+1,Size>::run(lhs,rhs); + } +}; + +template<typename Lhs, typename Rhs, int Mode, int Index, int Size> +struct triangular_solver_unroller<Lhs,Rhs,Mode,Index,Size,true> { + static void run(const Lhs&, Rhs&) {} +}; + +template<typename Lhs, typename Rhs, int Mode> +struct triangular_solver_selector<Lhs,Rhs,OnTheLeft,Mode,CompleteUnrolling,1> { + static 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 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 +***************************************************************************/ + +/** "in-place" version of TriangularView::solve() where the result is written in \a other + * + * \warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here. + * This function will const_cast it, so constness isn't honored here. + * + * See TriangularView:solve() for the details. + */ +template<typename MatrixType, unsigned int Mode> +template<int Side, typename OtherDerived> +void TriangularView<MatrixType,Mode>::solveInPlace(const MatrixBase<OtherDerived>& _other) const +{ + OtherDerived& other = _other.const_cast_derived(); + eigen_assert(cols() == rows()); + eigen_assert( (Side==OnTheLeft && cols() == other.rows()) || (Side==OnTheRight && cols() == other.cols()) ); + eigen_assert(!(Mode & ZeroDiag)); + eigen_assert(Mode & (Upper|Lower)); + + enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit && OtherDerived::IsVectorAtCompileTime }; + 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(nestedExpression(), otherCopy); + + if (copy) + other = otherCopy; +} + +/** \returns the product of the inverse of \c *this with \a other, \a *this being triangular. + * + * This function computes the inverse-matrix matrix product inverse(\c *this) * \a other if + * \a Side==OnTheLeft (the default), or the right-inverse-multiply \a other * inverse(\c *this) if + * \a Side==OnTheRight. + * + * The matrix \c *this must be triangular and invertible (i.e., all the coefficients of the + * diagonal must be non zero). It works as a forward (resp. backward) substitution if \c *this + * is an upper (resp. lower) triangular matrix. + * + * Example: \include MatrixBase_marked.cpp + * Output: \verbinclude MatrixBase_marked.out + * + * This function returns an expression of the inverse-multiply and can works in-place if it is assigned + * to the same matrix or vector \a other. + * + * For users coming from BLAS, this function (and more specifically solveInPlace()) offer + * all the operations supported by the \c *TRSV and \c *TRSM BLAS routines. + * + * \sa TriangularView::solveInPlace() + */ +template<typename Derived, unsigned int Mode> +template<int Side, typename Other> +const internal::triangular_solve_retval<Side,TriangularView<Derived,Mode>,Other> +TriangularView<Derived,Mode>::solve(const MatrixBase<Other>& other) const +{ + return internal::triangular_solve_retval<Side,TriangularView,Other>(*this, other.derived()); +} + +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; + typedef typename Base::Index Index; + + triangular_solve_retval(const TriangularType& tri, const Rhs& rhs) + : m_triangularMatrix(tri), m_rhs(rhs) + {} + + inline Index rows() const { return m_rhs.rows(); } + inline Index cols() const { return m_rhs.cols(); } + + template<typename Dest> inline void evalTo(Dest& dst) const + { + if(!(is_same<RhsNestedCleaned,Dest>::value && extract_data(dst) == extract_data(m_rhs))) + dst = m_rhs; + m_triangularMatrix.template solveInPlace<Side>(dst); + } + + protected: + const TriangularType& m_triangularMatrix; + const typename Rhs::Nested m_rhs; +}; + +} // namespace internal + +#endif // EIGEN_SOLVETRIANGULAR_H |