Diff: src/Core/VectorwiseOp.h
- Revision:
- 0:13a5d365ba16
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Core/VectorwiseOp.h Thu Oct 13 04:07:23 2016 +0000
@@ -0,0 +1,642 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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_PARTIAL_REDUX_H
+#define EIGEN_PARTIAL_REDUX_H
+
+namespace Eigen {
+
+/** \class PartialReduxExpr
+ * \ingroup Core_Module
+ *
+ * \brief Generic expression of a partially reduxed matrix
+ *
+ * \tparam MatrixType the type of the matrix we are applying the redux operation
+ * \tparam MemberOp type of the member functor
+ * \tparam Direction indicates the direction of the redux (#Vertical or #Horizontal)
+ *
+ * This class represents an expression of a partial redux operator of a matrix.
+ * It is the return type of some VectorwiseOp functions,
+ * and most of the time this is the only way it is used.
+ *
+ * \sa class VectorwiseOp
+ */
+
+template< typename MatrixType, typename MemberOp, int Direction>
+class PartialReduxExpr;
+
+namespace internal {
+template<typename MatrixType, typename MemberOp, int Direction>
+struct traits<PartialReduxExpr<MatrixType, MemberOp, Direction> >
+ : traits<MatrixType>
+{
+ typedef typename MemberOp::result_type Scalar;
+ typedef typename traits<MatrixType>::StorageKind StorageKind;
+ typedef typename traits<MatrixType>::XprKind XprKind;
+ typedef typename MatrixType::Scalar InputScalar;
+ typedef typename nested<MatrixType>::type MatrixTypeNested;
+ typedef typename remove_all<MatrixTypeNested>::type _MatrixTypeNested;
+ enum {
+ RowsAtCompileTime = Direction==Vertical ? 1 : MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = Direction==Vertical ? 1 : MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::MaxColsAtCompileTime,
+ Flags0 = (unsigned int)_MatrixTypeNested::Flags & HereditaryBits,
+ Flags = (Flags0 & ~RowMajorBit) | (RowsAtCompileTime == 1 ? RowMajorBit : 0),
+ TraversalSize = Direction==Vertical ? MatrixType::RowsAtCompileTime : MatrixType::ColsAtCompileTime
+ };
+ #if EIGEN_GNUC_AT_LEAST(3,4)
+ typedef typename MemberOp::template Cost<InputScalar,int(TraversalSize)> CostOpType;
+ #else
+ typedef typename MemberOp::template Cost<InputScalar,TraversalSize> CostOpType;
+ #endif
+ enum {
+ CoeffReadCost = TraversalSize==Dynamic ? Dynamic
+ : TraversalSize * traits<_MatrixTypeNested>::CoeffReadCost + int(CostOpType::value)
+ };
+};
+}
+
+template< typename MatrixType, typename MemberOp, int Direction>
+class PartialReduxExpr : internal::no_assignment_operator,
+ public internal::dense_xpr_base< PartialReduxExpr<MatrixType, MemberOp, Direction> >::type
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<PartialReduxExpr>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(PartialReduxExpr)
+ typedef typename internal::traits<PartialReduxExpr>::MatrixTypeNested MatrixTypeNested;
+ typedef typename internal::traits<PartialReduxExpr>::_MatrixTypeNested _MatrixTypeNested;
+
+ PartialReduxExpr(const MatrixType& mat, const MemberOp& func = MemberOp())
+ : m_matrix(mat), m_functor(func) {}
+
+ Index rows() const { return (Direction==Vertical ? 1 : m_matrix.rows()); }
+ Index cols() const { return (Direction==Horizontal ? 1 : m_matrix.cols()); }
+
+ EIGEN_STRONG_INLINE const Scalar coeff(Index i, Index j) const
+ {
+ if (Direction==Vertical)
+ return m_functor(m_matrix.col(j));
+ else
+ return m_functor(m_matrix.row(i));
+ }
+
+ const Scalar coeff(Index index) const
+ {
+ if (Direction==Vertical)
+ return m_functor(m_matrix.col(index));
+ else
+ return m_functor(m_matrix.row(index));
+ }
+
+ protected:
+ MatrixTypeNested m_matrix;
+ const MemberOp m_functor;
+};
+
+#define EIGEN_MEMBER_FUNCTOR(MEMBER,COST) \
+ template <typename ResultType> \
+ struct member_##MEMBER { \
+ EIGEN_EMPTY_STRUCT_CTOR(member_##MEMBER) \
+ typedef ResultType result_type; \
+ template<typename Scalar, int Size> struct Cost \
+ { enum { value = COST }; }; \
+ template<typename XprType> \
+ EIGEN_STRONG_INLINE ResultType operator()(const XprType& mat) const \
+ { return mat.MEMBER(); } \
+ }
+
+namespace internal {
+
+EIGEN_MEMBER_FUNCTOR(squaredNorm, Size * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(norm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(stableNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(blueNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(hypotNorm, (Size-1) * functor_traits<scalar_hypot_op<Scalar> >::Cost );
+EIGEN_MEMBER_FUNCTOR(sum, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(mean, (Size-1)*NumTraits<Scalar>::AddCost + NumTraits<Scalar>::MulCost);
+EIGEN_MEMBER_FUNCTOR(minCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(maxCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(all, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(any, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(count, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(prod, (Size-1)*NumTraits<Scalar>::MulCost);
+
+
+template <typename BinaryOp, typename Scalar>
+struct member_redux {
+ typedef typename result_of<
+ BinaryOp(Scalar)
+ >::type result_type;
+ template<typename _Scalar, int Size> struct Cost
+ { enum { value = (Size-1) * functor_traits<BinaryOp>::Cost }; };
+ member_redux(const BinaryOp func) : m_functor(func) {}
+ template<typename Derived>
+ inline result_type operator()(const DenseBase<Derived>& mat) const
+ { return mat.redux(m_functor); }
+ const BinaryOp m_functor;
+};
+}
+
+/** \class VectorwiseOp
+ * \ingroup Core_Module
+ *
+ * \brief Pseudo expression providing partial reduction operations
+ *
+ * \param ExpressionType the type of the object on which to do partial reductions
+ * \param Direction indicates the direction of the redux (#Vertical or #Horizontal)
+ *
+ * This class represents a pseudo expression with partial reduction features.
+ * It is the return type of DenseBase::colwise() and DenseBase::rowwise()
+ * and most of the time this is the only way it is used.
+ *
+ * Example: \include MatrixBase_colwise.cpp
+ * Output: \verbinclude MatrixBase_colwise.out
+ *
+ * \sa DenseBase::colwise(), DenseBase::rowwise(), class PartialReduxExpr
+ */
+template<typename ExpressionType, int Direction> class VectorwiseOp
+{
+ public:
+
+ typedef typename ExpressionType::Scalar Scalar;
+ typedef typename ExpressionType::RealScalar RealScalar;
+ typedef typename ExpressionType::Index Index;
+ typedef typename internal::conditional<internal::must_nest_by_value<ExpressionType>::ret,
+ ExpressionType, ExpressionType&>::type ExpressionTypeNested;
+ typedef typename internal::remove_all<ExpressionTypeNested>::type ExpressionTypeNestedCleaned;
+
+ template<template<typename _Scalar> class Functor,
+ typename Scalar=typename internal::traits<ExpressionType>::Scalar> struct ReturnType
+ {
+ typedef PartialReduxExpr<ExpressionType,
+ Functor<Scalar>,
+ Direction
+ > Type;
+ };
+
+ template<typename BinaryOp> struct ReduxReturnType
+ {
+ typedef PartialReduxExpr<ExpressionType,
+ internal::member_redux<BinaryOp,typename internal::traits<ExpressionType>::Scalar>,
+ Direction
+ > Type;
+ };
+
+ enum {
+ IsVertical = (Direction==Vertical) ? 1 : 0,
+ IsHorizontal = (Direction==Horizontal) ? 1 : 0
+ };
+
+ protected:
+
+ /** \internal
+ * \returns the i-th subvector according to the \c Direction */
+ typedef typename internal::conditional<Direction==Vertical,
+ typename ExpressionType::ColXpr,
+ typename ExpressionType::RowXpr>::type SubVector;
+ SubVector subVector(Index i)
+ {
+ return SubVector(m_matrix.derived(),i);
+ }
+
+ /** \internal
+ * \returns the number of subvectors in the direction \c Direction */
+ Index subVectors() const
+ { return Direction==Vertical?m_matrix.cols():m_matrix.rows(); }
+
+ template<typename OtherDerived> struct ExtendedType {
+ typedef Replicate<OtherDerived,
+ Direction==Vertical ? 1 : ExpressionType::RowsAtCompileTime,
+ Direction==Horizontal ? 1 : ExpressionType::ColsAtCompileTime> Type;
+ };
+
+ /** \internal
+ * Replicates a vector to match the size of \c *this */
+ template<typename OtherDerived>
+ typename ExtendedType<OtherDerived>::Type
+ extendedTo(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(Direction==Vertical, OtherDerived::MaxColsAtCompileTime==1),
+ YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED)
+ EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(Direction==Horizontal, OtherDerived::MaxRowsAtCompileTime==1),
+ YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED)
+ return typename ExtendedType<OtherDerived>::Type
+ (other.derived(),
+ Direction==Vertical ? 1 : m_matrix.rows(),
+ Direction==Horizontal ? 1 : m_matrix.cols());
+ }
+
+ template<typename OtherDerived> struct OppositeExtendedType {
+ typedef Replicate<OtherDerived,
+ Direction==Horizontal ? 1 : ExpressionType::RowsAtCompileTime,
+ Direction==Vertical ? 1 : ExpressionType::ColsAtCompileTime> Type;
+ };
+
+ /** \internal
+ * Replicates a vector in the opposite direction to match the size of \c *this */
+ template<typename OtherDerived>
+ typename OppositeExtendedType<OtherDerived>::Type
+ extendedToOpposite(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(Direction==Horizontal, OtherDerived::MaxColsAtCompileTime==1),
+ YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED)
+ EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(Direction==Vertical, OtherDerived::MaxRowsAtCompileTime==1),
+ YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED)
+ return typename OppositeExtendedType<OtherDerived>::Type
+ (other.derived(),
+ Direction==Horizontal ? 1 : m_matrix.rows(),
+ Direction==Vertical ? 1 : m_matrix.cols());
+ }
+
+ public:
+
+ inline VectorwiseOp(ExpressionType& matrix) : m_matrix(matrix) {}
+
+ /** \internal */
+ inline const ExpressionType& _expression() const { return m_matrix; }
+
+ /** \returns a row or column vector expression of \c *this reduxed by \a func
+ *
+ * The template parameter \a BinaryOp is the type of the functor
+ * of the custom redux operator. Note that func must be an associative operator.
+ *
+ * \sa class VectorwiseOp, DenseBase::colwise(), DenseBase::rowwise()
+ */
+ template<typename BinaryOp>
+ const typename ReduxReturnType<BinaryOp>::Type
+ redux(const BinaryOp& func = BinaryOp()) const
+ { return typename ReduxReturnType<BinaryOp>::Type(_expression(), func); }
+
+ /** \returns a row (or column) vector expression of the smallest coefficient
+ * of each column (or row) of the referenced expression.
+ *
+ * \warning the result is undefined if \c *this contains NaN.
+ *
+ * Example: \include PartialRedux_minCoeff.cpp
+ * Output: \verbinclude PartialRedux_minCoeff.out
+ *
+ * \sa DenseBase::minCoeff() */
+ const typename ReturnType<internal::member_minCoeff>::Type minCoeff() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression of the largest coefficient
+ * of each column (or row) of the referenced expression.
+ *
+ * \warning the result is undefined if \c *this contains NaN.
+ *
+ * Example: \include PartialRedux_maxCoeff.cpp
+ * Output: \verbinclude PartialRedux_maxCoeff.out
+ *
+ * \sa DenseBase::maxCoeff() */
+ const typename ReturnType<internal::member_maxCoeff>::Type maxCoeff() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression of the squared norm
+ * of each column (or row) of the referenced expression.
+ *
+ * Example: \include PartialRedux_squaredNorm.cpp
+ * Output: \verbinclude PartialRedux_squaredNorm.out
+ *
+ * \sa DenseBase::squaredNorm() */
+ const typename ReturnType<internal::member_squaredNorm,RealScalar>::Type squaredNorm() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression of the norm
+ * of each column (or row) of the referenced expression.
+ *
+ * Example: \include PartialRedux_norm.cpp
+ * Output: \verbinclude PartialRedux_norm.out
+ *
+ * \sa DenseBase::norm() */
+ const typename ReturnType<internal::member_norm,RealScalar>::Type norm() const
+ { return _expression(); }
+
+
+ /** \returns a row (or column) vector expression of the norm
+ * of each column (or row) of the referenced expression, using
+ * blue's algorithm.
+ *
+ * \sa DenseBase::blueNorm() */
+ const typename ReturnType<internal::member_blueNorm,RealScalar>::Type blueNorm() const
+ { return _expression(); }
+
+
+ /** \returns a row (or column) vector expression of the norm
+ * of each column (or row) of the referenced expression, avoiding
+ * underflow and overflow.
+ *
+ * \sa DenseBase::stableNorm() */
+ const typename ReturnType<internal::member_stableNorm,RealScalar>::Type stableNorm() const
+ { return _expression(); }
+
+
+ /** \returns a row (or column) vector expression of the norm
+ * of each column (or row) of the referenced expression, avoiding
+ * underflow and overflow using a concatenation of hypot() calls.
+ *
+ * \sa DenseBase::hypotNorm() */
+ const typename ReturnType<internal::member_hypotNorm,RealScalar>::Type hypotNorm() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression of the sum
+ * of each column (or row) of the referenced expression.
+ *
+ * Example: \include PartialRedux_sum.cpp
+ * Output: \verbinclude PartialRedux_sum.out
+ *
+ * \sa DenseBase::sum() */
+ const typename ReturnType<internal::member_sum>::Type sum() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression of the mean
+ * of each column (or row) of the referenced expression.
+ *
+ * \sa DenseBase::mean() */
+ const typename ReturnType<internal::member_mean>::Type mean() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression representing
+ * whether \b all coefficients of each respective column (or row) are \c true.
+ *
+ * \sa DenseBase::all() */
+ const typename ReturnType<internal::member_all>::Type all() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression representing
+ * whether \b at \b least one coefficient of each respective column (or row) is \c true.
+ *
+ * \sa DenseBase::any() */
+ const typename ReturnType<internal::member_any>::Type any() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression representing
+ * the number of \c true coefficients of each respective column (or row).
+ *
+ * Example: \include PartialRedux_count.cpp
+ * Output: \verbinclude PartialRedux_count.out
+ *
+ * \sa DenseBase::count() */
+ const PartialReduxExpr<ExpressionType, internal::member_count<Index>, Direction> count() const
+ { return _expression(); }
+
+ /** \returns a row (or column) vector expression of the product
+ * of each column (or row) of the referenced expression.
+ *
+ * Example: \include PartialRedux_prod.cpp
+ * Output: \verbinclude PartialRedux_prod.out
+ *
+ * \sa DenseBase::prod() */
+ const typename ReturnType<internal::member_prod>::Type prod() const
+ { return _expression(); }
+
+
+ /** \returns a matrix expression
+ * where each column (or row) are reversed.
+ *
+ * Example: \include Vectorwise_reverse.cpp
+ * Output: \verbinclude Vectorwise_reverse.out
+ *
+ * \sa DenseBase::reverse() */
+ const Reverse<ExpressionType, Direction> reverse() const
+ { return Reverse<ExpressionType, Direction>( _expression() ); }
+
+ typedef Replicate<ExpressionType,Direction==Vertical?Dynamic:1,Direction==Horizontal?Dynamic:1> ReplicateReturnType;
+ const ReplicateReturnType replicate(Index factor) const;
+
+ /**
+ * \return an expression of the replication of each column (or row) of \c *this
+ *
+ * Example: \include DirectionWise_replicate.cpp
+ * Output: \verbinclude DirectionWise_replicate.out
+ *
+ * \sa VectorwiseOp::replicate(Index), DenseBase::replicate(), class Replicate
+ */
+ // NOTE implemented here because of sunstudio's compilation errors
+ template<int Factor> const Replicate<ExpressionType,(IsVertical?Factor:1),(IsHorizontal?Factor:1)>
+ replicate(Index factor = Factor) const
+ {
+ return Replicate<ExpressionType,Direction==Vertical?Factor:1,Direction==Horizontal?Factor:1>
+ (_expression(),Direction==Vertical?factor:1,Direction==Horizontal?factor:1);
+ }
+
+/////////// Artithmetic operators ///////////
+
+ /** Copies the vector \a other to each subvector of \c *this */
+ template<typename OtherDerived>
+ ExpressionType& operator=(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ //eigen_assert((m_matrix.isNull()) == (other.isNull())); FIXME
+ return const_cast<ExpressionType&>(m_matrix = extendedTo(other.derived()));
+ }
+
+ /** Adds the vector \a other to each subvector of \c *this */
+ template<typename OtherDerived>
+ ExpressionType& operator+=(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return const_cast<ExpressionType&>(m_matrix += extendedTo(other.derived()));
+ }
+
+ /** Substracts the vector \a other to each subvector of \c *this */
+ template<typename OtherDerived>
+ ExpressionType& operator-=(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return const_cast<ExpressionType&>(m_matrix -= extendedTo(other.derived()));
+ }
+
+ /** Multiples each subvector of \c *this by the vector \a other */
+ template<typename OtherDerived>
+ ExpressionType& operator*=(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ m_matrix *= extendedTo(other.derived());
+ return const_cast<ExpressionType&>(m_matrix);
+ }
+
+ /** Divides each subvector of \c *this by the vector \a other */
+ template<typename OtherDerived>
+ ExpressionType& operator/=(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ m_matrix /= extendedTo(other.derived());
+ return const_cast<ExpressionType&>(m_matrix);
+ }
+
+ /** Returns the expression of the sum of the vector \a other to each subvector of \c *this */
+ template<typename OtherDerived> EIGEN_STRONG_INLINE
+ CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
+ const ExpressionTypeNestedCleaned,
+ const typename ExtendedType<OtherDerived>::Type>
+ operator+(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return m_matrix + extendedTo(other.derived());
+ }
+
+ /** Returns the expression of the difference between each subvector of \c *this and the vector \a other */
+ template<typename OtherDerived>
+ CwiseBinaryOp<internal::scalar_difference_op<Scalar>,
+ const ExpressionTypeNestedCleaned,
+ const typename ExtendedType<OtherDerived>::Type>
+ operator-(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return m_matrix - extendedTo(other.derived());
+ }
+
+ /** Returns the expression where each subvector is the product of the vector \a other
+ * by the corresponding subvector of \c *this */
+ template<typename OtherDerived> EIGEN_STRONG_INLINE
+ CwiseBinaryOp<internal::scalar_product_op<Scalar>,
+ const ExpressionTypeNestedCleaned,
+ const typename ExtendedType<OtherDerived>::Type>
+ operator*(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return m_matrix * extendedTo(other.derived());
+ }
+
+ /** Returns the expression where each subvector is the quotient of the corresponding
+ * subvector of \c *this by the vector \a other */
+ template<typename OtherDerived>
+ CwiseBinaryOp<internal::scalar_quotient_op<Scalar>,
+ const ExpressionTypeNestedCleaned,
+ const typename ExtendedType<OtherDerived>::Type>
+ operator/(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return m_matrix / extendedTo(other.derived());
+ }
+
+ /** \returns an expression where each column of row of the referenced matrix are normalized.
+ * The referenced matrix is \b not modified.
+ * \sa MatrixBase::normalized(), normalize()
+ */
+ CwiseBinaryOp<internal::scalar_quotient_op<Scalar>,
+ const ExpressionTypeNestedCleaned,
+ const typename OppositeExtendedType<typename ReturnType<internal::member_norm,RealScalar>::Type>::Type>
+ normalized() const { return m_matrix.cwiseQuotient(extendedToOpposite(this->norm())); }
+
+
+ /** Normalize in-place each row or columns of the referenced matrix.
+ * \sa MatrixBase::normalize(), normalized()
+ */
+ void normalize() {
+ m_matrix = this->normalized();
+ }
+
+/////////// Geometry module ///////////
+
+ #if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
+ Homogeneous<ExpressionType,Direction> homogeneous() const;
+ #endif
+
+ typedef typename ExpressionType::PlainObject CrossReturnType;
+ template<typename OtherDerived>
+ const CrossReturnType cross(const MatrixBase<OtherDerived>& other) const;
+
+ enum {
+ HNormalized_Size = Direction==Vertical ? internal::traits<ExpressionType>::RowsAtCompileTime
+ : internal::traits<ExpressionType>::ColsAtCompileTime,
+ HNormalized_SizeMinusOne = HNormalized_Size==Dynamic ? Dynamic : HNormalized_Size-1
+ };
+ typedef Block<const ExpressionType,
+ Direction==Vertical ? int(HNormalized_SizeMinusOne)
+ : int(internal::traits<ExpressionType>::RowsAtCompileTime),
+ Direction==Horizontal ? int(HNormalized_SizeMinusOne)
+ : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
+ HNormalized_Block;
+ typedef Block<const ExpressionType,
+ Direction==Vertical ? 1 : int(internal::traits<ExpressionType>::RowsAtCompileTime),
+ Direction==Horizontal ? 1 : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
+ HNormalized_Factors;
+ typedef CwiseBinaryOp<internal::scalar_quotient_op<typename internal::traits<ExpressionType>::Scalar>,
+ const HNormalized_Block,
+ const Replicate<HNormalized_Factors,
+ Direction==Vertical ? HNormalized_SizeMinusOne : 1,
+ Direction==Horizontal ? HNormalized_SizeMinusOne : 1> >
+ HNormalizedReturnType;
+
+ const HNormalizedReturnType hnormalized() const;
+
+ protected:
+ ExpressionTypeNested m_matrix;
+};
+
+/** \returns a VectorwiseOp wrapper of *this providing additional partial reduction operations
+ *
+ * Example: \include MatrixBase_colwise.cpp
+ * Output: \verbinclude MatrixBase_colwise.out
+ *
+ * \sa rowwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
+ */
+template<typename Derived>
+inline const typename DenseBase<Derived>::ConstColwiseReturnType
+DenseBase<Derived>::colwise() const
+{
+ return derived();
+}
+
+/** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
+ *
+ * \sa rowwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
+ */
+template<typename Derived>
+inline typename DenseBase<Derived>::ColwiseReturnType
+DenseBase<Derived>::colwise()
+{
+ return derived();
+}
+
+/** \returns a VectorwiseOp wrapper of *this providing additional partial reduction operations
+ *
+ * Example: \include MatrixBase_rowwise.cpp
+ * Output: \verbinclude MatrixBase_rowwise.out
+ *
+ * \sa colwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
+ */
+template<typename Derived>
+inline const typename DenseBase<Derived>::ConstRowwiseReturnType
+DenseBase<Derived>::rowwise() const
+{
+ return derived();
+}
+
+/** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
+ *
+ * \sa colwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
+ */
+template<typename Derived>
+inline typename DenseBase<Derived>::RowwiseReturnType
+DenseBase<Derived>::rowwise()
+{
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_PARTIAL_REDUX_H
\ No newline at end of file