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Eigen  3.4.0
 
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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
13namespace Eigen {
14
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
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 EIGEN_CONSTEXPR
76 inline Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows() + (int(Direction)==Vertical ? 1 : 0); }
77 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
78 inline Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols() + (int(Direction)==Horizontal ? 1 : 0); }
79
80 EIGEN_DEVICE_FUNC const NestedExpression& nestedExpression() const { return m_matrix; }
81
82 template<typename Rhs>
83 EIGEN_DEVICE_FUNC inline const Product<Homogeneous,Rhs>
84 operator* (const MatrixBase<Rhs>& rhs) const
85 {
86 eigen_assert(int(Direction)==Horizontal);
87 return Product<Homogeneous,Rhs>(*this,rhs.derived());
88 }
89
90 template<typename Lhs> friend
91 EIGEN_DEVICE_FUNC inline const Product<Lhs,Homogeneous>
92 operator* (const MatrixBase<Lhs>& lhs, const Homogeneous& rhs)
93 {
94 eigen_assert(int(Direction)==Vertical);
95 return Product<Lhs,Homogeneous>(lhs.derived(),rhs);
96 }
97
98 template<typename Scalar, int Dim, int Mode, int Options> friend
99 EIGEN_DEVICE_FUNC inline const Product<Transform<Scalar,Dim,Mode,Options>, Homogeneous >
100 operator* (const Transform<Scalar,Dim,Mode,Options>& lhs, const Homogeneous& rhs)
101 {
102 eigen_assert(int(Direction)==Vertical);
104 }
105
106 template<typename Func>
107 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::result_of<Func(Scalar,Scalar)>::type
108 redux(const Func& func) const
109 {
110 return func(m_matrix.redux(func), Scalar(1));
111 }
112
113 protected:
114 typename MatrixType::Nested m_matrix;
115};
116
130template<typename Derived>
131EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::HomogeneousReturnType
133{
134 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
135 return HomogeneousReturnType(derived());
136}
137
148template<typename ExpressionType, int Direction>
149EIGEN_DEVICE_FUNC inline Homogeneous<ExpressionType,Direction>
151{
152 return HomogeneousReturnType(_expression());
153}
154
172template<typename Derived>
173EIGEN_DEVICE_FUNC inline const typename MatrixBase<Derived>::HNormalizedReturnType
175{
176 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
177 return ConstStartMinusOne(derived(),0,0,
178 ColsAtCompileTime==1?size()-1:1,
179 ColsAtCompileTime==1?1:size()-1) / coeff(size()-1);
180}
181
196template<typename ExpressionType, int Direction>
197EIGEN_DEVICE_FUNC inline const typename VectorwiseOp<ExpressionType,Direction>::HNormalizedReturnType
199{
200 return HNormalized_Block(_expression(),0,0,
201 Direction==Vertical ? _expression().rows()-1 : _expression().rows(),
202 Direction==Horizontal ? _expression().cols()-1 : _expression().cols()).cwiseQuotient(
204 Direction==Vertical ? HNormalized_SizeMinusOne : 1,
205 Direction==Horizontal ? HNormalized_SizeMinusOne : 1>
206 (HNormalized_Factors(_expression(),
207 Direction==Vertical ? _expression().rows()-1:0,
208 Direction==Horizontal ? _expression().cols()-1:0,
209 Direction==Vertical ? 1 : _expression().rows(),
210 Direction==Horizontal ? 1 : _expression().cols()),
211 Direction==Vertical ? _expression().rows()-1 : 1,
212 Direction==Horizontal ? _expression().cols()-1 : 1));
213}
214
215namespace internal {
216
217template<typename MatrixOrTransformType>
218struct take_matrix_for_product
219{
220 typedef MatrixOrTransformType type;
221 EIGEN_DEVICE_FUNC static const type& run(const type &x) { return x; }
222};
223
224template<typename Scalar, int Dim, int Mode,int Options>
225struct take_matrix_for_product<Transform<Scalar, Dim, Mode, Options> >
226{
227 typedef Transform<Scalar, Dim, Mode, Options> TransformType;
228 typedef typename internal::add_const<typename TransformType::ConstAffinePart>::type type;
229 EIGEN_DEVICE_FUNC static type run (const TransformType& x) { return x.affine(); }
230};
231
232template<typename Scalar, int Dim, int Options>
233struct take_matrix_for_product<Transform<Scalar, Dim, Projective, Options> >
234{
235 typedef Transform<Scalar, Dim, Projective, Options> TransformType;
236 typedef typename TransformType::MatrixType type;
237 EIGEN_DEVICE_FUNC static const type& run (const TransformType& x) { return x.matrix(); }
238};
239
240template<typename MatrixType,typename Lhs>
241struct traits<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
242{
243 typedef typename take_matrix_for_product<Lhs>::type LhsMatrixType;
244 typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;
245 typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
246 typedef typename make_proper_matrix_type<
247 typename traits<MatrixTypeCleaned>::Scalar,
248 LhsMatrixTypeCleaned::RowsAtCompileTime,
249 MatrixTypeCleaned::ColsAtCompileTime,
250 MatrixTypeCleaned::PlainObject::Options,
251 LhsMatrixTypeCleaned::MaxRowsAtCompileTime,
252 MatrixTypeCleaned::MaxColsAtCompileTime>::type ReturnType;
253};
254
255template<typename MatrixType,typename Lhs>
256struct homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs>
257 : public ReturnByValue<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
258{
259 typedef typename traits<homogeneous_left_product_impl>::LhsMatrixType LhsMatrixType;
260 typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
261 typedef typename remove_all<typename LhsMatrixTypeCleaned::Nested>::type LhsMatrixTypeNested;
262 EIGEN_DEVICE_FUNC homogeneous_left_product_impl(const Lhs& lhs, const MatrixType& rhs)
263 : m_lhs(take_matrix_for_product<Lhs>::run(lhs)),
264 m_rhs(rhs)
265 {}
266
267 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
268 inline Index rows() const EIGEN_NOEXCEPT { return m_lhs.rows(); }
269 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
270 inline Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }
271
272 template<typename Dest> EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const
273 {
274 // FIXME investigate how to allow lazy evaluation of this product when possible
275 dst = Block<const LhsMatrixTypeNested,
276 LhsMatrixTypeNested::RowsAtCompileTime,
277 LhsMatrixTypeNested::ColsAtCompileTime==Dynamic?Dynamic:LhsMatrixTypeNested::ColsAtCompileTime-1>
278 (m_lhs,0,0,m_lhs.rows(),m_lhs.cols()-1) * m_rhs;
279 dst += m_lhs.col(m_lhs.cols()-1).rowwise()
280 .template replicate<MatrixType::ColsAtCompileTime>(m_rhs.cols());
281 }
282
283 typename LhsMatrixTypeCleaned::Nested m_lhs;
284 typename MatrixType::Nested m_rhs;
285};
286
287template<typename MatrixType,typename Rhs>
288struct traits<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
289{
290 typedef typename make_proper_matrix_type<typename traits<MatrixType>::Scalar,
291 MatrixType::RowsAtCompileTime,
292 Rhs::ColsAtCompileTime,
293 MatrixType::PlainObject::Options,
294 MatrixType::MaxRowsAtCompileTime,
295 Rhs::MaxColsAtCompileTime>::type ReturnType;
296};
297
298template<typename MatrixType,typename Rhs>
299struct homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs>
300 : public ReturnByValue<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
301{
302 typedef typename remove_all<typename Rhs::Nested>::type RhsNested;
303 EIGEN_DEVICE_FUNC homogeneous_right_product_impl(const MatrixType& lhs, const Rhs& rhs)
304 : m_lhs(lhs), m_rhs(rhs)
305 {}
306
307 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_lhs.rows(); }
308 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }
309
310 template<typename Dest> EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const
311 {
312 // FIXME investigate how to allow lazy evaluation of this product when possible
313 dst = m_lhs * Block<const RhsNested,
314 RhsNested::RowsAtCompileTime==Dynamic?Dynamic:RhsNested::RowsAtCompileTime-1,
315 RhsNested::ColsAtCompileTime>
316 (m_rhs,0,0,m_rhs.rows()-1,m_rhs.cols());
317 dst += m_rhs.row(m_rhs.rows()-1).colwise()
318 .template replicate<MatrixType::RowsAtCompileTime>(m_lhs.rows());
319 }
320
321 typename MatrixType::Nested m_lhs;
322 typename Rhs::Nested m_rhs;
323};
324
325template<typename ArgType,int Direction>
326struct evaluator_traits<Homogeneous<ArgType,Direction> >
327{
328 typedef typename storage_kind_to_evaluator_kind<typename ArgType::StorageKind>::Kind Kind;
329 typedef HomogeneousShape Shape;
330};
331
332template<> struct AssignmentKind<DenseShape,HomogeneousShape> { typedef Dense2Dense Kind; };
333
334
335template<typename ArgType,int Direction>
336struct unary_evaluator<Homogeneous<ArgType,Direction>, IndexBased>
337 : evaluator<typename Homogeneous<ArgType,Direction>::PlainObject >
338{
339 typedef Homogeneous<ArgType,Direction> XprType;
340 typedef typename XprType::PlainObject PlainObject;
341 typedef evaluator<PlainObject> Base;
342
343 EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& op)
344 : Base(), m_temp(op)
345 {
346 ::new (static_cast<Base*>(this)) Base(m_temp);
347 }
348
349protected:
350 PlainObject m_temp;
351};
352
353// dense = homogeneous
354template< typename DstXprType, typename ArgType, typename Scalar>
355struct Assignment<DstXprType, Homogeneous<ArgType,Vertical>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
356{
357 typedef Homogeneous<ArgType,Vertical> SrcXprType;
358 EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
359 {
360 Index dstRows = src.rows();
361 Index dstCols = src.cols();
362 if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
363 dst.resize(dstRows, dstCols);
364
365 dst.template topRows<ArgType::RowsAtCompileTime>(src.nestedExpression().rows()) = src.nestedExpression();
366 dst.row(dst.rows()-1).setOnes();
367 }
368};
369
370// dense = homogeneous
371template< typename DstXprType, typename ArgType, typename Scalar>
372struct Assignment<DstXprType, Homogeneous<ArgType,Horizontal>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
373{
374 typedef Homogeneous<ArgType,Horizontal> SrcXprType;
375 EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
376 {
377 Index dstRows = src.rows();
378 Index dstCols = src.cols();
379 if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
380 dst.resize(dstRows, dstCols);
381
382 dst.template leftCols<ArgType::ColsAtCompileTime>(src.nestedExpression().cols()) = src.nestedExpression();
383 dst.col(dst.cols()-1).setOnes();
384 }
385};
386
387template<typename LhsArg, typename Rhs, int ProductTag>
388struct generic_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs, HomogeneousShape, DenseShape, ProductTag>
389{
390 template<typename Dest>
391 EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Homogeneous<LhsArg,Horizontal>& lhs, const Rhs& rhs)
392 {
393 homogeneous_right_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs>(lhs.nestedExpression(), rhs).evalTo(dst);
394 }
395};
396
397template<typename Lhs,typename Rhs>
398struct homogeneous_right_product_refactoring_helper
399{
400 enum {
401 Dim = Lhs::ColsAtCompileTime,
402 Rows = Lhs::RowsAtCompileTime
403 };
404 typedef typename Rhs::template ConstNRowsBlockXpr<Dim>::Type LinearBlockConst;
405 typedef typename remove_const<LinearBlockConst>::type LinearBlock;
406 typedef typename Rhs::ConstRowXpr ConstantColumn;
408 typedef Product<Lhs,LinearBlock,LazyProduct> LinearProduct;
409 typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
410};
411
412template<typename Lhs, typename Rhs, int ProductTag>
413struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, HomogeneousShape, DenseShape>
414 : public evaluator<typename homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs>::Xpr>
415{
416 typedef Product<Lhs, Rhs, LazyProduct> XprType;
417 typedef homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs> helper;
418 typedef typename helper::ConstantBlock ConstantBlock;
419 typedef typename helper::Xpr RefactoredXpr;
420 typedef evaluator<RefactoredXpr> Base;
421
422 EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
423 : Base( xpr.lhs().nestedExpression() .lazyProduct( xpr.rhs().template topRows<helper::Dim>(xpr.lhs().nestedExpression().cols()) )
424 + ConstantBlock(xpr.rhs().row(xpr.rhs().rows()-1),xpr.lhs().rows(), 1) )
425 {}
426};
427
428template<typename Lhs, typename RhsArg, int ProductTag>
429struct generic_product_impl<Lhs, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>
430{
431 template<typename Dest>
432 EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
433 {
434 homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, Lhs>(lhs, rhs.nestedExpression()).evalTo(dst);
435 }
436};
437
438// TODO: the following specialization is to address a regression from 3.2 to 3.3
439// In the future, this path should be optimized.
440template<typename Lhs, typename RhsArg, int ProductTag>
441struct generic_product_impl<Lhs, Homogeneous<RhsArg,Vertical>, TriangularShape, HomogeneousShape, ProductTag>
442{
443 template<typename Dest>
444 static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
445 {
446 dst.noalias() = lhs * rhs.eval();
447 }
448};
449
450template<typename Lhs,typename Rhs>
451struct homogeneous_left_product_refactoring_helper
452{
453 enum {
454 Dim = Rhs::RowsAtCompileTime,
455 Cols = Rhs::ColsAtCompileTime
456 };
457 typedef typename Lhs::template ConstNColsBlockXpr<Dim>::Type LinearBlockConst;
458 typedef typename remove_const<LinearBlockConst>::type LinearBlock;
459 typedef typename Lhs::ConstColXpr ConstantColumn;
460 typedef Replicate<const ConstantColumn,1,Cols> ConstantBlock;
461 typedef Product<LinearBlock,Rhs,LazyProduct> LinearProduct;
462 typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
463};
464
465template<typename Lhs, typename Rhs, int ProductTag>
466struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, DenseShape, HomogeneousShape>
467 : public evaluator<typename homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression>::Xpr>
468{
469 typedef Product<Lhs, Rhs, LazyProduct> XprType;
470 typedef homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression> helper;
471 typedef typename helper::ConstantBlock ConstantBlock;
472 typedef typename helper::Xpr RefactoredXpr;
473 typedef evaluator<RefactoredXpr> Base;
474
475 EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
476 : Base( xpr.lhs().template leftCols<helper::Dim>(xpr.rhs().nestedExpression().rows()) .lazyProduct( xpr.rhs().nestedExpression() )
477 + ConstantBlock(xpr.lhs().col(xpr.lhs().cols()-1),1,xpr.rhs().cols()) )
478 {}
479};
480
481template<typename Scalar, int Dim, int Mode,int Options, typename RhsArg, int ProductTag>
482struct generic_product_impl<Transform<Scalar,Dim,Mode,Options>, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>
483{
484 typedef Transform<Scalar,Dim,Mode,Options> TransformType;
485 template<typename Dest>
486 EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const TransformType& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
487 {
488 homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, TransformType>(lhs, rhs.nestedExpression()).evalTo(dst);
489 }
490};
491
492template<typename ExpressionType, int Side, bool Transposed>
493struct permutation_matrix_product<ExpressionType, Side, Transposed, HomogeneousShape>
494 : public permutation_matrix_product<ExpressionType, Side, Transposed, DenseShape>
495{};
496
497} // end namespace internal
498
499} // end namespace Eigen
500
501#endif // EIGEN_HOMOGENEOUS_H
Expression of a fixed-size or dynamic-size block.
Definition: Block.h:105
Generic expression where a coefficient-wise binary operator is applied to two expressions.
Definition: CwiseBinaryOp.h:84
internal::traits< Derived >::Scalar Scalar
Definition: DenseBase.h:66
Derived & derived()
Definition: EigenBase.h:46
Expression of one (or a set of) homogeneous vector(s)
Definition: Homogeneous.h:62
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:50
Expression of the product of two arbitrary matrices or vectors.
Definition: Product.h:75
Expression of the multiple replication of a matrix or vector.
Definition: Replicate.h:63
Represents an homogeneous transformation in a N dimensional space.
Definition: Transform.h:205
Pseudo expression providing broadcasting and partial reduction operations.
Definition: VectorwiseOp.h:187
@ Horizontal
Definition: Constants.h:267
@ Vertical
Definition: Constants.h:264
@ Projective
Definition: Constants.h:464
Namespace containing all symbols from the Eigen library.
Definition: Core:141
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
const int Dynamic
Definition: Constants.h:22