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eigen/Eigen/src/Core/TriangularMatrix.h

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// 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_TRIANGULARMATRIX_H
#define EIGEN_TRIANGULARMATRIX_H
namespace Eigen {
namespace internal {
template<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval;
}
/** \internal
*
* \class TriangularBase
* \ingroup Core_Module
*
* \brief Base class for triangular part in a matrix
*/
template<typename Derived> class TriangularBase : public EigenBase<Derived>
{
public:
enum {
Mode = internal::traits<Derived>::Mode,
CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime
};
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Index Index;
typedef typename internal::traits<Derived>::DenseMatrixType DenseMatrixType;
typedef DenseMatrixType DenseType;
EIGEN_DEVICE_FUNC
inline TriangularBase() { eigen_assert(!((Mode&UnitDiag) && (Mode&ZeroDiag))); }
EIGEN_DEVICE_FUNC
inline Index rows() const { return derived().rows(); }
EIGEN_DEVICE_FUNC
inline Index cols() const { return derived().cols(); }
EIGEN_DEVICE_FUNC
inline Index outerStride() const { return derived().outerStride(); }
EIGEN_DEVICE_FUNC
inline Index innerStride() const { return derived().innerStride(); }
EIGEN_DEVICE_FUNC
inline Scalar coeff(Index row, Index col) const { return derived().coeff(row,col); }
EIGEN_DEVICE_FUNC
inline Scalar& coeffRef(Index row, Index col) { return derived().coeffRef(row,col); }
/** \see MatrixBase::copyCoeff(row,col)
*/
template<typename Other>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE void copyCoeff(Index row, Index col, Other& other)
{
derived().coeffRef(row, col) = other.coeff(row, col);
}
EIGEN_DEVICE_FUNC
inline Scalar operator()(Index row, Index col) const
{
check_coordinates(row, col);
return coeff(row,col);
}
EIGEN_DEVICE_FUNC
inline Scalar& operator()(Index row, Index col)
{
check_coordinates(row, col);
return coeffRef(row,col);
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
EIGEN_DEVICE_FUNC
inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
EIGEN_DEVICE_FUNC
inline Derived& derived() { return *static_cast<Derived*>(this); }
#endif // not EIGEN_PARSED_BY_DOXYGEN
template<typename DenseDerived>
EIGEN_DEVICE_FUNC
void evalTo(MatrixBase<DenseDerived> &other) const;
template<typename DenseDerived>
EIGEN_DEVICE_FUNC
void evalToLazy(MatrixBase<DenseDerived> &other) const;
EIGEN_DEVICE_FUNC
DenseMatrixType toDenseMatrix() const
{
DenseMatrixType res(rows(), cols());
evalToLazy(res);
return res;
}
protected:
void check_coordinates(Index row, Index col) const
{
EIGEN_ONLY_USED_FOR_DEBUG(row);
EIGEN_ONLY_USED_FOR_DEBUG(col);
eigen_assert(col>=0 && col<cols() && row>=0 && row<rows());
const int mode = int(Mode) & ~SelfAdjoint;
EIGEN_ONLY_USED_FOR_DEBUG(mode);
eigen_assert((mode==Upper && col>=row)
|| (mode==Lower && col<=row)
|| ((mode==StrictlyUpper || mode==UnitUpper) && col>row)
|| ((mode==StrictlyLower || mode==UnitLower) && col<row));
}
#ifdef EIGEN_INTERNAL_DEBUGGING
void check_coordinates_internal(Index row, Index col) const
{
check_coordinates(row, col);
}
#else
void check_coordinates_internal(Index , Index ) const {}
#endif
};
/** \class TriangularView
* \ingroup Core_Module
*
* \brief Base class for triangular part in a matrix
*
* \param MatrixType the type of the object in which we are taking the triangular part
* \param Mode the kind of triangular matrix expression to construct. Can be #Upper,
* #Lower, #UnitUpper, #UnitLower, #StrictlyUpper, or #StrictlyLower.
* This is in fact a bit field; it must have either #Upper or #Lower,
* and additionnaly it may have #UnitDiag or #ZeroDiag or neither.
*
* This class represents a triangular part of a matrix, not necessarily square. Strictly speaking, for rectangular
* matrices one should speak of "trapezoid" parts. This class is the return type
* of MatrixBase::triangularView() and most of the time this is the only way it is used.
*
* \sa MatrixBase::triangularView()
*/
namespace internal {
template<typename MatrixType, unsigned int _Mode>
struct traits<TriangularView<MatrixType, _Mode> > : traits<MatrixType>
{
typedef typename nested<MatrixType>::type MatrixTypeNested;
typedef typename remove_reference<MatrixTypeNested>::type MatrixTypeNestedNonRef;
typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;
typedef MatrixType ExpressionType;
typedef typename MatrixType::PlainObject DenseMatrixType;
enum {
Mode = _Mode,
Flags = (MatrixTypeNestedCleaned::Flags & (HereditaryBits) & (~(PacketAccessBit | DirectAccessBit | LinearAccessBit))) | Mode,
CoeffReadCost = MatrixTypeNestedCleaned::CoeffReadCost
};
};
}
template<int Mode, bool LhsIsTriangular,
typename Lhs, bool LhsIsVector,
typename Rhs, bool RhsIsVector>
struct TriangularProduct;
template<typename _MatrixType, unsigned int _Mode> class TriangularView
: public TriangularBase<TriangularView<_MatrixType, _Mode> >
{
public:
typedef TriangularBase<TriangularView> Base;
typedef typename internal::traits<TriangularView>::Scalar Scalar;
typedef _MatrixType MatrixType;
typedef typename internal::traits<TriangularView>::DenseMatrixType DenseMatrixType;
typedef DenseMatrixType PlainObject;
protected:
typedef typename internal::traits<TriangularView>::MatrixTypeNested MatrixTypeNested;
typedef typename internal::traits<TriangularView>::MatrixTypeNestedNonRef MatrixTypeNestedNonRef;
typedef typename internal::traits<TriangularView>::MatrixTypeNestedCleaned MatrixTypeNestedCleaned;
typedef typename internal::remove_all<typename MatrixType::ConjugateReturnType>::type MatrixConjugateReturnType;
public:
using Base::evalToLazy;
typedef typename internal::traits<TriangularView>::StorageKind StorageKind;
typedef typename internal::traits<TriangularView>::Index Index;
enum {
Mode = _Mode,
TransposeMode = (Mode & Upper ? Lower : 0)
| (Mode & Lower ? Upper : 0)
| (Mode & (UnitDiag))
| (Mode & (ZeroDiag))
};
EIGEN_DEVICE_FUNC
inline TriangularView(const MatrixType& matrix) : m_matrix(matrix)
{}
EIGEN_DEVICE_FUNC
inline Index rows() const { return m_matrix.rows(); }
EIGEN_DEVICE_FUNC
inline Index cols() const { return m_matrix.cols(); }
EIGEN_DEVICE_FUNC
inline Index outerStride() const { return m_matrix.outerStride(); }
EIGEN_DEVICE_FUNC
inline Index innerStride() const { return m_matrix.innerStride(); }
/** \sa MatrixBase::operator+=() */
template<typename Other>
EIGEN_DEVICE_FUNC
TriangularView& operator+=(const DenseBase<Other>& other) { return *this = m_matrix + other.derived(); }
/** \sa MatrixBase::operator-=() */
template<typename Other>
EIGEN_DEVICE_FUNC
TriangularView& operator-=(const DenseBase<Other>& other) { return *this = m_matrix - other.derived(); }
/** \sa MatrixBase::operator*=() */
EIGEN_DEVICE_FUNC
TriangularView& operator*=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = m_matrix * other; }
/** \sa MatrixBase::operator/=() */
EIGEN_DEVICE_FUNC
TriangularView& operator/=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = m_matrix / other; }
/** \sa MatrixBase::fill() */
EIGEN_DEVICE_FUNC
void fill(const Scalar& value) { setConstant(value); }
/** \sa MatrixBase::setConstant() */
EIGEN_DEVICE_FUNC
TriangularView& setConstant(const Scalar& value)
{ return *this = MatrixType::Constant(rows(), cols(), value); }
/** \sa MatrixBase::setZero() */
EIGEN_DEVICE_FUNC
TriangularView& setZero() { return setConstant(Scalar(0)); }
/** \sa MatrixBase::setOnes() */
EIGEN_DEVICE_FUNC
TriangularView& setOnes() { return setConstant(Scalar(1)); }
/** \sa MatrixBase::coeff()
* \warning the coordinates must fit into the referenced triangular part
*/
EIGEN_DEVICE_FUNC
inline Scalar coeff(Index row, Index col) const
{
Base::check_coordinates_internal(row, col);
return m_matrix.coeff(row, col);
}
/** \sa MatrixBase::coeffRef()
* \warning the coordinates must fit into the referenced triangular part
*/
EIGEN_DEVICE_FUNC
inline Scalar& coeffRef(Index row, Index col)
{
Base::check_coordinates_internal(row, col);
return m_matrix.const_cast_derived().coeffRef(row, col);
}
EIGEN_DEVICE_FUNC
const MatrixTypeNestedCleaned& nestedExpression() const { return m_matrix; }
EIGEN_DEVICE_FUNC
MatrixTypeNestedCleaned& nestedExpression() { return *const_cast<MatrixTypeNestedCleaned*>(&m_matrix); }
/** Assigns a triangular matrix to a triangular part of a dense matrix */
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
TriangularView& operator=(const TriangularBase<OtherDerived>& other);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
TriangularView& operator=(const MatrixBase<OtherDerived>& other);
EIGEN_DEVICE_FUNC
TriangularView& operator=(const TriangularView& other)
{ return *this = other.nestedExpression(); }
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
void lazyAssign(const TriangularBase<OtherDerived>& other);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
void lazyAssign(const MatrixBase<OtherDerived>& other);
/** \sa MatrixBase::conjugate() */
EIGEN_DEVICE_FUNC
inline TriangularView<MatrixConjugateReturnType,Mode> conjugate()
{ return m_matrix.conjugate(); }
/** \sa MatrixBase::conjugate() const */
EIGEN_DEVICE_FUNC
inline const TriangularView<MatrixConjugateReturnType,Mode> conjugate() const
{ return m_matrix.conjugate(); }
/** \sa MatrixBase::adjoint() const */
EIGEN_DEVICE_FUNC
inline const TriangularView<const typename MatrixType::AdjointReturnType,TransposeMode> adjoint() const
{ return m_matrix.adjoint(); }
/** \sa MatrixBase::transpose() */
EIGEN_DEVICE_FUNC
inline TriangularView<Transpose<MatrixType>,TransposeMode> transpose()
{
EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
return m_matrix.const_cast_derived().transpose();
}
/** \sa MatrixBase::transpose() const */
EIGEN_DEVICE_FUNC
inline const TriangularView<Transpose<MatrixType>,TransposeMode> transpose() const
{
return m_matrix.transpose();
}
/** Efficient triangular matrix times vector/matrix product */
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
TriangularProduct<Mode,true,MatrixType,false,OtherDerived, OtherDerived::IsVectorAtCompileTime>
operator*(const MatrixBase<OtherDerived>& rhs) const
{
return TriangularProduct
<Mode,true,MatrixType,false,OtherDerived,OtherDerived::IsVectorAtCompileTime>
(m_matrix, rhs.derived());
}
/** Efficient vector/matrix times triangular matrix product */
template<typename OtherDerived> friend
EIGEN_DEVICE_FUNC
TriangularProduct<Mode,false,OtherDerived,OtherDerived::IsVectorAtCompileTime,MatrixType,false>
operator*(const MatrixBase<OtherDerived>& lhs, const TriangularView& rhs)
{
return TriangularProduct
<Mode,false,OtherDerived,OtherDerived::IsVectorAtCompileTime,MatrixType,false>
(lhs.derived(),rhs.m_matrix);
}
#ifdef EIGEN2_SUPPORT
template<typename OtherDerived>
struct eigen2_product_return_type
{
typedef typename TriangularView<MatrixType,Mode>::DenseMatrixType DenseMatrixType;
typedef typename OtherDerived::PlainObject::DenseType OtherPlainObject;
typedef typename ProductReturnType<DenseMatrixType, OtherPlainObject>::Type ProdRetType;
typedef typename ProdRetType::PlainObject type;
};
template<typename OtherDerived>
const typename eigen2_product_return_type<OtherDerived>::type
operator*(const EigenBase<OtherDerived>& rhs) const
{
typename OtherDerived::PlainObject::DenseType rhsPlainObject;
rhs.evalTo(rhsPlainObject);
return this->toDenseMatrix() * rhsPlainObject;
}
template<typename OtherMatrixType>
bool isApprox(const TriangularView<OtherMatrixType, Mode>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
{
return this->toDenseMatrix().isApprox(other.toDenseMatrix(), precision);
}
template<typename OtherDerived>
bool isApprox(const MatrixBase<OtherDerived>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
{
return this->toDenseMatrix().isApprox(other, precision);
}
#endif // EIGEN2_SUPPORT
template<int Side, typename Other>
EIGEN_DEVICE_FUNC
inline const internal::triangular_solve_retval<Side,TriangularView, Other>
solve(const MatrixBase<Other>& other) const;
template<int Side, typename OtherDerived>
EIGEN_DEVICE_FUNC
void solveInPlace(const MatrixBase<OtherDerived>& other) const;
template<typename Other>
EIGEN_DEVICE_FUNC
inline const internal::triangular_solve_retval<OnTheLeft,TriangularView, Other>
solve(const MatrixBase<Other>& other) const
{ return solve<OnTheLeft>(other); }
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
void solveInPlace(const MatrixBase<OtherDerived>& other) const
{ return solveInPlace<OnTheLeft>(other); }
EIGEN_DEVICE_FUNC
const SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView() const
{
EIGEN_STATIC_ASSERT((Mode&UnitDiag)==0,PROGRAMMING_ERROR);
return SelfAdjointView<MatrixTypeNestedNonRef,Mode>(m_matrix);
}
EIGEN_DEVICE_FUNC
SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView()
{
EIGEN_STATIC_ASSERT((Mode&UnitDiag)==0,PROGRAMMING_ERROR);
return SelfAdjointView<MatrixTypeNestedNonRef,Mode>(m_matrix);
}
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
void swap(TriangularBase<OtherDerived> const & other)
{
TriangularView<SwapWrapper<MatrixType>,Mode>(const_cast<MatrixType&>(m_matrix)).lazyAssign(other.derived());
}
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
void swap(MatrixBase<OtherDerived> const & other)
{
SwapWrapper<MatrixType> swaper(const_cast<MatrixType&>(m_matrix));
TriangularView<SwapWrapper<MatrixType>,Mode>(swaper).lazyAssign(other.derived());
}
EIGEN_DEVICE_FUNC
Scalar determinant() const
{
if (Mode & UnitDiag)
return 1;
else if (Mode & ZeroDiag)
return 0;
else
return m_matrix.diagonal().prod();
}
// TODO simplify the following:
template<typename ProductDerived, typename Lhs, typename Rhs>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE TriangularView& operator=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
{
setZero();
return assignProduct(other,1);
}
template<typename ProductDerived, typename Lhs, typename Rhs>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE TriangularView& operator+=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
{
return assignProduct(other,1);
}
template<typename ProductDerived, typename Lhs, typename Rhs>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE TriangularView& operator-=(const ProductBase<ProductDerived, Lhs,Rhs>& other)
{
return assignProduct(other,-1);
}
template<typename ProductDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE TriangularView& operator=(const ScaledProduct<ProductDerived>& other)
{
setZero();
return assignProduct(other,other.alpha());
}
template<typename ProductDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE TriangularView& operator+=(const ScaledProduct<ProductDerived>& other)
{
return assignProduct(other,other.alpha());
}
template<typename ProductDerived>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE TriangularView& operator-=(const ScaledProduct<ProductDerived>& other)
{
return assignProduct(other,-other.alpha());
}
protected:
template<typename ProductDerived, typename Lhs, typename Rhs>
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE TriangularView& assignProduct(const ProductBase<ProductDerived, Lhs,Rhs>& prod, const Scalar& alpha);
MatrixTypeNested m_matrix;
};
/***************************************************************************
* Implementation of triangular evaluation/assignment
***************************************************************************/
namespace internal {
template<typename Derived1, typename Derived2, unsigned int Mode, int UnrollCount, bool ClearOpposite>
struct triangular_assignment_selector
{
enum {
col = (UnrollCount-1) / Derived1::RowsAtCompileTime,
row = (UnrollCount-1) % Derived1::RowsAtCompileTime
};
typedef typename Derived1::Scalar Scalar;
EIGEN_DEVICE_FUNC
static inline void run(Derived1 &dst, const Derived2 &src)
{
triangular_assignment_selector<Derived1, Derived2, Mode, UnrollCount-1, ClearOpposite>::run(dst, src);
eigen_assert( Mode == Upper || Mode == Lower
|| Mode == StrictlyUpper || Mode == StrictlyLower
|| Mode == UnitUpper || Mode == UnitLower);
if((Mode == Upper && row <= col)
|| (Mode == Lower && row >= col)
|| (Mode == StrictlyUpper && row < col)
|| (Mode == StrictlyLower && row > col)
|| (Mode == UnitUpper && row < col)
|| (Mode == UnitLower && row > col))
dst.copyCoeff(row, col, src);
else if(ClearOpposite)
{
if (Mode&UnitDiag && row==col)
dst.coeffRef(row, col) = Scalar(1);
else
dst.coeffRef(row, col) = Scalar(0);
}
}
};
// prevent buggy user code from causing an infinite recursion
template<typename Derived1, typename Derived2, unsigned int Mode, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, Mode, 0, ClearOpposite>
{
EIGEN_DEVICE_FUNC
static inline void run(Derived1 &, const Derived2 &) {}
};
template<typename Derived1, typename Derived2, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, Upper, Dynamic, ClearOpposite>
{
typedef typename Derived1::Index Index;
typedef typename Derived1::Scalar Scalar;
EIGEN_DEVICE_FUNC
static inline void run(Derived1 &dst, const Derived2 &src)
{
for(Index j = 0; j < dst.cols(); ++j)
{
Index maxi = (std::min)(j, dst.rows()-1);
for(Index i = 0; i <= maxi; ++i)
dst.copyCoeff(i, j, src);
if (ClearOpposite)
for(Index i = maxi+1; i < dst.rows(); ++i)
dst.coeffRef(i, j) = Scalar(0);
}
}
};
template<typename Derived1, typename Derived2, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, Lower, Dynamic, ClearOpposite>
{
typedef typename Derived1::Index Index;
EIGEN_DEVICE_FUNC
static inline void run(Derived1 &dst, const Derived2 &src)
{
for(Index j = 0; j < dst.cols(); ++j)
{
for(Index i = j; i < dst.rows(); ++i)
dst.copyCoeff(i, j, src);
Index maxi = (std::min)(j, dst.rows());
if (ClearOpposite)
for(Index i = 0; i < maxi; ++i)
dst.coeffRef(i, j) = static_cast<typename Derived1::Scalar>(0);
}
}
};
template<typename Derived1, typename Derived2, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, StrictlyUpper, Dynamic, ClearOpposite>
{
typedef typename Derived1::Index Index;
typedef typename Derived1::Scalar Scalar;
EIGEN_DEVICE_FUNC
static inline void run(Derived1 &dst, const Derived2 &src)
{
for(Index j = 0; j < dst.cols(); ++j)
{
Index maxi = (std::min)(j, dst.rows());
for(Index i = 0; i < maxi; ++i)
dst.copyCoeff(i, j, src);
if (ClearOpposite)
for(Index i = maxi; i < dst.rows(); ++i)
dst.coeffRef(i, j) = Scalar(0);
}
}
};
template<typename Derived1, typename Derived2, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, StrictlyLower, Dynamic, ClearOpposite>
{
typedef typename Derived1::Index Index;
EIGEN_DEVICE_FUNC
static inline void run(Derived1 &dst, const Derived2 &src)
{
for(Index j = 0; j < dst.cols(); ++j)
{
for(Index i = j+1; i < dst.rows(); ++i)
dst.copyCoeff(i, j, src);
Index maxi = (std::min)(j, dst.rows()-1);
if (ClearOpposite)
for(Index i = 0; i <= maxi; ++i)
dst.coeffRef(i, j) = static_cast<typename Derived1::Scalar>(0);
}
}
};
template<typename Derived1, typename Derived2, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, UnitUpper, Dynamic, ClearOpposite>
{
typedef typename Derived1::Index Index;
EIGEN_DEVICE_FUNC
static inline void run(Derived1 &dst, const Derived2 &src)
{
for(Index j = 0; j < dst.cols(); ++j)
{
Index maxi = (std::min)(j, dst.rows());
for(Index i = 0; i < maxi; ++i)
dst.copyCoeff(i, j, src);
if (ClearOpposite)
{
for(Index i = maxi+1; i < dst.rows(); ++i)
dst.coeffRef(i, j) = 0;
}
}
dst.diagonal().setOnes();
}
};
template<typename Derived1, typename Derived2, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, UnitLower, Dynamic, ClearOpposite>
{
typedef typename Derived1::Index Index;
EIGEN_DEVICE_FUNC
static inline void run(Derived1 &dst, const Derived2 &src)
{
for(Index j = 0; j < dst.cols(); ++j)
{
Index maxi = (std::min)(j, dst.rows());
for(Index i = maxi+1; i < dst.rows(); ++i)
dst.copyCoeff(i, j, src);
if (ClearOpposite)
{
for(Index i = 0; i < maxi; ++i)
dst.coeffRef(i, j) = 0;
}
}
dst.diagonal().setOnes();
}
};
} // end namespace internal
// FIXME should we keep that possibility
template<typename MatrixType, unsigned int Mode>
template<typename OtherDerived>
inline TriangularView<MatrixType, Mode>&
TriangularView<MatrixType, Mode>::operator=(const MatrixBase<OtherDerived>& other)
{
if(OtherDerived::Flags & EvalBeforeAssigningBit)
{
typename internal::plain_matrix_type<OtherDerived>::type other_evaluated(other.rows(), other.cols());
other_evaluated.template triangularView<Mode>().lazyAssign(other.derived());
lazyAssign(other_evaluated);
}
else
lazyAssign(other.derived());
return *this;
}
// FIXME should we keep that possibility
template<typename MatrixType, unsigned int Mode>
template<typename OtherDerived>
void TriangularView<MatrixType, Mode>::lazyAssign(const MatrixBase<OtherDerived>& other)
{
enum {
unroll = MatrixType::SizeAtCompileTime != Dynamic
&& internal::traits<OtherDerived>::CoeffReadCost != Dynamic
&& MatrixType::SizeAtCompileTime*internal::traits<OtherDerived>::CoeffReadCost/2 <= EIGEN_UNROLLING_LIMIT
};
eigen_assert(m_matrix.rows() == other.rows() && m_matrix.cols() == other.cols());
internal::triangular_assignment_selector
<MatrixType, OtherDerived, int(Mode),
unroll ? int(MatrixType::SizeAtCompileTime) : Dynamic,
false // do not change the opposite triangular part
>::run(m_matrix.const_cast_derived(), other.derived());
}
template<typename MatrixType, unsigned int Mode>
template<typename OtherDerived>
inline TriangularView<MatrixType, Mode>&
TriangularView<MatrixType, Mode>::operator=(const TriangularBase<OtherDerived>& other)
{
eigen_assert(Mode == int(OtherDerived::Mode));
if(internal::traits<OtherDerived>::Flags & EvalBeforeAssigningBit)
{
typename OtherDerived::DenseMatrixType other_evaluated(other.rows(), other.cols());
other_evaluated.template triangularView<Mode>().lazyAssign(other.derived().nestedExpression());
lazyAssign(other_evaluated);
}
else
lazyAssign(other.derived().nestedExpression());
return *this;
}
template<typename MatrixType, unsigned int Mode>
template<typename OtherDerived>
void TriangularView<MatrixType, Mode>::lazyAssign(const TriangularBase<OtherDerived>& other)
{
enum {
unroll = MatrixType::SizeAtCompileTime != Dynamic
&& internal::traits<OtherDerived>::CoeffReadCost != Dynamic
&& MatrixType::SizeAtCompileTime * internal::traits<OtherDerived>::CoeffReadCost / 2
<= EIGEN_UNROLLING_LIMIT
};
eigen_assert(m_matrix.rows() == other.rows() && m_matrix.cols() == other.cols());
internal::triangular_assignment_selector
<MatrixType, OtherDerived, int(Mode),
unroll ? int(MatrixType::SizeAtCompileTime) : Dynamic,
false // preserve the opposite triangular part
>::run(m_matrix.const_cast_derived(), other.derived().nestedExpression());
}
/***************************************************************************
* Implementation of TriangularBase methods
***************************************************************************/
/** Assigns a triangular or selfadjoint matrix to a dense matrix.
* If the matrix is triangular, the opposite part is set to zero. */
template<typename Derived>
template<typename DenseDerived>
void TriangularBase<Derived>::evalTo(MatrixBase<DenseDerived> &other) const
{
if(internal::traits<Derived>::Flags & EvalBeforeAssigningBit)
{
typename internal::plain_matrix_type<Derived>::type other_evaluated(rows(), cols());
evalToLazy(other_evaluated);
other.derived().swap(other_evaluated);
}
else
evalToLazy(other.derived());
}
/** Assigns a triangular or selfadjoint matrix to a dense matrix.
* If the matrix is triangular, the opposite part is set to zero. */
template<typename Derived>
template<typename DenseDerived>
void TriangularBase<Derived>::evalToLazy(MatrixBase<DenseDerived> &other) const
{
enum {
unroll = DenseDerived::SizeAtCompileTime != Dynamic
&& internal::traits<Derived>::CoeffReadCost != Dynamic
&& DenseDerived::SizeAtCompileTime * internal::traits<Derived>::CoeffReadCost / 2
<= EIGEN_UNROLLING_LIMIT
};
other.derived().resize(this->rows(), this->cols());
internal::triangular_assignment_selector
<DenseDerived, typename internal::traits<Derived>::MatrixTypeNestedCleaned, Derived::Mode,
unroll ? int(DenseDerived::SizeAtCompileTime) : Dynamic,
true // clear the opposite triangular part
>::run(other.derived(), derived().nestedExpression());
}
/***************************************************************************
* Implementation of TriangularView methods
***************************************************************************/
/***************************************************************************
* Implementation of MatrixBase methods
***************************************************************************/
#ifdef EIGEN2_SUPPORT
// implementation of part<>(), including the SelfAdjoint case.
namespace internal {
template<typename MatrixType, unsigned int Mode>
struct eigen2_part_return_type
{
typedef TriangularView<MatrixType, Mode> type;
};
template<typename MatrixType>
struct eigen2_part_return_type<MatrixType, SelfAdjoint>
{
typedef SelfAdjointView<MatrixType, Upper> type;
};
}
/** \deprecated use MatrixBase::triangularView() */
template<typename Derived>
template<unsigned int Mode>
const typename internal::eigen2_part_return_type<Derived, Mode>::type MatrixBase<Derived>::part() const
{
return derived();
}
/** \deprecated use MatrixBase::triangularView() */
template<typename Derived>
template<unsigned int Mode>
typename internal::eigen2_part_return_type<Derived, Mode>::type MatrixBase<Derived>::part()
{
return derived();
}
#endif
/**
* \returns an expression of a triangular view extracted from the current matrix
*
* The parameter \a Mode can have the following values: \c #Upper, \c #StrictlyUpper, \c #UnitUpper,
* \c #Lower, \c #StrictlyLower, \c #UnitLower.
*
* Example: \include MatrixBase_extract.cpp
* Output: \verbinclude MatrixBase_extract.out
*
* \sa class TriangularView
*/
template<typename Derived>
template<unsigned int Mode>
typename MatrixBase<Derived>::template TriangularViewReturnType<Mode>::Type
MatrixBase<Derived>::triangularView()
{
return derived();
}
/** This is the const version of MatrixBase::triangularView() */
template<typename Derived>
template<unsigned int Mode>
typename MatrixBase<Derived>::template ConstTriangularViewReturnType<Mode>::Type
MatrixBase<Derived>::triangularView() const
{
return derived();
}
/** \returns true if *this is approximately equal to an upper triangular matrix,
* within the precision given by \a prec.
*
* \sa isLowerTriangular()
*/
template<typename Derived>
bool MatrixBase<Derived>::isUpperTriangular(const RealScalar& prec) const
{
using std::abs;
RealScalar maxAbsOnUpperPart = static_cast<RealScalar>(-1);
for(Index j = 0; j < cols(); ++j)
{
Index maxi = (std::min)(j, rows()-1);
for(Index i = 0; i <= maxi; ++i)
{
RealScalar absValue = abs(coeff(i,j));
if(absValue > maxAbsOnUpperPart) maxAbsOnUpperPart = absValue;
}
}
RealScalar threshold = maxAbsOnUpperPart * prec;
for(Index j = 0; j < cols(); ++j)
for(Index i = j+1; i < rows(); ++i)
if(abs(coeff(i, j)) > threshold) return false;
return true;
}
/** \returns true if *this is approximately equal to a lower triangular matrix,
* within the precision given by \a prec.
*
* \sa isUpperTriangular()
*/
template<typename Derived>
bool MatrixBase<Derived>::isLowerTriangular(const RealScalar& prec) const
{
using std::abs;
RealScalar maxAbsOnLowerPart = static_cast<RealScalar>(-1);
for(Index j = 0; j < cols(); ++j)
for(Index i = j; i < rows(); ++i)
{
RealScalar absValue = abs(coeff(i,j));
if(absValue > maxAbsOnLowerPart) maxAbsOnLowerPart = absValue;
}
RealScalar threshold = maxAbsOnLowerPart * prec;
for(Index j = 1; j < cols(); ++j)
{
Index maxi = (std::min)(j, rows()-1);
for(Index i = 0; i < maxi; ++i)
if(abs(coeff(i, j)) > threshold) return false;
}
return true;
}
} // end namespace Eigen
#endif // EIGEN_TRIANGULARMATRIX_H
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