diff options
Diffstat (limited to 'Eigen/src/Core/TriangularMatrix.h')
| -rw-r--r-- | Eigen/src/Core/TriangularMatrix.h | 883 |
1 files changed, 482 insertions, 401 deletions
diff --git a/Eigen/src/Core/TriangularMatrix.h b/Eigen/src/Core/TriangularMatrix.h index 72792d21b..cf0255bce 100644 --- a/Eigen/src/Core/TriangularMatrix.h +++ b/Eigen/src/Core/TriangularMatrix.h @@ -32,17 +32,23 @@ template<typename Derived> class TriangularBase : public EigenBase<Derived> 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 + MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime, + + SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime, + internal::traits<Derived>::ColsAtCompileTime>::ret) + /**< This is equal to the number of coefficients, i.e. the number of + * rows times the number of columns, or to \a Dynamic if this is not + * known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */ }; 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 typename internal::traits<Derived>::FullMatrixType DenseMatrixType; typedef DenseMatrixType DenseType; + typedef Derived const& Nested; EIGEN_DEVICE_FUNC inline TriangularBase() { eigen_assert(!((Mode&UnitDiag) && (Mode&ZeroDiag))); } @@ -55,6 +61,14 @@ template<typename Derived> class TriangularBase : public EigenBase<Derived> inline Index outerStride() const { return derived().outerStride(); } EIGEN_DEVICE_FUNC inline Index innerStride() const { return derived().innerStride(); } + + // dummy resize function + void resize(Index nbRows, Index nbCols) + { + EIGEN_UNUSED_VARIABLE(nbRows); + EIGEN_UNUSED_VARIABLE(nbCols); + eigen_assert(nbRows==rows() && nbCols==nbCols); + } EIGEN_DEVICE_FUNC inline Scalar coeff(Index row, Index col) const { return derived().coeff(row,col); } @@ -155,96 +169,209 @@ 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 typename MatrixType::PlainObject FullMatrixType; typedef MatrixType ExpressionType; - typedef typename MatrixType::PlainObject DenseMatrixType; enum { Mode = _Mode, - Flags = (MatrixTypeNestedCleaned::Flags & (HereditaryBits) & (~(PacketAccessBit | DirectAccessBit | LinearAccessBit))) | Mode, - CoeffReadCost = MatrixTypeNestedCleaned::CoeffReadCost + FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0, + Flags = (MatrixTypeNestedCleaned::Flags & (HereditaryBits | FlagsLvalueBit) & (~(PacketAccessBit | DirectAccessBit | LinearAccessBit))) }; }; } -template<int Mode, bool LhsIsTriangular, - typename Lhs, bool LhsIsVector, - typename Rhs, bool RhsIsVector> -struct TriangularProduct; +template<typename _MatrixType, unsigned int _Mode, typename StorageKind> class TriangularViewImpl; template<typename _MatrixType, unsigned int _Mode> class TriangularView - : public TriangularBase<TriangularView<_MatrixType, _Mode> > + : public TriangularViewImpl<_MatrixType, _Mode, typename internal::traits<_MatrixType>::StorageKind > { public: - typedef TriangularBase<TriangularView> Base; + typedef TriangularViewImpl<_MatrixType, _Mode, typename internal::traits<_MatrixType>::StorageKind > 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; + typedef typename internal::traits<TriangularView>::MatrixTypeNestedCleaned NestedExpression; enum { Mode = _Mode, + Flags = internal::traits<TriangularView>::Flags, TransposeMode = (Mode & Upper ? Lower : 0) | (Mode & Lower ? Upper : 0) | (Mode & (UnitDiag)) - | (Mode & (ZeroDiag)) + | (Mode & (ZeroDiag)), + IsVectorAtCompileTime = false }; + // FIXME This, combined with const_cast_derived in transpose() leads to a const-correctness loophole EIGEN_DEVICE_FUNC - inline TriangularView(const MatrixType& matrix) : m_matrix(matrix) + explicit inline TriangularView(MatrixType& matrix) : m_matrix(matrix) {} + + using Base::operator=; + TriangularView& operator=(const TriangularView &other) + { return Base::operator=(other); } 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 + const NestedExpression& nestedExpression() const { return m_matrix; } + EIGEN_DEVICE_FUNC + NestedExpression& nestedExpression() { return *const_cast<NestedExpression*>(&m_matrix); } + + /** \sa MatrixBase::conjugate() const */ + typedef TriangularView<const MatrixConjugateReturnType,Mode> ConjugateReturnType; + EIGEN_DEVICE_FUNC + inline const ConjugateReturnType conjugate() const + { return ConjugateReturnType(m_matrix.conjugate()); } + + typedef TriangularView<const typename MatrixType::AdjointReturnType,TransposeMode> AdjointReturnType; + /** \sa MatrixBase::adjoint() const */ + EIGEN_DEVICE_FUNC + inline const AdjointReturnType adjoint() const + { return AdjointReturnType(m_matrix.adjoint()); } + + typedef TriangularView<typename MatrixType::TransposeReturnType,TransposeMode> TransposeReturnType; + /** \sa MatrixBase::transpose() */ + EIGEN_DEVICE_FUNC + inline TransposeReturnType transpose() + { + EIGEN_STATIC_ASSERT_LVALUE(MatrixType) + typename MatrixType::TransposeReturnType tmp(m_matrix.const_cast_derived()); + return TransposeReturnType(tmp); + } + + typedef TriangularView<const typename MatrixType::ConstTransposeReturnType,TransposeMode> ConstTransposeReturnType; + /** \sa MatrixBase::transpose() const */ EIGEN_DEVICE_FUNC - inline Index outerStride() const { return m_matrix.outerStride(); } + inline const ConstTransposeReturnType transpose() const + { + return ConstTransposeReturnType(m_matrix.transpose()); + } + + template<typename Other> EIGEN_DEVICE_FUNC - inline Index innerStride() const { return m_matrix.innerStride(); } + inline const Solve<TriangularView, Other> + solve(const MatrixBase<Other>& other) const + { return Solve<TriangularView, Other>(*this, other.derived()); } + + // workaround MSVC ICE + #if EIGEN_COMP_MSVC + template<int Side, typename Other> + EIGEN_DEVICE_FUNC + inline const internal::triangular_solve_retval<Side,TriangularView, Other> + solve(const MatrixBase<Other>& other) const + { return Base::template solve<Side>(other); } + #else + using Base::solve; + #endif + + 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); + } + + EIGEN_DEVICE_FUNC + Scalar determinant() const + { + if (Mode & UnitDiag) + return 1; + else if (Mode & ZeroDiag) + return 0; + else + return m_matrix.diagonal().prod(); + } + + protected: + + MatrixTypeNested m_matrix; +}; + +template<typename _MatrixType, unsigned int _Mode> class TriangularViewImpl<_MatrixType,_Mode,Dense> + : public TriangularBase<TriangularView<_MatrixType, _Mode> > +{ + public: + + typedef TriangularView<_MatrixType, _Mode> TriangularViewType; + typedef TriangularBase<TriangularViewType> Base; + typedef typename internal::traits<TriangularViewType>::Scalar Scalar; + + typedef _MatrixType MatrixType; + typedef typename MatrixType::PlainObject DenseMatrixType; + typedef DenseMatrixType PlainObject; + + public: + using Base::evalToLazy; + using Base::derived; + + typedef typename internal::traits<TriangularViewType>::StorageKind StorageKind; + typedef typename internal::traits<TriangularViewType>::Index Index; + + enum { + Mode = _Mode, + Flags = internal::traits<TriangularViewType>::Flags + }; + + EIGEN_DEVICE_FUNC + inline Index outerStride() const { return derived().nestedExpression().outerStride(); } + EIGEN_DEVICE_FUNC + inline Index innerStride() const { return derived().nestedExpression().innerStride(); } /** \sa MatrixBase::operator+=() */ template<typename Other> EIGEN_DEVICE_FUNC - TriangularView& operator+=(const DenseBase<Other>& other) { return *this = m_matrix + other.derived(); } + TriangularViewType& operator+=(const DenseBase<Other>& other) { + internal::call_assignment_no_alias(derived(), other.derived(), internal::add_assign_op<Scalar>()); + return derived(); + } /** \sa MatrixBase::operator-=() */ template<typename Other> EIGEN_DEVICE_FUNC - TriangularView& operator-=(const DenseBase<Other>& other) { return *this = m_matrix - other.derived(); } + TriangularViewType& operator-=(const DenseBase<Other>& other) { + internal::call_assignment_no_alias(derived(), other.derived(), internal::sub_assign_op<Scalar>()); + return derived(); + } + /** \sa MatrixBase::operator*=() */ EIGEN_DEVICE_FUNC - TriangularView& operator*=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = m_matrix * other; } + TriangularViewType& operator*=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = derived().nestedExpression() * other; } /** \sa MatrixBase::operator/=() */ EIGEN_DEVICE_FUNC - TriangularView& operator/=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = m_matrix / other; } + TriangularViewType& operator/=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = derived().nestedExpression() / 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); } + TriangularViewType& setConstant(const Scalar& value) + { return *this = MatrixType::Constant(derived().rows(), derived().cols(), value); } /** \sa MatrixBase::setZero() */ EIGEN_DEVICE_FUNC - TriangularView& setZero() { return setConstant(Scalar(0)); } + TriangularViewType& setZero() { return setConstant(Scalar(0)); } /** \sa MatrixBase::setOnes() */ EIGEN_DEVICE_FUNC - TriangularView& setOnes() { return setConstant(Scalar(1)); } + TriangularViewType& setOnes() { return setConstant(Scalar(1)); } /** \sa MatrixBase::coeff() * \warning the coordinates must fit into the referenced triangular part @@ -253,7 +380,7 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView inline Scalar coeff(Index row, Index col) const { Base::check_coordinates_internal(row, col); - return m_matrix.coeff(row, col); + return derived().nestedExpression().coeff(row, col); } /** \sa MatrixBase::coeffRef() @@ -262,27 +389,23 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index row, Index col) { + EIGEN_STATIC_ASSERT_LVALUE(TriangularViewType); Base::check_coordinates_internal(row, col); - return m_matrix.const_cast_derived().coeffRef(row, col); + return derived().nestedExpression().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); + TriangularViewType& operator=(const TriangularBase<OtherDerived>& other); template<typename OtherDerived> EIGEN_DEVICE_FUNC - TriangularView& operator=(const MatrixBase<OtherDerived>& other); + TriangularViewType& operator=(const MatrixBase<OtherDerived>& other); EIGEN_DEVICE_FUNC - TriangularView& operator=(const TriangularView& other) - { return *this = other.nestedExpression(); } + TriangularViewType& operator=(const TriangularViewImpl& other) + { return *this = other.derived().nestedExpression(); } template<typename OtherDerived> EIGEN_DEVICE_FUNC @@ -290,378 +413,88 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView 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(); - } + void lazyAssign(const MatrixBase<OtherDerived>& other); /** Efficient triangular matrix times vector/matrix product */ template<typename OtherDerived> EIGEN_DEVICE_FUNC - TriangularProduct<Mode, true, MatrixType, false, OtherDerived, OtherDerived::ColsAtCompileTime==1> + const Product<TriangularViewType,OtherDerived> operator*(const MatrixBase<OtherDerived>& rhs) const { - return TriangularProduct - <Mode, true, MatrixType, false, OtherDerived, OtherDerived::ColsAtCompileTime==1> - (m_matrix, rhs.derived()); + return Product<TriangularViewType,OtherDerived>(derived(), rhs.derived()); } /** Efficient vector/matrix times triangular matrix product */ template<typename OtherDerived> friend EIGEN_DEVICE_FUNC - TriangularProduct<Mode, false, OtherDerived, OtherDerived::RowsAtCompileTime==1, MatrixType, false> - operator*(const MatrixBase<OtherDerived>& lhs, const TriangularView& rhs) + const Product<OtherDerived,TriangularViewType> + operator*(const MatrixBase<OtherDerived>& lhs, const TriangularViewImpl& rhs) { - return TriangularProduct - <Mode, false, OtherDerived, OtherDerived::RowsAtCompileTime==1, MatrixType, false> - (lhs.derived(),rhs.m_matrix); + return Product<OtherDerived,TriangularViewType>(lhs.derived(),rhs.derived()); } template<int Side, typename Other> EIGEN_DEVICE_FUNC - inline const internal::triangular_solve_retval<Side,TriangularView, Other> + inline const internal::triangular_solve_retval<Side,TriangularViewType, 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()); + call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op<Scalar>()); } + // TODO: this overload is ambiguous and it should be deprecated (Gael) 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()); + call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op<Scalar>()); } + template<typename RhsType, typename DstType> 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()); + EIGEN_STRONG_INLINE void _solve_impl(const RhsType &rhs, DstType &dst) const { + if(!(internal::is_same<RhsType,DstType>::value && internal::extract_data(dst) == internal::extract_data(rhs))) + dst = rhs; + this->solveInPlace(dst); } - - 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; + template<typename ProductType> + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE TriangularViewType& _assignProduct(const ProductType& prod, const Scalar& alpha); }; /*************************************************************************** * 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) +TriangularViewImpl<MatrixType, Mode, Dense>::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; + internal::call_assignment_no_alias(derived(), other.derived(), internal::assign_op<Scalar>()); + return derived(); } // FIXME should we keep that possibility template<typename MatrixType, unsigned int Mode> template<typename OtherDerived> -void TriangularView<MatrixType, Mode>::lazyAssign(const MatrixBase<OtherDerived>& other) +void TriangularViewImpl<MatrixType, Mode, Dense>::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()); + internal::call_assignment(derived().noalias(), other.template triangularView<Mode>()); } @@ -669,37 +502,19 @@ void TriangularView<MatrixType, Mode>::lazyAssign(const MatrixBase<OtherDerived> template<typename MatrixType, unsigned int Mode> template<typename OtherDerived> inline TriangularView<MatrixType, Mode>& -TriangularView<MatrixType, Mode>::operator=(const TriangularBase<OtherDerived>& other) +TriangularViewImpl<MatrixType, Mode, Dense>::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; + internal::call_assignment(derived(), other.derived()); + return derived(); } template<typename MatrixType, unsigned int Mode> template<typename OtherDerived> -void TriangularView<MatrixType, Mode>::lazyAssign(const TriangularBase<OtherDerived>& other) +void TriangularViewImpl<MatrixType, Mode, Dense>::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()); + eigen_assert(Mode == int(OtherDerived::Mode)); + internal::call_assignment(derived().noalias(), other.derived()); } /*************************************************************************** @@ -722,27 +537,6 @@ void TriangularBase<Derived>::evalTo(MatrixBase<DenseDerived> &other) const 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 ***************************************************************************/ @@ -767,7 +561,7 @@ template<unsigned int Mode> typename MatrixBase<Derived>::template TriangularViewReturnType<Mode>::Type MatrixBase<Derived>::triangularView() { - return derived(); + return typename TriangularViewReturnType<Mode>::Type(derived()); } /** This is the const version of MatrixBase::triangularView() */ @@ -776,7 +570,7 @@ template<unsigned int Mode> typename MatrixBase<Derived>::template ConstTriangularViewReturnType<Mode>::Type MatrixBase<Derived>::triangularView() const { - return derived(); + return typename ConstTriangularViewReturnType<Mode>::Type(derived()); } /** \returns true if *this is approximately equal to an upper triangular matrix, @@ -831,6 +625,293 @@ bool MatrixBase<Derived>::isLowerTriangular(const RealScalar& prec) const return true; } + +/*************************************************************************** +**************************************************************************** +* Evaluators and Assignment of triangular expressions +*************************************************************************** +***************************************************************************/ + +namespace internal { + + +// TODO currently a triangular expression has the form TriangularView<.,.> +// in the future triangular-ness should be defined by the expression traits +// such that Transpose<TriangularView<.,.> > is valid. (currently TriangularBase::transpose() is overloaded to make it work) +template<typename MatrixType, unsigned int Mode> +struct evaluator_traits<TriangularView<MatrixType,Mode> > +{ + typedef typename storage_kind_to_evaluator_kind<typename MatrixType::StorageKind>::Kind Kind; + typedef typename glue_shapes<typename evaluator_traits<MatrixType>::Shape, TriangularShape>::type Shape; + + // 1 if assignment A = B assumes aliasing when B is of type T and thus B needs to be evaluated into a + // temporary; 0 if not. + static const int AssumeAliasing = 0; +}; + +template<typename MatrixType, unsigned int Mode> +struct unary_evaluator<TriangularView<MatrixType,Mode>, IndexBased> + : evaluator<typename internal::remove_all<MatrixType>::type> +{ + typedef TriangularView<MatrixType,Mode> XprType; + typedef evaluator<typename internal::remove_all<MatrixType>::type> Base; + typedef evaluator<XprType> type; + unary_evaluator(const XprType &xpr) : Base(xpr.nestedExpression()) {} +}; + +// Additional assignment kinds: +struct Triangular2Triangular {}; +struct Triangular2Dense {}; +struct Dense2Triangular {}; + + +template<typename Kernel, unsigned int Mode, int UnrollCount, bool ClearOpposite> struct triangular_assignment_loop; + + +/** \internal Specialization of the dense assignment kernel for triangular matrices. + * The main difference is that the triangular, diagonal, and opposite parts are processed through three different functions. + * \tparam UpLo must be either Lower or Upper + * \tparam Mode must be either 0, UnitDiag, ZeroDiag, or SelfAdjoint + */ +template<int UpLo, int Mode, int SetOpposite, typename DstEvaluatorTypeT, typename SrcEvaluatorTypeT, typename Functor, int Version = Specialized> +class triangular_dense_assignment_kernel : public generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, Version> +{ +protected: + typedef generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, Version> Base; + typedef typename Base::DstXprType DstXprType; + typedef typename Base::SrcXprType SrcXprType; + using Base::m_dst; + using Base::m_src; + using Base::m_functor; +public: + + typedef typename Base::DstEvaluatorType DstEvaluatorType; + typedef typename Base::SrcEvaluatorType SrcEvaluatorType; + typedef typename Base::Scalar Scalar; + typedef typename Base::Index Index; + typedef typename Base::AssignmentTraits AssignmentTraits; + + + EIGEN_DEVICE_FUNC triangular_dense_assignment_kernel(DstEvaluatorType &dst, const SrcEvaluatorType &src, const Functor &func, DstXprType& dstExpr) + : Base(dst, src, func, dstExpr) + {} + +#ifdef EIGEN_INTERNAL_DEBUGGING + EIGEN_DEVICE_FUNC void assignCoeff(Index row, Index col) + { + eigen_internal_assert(row!=col); + Base::assignCoeff(row,col); + } +#else + using Base::assignCoeff; +#endif + + EIGEN_DEVICE_FUNC void assignDiagonalCoeff(Index id) + { + if(Mode==UnitDiag && SetOpposite) m_functor.assignCoeff(m_dst.coeffRef(id,id), Scalar(1)); + else if(Mode==ZeroDiag && SetOpposite) m_functor.assignCoeff(m_dst.coeffRef(id,id), Scalar(0)); + else if(Mode==0) Base::assignCoeff(id,id); + } + + EIGEN_DEVICE_FUNC void assignOppositeCoeff(Index row, Index col) + { + eigen_internal_assert(row!=col); + if(SetOpposite) + m_functor.assignCoeff(m_dst.coeffRef(row,col), Scalar(0)); + } +}; + +template<int Mode, bool SetOpposite, typename DstXprType, typename SrcXprType, typename Functor> +EIGEN_DEVICE_FUNC void call_triangular_assignment_loop(const DstXprType& dst, const SrcXprType& src, const Functor &func) +{ + eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); + + typedef typename evaluator<DstXprType>::type DstEvaluatorType; + typedef typename evaluator<SrcXprType>::type SrcEvaluatorType; + + DstEvaluatorType dstEvaluator(dst); + SrcEvaluatorType srcEvaluator(src); + + typedef triangular_dense_assignment_kernel< Mode&(Lower|Upper),Mode&(UnitDiag|ZeroDiag|SelfAdjoint),SetOpposite, + DstEvaluatorType,SrcEvaluatorType,Functor> Kernel; + Kernel kernel(dstEvaluator, srcEvaluator, func, dst.const_cast_derived()); + + enum { + unroll = DstXprType::SizeAtCompileTime != Dynamic + && SrcEvaluatorType::CoeffReadCost != Dynamic + && DstXprType::SizeAtCompileTime * SrcEvaluatorType::CoeffReadCost / 2 <= EIGEN_UNROLLING_LIMIT + }; + + triangular_assignment_loop<Kernel, Mode, unroll ? int(DstXprType::SizeAtCompileTime) : Dynamic, SetOpposite>::run(kernel); +} + +template<int Mode, bool SetOpposite, typename DstXprType, typename SrcXprType> +EIGEN_DEVICE_FUNC void call_triangular_assignment_loop(const DstXprType& dst, const SrcXprType& src) +{ + call_triangular_assignment_loop<Mode,SetOpposite>(dst, src, internal::assign_op<typename DstXprType::Scalar>()); +} + +template<> struct AssignmentKind<TriangularShape,TriangularShape> { typedef Triangular2Triangular Kind; }; +template<> struct AssignmentKind<DenseShape,TriangularShape> { typedef Triangular2Dense Kind; }; +template<> struct AssignmentKind<TriangularShape,DenseShape> { typedef Dense2Triangular Kind; }; + + +template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar> +struct Assignment<DstXprType, SrcXprType, Functor, Triangular2Triangular, Scalar> +{ + EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func) + { + eigen_assert(int(DstXprType::Mode) == int(SrcXprType::Mode)); + + call_triangular_assignment_loop<DstXprType::Mode, false>(dst, src, func); + } +}; + +template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar> +struct Assignment<DstXprType, SrcXprType, Functor, Triangular2Dense, Scalar> +{ + EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func) + { + call_triangular_assignment_loop<SrcXprType::Mode, (SrcXprType::Mode&SelfAdjoint)==0>(dst, src, func); + } +}; + +template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar> +struct Assignment<DstXprType, SrcXprType, Functor, Dense2Triangular, Scalar> +{ + EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func) + { + call_triangular_assignment_loop<DstXprType::Mode, false>(dst, src, func); + } +}; + + +template<typename Kernel, unsigned int Mode, int UnrollCount, bool SetOpposite> +struct triangular_assignment_loop +{ + // FIXME: this is not very clean, perhaps this information should be provided by the kernel? + typedef typename Kernel::DstEvaluatorType DstEvaluatorType; + typedef typename DstEvaluatorType::XprType DstXprType; + + enum { + col = (UnrollCount-1) / DstXprType::RowsAtCompileTime, + row = (UnrollCount-1) % DstXprType::RowsAtCompileTime + }; + + typedef typename Kernel::Scalar Scalar; + + EIGEN_DEVICE_FUNC + static inline void run(Kernel &kernel) + { + triangular_assignment_loop<Kernel, Mode, UnrollCount-1, SetOpposite>::run(kernel); + + if(row==col) + kernel.assignDiagonalCoeff(row); + else if( ((Mode&Lower) && row>col) || ((Mode&Upper) && row<col) ) + kernel.assignCoeff(row,col); + else if(SetOpposite) + kernel.assignOppositeCoeff(row,col); + } +}; + +// prevent buggy user code from causing an infinite recursion +template<typename Kernel, unsigned int Mode, bool SetOpposite> +struct triangular_assignment_loop<Kernel, Mode, 0, SetOpposite> +{ + EIGEN_DEVICE_FUNC + static inline void run(Kernel &) {} +}; + + + +// TODO: experiment with a recursive assignment procedure splitting the current +// triangular part into one rectangular and two triangular parts. + + +template<typename Kernel, unsigned int Mode, bool SetOpposite> +struct triangular_assignment_loop<Kernel, Mode, Dynamic, SetOpposite> +{ + typedef typename Kernel::Index Index; + typedef typename Kernel::Scalar Scalar; + EIGEN_DEVICE_FUNC + static inline void run(Kernel &kernel) + { + for(Index j = 0; j < kernel.cols(); ++j) + { + Index maxi = (std::min)(j, kernel.rows()); + Index i = 0; + if (((Mode&Lower) && SetOpposite) || (Mode&Upper)) + { + for(; i < maxi; ++i) + if(Mode&Upper) kernel.assignCoeff(i, j); + else kernel.assignOppositeCoeff(i, j); + } + else + i = maxi; + + if(i<kernel.rows()) // then i==j + kernel.assignDiagonalCoeff(i++); + + if (((Mode&Upper) && SetOpposite) || (Mode&Lower)) + { + for(; i < kernel.rows(); ++i) + if(Mode&Lower) kernel.assignCoeff(i, j); + else kernel.assignOppositeCoeff(i, j); + } + } + } +}; + +} // end namespace internal + +/** 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 +{ + other.derived().resize(this->rows(), this->cols()); + internal::call_triangular_assignment_loop<Derived::Mode,(Derived::Mode&SelfAdjoint)==0 /* SetOpposite */>(other.derived(), derived().nestedExpression()); +} + +namespace internal { + +// Triangular = Product +template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar> +struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::assign_op<Scalar>, Dense2Triangular, Scalar> +{ + typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType; + static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &) + { + dst.setZero(); + dst._assignProduct(src, 1); + } +}; + +// Triangular += Product +template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar> +struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::add_assign_op<Scalar>, Dense2Triangular, Scalar> +{ + typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType; + static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<Scalar> &) + { + dst._assignProduct(src, 1); + } +}; + +// Triangular -= Product +template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar> +struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::sub_assign_op<Scalar>, Dense2Triangular, Scalar> +{ + typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType; + static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<Scalar> &) + { + dst._assignProduct(src, -1); + } +}; + +} // end namespace internal + } // end namespace Eigen #endif // EIGEN_TRIANGULARMATRIX_H |