VectorwiseOp.h

00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
00005 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
00006 //
00007 // This Source Code Form is subject to the terms of the Mozilla
00008 // Public License v. 2.0. If a copy of the MPL was not distributed
00009 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
00010 
00011 #ifndef EIGEN_PARTIAL_REDUX_H
00012 #define EIGEN_PARTIAL_REDUX_H
00013 
00014 namespace Eigen { 
00015 
00016 /** \class PartialReduxExpr
00017   * \ingroup Core_Module
00018   *
00019   * \brief Generic expression of a partially reduxed matrix
00020   *
00021   * \tparam MatrixType the type of the matrix we are applying the redux operation
00022   * \tparam MemberOp type of the member functor
00023   * \tparam Direction indicates the direction of the redux (#Vertical or #Horizontal)
00024   *
00025   * This class represents an expression of a partial redux operator of a matrix.
00026   * It is the return type of some VectorwiseOp functions,
00027   * and most of the time this is the only way it is used.
00028   *
00029   * \sa class VectorwiseOp
00030   */
00031 
00032 template< typename MatrixType, typename MemberOp, int Direction>
00033 class PartialReduxExpr;
00034 
00035 namespace internal {
00036 template<typename MatrixType, typename MemberOp, int Direction>
00037 struct traits<PartialReduxExpr<MatrixType, MemberOp, Direction> >
00038  : traits<MatrixType>
00039 {
00040   typedef typename MemberOp::result_type Scalar;
00041   typedef typename traits<MatrixType>::StorageKind StorageKind;
00042   typedef typename traits<MatrixType>::XprKind XprKind;
00043   typedef typename MatrixType::Scalar InputScalar;
00044   typedef typename nested<MatrixType>::type MatrixTypeNested;
00045   typedef typename remove_all<MatrixTypeNested>::type _MatrixTypeNested;
00046   enum {
00047     RowsAtCompileTime = Direction==Vertical   ? 1 : MatrixType::RowsAtCompileTime,
00048     ColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::ColsAtCompileTime,
00049     MaxRowsAtCompileTime = Direction==Vertical   ? 1 : MatrixType::MaxRowsAtCompileTime,
00050     MaxColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::MaxColsAtCompileTime,
00051     Flags0 = (unsigned int)_MatrixTypeNested::Flags & HereditaryBits,
00052     Flags = (Flags0 & ~RowMajorBit) | (RowsAtCompileTime == 1 ? RowMajorBit : 0),
00053     TraversalSize = Direction==Vertical ? MatrixType::RowsAtCompileTime :  MatrixType::ColsAtCompileTime
00054   };
00055   #if EIGEN_GNUC_AT_LEAST(3,4)
00056   typedef typename MemberOp::template Cost<InputScalar,int(TraversalSize)> CostOpType;
00057   #else
00058   typedef typename MemberOp::template Cost<InputScalar,TraversalSize> CostOpType;
00059   #endif
00060   enum {
00061     CoeffReadCost = TraversalSize==Dynamic ? Dynamic
00062                   : TraversalSize * traits<_MatrixTypeNested>::CoeffReadCost + int(CostOpType::value)
00063   };
00064 };
00065 }
00066 
00067 template< typename MatrixType, typename MemberOp, int Direction>
00068 class PartialReduxExpr : internal::no_assignment_operator,
00069   public internal::dense_xpr_base< PartialReduxExpr<MatrixType, MemberOp, Direction> >::type
00070 {
00071   public:
00072 
00073     typedef typename internal::dense_xpr_base<PartialReduxExpr>::type Base;
00074     EIGEN_DENSE_PUBLIC_INTERFACE(PartialReduxExpr)
00075     typedef typename internal::traits<PartialReduxExpr>::MatrixTypeNested MatrixTypeNested;
00076     typedef typename internal::traits<PartialReduxExpr>::_MatrixTypeNested _MatrixTypeNested;
00077 
00078     PartialReduxExpr(const MatrixType& mat, const MemberOp& func = MemberOp())
00079       : m_matrix(mat), m_functor(func) {}
00080 
00081     Index rows() const { return (Direction==Vertical   ? 1 : m_matrix.rows()); }
00082     Index cols() const { return (Direction==Horizontal ? 1 : m_matrix.cols()); }
00083 
00084     EIGEN_STRONG_INLINE const Scalar coeff(Index i, Index j) const
00085     {
00086       if (Direction==Vertical)
00087         return m_functor(m_matrix.col(j));
00088       else
00089         return m_functor(m_matrix.row(i));
00090     }
00091 
00092     const Scalar coeff(Index index) const
00093     {
00094       if (Direction==Vertical)
00095         return m_functor(m_matrix.col(index));
00096       else
00097         return m_functor(m_matrix.row(index));
00098     }
00099 
00100   protected:
00101     MatrixTypeNested m_matrix;
00102     const MemberOp m_functor;
00103 };
00104 
00105 #define EIGEN_MEMBER_FUNCTOR(MEMBER,COST)                               \
00106   template <typename ResultType>                                        \
00107   struct member_##MEMBER {                                              \
00108     EIGEN_EMPTY_STRUCT_CTOR(member_##MEMBER)                            \
00109     typedef ResultType result_type;                                     \
00110     template<typename Scalar, int Size> struct Cost                     \
00111     { enum { value = COST }; };                                         \
00112     template<typename XprType>                                          \
00113     EIGEN_STRONG_INLINE ResultType operator()(const XprType& mat) const \
00114     { return mat.MEMBER(); } \
00115   }
00116 
00117 namespace internal {
00118 
00119 EIGEN_MEMBER_FUNCTOR(squaredNorm, Size * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
00120 EIGEN_MEMBER_FUNCTOR(norm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
00121 EIGEN_MEMBER_FUNCTOR(stableNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
00122 EIGEN_MEMBER_FUNCTOR(blueNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
00123 EIGEN_MEMBER_FUNCTOR(hypotNorm, (Size-1) * functor_traits<scalar_hypot_op<Scalar> >::Cost );
00124 EIGEN_MEMBER_FUNCTOR(sum, (Size-1)*NumTraits<Scalar>::AddCost);
00125 EIGEN_MEMBER_FUNCTOR(mean, (Size-1)*NumTraits<Scalar>::AddCost + NumTraits<Scalar>::MulCost);
00126 EIGEN_MEMBER_FUNCTOR(minCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
00127 EIGEN_MEMBER_FUNCTOR(maxCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
00128 EIGEN_MEMBER_FUNCTOR(all, (Size-1)*NumTraits<Scalar>::AddCost);
00129 EIGEN_MEMBER_FUNCTOR(any, (Size-1)*NumTraits<Scalar>::AddCost);
00130 EIGEN_MEMBER_FUNCTOR(count, (Size-1)*NumTraits<Scalar>::AddCost);
00131 EIGEN_MEMBER_FUNCTOR(prod, (Size-1)*NumTraits<Scalar>::MulCost);
00132 
00133 
00134 template <typename BinaryOp, typename Scalar>
00135 struct member_redux {
00136   typedef typename result_of<
00137                      BinaryOp(Scalar)
00138                    >::type  result_type;
00139   template<typename _Scalar, int Size> struct Cost
00140   { enum { value = (Size-1) * functor_traits<BinaryOp>::Cost }; };
00141   member_redux(const BinaryOp func) : m_functor(func) {}
00142   template<typename Derived>
00143   inline result_type operator()(const DenseBase<Derived> & mat) const
00144   { return mat.redux(m_functor); }
00145   const BinaryOp m_functor;
00146 };
00147 }
00148 
00149 /** \class VectorwiseOp
00150   * \ingroup Core_Module
00151   *
00152   * \brief Pseudo expression providing partial reduction operations
00153   *
00154   * \param ExpressionType the type of the object on which to do partial reductions
00155   * \param Direction indicates the direction of the redux (#Vertical or #Horizontal)
00156   *
00157   * This class represents a pseudo expression with partial reduction features.
00158   * It is the return type of DenseBase::colwise() and DenseBase::rowwise()
00159   * and most of the time this is the only way it is used.
00160   *
00161   * Example: \include MatrixBase_colwise.cpp
00162   * Output: \verbinclude MatrixBase_colwise.out
00163   *
00164   * \sa DenseBase::colwise(), DenseBase::rowwise(), class PartialReduxExpr
00165   */
00166 template<typename ExpressionType, int Direction> class VectorwiseOp
00167 {
00168   public:
00169 
00170     typedef typename ExpressionType::Scalar Scalar;
00171     typedef typename ExpressionType::RealScalar RealScalar;
00172     typedef typename ExpressionType::Index Index;
00173     typedef typename internal::conditional<internal::must_nest_by_value<ExpressionType>::ret,
00174         ExpressionType, ExpressionType&>::type ExpressionTypeNested;
00175     typedef typename internal::remove_all<ExpressionTypeNested>::type ExpressionTypeNestedCleaned;
00176 
00177     template<template<typename _Scalar> class Functor,
00178                       typename Scalar=typename internal::traits<ExpressionType>::Scalar> struct ReturnType
00179     {
00180       typedef PartialReduxExpr<ExpressionType,
00181                                Functor<Scalar>,
00182                                Direction
00183                               > Type;
00184     };
00185 
00186     template<typename BinaryOp> struct ReduxReturnType
00187     {
00188       typedef PartialReduxExpr<ExpressionType,
00189                                internal::member_redux<BinaryOp,typename internal::traits<ExpressionType>::Scalar>,
00190                                Direction
00191                               > Type;
00192     };
00193 
00194     enum {
00195       IsVertical   = (Direction==Vertical) ? 1 : 0,
00196       IsHorizontal = (Direction==Horizontal) ? 1 : 0
00197     };
00198 
00199   protected:
00200 
00201     /** \internal
00202       * \returns the i-th subvector according to the \c Direction */
00203     typedef typename internal::conditional<Direction==Vertical,
00204                                typename ExpressionType::ColXpr,
00205                                typename ExpressionType::RowXpr>::type SubVector;
00206     SubVector subVector(Index i)
00207     {
00208       return SubVector(m_matrix.derived(),i);
00209     }
00210 
00211     /** \internal
00212       * \returns the number of subvectors in the direction \c Direction */
00213     Index subVectors() const
00214     { return Direction==Vertical?m_matrix.cols():m_matrix.rows(); }
00215 
00216     template<typename OtherDerived> struct ExtendedType {
00217       typedef Replicate<OtherDerived,
00218                         Direction==Vertical   ? 1 : ExpressionType::RowsAtCompileTime,
00219                         Direction==Horizontal ? 1 : ExpressionType::ColsAtCompileTime> Type;
00220     };
00221 
00222     /** \internal
00223       * Replicates a vector to match the size of \c *this */
00224     template<typename OtherDerived>
00225     typename ExtendedType<OtherDerived>::Type
00226     extendedTo(const DenseBase<OtherDerived>& other) const
00227     {
00228       EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(Direction==Vertical, OtherDerived::MaxColsAtCompileTime==1),
00229                           YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED)
00230       EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(Direction==Horizontal, OtherDerived::MaxRowsAtCompileTime==1),
00231                           YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED)
00232       return typename ExtendedType<OtherDerived>::Type
00233                       (other.derived(),
00234                        Direction==Vertical   ? 1 : m_matrix.rows(),
00235                        Direction==Horizontal ? 1 : m_matrix.cols());
00236     }
00237     
00238     template<typename OtherDerived> struct OppositeExtendedType {
00239       typedef Replicate<OtherDerived,
00240                         Direction==Horizontal ? 1 : ExpressionType::RowsAtCompileTime,
00241                         Direction==Vertical   ? 1 : ExpressionType::ColsAtCompileTime> Type;
00242     };
00243 
00244     /** \internal
00245       * Replicates a vector in the opposite direction to match the size of \c *this */
00246     template<typename OtherDerived>
00247     typename OppositeExtendedType<OtherDerived>::Type
00248     extendedToOpposite(const DenseBase<OtherDerived>& other) const
00249     {
00250       EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(Direction==Horizontal, OtherDerived::MaxColsAtCompileTime==1),
00251                           YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED)
00252       EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(Direction==Vertical, OtherDerived::MaxRowsAtCompileTime==1),
00253                           YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED)
00254       return typename OppositeExtendedType<OtherDerived>::Type
00255                       (other.derived(),
00256                        Direction==Horizontal  ? 1 : m_matrix.rows(),
00257                        Direction==Vertical    ? 1 : m_matrix.cols());
00258     }
00259 
00260   public:
00261 
00262     inline VectorwiseOp(ExpressionType& matrix) : m_matrix(matrix) {}
00263 
00264     /** \internal */
00265     inline const ExpressionType& _expression() const { return m_matrix; }
00266 
00267     /** \returns a row or column vector expression of \c *this reduxed by \a func
00268       *
00269       * The template parameter \a BinaryOp is the type of the functor
00270       * of the custom redux operator. Note that func must be an associative operator.
00271       *
00272       * \sa class VectorwiseOp, DenseBase::colwise(), DenseBase::rowwise()
00273       */
00274     template<typename BinaryOp>
00275     const typename ReduxReturnType<BinaryOp>::Type
00276     redux(const BinaryOp& func = BinaryOp()) const
00277     { return typename ReduxReturnType<BinaryOp>::Type(_expression(), func); }
00278 
00279     /** \returns a row (or column) vector expression of the smallest coefficient
00280       * of each column (or row) of the referenced expression.
00281       * 
00282       * \warning the result is undefined if \c *this contains NaN.
00283       *
00284       * Example: \include PartialRedux_minCoeff.cpp
00285       * Output: \verbinclude PartialRedux_minCoeff.out
00286       *
00287       * \sa DenseBase::minCoeff() */
00288     const typename ReturnType<internal::member_minCoeff>::Type minCoeff() const
00289     { return _expression(); }
00290 
00291     /** \returns a row (or column) vector expression of the largest coefficient
00292       * of each column (or row) of the referenced expression.
00293       * 
00294       * \warning the result is undefined if \c *this contains NaN.
00295       *
00296       * Example: \include PartialRedux_maxCoeff.cpp
00297       * Output: \verbinclude PartialRedux_maxCoeff.out
00298       *
00299       * \sa DenseBase::maxCoeff() */
00300     const typename ReturnType<internal::member_maxCoeff>::Type maxCoeff() const
00301     { return _expression(); }
00302 
00303     /** \returns a row (or column) vector expression of the squared norm
00304       * of each column (or row) of the referenced expression.
00305       *
00306       * Example: \include PartialRedux_squaredNorm.cpp
00307       * Output: \verbinclude PartialRedux_squaredNorm.out
00308       *
00309       * \sa DenseBase::squaredNorm() */
00310     const typename ReturnType<internal::member_squaredNorm,RealScalar>::Type squaredNorm() const
00311     { return _expression(); }
00312 
00313     /** \returns a row (or column) vector expression of the norm
00314       * of each column (or row) of the referenced expression.
00315       *
00316       * Example: \include PartialRedux_norm.cpp
00317       * Output: \verbinclude PartialRedux_norm.out
00318       *
00319       * \sa DenseBase::norm() */
00320     const typename ReturnType<internal::member_norm,RealScalar>::Type norm() const
00321     { return _expression(); }
00322 
00323 
00324     /** \returns a row (or column) vector expression of the norm
00325       * of each column (or row) of the referenced expression, using
00326       * blue's algorithm.
00327       *
00328       * \sa DenseBase::blueNorm() */
00329     const typename ReturnType<internal::member_blueNorm,RealScalar>::Type blueNorm() const
00330     { return _expression(); }
00331 
00332 
00333     /** \returns a row (or column) vector expression of the norm
00334       * of each column (or row) of the referenced expression, avoiding
00335       * underflow and overflow.
00336       *
00337       * \sa DenseBase::stableNorm() */
00338     const typename ReturnType<internal::member_stableNorm,RealScalar>::Type stableNorm() const
00339     { return _expression(); }
00340 
00341 
00342     /** \returns a row (or column) vector expression of the norm
00343       * of each column (or row) of the referenced expression, avoiding
00344       * underflow and overflow using a concatenation of hypot() calls.
00345       *
00346       * \sa DenseBase::hypotNorm() */
00347     const typename ReturnType<internal::member_hypotNorm,RealScalar>::Type hypotNorm() const
00348     { return _expression(); }
00349 
00350     /** \returns a row (or column) vector expression of the sum
00351       * of each column (or row) of the referenced expression.
00352       *
00353       * Example: \include PartialRedux_sum.cpp
00354       * Output: \verbinclude PartialRedux_sum.out
00355       *
00356       * \sa DenseBase::sum() */
00357     const typename ReturnType<internal::member_sum>::Type sum() const
00358     { return _expression(); }
00359 
00360     /** \returns a row (or column) vector expression of the mean
00361     * of each column (or row) of the referenced expression.
00362     *
00363     * \sa DenseBase::mean() */
00364     const typename ReturnType<internal::member_mean>::Type mean() const
00365     { return _expression(); }
00366 
00367     /** \returns a row (or column) vector expression representing
00368       * whether \b all coefficients of each respective column (or row) are \c true.
00369       *
00370       * \sa DenseBase::all() */
00371     const typename ReturnType<internal::member_all>::Type all() const
00372     { return _expression(); }
00373 
00374     /** \returns a row (or column) vector expression representing
00375       * whether \b at \b least one coefficient of each respective column (or row) is \c true.
00376       *
00377       * \sa DenseBase::any() */
00378     const typename ReturnType<internal::member_any>::Type any() const
00379     { return _expression(); }
00380 
00381     /** \returns a row (or column) vector expression representing
00382       * the number of \c true coefficients of each respective column (or row).
00383       *
00384       * Example: \include PartialRedux_count.cpp
00385       * Output: \verbinclude PartialRedux_count.out
00386       *
00387       * \sa DenseBase::count() */
00388     const PartialReduxExpr<ExpressionType, internal::member_count<Index>, Direction> count() const
00389     { return _expression(); }
00390 
00391     /** \returns a row (or column) vector expression of the product
00392       * of each column (or row) of the referenced expression.
00393       *
00394       * Example: \include PartialRedux_prod.cpp
00395       * Output: \verbinclude PartialRedux_prod.out
00396       *
00397       * \sa DenseBase::prod() */
00398     const typename ReturnType<internal::member_prod>::Type prod() const
00399     { return _expression(); }
00400 
00401 
00402     /** \returns a matrix expression
00403       * where each column (or row) are reversed.
00404       *
00405       * Example: \include Vectorwise_reverse.cpp
00406       * Output: \verbinclude Vectorwise_reverse.out
00407       *
00408       * \sa DenseBase::reverse() */
00409     const Reverse<ExpressionType, Direction> reverse() const
00410     { return Reverse<ExpressionType, Direction>( _expression() ); }
00411 
00412     typedef Replicate<ExpressionType,Direction==Vertical?Dynamic:1,Direction==Horizontal?Dynamic:1> ReplicateReturnType;
00413     const ReplicateReturnType replicate(Index factor) const;
00414 
00415     /**
00416       * \return an expression of the replication of each column (or row) of \c *this
00417       *
00418       * Example: \include DirectionWise_replicate.cpp
00419       * Output: \verbinclude DirectionWise_replicate.out
00420       *
00421       * \sa VectorwiseOp::replicate(Index), DenseBase::replicate(), class Replicate
00422       */
00423     // NOTE implemented here because of sunstudio's compilation errors
00424     template<int Factor> const Replicate<ExpressionType,(IsVertical?Factor:1),(IsHorizontal?Factor:1)>
00425     replicate(Index factor = Factor) const
00426     {
00427       return Replicate<ExpressionType,Direction==Vertical?Factor:1,Direction==Horizontal?Factor:1>
00428           (_expression(),Direction==Vertical?factor:1,Direction==Horizontal?factor:1);
00429     }
00430 
00431 /////////// Artithmetic operators ///////////
00432 
00433     /** Copies the vector \a other to each subvector of \c *this */
00434     template<typename OtherDerived>
00435     ExpressionType& operator=(const DenseBase<OtherDerived>& other)
00436     {
00437       EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
00438       EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
00439       //eigen_assert((m_matrix.isNull()) == (other.isNull())); FIXME
00440       return const_cast<ExpressionType&>(m_matrix = extendedTo(other.derived()));
00441     }
00442 
00443     /** Adds the vector \a other to each subvector of \c *this */
00444     template<typename OtherDerived>
00445     ExpressionType& operator+=(const DenseBase<OtherDerived>& other)
00446     {
00447       EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
00448       EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
00449       return const_cast<ExpressionType&>(m_matrix += extendedTo(other.derived()));
00450     }
00451 
00452     /** Substracts the vector \a other to each subvector of \c *this */
00453     template<typename OtherDerived>
00454     ExpressionType& operator-=(const DenseBase<OtherDerived>& other)
00455     {
00456       EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
00457       EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
00458       return const_cast<ExpressionType&>(m_matrix -= extendedTo(other.derived()));
00459     }
00460 
00461     /** Multiples each subvector of \c *this by the vector \a other */
00462     template<typename OtherDerived>
00463     ExpressionType& operator*=(const DenseBase<OtherDerived>& other)
00464     {
00465       EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
00466       EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
00467       EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
00468       m_matrix *= extendedTo(other.derived());
00469       return const_cast<ExpressionType&>(m_matrix);
00470     }
00471 
00472     /** Divides each subvector of \c *this by the vector \a other */
00473     template<typename OtherDerived>
00474     ExpressionType& operator/=(const DenseBase<OtherDerived>& other)
00475     {
00476       EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
00477       EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
00478       EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
00479       m_matrix /= extendedTo(other.derived());
00480       return const_cast<ExpressionType&>(m_matrix);
00481     }
00482 
00483     /** Returns the expression of the sum of the vector \a other to each subvector of \c *this */
00484     template<typename OtherDerived> EIGEN_STRONG_INLINE
00485     CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
00486                   const ExpressionTypeNestedCleaned,
00487                   const typename ExtendedType<OtherDerived>::Type>
00488     operator+(const DenseBase<OtherDerived>& other) const
00489     {
00490       EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
00491       EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
00492       return m_matrix + extendedTo(other.derived());
00493     }
00494 
00495     /** Returns the expression of the difference between each subvector of \c *this and the vector \a other */
00496     template<typename OtherDerived>
00497     CwiseBinaryOp<internal::scalar_difference_op<Scalar>,
00498                   const ExpressionTypeNestedCleaned,
00499                   const typename ExtendedType<OtherDerived>::Type>
00500     operator-(const DenseBase<OtherDerived>& other) const
00501     {
00502       EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
00503       EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
00504       return m_matrix - extendedTo(other.derived());
00505     }
00506 
00507     /** Returns the expression where each subvector is the product of the vector \a other
00508       * by the corresponding subvector of \c *this */
00509     template<typename OtherDerived> EIGEN_STRONG_INLINE
00510     CwiseBinaryOp<internal::scalar_product_op<Scalar>,
00511                   const ExpressionTypeNestedCleaned,
00512                   const typename ExtendedType<OtherDerived>::Type>
00513     operator* (const DenseBase<OtherDerived>& other) const
00514     {
00515       EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
00516       EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
00517       EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
00518       return m_matrix * extendedTo(other.derived());
00519     }
00520 
00521     /** Returns the expression where each subvector is the quotient of the corresponding
00522       * subvector of \c *this by the vector \a other */
00523     template<typename OtherDerived>
00524     CwiseBinaryOp<internal::scalar_quotient_op<Scalar>,
00525                   const ExpressionTypeNestedCleaned,
00526                   const typename ExtendedType<OtherDerived>::Type>
00527     operator/(const DenseBase<OtherDerived>& other) const
00528     {
00529       EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
00530       EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
00531       EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
00532       return m_matrix / extendedTo(other.derived());
00533     }
00534     
00535     /** \returns an expression where each column of row of the referenced matrix are normalized.
00536       * The referenced matrix is \b not modified.
00537       * \sa MatrixBase::normalized(), normalize()
00538       */
00539     CwiseBinaryOp<internal::scalar_quotient_op<Scalar>,
00540                   const ExpressionTypeNestedCleaned,
00541                   const typename OppositeExtendedType<typename ReturnType<internal::member_norm,RealScalar>::Type>::Type>
00542     normalized () const { return m_matrix.cwiseQuotient(extendedToOpposite(this->norm())); }
00543     
00544     
00545     /** Normalize in-place each row or columns of the referenced matrix.
00546       * \sa MatrixBase::normalize(), normalized()
00547       */
00548     void normalize() {
00549       m_matrix = this->normalized();
00550     }
00551 
00552 /////////// Geometry module ///////////
00553 
00554     #if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
00555     Homogeneous<ExpressionType,Direction>  homogeneous() const;
00556     #endif
00557 
00558     typedef typename ExpressionType::PlainObject CrossReturnType;
00559     template<typename OtherDerived>
00560     const CrossReturnType cross(const MatrixBase<OtherDerived>& other) const;
00561 
00562     enum {
00563       HNormalized_Size = Direction==Vertical ? internal::traits<ExpressionType>::RowsAtCompileTime
00564                                              : internal::traits<ExpressionType>::ColsAtCompileTime,
00565       HNormalized_SizeMinusOne = HNormalized_Size==Dynamic ? Dynamic : HNormalized_Size-1
00566     };
00567     typedef Block<const ExpressionType,
00568                   Direction==Vertical   ? int(HNormalized_SizeMinusOne)
00569                                         : int(internal::traits<ExpressionType>::RowsAtCompileTime),
00570                   Direction==Horizontal ? int(HNormalized_SizeMinusOne)
00571                                         : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
00572             HNormalized_Block;
00573     typedef Block<const ExpressionType,
00574                   Direction==Vertical   ? 1 : int(internal::traits<ExpressionType>::RowsAtCompileTime),
00575                   Direction==Horizontal ? 1 : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
00576             HNormalized_Factors;
00577     typedef CwiseBinaryOp<internal::scalar_quotient_op<typename internal::traits<ExpressionType>::Scalar>,
00578                 const HNormalized_Block,
00579                 const Replicate<HNormalized_Factors,
00580                   Direction==Vertical   ? HNormalized_SizeMinusOne : 1,
00581                   Direction==Horizontal ? HNormalized_SizeMinusOne : 1> >
00582             HNormalizedReturnType;
00583 
00584     const HNormalizedReturnType hnormalized() const;
00585 
00586   protected:
00587     ExpressionTypeNested m_matrix;
00588 };
00589 
00590 /** \returns a VectorwiseOp wrapper of *this providing additional partial reduction operations
00591   *
00592   * Example: \include MatrixBase_colwise.cpp
00593   * Output: \verbinclude MatrixBase_colwise.out
00594   *
00595   * \sa rowwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
00596   */
00597 template<typename Derived>
00598 inline const typename DenseBase<Derived>::ConstColwiseReturnType
00599 DenseBase<Derived>::colwise() const
00600 {
00601   return derived();
00602 }
00603 
00604 /** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
00605   *
00606   * \sa rowwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
00607   */
00608 template<typename Derived>
00609 inline typename DenseBase<Derived>::ColwiseReturnType
00610 DenseBase<Derived>::colwise()
00611 {
00612   return derived();
00613 }
00614 
00615 /** \returns a VectorwiseOp wrapper of *this providing additional partial reduction operations
00616   *
00617   * Example: \include MatrixBase_rowwise.cpp
00618   * Output: \verbinclude MatrixBase_rowwise.out
00619   *
00620   * \sa colwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
00621   */
00622 template<typename Derived>
00623 inline const typename DenseBase<Derived>::ConstRowwiseReturnType
00624 DenseBase<Derived>::rowwise() const
00625 {
00626   return derived();
00627 }
00628 
00629 /** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
00630   *
00631   * \sa colwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
00632   */
00633 template<typename Derived>
00634 inline typename DenseBase<Derived>::RowwiseReturnType
00635 DenseBase<Derived>::rowwise()
00636 {
00637   return derived();
00638 }
00639 
00640 } // end namespace Eigen
00641 
00642 #endif // EIGEN_PARTIAL_REDUX_H