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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>
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)
{
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);
triangular_solve_matrix<Scalar,Index,Side,Mode,LhsProductTraits::NeedToConjugate,(int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor,
(Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor>
::run(size, othersize, &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &rhs.coeffRef(0,0), rhs.outerStride(), blocking);
}
};
/***************************************************************************
* 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),
RowIndex = IsLower ? Index : Size - Index - 1,
S = IsLower ? 0 : RowIndex+1
};
static void run(const Lhs& lhs, Rhs& rhs)
{
if (Index>0)
rhs.coeffRef(RowIndex) -= lhs.row(RowIndex).template segment<Index>(S).transpose()
.cwiseProduct(rhs.template segment<Index>(S)).sum();
if(!(Mode & UnitDiag))
rhs.coeffRef(RowIndex) /= lhs.coeff(RowIndex,RowIndex);
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() && ((Side==OnTheLeft && cols() == other.rows()) || (Side==OnTheRight && cols() == other.cols())) );
eigen_assert((!(Mode & ZeroDiag)) && bool(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;
typename Rhs::Nested m_rhs;
};
} // namespace internal
} // end namespace Eigen
#endif // EIGEN_SOLVETRIANGULAR_H
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