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