Eigen  3.3.7
Homogeneous.h
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 
13 namespace Eigen {
14 
30 namespace internal {
31 
32 template<typename MatrixType,int Direction>
33 struct 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 
55 template<typename MatrixType,typename Lhs> struct homogeneous_left_product_impl;
56 template<typename MatrixType,typename Rhs> struct homogeneous_right_product_impl;
57 
58 } // end namespace internal
59 
60 template<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 
128 template<typename Derived>
129 EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::HomogeneousReturnType
131 {
132  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
133  return HomogeneousReturnType(derived());
134 }
135 
146 template<typename ExpressionType, int Direction>
147 EIGEN_DEVICE_FUNC inline Homogeneous<ExpressionType,Direction>
149 {
150  return HomogeneousReturnType(_expression());
151 }
152 
170 template<typename Derived>
171 EIGEN_DEVICE_FUNC inline const typename MatrixBase<Derived>::HNormalizedReturnType
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 
194 template<typename ExpressionType, int Direction>
195 EIGEN_DEVICE_FUNC inline const typename VectorwiseOp<ExpressionType,Direction>::HNormalizedReturnType
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(
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 
213 namespace internal {
214 
215 template<typename MatrixOrTransformType>
216 struct take_matrix_for_product
217 {
218  typedef MatrixOrTransformType type;
219  EIGEN_DEVICE_FUNC static const type& run(const type &x) { return x; }
220 };
221 
222 template<typename Scalar, int Dim, int Mode,int Options>
223 struct 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 
230 template<typename Scalar, int Dim, int Options>
231 struct 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 
238 template<typename MatrixType,typename Lhs>
239 struct 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 
253 template<typename MatrixType,typename Lhs>
254 struct 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 
283 template<typename MatrixType,typename Rhs>
284 struct 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 
294 template<typename MatrixType,typename Rhs>
295 struct 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 
321 template<typename ArgType,int Direction>
322 struct 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 
328 template<> struct AssignmentKind<DenseShape,HomogeneousShape> { typedef Dense2Dense Kind; };
329 
330 
331 template<typename ArgType,int Direction>
332 struct 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 
345 protected:
346  PlainObject m_temp;
347 };
348 
349 // dense = homogeneous
350 template< typename DstXprType, typename ArgType, typename Scalar>
351 struct 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
367 template< typename DstXprType, typename ArgType, typename Scalar>
368 struct 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 
383 template<typename LhsArg, typename Rhs, int ProductTag>
384 struct 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 
393 template<typename Lhs,typename Rhs>
394 struct 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 
408 template<typename Lhs, typename Rhs, int ProductTag>
409 struct 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 
424 template<typename Lhs, typename RhsArg, int ProductTag>
425 struct 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.
436 template<typename Lhs, typename RhsArg, int ProductTag>
437 struct 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 
446 template<typename Lhs,typename Rhs>
447 struct 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 
461 template<typename Lhs, typename Rhs, int ProductTag>
462 struct 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 
477 template<typename Scalar, int Dim, int Mode,int Options, typename RhsArg, int ProductTag>
478 struct 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 
488 template<typename ExpressionType, int Side, bool Transposed>
489 struct 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
internal::traits< Derived >::Scalar Scalar
Definition: DenseBase.h:66
Definition: Constants.h:265
HomogeneousReturnType homogeneous() const
Definition: Homogeneous.h:148
const HNormalizedReturnType hnormalized() const
column or row-wise homogeneous normalization
Definition: Homogeneous.h:196
Namespace containing all symbols from the Eigen library.
Definition: Core:306
Eigen::Index Index
The interface type of indices.
Definition: EigenBase.h:38
const unsigned int RowMajorBit
Definition: Constants.h:61
Definition: Constants.h:454
Generic expression where a coefficient-wise binary operator is applied to two expressions.
Definition: CwiseBinaryOp.h:77
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33
Expression of the multiple replication of a matrix or vector.
Definition: Replicate.h:61
Definition: Constants.h:268
Definition: Eigen_Colamd.h:50
const HNormalizedReturnType hnormalized() const
homogeneous normalization
Definition: Homogeneous.h:172
Expression of a fixed-size or dynamic-size block.
Definition: Block.h:103
const int Dynamic
Definition: Constants.h:21
HomogeneousReturnType homogeneous() const
Definition: Homogeneous.h:130
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
Expression of one (or a set of) homogeneous vector(s)
Definition: ForwardDeclarations.h:274