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// This file is part of Eigen, a lightweight C++ template library
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// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
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// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#ifndef EIGEN_PARTIAL_REDUX_H
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#define EIGEN_PARTIAL_REDUX_H
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/** \class PartialReduxExpr
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* \ingroup Core_Module
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* \brief Generic expression of a partially reduxed matrix
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* \tparam MatrixType the type of the matrix we are applying the redux operation
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* \tparam MemberOp type of the member functor
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* \tparam Direction indicates the direction of the redux (#Vertical or #Horizontal)
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* This class represents an expression of a partial redux operator of a matrix.
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* It is the return type of some VectorwiseOp functions,
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* and most of the time this is the only way it is used.
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* \sa class VectorwiseOp
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template< typename MatrixType, typename MemberOp, int Direction>
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class PartialReduxExpr;
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template<typename MatrixType, typename MemberOp, int Direction>
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struct traits<PartialReduxExpr<MatrixType, MemberOp, Direction> >
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typedef typename MemberOp::result_type Scalar;
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typedef typename traits<MatrixType>::StorageKind StorageKind;
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typedef typename traits<MatrixType>::XprKind XprKind;
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typedef typename MatrixType::Scalar InputScalar;
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typedef typename nested<MatrixType>::type MatrixTypeNested;
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typedef typename remove_all<MatrixTypeNested>::type _MatrixTypeNested;
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RowsAtCompileTime = Direction==Vertical ? 1 : MatrixType::RowsAtCompileTime,
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ColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::ColsAtCompileTime,
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MaxRowsAtCompileTime = Direction==Vertical ? 1 : MatrixType::MaxRowsAtCompileTime,
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MaxColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::MaxColsAtCompileTime,
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Flags0 = (unsigned int)_MatrixTypeNested::Flags & HereditaryBits,
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Flags = (Flags0 & ~RowMajorBit) | (RowsAtCompileTime == 1 ? RowMajorBit : 0),
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TraversalSize = Direction==Vertical ? RowsAtCompileTime : ColsAtCompileTime
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#if EIGEN_GNUC_AT_LEAST(3,4)
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typedef typename MemberOp::template Cost<InputScalar,int(TraversalSize)> CostOpType;
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typedef typename MemberOp::template Cost<InputScalar,TraversalSize> CostOpType;
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CoeffReadCost = TraversalSize * traits<_MatrixTypeNested>::CoeffReadCost + int(CostOpType::value)
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template< typename MatrixType, typename MemberOp, int Direction>
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class PartialReduxExpr : internal::no_assignment_operator,
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public internal::dense_xpr_base< PartialReduxExpr<MatrixType, MemberOp, Direction> >::type
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typedef typename internal::dense_xpr_base<PartialReduxExpr>::type Base;
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EIGEN_DENSE_PUBLIC_INTERFACE(PartialReduxExpr)
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typedef typename internal::traits<PartialReduxExpr>::MatrixTypeNested MatrixTypeNested;
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typedef typename internal::traits<PartialReduxExpr>::_MatrixTypeNested _MatrixTypeNested;
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PartialReduxExpr(const MatrixType& mat, const MemberOp& func = MemberOp())
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: m_matrix(mat), m_functor(func) {}
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Index rows() const { return (Direction==Vertical ? 1 : m_matrix.rows()); }
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Index cols() const { return (Direction==Horizontal ? 1 : m_matrix.cols()); }
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EIGEN_STRONG_INLINE const Scalar coeff(Index i, Index j) const
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if (Direction==Vertical)
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return m_functor(m_matrix.col(j));
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return m_functor(m_matrix.row(i));
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const Scalar coeff(Index index) const
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if (Direction==Vertical)
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return m_functor(m_matrix.col(index));
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return m_functor(m_matrix.row(index));
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const MatrixTypeNested m_matrix;
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const MemberOp m_functor;
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#define EIGEN_MEMBER_FUNCTOR(MEMBER,COST) \
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template <typename ResultType> \
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struct member_##MEMBER { \
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EIGEN_EMPTY_STRUCT_CTOR(member_##MEMBER) \
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typedef ResultType result_type; \
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template<typename Scalar, int Size> struct Cost \
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{ enum { value = COST }; }; \
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template<typename XprType> \
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EIGEN_STRONG_INLINE ResultType operator()(const XprType& mat) const \
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{ return mat.MEMBER(); } \
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EIGEN_MEMBER_FUNCTOR(squaredNorm, Size * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
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EIGEN_MEMBER_FUNCTOR(norm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
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EIGEN_MEMBER_FUNCTOR(stableNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
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EIGEN_MEMBER_FUNCTOR(blueNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
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EIGEN_MEMBER_FUNCTOR(hypotNorm, (Size-1) * functor_traits<scalar_hypot_op<Scalar> >::Cost );
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EIGEN_MEMBER_FUNCTOR(sum, (Size-1)*NumTraits<Scalar>::AddCost);
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EIGEN_MEMBER_FUNCTOR(mean, (Size-1)*NumTraits<Scalar>::AddCost + NumTraits<Scalar>::MulCost);
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EIGEN_MEMBER_FUNCTOR(minCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
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EIGEN_MEMBER_FUNCTOR(maxCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
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EIGEN_MEMBER_FUNCTOR(all, (Size-1)*NumTraits<Scalar>::AddCost);
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EIGEN_MEMBER_FUNCTOR(any, (Size-1)*NumTraits<Scalar>::AddCost);
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EIGEN_MEMBER_FUNCTOR(count, (Size-1)*NumTraits<Scalar>::AddCost);
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EIGEN_MEMBER_FUNCTOR(prod, (Size-1)*NumTraits<Scalar>::MulCost);
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template <typename BinaryOp, typename Scalar>
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struct member_redux {
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typedef typename result_of<
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template<typename _Scalar, int Size> struct Cost
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{ enum { value = (Size-1) * functor_traits<BinaryOp>::Cost }; };
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member_redux(const BinaryOp func) : m_functor(func) {}
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template<typename Derived>
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inline result_type operator()(const DenseBase<Derived>& mat) const
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{ return mat.redux(m_functor); }
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const BinaryOp m_functor;
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/** \class VectorwiseOp
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* \ingroup Core_Module
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* \brief Pseudo expression providing partial reduction operations
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* \param ExpressionType the type of the object on which to do partial reductions
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* \param Direction indicates the direction of the redux (#Vertical or #Horizontal)
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* This class represents a pseudo expression with partial reduction features.
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* It is the return type of DenseBase::colwise() and DenseBase::rowwise()
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* and most of the time this is the only way it is used.
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* Example: \include MatrixBase_colwise.cpp
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* Output: \verbinclude MatrixBase_colwise.out
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* \sa DenseBase::colwise(), DenseBase::rowwise(), class PartialReduxExpr
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template<typename ExpressionType, int Direction> class VectorwiseOp
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typedef typename ExpressionType::Scalar Scalar;
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typedef typename ExpressionType::RealScalar RealScalar;
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typedef typename ExpressionType::Index Index;
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typedef typename internal::conditional<internal::must_nest_by_value<ExpressionType>::ret,
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ExpressionType, ExpressionType&>::type ExpressionTypeNested;
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typedef typename internal::remove_all<ExpressionTypeNested>::type ExpressionTypeNestedCleaned;
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template<template<typename _Scalar> class Functor,
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typename Scalar=typename internal::traits<ExpressionType>::Scalar> struct ReturnType
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typedef PartialReduxExpr<ExpressionType,
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template<typename BinaryOp> struct ReduxReturnType
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typedef PartialReduxExpr<ExpressionType,
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internal::member_redux<BinaryOp,typename internal::traits<ExpressionType>::Scalar>,
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IsVertical = (Direction==Vertical) ? 1 : 0,
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IsHorizontal = (Direction==Horizontal) ? 1 : 0
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* \returns the i-th subvector according to the \c Direction */
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typedef typename internal::conditional<Direction==Vertical,
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typename ExpressionType::ColXpr,
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typename ExpressionType::RowXpr>::type SubVector;
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SubVector subVector(Index i)
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return SubVector(m_matrix.derived(),i);
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* \returns the number of subvectors in the direction \c Direction */
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Index subVectors() const
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{ return Direction==Vertical?m_matrix.cols():m_matrix.rows(); }
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template<typename OtherDerived> struct ExtendedType {
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typedef Replicate<OtherDerived,
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Direction==Vertical ? 1 : ExpressionType::RowsAtCompileTime,
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Direction==Horizontal ? 1 : ExpressionType::ColsAtCompileTime> Type;
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* Replicates a vector to match the size of \c *this */
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template<typename OtherDerived>
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typename ExtendedType<OtherDerived>::Type
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extendedTo(const DenseBase<OtherDerived>& other) const
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived);
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return typename ExtendedType<OtherDerived>::Type
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Direction==Vertical ? 1 : m_matrix.rows(),
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Direction==Horizontal ? 1 : m_matrix.cols());
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inline VectorwiseOp(ExpressionType& matrix) : m_matrix(matrix) {}
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inline const ExpressionType& _expression() const { return m_matrix; }
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/** \returns a row or column vector expression of \c *this reduxed by \a func
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* The template parameter \a BinaryOp is the type of the functor
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* of the custom redux operator. Note that func must be an associative operator.
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* \sa class VectorwiseOp, DenseBase::colwise(), DenseBase::rowwise()
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template<typename BinaryOp>
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const typename ReduxReturnType<BinaryOp>::Type
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redux(const BinaryOp& func = BinaryOp()) const
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{ return typename ReduxReturnType<BinaryOp>::Type(_expression(), func); }
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/** \returns a row (or column) vector expression of the smallest coefficient
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* of each column (or row) of the referenced expression.
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* Example: \include PartialRedux_minCoeff.cpp
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* Output: \verbinclude PartialRedux_minCoeff.out
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* \sa DenseBase::minCoeff() */
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const typename ReturnType<internal::member_minCoeff>::Type minCoeff() const
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{ return _expression(); }
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/** \returns a row (or column) vector expression of the largest coefficient
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* of each column (or row) of the referenced expression.
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* Example: \include PartialRedux_maxCoeff.cpp
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* Output: \verbinclude PartialRedux_maxCoeff.out
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* \sa DenseBase::maxCoeff() */
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const typename ReturnType<internal::member_maxCoeff>::Type maxCoeff() const
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{ return _expression(); }
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/** \returns a row (or column) vector expression of the squared norm
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* of each column (or row) of the referenced expression.
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* Example: \include PartialRedux_squaredNorm.cpp
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* Output: \verbinclude PartialRedux_squaredNorm.out
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* \sa DenseBase::squaredNorm() */
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const typename ReturnType<internal::member_squaredNorm,RealScalar>::Type squaredNorm() const
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{ return _expression(); }
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/** \returns a row (or column) vector expression of the norm
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* of each column (or row) of the referenced expression.
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* Example: \include PartialRedux_norm.cpp
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* Output: \verbinclude PartialRedux_norm.out
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* \sa DenseBase::norm() */
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const typename ReturnType<internal::member_norm,RealScalar>::Type norm() const
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{ return _expression(); }
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/** \returns a row (or column) vector expression of the norm
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* of each column (or row) of the referenced expression, using
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* \sa DenseBase::blueNorm() */
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const typename ReturnType<internal::member_blueNorm,RealScalar>::Type blueNorm() const
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{ return _expression(); }
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/** \returns a row (or column) vector expression of the norm
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* of each column (or row) of the referenced expression, avoiding
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* underflow and overflow.
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* \sa DenseBase::stableNorm() */
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const typename ReturnType<internal::member_stableNorm,RealScalar>::Type stableNorm() const
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{ return _expression(); }
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/** \returns a row (or column) vector expression of the norm
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* of each column (or row) of the referenced expression, avoiding
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* underflow and overflow using a concatenation of hypot() calls.
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* \sa DenseBase::hypotNorm() */
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const typename ReturnType<internal::member_hypotNorm,RealScalar>::Type hypotNorm() const
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{ return _expression(); }
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/** \returns a row (or column) vector expression of the sum
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* of each column (or row) of the referenced expression.
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* Example: \include PartialRedux_sum.cpp
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* Output: \verbinclude PartialRedux_sum.out
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* \sa DenseBase::sum() */
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const typename ReturnType<internal::member_sum>::Type sum() const
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{ return _expression(); }
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/** \returns a row (or column) vector expression of the mean
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* of each column (or row) of the referenced expression.
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* \sa DenseBase::mean() */
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const typename ReturnType<internal::member_mean>::Type mean() const
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{ return _expression(); }
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/** \returns a row (or column) vector expression representing
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* whether \b all coefficients of each respective column (or row) are \c true.
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* \sa DenseBase::all() */
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const typename ReturnType<internal::member_all>::Type all() const
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{ return _expression(); }
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/** \returns a row (or column) vector expression representing
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* whether \b at \b least one coefficient of each respective column (or row) is \c true.
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* \sa DenseBase::any() */
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const typename ReturnType<internal::member_any>::Type any() const
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{ return _expression(); }
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/** \returns a row (or column) vector expression representing
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* the number of \c true coefficients of each respective column (or row).
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* Example: \include PartialRedux_count.cpp
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* Output: \verbinclude PartialRedux_count.out
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* \sa DenseBase::count() */
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const PartialReduxExpr<ExpressionType, internal::member_count<Index>, Direction> count() const
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{ return _expression(); }
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/** \returns a row (or column) vector expression of the product
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* of each column (or row) of the referenced expression.
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* Example: \include PartialRedux_prod.cpp
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* Output: \verbinclude PartialRedux_prod.out
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* \sa DenseBase::prod() */
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const typename ReturnType<internal::member_prod>::Type prod() const
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{ return _expression(); }
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/** \returns a matrix expression
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* where each column (or row) are reversed.
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* Example: \include Vectorwise_reverse.cpp
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* Output: \verbinclude Vectorwise_reverse.out
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* \sa DenseBase::reverse() */
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const Reverse<ExpressionType, Direction> reverse() const
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{ return Reverse<ExpressionType, Direction>( _expression() ); }
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typedef Replicate<ExpressionType,Direction==Vertical?Dynamic:1,Direction==Horizontal?Dynamic:1> ReplicateReturnType;
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const ReplicateReturnType replicate(Index factor) const;
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* \return an expression of the replication of each column (or row) of \c *this
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* Example: \include DirectionWise_replicate.cpp
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* Output: \verbinclude DirectionWise_replicate.out
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* \sa VectorwiseOp::replicate(Index), DenseBase::replicate(), class Replicate
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// NOTE implemented here because of sunstudio's compilation errors
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template<int Factor> const Replicate<ExpressionType,(IsVertical?Factor:1),(IsHorizontal?Factor:1)>
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replicate(Index factor = Factor) const
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return Replicate<ExpressionType,Direction==Vertical?Factor:1,Direction==Horizontal?Factor:1>
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(_expression(),Direction==Vertical?factor:1,Direction==Horizontal?factor:1);
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/////////// Artithmetic operators ///////////
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/** Copies the vector \a other to each subvector of \c *this */
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template<typename OtherDerived>
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ExpressionType& operator=(const DenseBase<OtherDerived>& other)
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
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//eigen_assert((m_matrix.isNull()) == (other.isNull())); FIXME
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for(Index j=0; j<subVectors(); ++j)
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subVector(j) = other;
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return const_cast<ExpressionType&>(m_matrix);
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/** Adds the vector \a other to each subvector of \c *this */
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template<typename OtherDerived>
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ExpressionType& operator+=(const DenseBase<OtherDerived>& other)
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
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for(Index j=0; j<subVectors(); ++j)
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subVector(j) += other.derived();
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return const_cast<ExpressionType&>(m_matrix);
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/** Substracts the vector \a other to each subvector of \c *this */
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template<typename OtherDerived>
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ExpressionType& operator-=(const DenseBase<OtherDerived>& other)
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
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for(Index j=0; j<subVectors(); ++j)
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subVector(j) -= other.derived();
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return const_cast<ExpressionType&>(m_matrix);
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/** Returns the expression of the sum of the vector \a other to each subvector of \c *this */
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template<typename OtherDerived> EIGEN_STRONG_INLINE
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CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
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const ExpressionTypeNestedCleaned,
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const typename ExtendedType<OtherDerived>::Type>
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operator+(const DenseBase<OtherDerived>& other) const
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived);
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return m_matrix + extendedTo(other.derived());
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/** Returns the expression of the difference between each subvector of \c *this and the vector \a other */
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template<typename OtherDerived>
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CwiseBinaryOp<internal::scalar_difference_op<Scalar>,
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const ExpressionTypeNestedCleaned,
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const typename ExtendedType<OtherDerived>::Type>
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operator-(const DenseBase<OtherDerived>& other) const
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived);
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return m_matrix - extendedTo(other.derived());
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/////////// Geometry module ///////////
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#if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
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Homogeneous<ExpressionType,Direction> homogeneous() const;
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typedef typename ExpressionType::PlainObject CrossReturnType;
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template<typename OtherDerived>
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const CrossReturnType cross(const MatrixBase<OtherDerived>& other) const;
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HNormalized_Size = Direction==Vertical ? internal::traits<ExpressionType>::RowsAtCompileTime
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: internal::traits<ExpressionType>::ColsAtCompileTime,
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HNormalized_SizeMinusOne = HNormalized_Size==Dynamic ? Dynamic : HNormalized_Size-1
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typedef Block<const ExpressionType,
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Direction==Vertical ? int(HNormalized_SizeMinusOne)
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: int(internal::traits<ExpressionType>::RowsAtCompileTime),
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Direction==Horizontal ? int(HNormalized_SizeMinusOne)
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: int(internal::traits<ExpressionType>::ColsAtCompileTime)>
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typedef Block<const ExpressionType,
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Direction==Vertical ? 1 : int(internal::traits<ExpressionType>::RowsAtCompileTime),
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Direction==Horizontal ? 1 : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
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typedef CwiseBinaryOp<internal::scalar_quotient_op<typename internal::traits<ExpressionType>::Scalar>,
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const HNormalized_Block,
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const Replicate<HNormalized_Factors,
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Direction==Vertical ? HNormalized_SizeMinusOne : 1,
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Direction==Horizontal ? HNormalized_SizeMinusOne : 1> >
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HNormalizedReturnType;
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const HNormalizedReturnType hnormalized() const;
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ExpressionTypeNested m_matrix;
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/** \returns a VectorwiseOp wrapper of *this providing additional partial reduction operations
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* Example: \include MatrixBase_colwise.cpp
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* Output: \verbinclude MatrixBase_colwise.out
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* \sa rowwise(), class VectorwiseOp
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template<typename Derived>
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inline const typename DenseBase<Derived>::ConstColwiseReturnType
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DenseBase<Derived>::colwise() const
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/** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
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* \sa rowwise(), class VectorwiseOp
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template<typename Derived>
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inline typename DenseBase<Derived>::ColwiseReturnType
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DenseBase<Derived>::colwise()
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/** \returns a VectorwiseOp wrapper of *this providing additional partial reduction operations
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* Example: \include MatrixBase_rowwise.cpp
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* Output: \verbinclude MatrixBase_rowwise.out
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* \sa colwise(), class VectorwiseOp
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template<typename Derived>
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inline const typename DenseBase<Derived>::ConstRowwiseReturnType
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DenseBase<Derived>::rowwise() const
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/** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
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* \sa colwise(), class VectorwiseOp
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template<typename Derived>
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inline typename DenseBase<Derived>::RowwiseReturnType
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DenseBase<Derived>::rowwise()
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#endif // EIGEN_PARTIAL_REDUX_H
added
removed
thirdparty/eigen3/Eigen/src/Core/VectorwiseOp.h
