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SolveTriangular.h
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SolveTriangular.h
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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

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