1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
5//
6// This Source Code Form is subject to the terms of the Mozilla
7// Public License v. 2.0. If a copy of the MPL was not distributed
8// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10#ifndef EIGEN_HOMOGENEOUS_H
11#define EIGEN_HOMOGENEOUS_H
12
13namespace Eigen {
14
15/** \geometry_module \ingroup Geometry_Module
16  *
17  * \class Homogeneous
18  *
19  * \brief Expression of one (or a set of) homogeneous vector(s)
20  *
21  * \param MatrixType the type of the object in which we are making homogeneous
22  *
23  * This class represents an expression of one (or a set of) homogeneous vector(s).
24  * It is the return type of MatrixBase::homogeneous() and most of the time
25  * this is the only way it is used.
26  *
27  * \sa MatrixBase::homogeneous()
28  */
29
30namespace internal {
31
32template<typename MatrixType,int Direction>
33struct traits<Homogeneous<MatrixType,Direction> >
34 : traits<MatrixType>
35{
36  typedef typename traits<MatrixType>::StorageKind StorageKind;
37  typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
38  typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
39  enum {
40    RowsPlusOne = (MatrixType::RowsAtCompileTime != Dynamic) ?
41                  int(MatrixType::RowsAtCompileTime) + 1 : Dynamic,
42    ColsPlusOne = (MatrixType::ColsAtCompileTime != Dynamic) ?
43                  int(MatrixType::ColsAtCompileTime) + 1 : Dynamic,
44    RowsAtCompileTime = Direction==Vertical  ?  RowsPlusOne : MatrixType::RowsAtCompileTime,
45    ColsAtCompileTime = Direction==Horizontal ? ColsPlusOne : MatrixType::ColsAtCompileTime,
46    MaxRowsAtCompileTime = RowsAtCompileTime,
47    MaxColsAtCompileTime = ColsAtCompileTime,
48    TmpFlags = _MatrixTypeNested::Flags & HereditaryBits,
49    Flags = ColsAtCompileTime==1 ? (TmpFlags & ~RowMajorBit)
50          : RowsAtCompileTime==1 ? (TmpFlags | RowMajorBit)
51          : TmpFlags
52  };
53};
54
55template<typename MatrixType,typename Lhs> struct homogeneous_left_product_impl;
56template<typename MatrixType,typename Rhs> struct homogeneous_right_product_impl;
57
58} // end namespace internal
59
60template<typename MatrixType,int _Direction> class Homogeneous
61  : public MatrixBase<Homogeneous<MatrixType,_Direction> >, internal::no_assignment_operator
62{
63  public:
64
65    typedef MatrixType NestedExpression;
66    enum { Direction = _Direction };
67
68    typedef MatrixBase<Homogeneous> Base;
69    EIGEN_DENSE_PUBLIC_INTERFACE(Homogeneous)
70
71    EIGEN_DEVICE_FUNC explicit inline Homogeneous(const MatrixType& matrix)
72      : m_matrix(matrix)
73    {}
74
75    EIGEN_DEVICE_FUNC inline Index rows() const { return m_matrix.rows() + (int(Direction)==Vertical   ? 1 : 0); }
76    EIGEN_DEVICE_FUNC inline Index cols() const { return m_matrix.cols() + (int(Direction)==Horizontal ? 1 : 0); }
77
78    EIGEN_DEVICE_FUNC const NestedExpression& nestedExpression() const { return m_matrix; }
79
80    template<typename Rhs>
81    EIGEN_DEVICE_FUNC inline const Product<Homogeneous,Rhs>
82    operator* (const MatrixBase<Rhs>& rhs) const
83    {
84      eigen_assert(int(Direction)==Horizontal);
85      return Product<Homogeneous,Rhs>(*this,rhs.derived());
86    }
87
88    template<typename Lhs> friend
89    EIGEN_DEVICE_FUNC inline const Product<Lhs,Homogeneous>
90    operator* (const MatrixBase<Lhs>& lhs, const Homogeneous& rhs)
91    {
92      eigen_assert(int(Direction)==Vertical);
93      return Product<Lhs,Homogeneous>(lhs.derived(),rhs);
94    }
95
96    template<typename Scalar, int Dim, int Mode, int Options> friend
97    EIGEN_DEVICE_FUNC inline const Product<Transform<Scalar,Dim,Mode,Options>, Homogeneous >
98    operator* (const Transform<Scalar,Dim,Mode,Options>& lhs, const Homogeneous& rhs)
99    {
100      eigen_assert(int(Direction)==Vertical);
101      return Product<Transform<Scalar,Dim,Mode,Options>, Homogeneous>(lhs,rhs);
102    }
103
104    template<typename Func>
105    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::result_of<Func(Scalar,Scalar)>::type
106    redux(const Func& func) const
107    {
108      return func(m_matrix.redux(func), Scalar(1));
109    }
110
111  protected:
112    typename MatrixType::Nested m_matrix;
113};
114
115/** \geometry_module \ingroup Geometry_Module
116  *
117  * \returns a vector expression that is one longer than the vector argument, with the value 1 symbolically appended as the last coefficient.
118  *
119  * This can be used to convert affine coordinates to homogeneous coordinates.
120  *
121  * \only_for_vectors
122  *
123  * Example: \include MatrixBase_homogeneous.cpp
124  * Output: \verbinclude MatrixBase_homogeneous.out
125  *
126  * \sa VectorwiseOp::homogeneous(), class Homogeneous
127  */
128template<typename Derived>
129EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::HomogeneousReturnType
130MatrixBase<Derived>::homogeneous() const
131{
132  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
133  return HomogeneousReturnType(derived());
134}
135
136/** \geometry_module \ingroup Geometry_Module
137  *
138  * \returns an expression where the value 1 is symbolically appended as the final coefficient to each column (or row) of the matrix.
139  *
140  * This can be used to convert affine coordinates to homogeneous coordinates.
141  *
142  * Example: \include VectorwiseOp_homogeneous.cpp
143  * Output: \verbinclude VectorwiseOp_homogeneous.out
144  *
145  * \sa MatrixBase::homogeneous(), class Homogeneous */
146template<typename ExpressionType, int Direction>
147EIGEN_DEVICE_FUNC inline Homogeneous<ExpressionType,Direction>
148VectorwiseOp<ExpressionType,Direction>::homogeneous() const
149{
150  return HomogeneousReturnType(_expression());
151}
152
153/** \geometry_module \ingroup Geometry_Module
154  *
155  * \brief homogeneous normalization
156  *
157  * \returns a vector expression of the N-1 first coefficients of \c *this divided by that last coefficient.
158  *
159  * This can be used to convert homogeneous coordinates to affine coordinates.
160  *
161  * It is essentially a shortcut for:
162  * \code
163    this->head(this->size()-1)/this->coeff(this->size()-1);
164    \endcode
165  *
166  * Example: \include MatrixBase_hnormalized.cpp
167  * Output: \verbinclude MatrixBase_hnormalized.out
168  *
169  * \sa VectorwiseOp::hnormalized() */
170template<typename Derived>
171EIGEN_DEVICE_FUNC inline const typename MatrixBase<Derived>::HNormalizedReturnType
172MatrixBase<Derived>::hnormalized() const
173{
174  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
175  return ConstStartMinusOne(derived(),0,0,
176    ColsAtCompileTime==1?size()-1:1,
177    ColsAtCompileTime==1?1:size()-1) / coeff(size()-1);
178}
179
180/** \geometry_module \ingroup Geometry_Module
181  *
182  * \brief column or row-wise homogeneous normalization
183  *
184  * \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).
185  *
186  * This can be used to convert homogeneous coordinates to affine coordinates.
187  *
188  * It is conceptually equivalent to calling MatrixBase::hnormalized() to each column (or row) of \c *this.
189  *
190  * Example: \include DirectionWise_hnormalized.cpp
191  * Output: \verbinclude DirectionWise_hnormalized.out
192  *
193  * \sa MatrixBase::hnormalized() */
194template<typename ExpressionType, int Direction>
195EIGEN_DEVICE_FUNC inline const typename VectorwiseOp<ExpressionType,Direction>::HNormalizedReturnType
196VectorwiseOp<ExpressionType,Direction>::hnormalized() const
197{
198  return HNormalized_Block(_expression(),0,0,
199      Direction==Vertical   ? _expression().rows()-1 : _expression().rows(),
200      Direction==Horizontal ? _expression().cols()-1 : _expression().cols()).cwiseQuotient(
201      Replicate<HNormalized_Factors,
202                Direction==Vertical   ? HNormalized_SizeMinusOne : 1,
203                Direction==Horizontal ? HNormalized_SizeMinusOne : 1>
204        (HNormalized_Factors(_expression(),
205          Direction==Vertical    ? _expression().rows()-1:0,
206          Direction==Horizontal  ? _expression().cols()-1:0,
207          Direction==Vertical    ? 1 : _expression().rows(),
208          Direction==Horizontal  ? 1 : _expression().cols()),
209         Direction==Vertical   ? _expression().rows()-1 : 1,
210         Direction==Horizontal ? _expression().cols()-1 : 1));
211}
212
213namespace internal {
214
215template<typename MatrixOrTransformType>
216struct take_matrix_for_product
217{
218  typedef MatrixOrTransformType type;
219  EIGEN_DEVICE_FUNC static const type& run(const type &x) { return x; }
220};
221
222template<typename Scalar, int Dim, int Mode,int Options>
223struct take_matrix_for_product<Transform<Scalar, Dim, Mode, Options> >
224{
225  typedef Transform<Scalar, Dim, Mode, Options> TransformType;
226  typedef typename internal::add_const<typename TransformType::ConstAffinePart>::type type;
227  EIGEN_DEVICE_FUNC static type run (const TransformType& x) { return x.affine(); }
228};
229
230template<typename Scalar, int Dim, int Options>
231struct take_matrix_for_product<Transform<Scalar, Dim, Projective, Options> >
232{
233  typedef Transform<Scalar, Dim, Projective, Options> TransformType;
234  typedef typename TransformType::MatrixType type;
235  EIGEN_DEVICE_FUNC static const type& run (const TransformType& x) { return x.matrix(); }
236};
237
238template<typename MatrixType,typename Lhs>
239struct traits<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
240{
241  typedef typename take_matrix_for_product<Lhs>::type LhsMatrixType;
242  typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;
243  typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
244  typedef typename make_proper_matrix_type<
245                 typename traits<MatrixTypeCleaned>::Scalar,
246                 LhsMatrixTypeCleaned::RowsAtCompileTime,
247                 MatrixTypeCleaned::ColsAtCompileTime,
248                 MatrixTypeCleaned::PlainObject::Options,
249                 LhsMatrixTypeCleaned::MaxRowsAtCompileTime,
250                 MatrixTypeCleaned::MaxColsAtCompileTime>::type ReturnType;
251};
252
253template<typename MatrixType,typename Lhs>
254struct homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs>
255  : public ReturnByValue<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
256{
257  typedef typename traits<homogeneous_left_product_impl>::LhsMatrixType LhsMatrixType;
258  typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
259  typedef typename remove_all<typename LhsMatrixTypeCleaned::Nested>::type LhsMatrixTypeNested;
260  EIGEN_DEVICE_FUNC homogeneous_left_product_impl(const Lhs& lhs, const MatrixType& rhs)
261    : m_lhs(take_matrix_for_product<Lhs>::run(lhs)),
262      m_rhs(rhs)
263  {}
264
265  EIGEN_DEVICE_FUNC inline Index rows() const { return m_lhs.rows(); }
266  EIGEN_DEVICE_FUNC inline Index cols() const { return m_rhs.cols(); }
267
268  template<typename Dest> EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const
269  {
270    // FIXME investigate how to allow lazy evaluation of this product when possible
271    dst = Block<const LhsMatrixTypeNested,
272              LhsMatrixTypeNested::RowsAtCompileTime,
273              LhsMatrixTypeNested::ColsAtCompileTime==Dynamic?Dynamic:LhsMatrixTypeNested::ColsAtCompileTime-1>
274            (m_lhs,0,0,m_lhs.rows(),m_lhs.cols()-1) * m_rhs;
275    dst += m_lhs.col(m_lhs.cols()-1).rowwise()
276            .template replicate<MatrixType::ColsAtCompileTime>(m_rhs.cols());
277  }
278
279  typename LhsMatrixTypeCleaned::Nested m_lhs;
280  typename MatrixType::Nested m_rhs;
281};
282
283template<typename MatrixType,typename Rhs>
284struct traits<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
285{
286  typedef typename make_proper_matrix_type<typename traits<MatrixType>::Scalar,
287                 MatrixType::RowsAtCompileTime,
288                 Rhs::ColsAtCompileTime,
289                 MatrixType::PlainObject::Options,
290                 MatrixType::MaxRowsAtCompileTime,
291                 Rhs::MaxColsAtCompileTime>::type ReturnType;
292};
293
294template<typename MatrixType,typename Rhs>
295struct homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs>
296  : public ReturnByValue<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
297{
298  typedef typename remove_all<typename Rhs::Nested>::type RhsNested;
299  EIGEN_DEVICE_FUNC homogeneous_right_product_impl(const MatrixType& lhs, const Rhs& rhs)
300    : m_lhs(lhs), m_rhs(rhs)
301  {}
302
303  EIGEN_DEVICE_FUNC inline Index rows() const { return m_lhs.rows(); }
304  EIGEN_DEVICE_FUNC inline Index cols() const { return m_rhs.cols(); }
305
306  template<typename Dest> EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const
307  {
308    // FIXME investigate how to allow lazy evaluation of this product when possible
309    dst = m_lhs * Block<const RhsNested,
310                        RhsNested::RowsAtCompileTime==Dynamic?Dynamic:RhsNested::RowsAtCompileTime-1,
311                        RhsNested::ColsAtCompileTime>
312            (m_rhs,0,0,m_rhs.rows()-1,m_rhs.cols());
313    dst += m_rhs.row(m_rhs.rows()-1).colwise()
314            .template replicate<MatrixType::RowsAtCompileTime>(m_lhs.rows());
315  }
316
317  typename MatrixType::Nested m_lhs;
318  typename Rhs::Nested m_rhs;
319};
320
321template<typename ArgType,int Direction>
322struct evaluator_traits<Homogeneous<ArgType,Direction> >
323{
324  typedef typename storage_kind_to_evaluator_kind<typename ArgType::StorageKind>::Kind Kind;
325  typedef HomogeneousShape Shape;
326};
327
328template<> struct AssignmentKind<DenseShape,HomogeneousShape> { typedef Dense2Dense Kind; };
329
330
331template<typename ArgType,int Direction>
332struct unary_evaluator<Homogeneous<ArgType,Direction>, IndexBased>
333  : evaluator<typename Homogeneous<ArgType,Direction>::PlainObject >
334{
335  typedef Homogeneous<ArgType,Direction> XprType;
336  typedef typename XprType::PlainObject PlainObject;
337  typedef evaluator<PlainObject> Base;
338
339  EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& op)
340    : Base(), m_temp(op)
341  {
342    ::new (static_cast<Base*>(this)) Base(m_temp);
343  }
344
345protected:
346  PlainObject m_temp;
347};
348
349// dense = homogeneous
350template< typename DstXprType, typename ArgType, typename Scalar>
351struct Assignment<DstXprType, Homogeneous<ArgType,Vertical>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
352{
353  typedef Homogeneous<ArgType,Vertical> SrcXprType;
354  EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
355  {
356    Index dstRows = src.rows();
357    Index dstCols = src.cols();
358    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
359      dst.resize(dstRows, dstCols);
360
361    dst.template topRows<ArgType::RowsAtCompileTime>(src.nestedExpression().rows()) = src.nestedExpression();
362    dst.row(dst.rows()-1).setOnes();
363  }
364};
365
366// dense = homogeneous
367template< typename DstXprType, typename ArgType, typename Scalar>
368struct Assignment<DstXprType, Homogeneous<ArgType,Horizontal>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
369{
370  typedef Homogeneous<ArgType,Horizontal> SrcXprType;
371  EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
372  {
373    Index dstRows = src.rows();
374    Index dstCols = src.cols();
375    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
376      dst.resize(dstRows, dstCols);
377
378    dst.template leftCols<ArgType::ColsAtCompileTime>(src.nestedExpression().cols()) = src.nestedExpression();
379    dst.col(dst.cols()-1).setOnes();
380  }
381};
382
383template<typename LhsArg, typename Rhs, int ProductTag>
384struct generic_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs, HomogeneousShape, DenseShape, ProductTag>
385{
386  template<typename Dest>
387  EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Homogeneous<LhsArg,Horizontal>& lhs, const Rhs& rhs)
388  {
389    homogeneous_right_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs>(lhs.nestedExpression(), rhs).evalTo(dst);
390  }
391};
392
393template<typename Lhs,typename Rhs>
394struct homogeneous_right_product_refactoring_helper
395{
396  enum {
397    Dim  = Lhs::ColsAtCompileTime,
398    Rows = Lhs::RowsAtCompileTime
399  };
400  typedef typename Rhs::template ConstNRowsBlockXpr<Dim>::Type          LinearBlockConst;
401  typedef typename remove_const<LinearBlockConst>::type                 LinearBlock;
402  typedef typename Rhs::ConstRowXpr                                     ConstantColumn;
403  typedef Replicate<const ConstantColumn,Rows,1>                        ConstantBlock;
404  typedef Product<Lhs,LinearBlock,LazyProduct>                          LinearProduct;
405  typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
406};
407
408template<typename Lhs, typename Rhs, int ProductTag>
409struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, HomogeneousShape, DenseShape>
410 : public evaluator<typename homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs>::Xpr>
411{
412  typedef Product<Lhs, Rhs, LazyProduct> XprType;
413  typedef homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs> helper;
414  typedef typename helper::ConstantBlock ConstantBlock;
415  typedef typename helper::Xpr RefactoredXpr;
416  typedef evaluator<RefactoredXpr> Base;
417
418  EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
419    : Base(  xpr.lhs().nestedExpression() .lazyProduct(  xpr.rhs().template topRows<helper::Dim>(xpr.lhs().nestedExpression().cols()) )
420            + ConstantBlock(xpr.rhs().row(xpr.rhs().rows()-1),xpr.lhs().rows(), 1) )
421  {}
422};
423
424template<typename Lhs, typename RhsArg, int ProductTag>
425struct generic_product_impl<Lhs, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>
426{
427  template<typename Dest>
428  EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
429  {
430    homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, Lhs>(lhs, rhs.nestedExpression()).evalTo(dst);
431  }
432};
433
434// TODO: the following specialization is to address a regression from 3.2 to 3.3
435// In the future, this path should be optimized.
436template<typename Lhs, typename RhsArg, int ProductTag>
437struct generic_product_impl<Lhs, Homogeneous<RhsArg,Vertical>, TriangularShape, HomogeneousShape, ProductTag>
438{
439  template<typename Dest>
440  static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
441  {
442    dst.noalias() = lhs * rhs.eval();
443  }
444};
445
446template<typename Lhs,typename Rhs>
447struct homogeneous_left_product_refactoring_helper
448{
449  enum {
450    Dim = Rhs::RowsAtCompileTime,
451    Cols = Rhs::ColsAtCompileTime
452  };
453  typedef typename Lhs::template ConstNColsBlockXpr<Dim>::Type          LinearBlockConst;
454  typedef typename remove_const<LinearBlockConst>::type                 LinearBlock;
455  typedef typename Lhs::ConstColXpr                                     ConstantColumn;
456  typedef Replicate<const ConstantColumn,1,Cols>                        ConstantBlock;
457  typedef Product<LinearBlock,Rhs,LazyProduct>                          LinearProduct;
458  typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
459};
460
461template<typename Lhs, typename Rhs, int ProductTag>
462struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, DenseShape, HomogeneousShape>
463 : public evaluator<typename homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression>::Xpr>
464{
465  typedef Product<Lhs, Rhs, LazyProduct> XprType;
466  typedef homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression> helper;
467  typedef typename helper::ConstantBlock ConstantBlock;
468  typedef typename helper::Xpr RefactoredXpr;
469  typedef evaluator<RefactoredXpr> Base;
470
471  EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
472    : Base(   xpr.lhs().template leftCols<helper::Dim>(xpr.rhs().nestedExpression().rows()) .lazyProduct( xpr.rhs().nestedExpression() )
473            + ConstantBlock(xpr.lhs().col(xpr.lhs().cols()-1),1,xpr.rhs().cols()) )
474  {}
475};
476
477template<typename Scalar, int Dim, int Mode,int Options, typename RhsArg, int ProductTag>
478struct generic_product_impl<Transform<Scalar,Dim,Mode,Options>, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>
479{
480  typedef Transform<Scalar,Dim,Mode,Options> TransformType;
481  template<typename Dest>
482  EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const TransformType& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
483  {
484    homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, TransformType>(lhs, rhs.nestedExpression()).evalTo(dst);
485  }
486};
487
488template<typename ExpressionType, int Side, bool Transposed>
489struct permutation_matrix_product<ExpressionType, Side, Transposed, HomogeneousShape>
490  : public permutation_matrix_product<ExpressionType, Side, Transposed, DenseShape>
491{};
492
493} // end namespace internal
494
495} // end namespace Eigen
496
497#endif // EIGEN_HOMOGENEOUS_H
498