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Warning, file /include/eigen3/Eigen/src/Geometry/Homogeneous.h was not indexed or was modified since last indexation (in which case cross-reference links may be missing, inaccurate or erroneous).

0001 // This file is part of Eigen, a lightweight C++ template library
0002 // for linear algebra.
0003 //
0004 // Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
0005 //
0006 // This Source Code Form is subject to the terms of the Mozilla
0007 // Public License v. 2.0. If a copy of the MPL was not distributed
0008 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
0009 
0010 #ifndef EIGEN_HOMOGENEOUS_H
0011 #define EIGEN_HOMOGENEOUS_H
0012 
0013 namespace Eigen {
0014 
0015 /** \geometry_module \ingroup Geometry_Module
0016   *
0017   * \class Homogeneous
0018   *
0019   * \brief Expression of one (or a set of) homogeneous vector(s)
0020   *
0021   * \param MatrixType the type of the object in which we are making homogeneous
0022   *
0023   * This class represents an expression of one (or a set of) homogeneous vector(s).
0024   * It is the return type of MatrixBase::homogeneous() and most of the time
0025   * this is the only way it is used.
0026   *
0027   * \sa MatrixBase::homogeneous()
0028   */
0029 
0030 namespace internal {
0031 
0032 template<typename MatrixType,int Direction>
0033 struct traits<Homogeneous<MatrixType,Direction> >
0034  : traits<MatrixType>
0035 {
0036   typedef typename traits<MatrixType>::StorageKind StorageKind;
0037   typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
0038   typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
0039   enum {
0040     RowsPlusOne = (MatrixType::RowsAtCompileTime != Dynamic) ?
0041                   int(MatrixType::RowsAtCompileTime) + 1 : Dynamic,
0042     ColsPlusOne = (MatrixType::ColsAtCompileTime != Dynamic) ?
0043                   int(MatrixType::ColsAtCompileTime) + 1 : Dynamic,
0044     RowsAtCompileTime = Direction==Vertical  ?  RowsPlusOne : MatrixType::RowsAtCompileTime,
0045     ColsAtCompileTime = Direction==Horizontal ? ColsPlusOne : MatrixType::ColsAtCompileTime,
0046     MaxRowsAtCompileTime = RowsAtCompileTime,
0047     MaxColsAtCompileTime = ColsAtCompileTime,
0048     TmpFlags = _MatrixTypeNested::Flags & HereditaryBits,
0049     Flags = ColsAtCompileTime==1 ? (TmpFlags & ~RowMajorBit)
0050           : RowsAtCompileTime==1 ? (TmpFlags | RowMajorBit)
0051           : TmpFlags
0052   };
0053 };
0054 
0055 template<typename MatrixType,typename Lhs> struct homogeneous_left_product_impl;
0056 template<typename MatrixType,typename Rhs> struct homogeneous_right_product_impl;
0057 
0058 } // end namespace internal
0059 
0060 template<typename MatrixType,int _Direction> class Homogeneous
0061   : public MatrixBase<Homogeneous<MatrixType,_Direction> >, internal::no_assignment_operator
0062 {
0063   public:
0064 
0065     typedef MatrixType NestedExpression;
0066     enum { Direction = _Direction };
0067 
0068     typedef MatrixBase<Homogeneous> Base;
0069     EIGEN_DENSE_PUBLIC_INTERFACE(Homogeneous)
0070 
0071     EIGEN_DEVICE_FUNC explicit inline Homogeneous(const MatrixType& matrix)
0072       : m_matrix(matrix)
0073     {}
0074 
0075     EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
0076     inline Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows() + (int(Direction)==Vertical   ? 1 : 0); }
0077     EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
0078     inline Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols() + (int(Direction)==Horizontal ? 1 : 0); }
0079 
0080     EIGEN_DEVICE_FUNC const NestedExpression& nestedExpression() const { return m_matrix; }
0081 
0082     template<typename Rhs>
0083     EIGEN_DEVICE_FUNC inline const Product<Homogeneous,Rhs>
0084     operator* (const MatrixBase<Rhs>& rhs) const
0085     {
0086       eigen_assert(int(Direction)==Horizontal);
0087       return Product<Homogeneous,Rhs>(*this,rhs.derived());
0088     }
0089 
0090     template<typename Lhs> friend
0091     EIGEN_DEVICE_FUNC inline const Product<Lhs,Homogeneous>
0092     operator* (const MatrixBase<Lhs>& lhs, const Homogeneous& rhs)
0093     {
0094       eigen_assert(int(Direction)==Vertical);
0095       return Product<Lhs,Homogeneous>(lhs.derived(),rhs);
0096     }
0097 
0098     template<typename Scalar, int Dim, int Mode, int Options> friend
0099     EIGEN_DEVICE_FUNC inline const Product<Transform<Scalar,Dim,Mode,Options>, Homogeneous >
0100     operator* (const Transform<Scalar,Dim,Mode,Options>& lhs, const Homogeneous& rhs)
0101     {
0102       eigen_assert(int(Direction)==Vertical);
0103       return Product<Transform<Scalar,Dim,Mode,Options>, Homogeneous>(lhs,rhs);
0104     }
0105 
0106     template<typename Func>
0107     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::result_of<Func(Scalar,Scalar)>::type
0108     redux(const Func& func) const
0109     {
0110       return func(m_matrix.redux(func), Scalar(1));
0111     }
0112 
0113   protected:
0114     typename MatrixType::Nested m_matrix;
0115 };
0116 
0117 /** \geometry_module \ingroup Geometry_Module
0118   *
0119   * \returns a vector expression that is one longer than the vector argument, with the value 1 symbolically appended as the last coefficient.
0120   *
0121   * This can be used to convert affine coordinates to homogeneous coordinates.
0122   *
0123   * \only_for_vectors
0124   *
0125   * Example: \include MatrixBase_homogeneous.cpp
0126   * Output: \verbinclude MatrixBase_homogeneous.out
0127   *
0128   * \sa VectorwiseOp::homogeneous(), class Homogeneous
0129   */
0130 template<typename Derived>
0131 EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::HomogeneousReturnType
0132 MatrixBase<Derived>::homogeneous() const
0133 {
0134   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
0135   return HomogeneousReturnType(derived());
0136 }
0137 
0138 /** \geometry_module \ingroup Geometry_Module
0139   *
0140   * \returns an expression where the value 1 is symbolically appended as the final coefficient to each column (or row) of the matrix.
0141   *
0142   * This can be used to convert affine coordinates to homogeneous coordinates.
0143   *
0144   * Example: \include VectorwiseOp_homogeneous.cpp
0145   * Output: \verbinclude VectorwiseOp_homogeneous.out
0146   *
0147   * \sa MatrixBase::homogeneous(), class Homogeneous */
0148 template<typename ExpressionType, int Direction>
0149 EIGEN_DEVICE_FUNC inline Homogeneous<ExpressionType,Direction>
0150 VectorwiseOp<ExpressionType,Direction>::homogeneous() const
0151 {
0152   return HomogeneousReturnType(_expression());
0153 }
0154 
0155 /** \geometry_module \ingroup Geometry_Module
0156   *
0157   * \brief homogeneous normalization
0158   *
0159   * \returns a vector expression of the N-1 first coefficients of \c *this divided by that last coefficient.
0160   *
0161   * This can be used to convert homogeneous coordinates to affine coordinates.
0162   *
0163   * It is essentially a shortcut for:
0164   * \code
0165     this->head(this->size()-1)/this->coeff(this->size()-1);
0166     \endcode
0167   *
0168   * Example: \include MatrixBase_hnormalized.cpp
0169   * Output: \verbinclude MatrixBase_hnormalized.out
0170   *
0171   * \sa VectorwiseOp::hnormalized() */
0172 template<typename Derived>
0173 EIGEN_DEVICE_FUNC inline const typename MatrixBase<Derived>::HNormalizedReturnType
0174 MatrixBase<Derived>::hnormalized() const
0175 {
0176   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
0177   return ConstStartMinusOne(derived(),0,0,
0178     ColsAtCompileTime==1?size()-1:1,
0179     ColsAtCompileTime==1?1:size()-1) / coeff(size()-1);
0180 }
0181 
0182 /** \geometry_module \ingroup Geometry_Module
0183   *
0184   * \brief column or row-wise homogeneous normalization
0185   *
0186   * \returns an expression of the first N-1 coefficients of each column (or row) of \c *this divided by the last coefficient of each column (or row).
0187   *
0188   * This can be used to convert homogeneous coordinates to affine coordinates.
0189   *
0190   * It is conceptually equivalent to calling MatrixBase::hnormalized() to each column (or row) of \c *this.
0191   *
0192   * Example: \include DirectionWise_hnormalized.cpp
0193   * Output: \verbinclude DirectionWise_hnormalized.out
0194   *
0195   * \sa MatrixBase::hnormalized() */
0196 template<typename ExpressionType, int Direction>
0197 EIGEN_DEVICE_FUNC inline const typename VectorwiseOp<ExpressionType,Direction>::HNormalizedReturnType
0198 VectorwiseOp<ExpressionType,Direction>::hnormalized() const
0199 {
0200   return HNormalized_Block(_expression(),0,0,
0201       Direction==Vertical   ? _expression().rows()-1 : _expression().rows(),
0202       Direction==Horizontal ? _expression().cols()-1 : _expression().cols()).cwiseQuotient(
0203       Replicate<HNormalized_Factors,
0204                 Direction==Vertical   ? HNormalized_SizeMinusOne : 1,
0205                 Direction==Horizontal ? HNormalized_SizeMinusOne : 1>
0206         (HNormalized_Factors(_expression(),
0207           Direction==Vertical    ? _expression().rows()-1:0,
0208           Direction==Horizontal  ? _expression().cols()-1:0,
0209           Direction==Vertical    ? 1 : _expression().rows(),
0210           Direction==Horizontal  ? 1 : _expression().cols()),
0211          Direction==Vertical   ? _expression().rows()-1 : 1,
0212          Direction==Horizontal ? _expression().cols()-1 : 1));
0213 }
0214 
0215 namespace internal {
0216 
0217 template<typename MatrixOrTransformType>
0218 struct take_matrix_for_product
0219 {
0220   typedef MatrixOrTransformType type;
0221   EIGEN_DEVICE_FUNC static const type& run(const type &x) { return x; }
0222 };
0223 
0224 template<typename Scalar, int Dim, int Mode,int Options>
0225 struct take_matrix_for_product<Transform<Scalar, Dim, Mode, Options> >
0226 {
0227   typedef Transform<Scalar, Dim, Mode, Options> TransformType;
0228   typedef typename internal::add_const<typename TransformType::ConstAffinePart>::type type;
0229   EIGEN_DEVICE_FUNC static type run (const TransformType& x) { return x.affine(); }
0230 };
0231 
0232 template<typename Scalar, int Dim, int Options>
0233 struct take_matrix_for_product<Transform<Scalar, Dim, Projective, Options> >
0234 {
0235   typedef Transform<Scalar, Dim, Projective, Options> TransformType;
0236   typedef typename TransformType::MatrixType type;
0237   EIGEN_DEVICE_FUNC static const type& run (const TransformType& x) { return x.matrix(); }
0238 };
0239 
0240 template<typename MatrixType,typename Lhs>
0241 struct traits<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
0242 {
0243   typedef typename take_matrix_for_product<Lhs>::type LhsMatrixType;
0244   typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;
0245   typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
0246   typedef typename make_proper_matrix_type<
0247                  typename traits<MatrixTypeCleaned>::Scalar,
0248                  LhsMatrixTypeCleaned::RowsAtCompileTime,
0249                  MatrixTypeCleaned::ColsAtCompileTime,
0250                  MatrixTypeCleaned::PlainObject::Options,
0251                  LhsMatrixTypeCleaned::MaxRowsAtCompileTime,
0252                  MatrixTypeCleaned::MaxColsAtCompileTime>::type ReturnType;
0253 };
0254 
0255 template<typename MatrixType,typename Lhs>
0256 struct homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs>
0257   : public ReturnByValue<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
0258 {
0259   typedef typename traits<homogeneous_left_product_impl>::LhsMatrixType LhsMatrixType;
0260   typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
0261   typedef typename remove_all<typename LhsMatrixTypeCleaned::Nested>::type LhsMatrixTypeNested;
0262   EIGEN_DEVICE_FUNC homogeneous_left_product_impl(const Lhs& lhs, const MatrixType& rhs)
0263     : m_lhs(take_matrix_for_product<Lhs>::run(lhs)),
0264       m_rhs(rhs)
0265   {}
0266 
0267   EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
0268   inline Index rows() const EIGEN_NOEXCEPT { return m_lhs.rows(); }
0269   EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
0270   inline Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }
0271 
0272   template<typename Dest> EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const
0273   {
0274     // FIXME investigate how to allow lazy evaluation of this product when possible
0275     dst = Block<const LhsMatrixTypeNested,
0276               LhsMatrixTypeNested::RowsAtCompileTime,
0277               LhsMatrixTypeNested::ColsAtCompileTime==Dynamic?Dynamic:LhsMatrixTypeNested::ColsAtCompileTime-1>
0278             (m_lhs,0,0,m_lhs.rows(),m_lhs.cols()-1) * m_rhs;
0279     dst += m_lhs.col(m_lhs.cols()-1).rowwise()
0280             .template replicate<MatrixType::ColsAtCompileTime>(m_rhs.cols());
0281   }
0282 
0283   typename LhsMatrixTypeCleaned::Nested m_lhs;
0284   typename MatrixType::Nested m_rhs;
0285 };
0286 
0287 template<typename MatrixType,typename Rhs>
0288 struct traits<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
0289 {
0290   typedef typename make_proper_matrix_type<typename traits<MatrixType>::Scalar,
0291                  MatrixType::RowsAtCompileTime,
0292                  Rhs::ColsAtCompileTime,
0293                  MatrixType::PlainObject::Options,
0294                  MatrixType::MaxRowsAtCompileTime,
0295                  Rhs::MaxColsAtCompileTime>::type ReturnType;
0296 };
0297 
0298 template<typename MatrixType,typename Rhs>
0299 struct homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs>
0300   : public ReturnByValue<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
0301 {
0302   typedef typename remove_all<typename Rhs::Nested>::type RhsNested;
0303   EIGEN_DEVICE_FUNC homogeneous_right_product_impl(const MatrixType& lhs, const Rhs& rhs)
0304     : m_lhs(lhs), m_rhs(rhs)
0305   {}
0306 
0307   EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_lhs.rows(); }
0308   EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }
0309 
0310   template<typename Dest> EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const
0311   {
0312     // FIXME investigate how to allow lazy evaluation of this product when possible
0313     dst = m_lhs * Block<const RhsNested,
0314                         RhsNested::RowsAtCompileTime==Dynamic?Dynamic:RhsNested::RowsAtCompileTime-1,
0315                         RhsNested::ColsAtCompileTime>
0316             (m_rhs,0,0,m_rhs.rows()-1,m_rhs.cols());
0317     dst += m_rhs.row(m_rhs.rows()-1).colwise()
0318             .template replicate<MatrixType::RowsAtCompileTime>(m_lhs.rows());
0319   }
0320 
0321   typename MatrixType::Nested m_lhs;
0322   typename Rhs::Nested m_rhs;
0323 };
0324 
0325 template<typename ArgType,int Direction>
0326 struct evaluator_traits<Homogeneous<ArgType,Direction> >
0327 {
0328   typedef typename storage_kind_to_evaluator_kind<typename ArgType::StorageKind>::Kind Kind;
0329   typedef HomogeneousShape Shape;
0330 };
0331 
0332 template<> struct AssignmentKind<DenseShape,HomogeneousShape> { typedef Dense2Dense Kind; };
0333 
0334 
0335 template<typename ArgType,int Direction>
0336 struct unary_evaluator<Homogeneous<ArgType,Direction>, IndexBased>
0337   : evaluator<typename Homogeneous<ArgType,Direction>::PlainObject >
0338 {
0339   typedef Homogeneous<ArgType,Direction> XprType;
0340   typedef typename XprType::PlainObject PlainObject;
0341   typedef evaluator<PlainObject> Base;
0342 
0343   EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& op)
0344     : Base(), m_temp(op)
0345   {
0346     ::new (static_cast<Base*>(this)) Base(m_temp);
0347   }
0348 
0349 protected:
0350   PlainObject m_temp;
0351 };
0352 
0353 // dense = homogeneous
0354 template< typename DstXprType, typename ArgType, typename Scalar>
0355 struct Assignment<DstXprType, Homogeneous<ArgType,Vertical>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
0356 {
0357   typedef Homogeneous<ArgType,Vertical> SrcXprType;
0358   EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
0359   {
0360     Index dstRows = src.rows();
0361     Index dstCols = src.cols();
0362     if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
0363       dst.resize(dstRows, dstCols);
0364 
0365     dst.template topRows<ArgType::RowsAtCompileTime>(src.nestedExpression().rows()) = src.nestedExpression();
0366     dst.row(dst.rows()-1).setOnes();
0367   }
0368 };
0369 
0370 // dense = homogeneous
0371 template< typename DstXprType, typename ArgType, typename Scalar>
0372 struct Assignment<DstXprType, Homogeneous<ArgType,Horizontal>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
0373 {
0374   typedef Homogeneous<ArgType,Horizontal> SrcXprType;
0375   EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
0376   {
0377     Index dstRows = src.rows();
0378     Index dstCols = src.cols();
0379     if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
0380       dst.resize(dstRows, dstCols);
0381 
0382     dst.template leftCols<ArgType::ColsAtCompileTime>(src.nestedExpression().cols()) = src.nestedExpression();
0383     dst.col(dst.cols()-1).setOnes();
0384   }
0385 };
0386 
0387 template<typename LhsArg, typename Rhs, int ProductTag>
0388 struct generic_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs, HomogeneousShape, DenseShape, ProductTag>
0389 {
0390   template<typename Dest>
0391   EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Homogeneous<LhsArg,Horizontal>& lhs, const Rhs& rhs)
0392   {
0393     homogeneous_right_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs>(lhs.nestedExpression(), rhs).evalTo(dst);
0394   }
0395 };
0396 
0397 template<typename Lhs,typename Rhs>
0398 struct homogeneous_right_product_refactoring_helper
0399 {
0400   enum {
0401     Dim  = Lhs::ColsAtCompileTime,
0402     Rows = Lhs::RowsAtCompileTime
0403   };
0404   typedef typename Rhs::template ConstNRowsBlockXpr<Dim>::Type          LinearBlockConst;
0405   typedef typename remove_const<LinearBlockConst>::type                 LinearBlock;
0406   typedef typename Rhs::ConstRowXpr                                     ConstantColumn;
0407   typedef Replicate<const ConstantColumn,Rows,1>                        ConstantBlock;
0408   typedef Product<Lhs,LinearBlock,LazyProduct>                          LinearProduct;
0409   typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
0410 };
0411 
0412 template<typename Lhs, typename Rhs, int ProductTag>
0413 struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, HomogeneousShape, DenseShape>
0414  : public evaluator<typename homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs>::Xpr>
0415 {
0416   typedef Product<Lhs, Rhs, LazyProduct> XprType;
0417   typedef homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs> helper;
0418   typedef typename helper::ConstantBlock ConstantBlock;
0419   typedef typename helper::Xpr RefactoredXpr;
0420   typedef evaluator<RefactoredXpr> Base;
0421 
0422   EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
0423     : Base(  xpr.lhs().nestedExpression() .lazyProduct(  xpr.rhs().template topRows<helper::Dim>(xpr.lhs().nestedExpression().cols()) )
0424             + ConstantBlock(xpr.rhs().row(xpr.rhs().rows()-1),xpr.lhs().rows(), 1) )
0425   {}
0426 };
0427 
0428 template<typename Lhs, typename RhsArg, int ProductTag>
0429 struct generic_product_impl<Lhs, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>
0430 {
0431   template<typename Dest>
0432   EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
0433   {
0434     homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, Lhs>(lhs, rhs.nestedExpression()).evalTo(dst);
0435   }
0436 };
0437 
0438 // TODO: the following specialization is to address a regression from 3.2 to 3.3
0439 // In the future, this path should be optimized.
0440 template<typename Lhs, typename RhsArg, int ProductTag>
0441 struct generic_product_impl<Lhs, Homogeneous<RhsArg,Vertical>, TriangularShape, HomogeneousShape, ProductTag>
0442 {
0443   template<typename Dest>
0444   static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
0445   {
0446     dst.noalias() = lhs * rhs.eval();
0447   }
0448 };
0449 
0450 template<typename Lhs,typename Rhs>
0451 struct homogeneous_left_product_refactoring_helper
0452 {
0453   enum {
0454     Dim = Rhs::RowsAtCompileTime,
0455     Cols = Rhs::ColsAtCompileTime
0456   };
0457   typedef typename Lhs::template ConstNColsBlockXpr<Dim>::Type          LinearBlockConst;
0458   typedef typename remove_const<LinearBlockConst>::type                 LinearBlock;
0459   typedef typename Lhs::ConstColXpr                                     ConstantColumn;
0460   typedef Replicate<const ConstantColumn,1,Cols>                        ConstantBlock;
0461   typedef Product<LinearBlock,Rhs,LazyProduct>                          LinearProduct;
0462   typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
0463 };
0464 
0465 template<typename Lhs, typename Rhs, int ProductTag>
0466 struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, DenseShape, HomogeneousShape>
0467  : public evaluator<typename homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression>::Xpr>
0468 {
0469   typedef Product<Lhs, Rhs, LazyProduct> XprType;
0470   typedef homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression> helper;
0471   typedef typename helper::ConstantBlock ConstantBlock;
0472   typedef typename helper::Xpr RefactoredXpr;
0473   typedef evaluator<RefactoredXpr> Base;
0474 
0475   EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
0476     : Base(   xpr.lhs().template leftCols<helper::Dim>(xpr.rhs().nestedExpression().rows()) .lazyProduct( xpr.rhs().nestedExpression() )
0477             + ConstantBlock(xpr.lhs().col(xpr.lhs().cols()-1),1,xpr.rhs().cols()) )
0478   {}
0479 };
0480 
0481 template<typename Scalar, int Dim, int Mode,int Options, typename RhsArg, int ProductTag>
0482 struct generic_product_impl<Transform<Scalar,Dim,Mode,Options>, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>
0483 {
0484   typedef Transform<Scalar,Dim,Mode,Options> TransformType;
0485   template<typename Dest>
0486   EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const TransformType& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
0487   {
0488     homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, TransformType>(lhs, rhs.nestedExpression()).evalTo(dst);
0489   }
0490 };
0491 
0492 template<typename ExpressionType, int Side, bool Transposed>
0493 struct permutation_matrix_product<ExpressionType, Side, Transposed, HomogeneousShape>
0494   : public permutation_matrix_product<ExpressionType, Side, Transposed, DenseShape>
0495 {};
0496 
0497 } // end namespace internal
0498 
0499 } // end namespace Eigen
0500 
0501 #endif // EIGEN_HOMOGENEOUS_H
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