10#ifndef EIGEN_HOMOGENEOUS_H
11#define EIGEN_HOMOGENEOUS_H
32template<
typename MatrixType,
int Direction>
33struct traits<Homogeneous<MatrixType,Direction> >
36 typedef typename traits<MatrixType>::StorageKind StorageKind;
37 typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
38 typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
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)
55template<
typename MatrixType,
typename Lhs>
struct homogeneous_left_product_impl;
56template<
typename MatrixType,
typename Rhs>
struct homogeneous_right_product_impl;
61 :
public MatrixBase<Homogeneous<MatrixType,_Direction> >, internal::no_assignment_operator
65 typedef MatrixType NestedExpression;
66 enum { Direction = _Direction };
71 EIGEN_DEVICE_FUNC
explicit inline Homogeneous(
const MatrixType& matrix)
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); }
80 EIGEN_DEVICE_FUNC
const NestedExpression& nestedExpression()
const {
return m_matrix; }
82 template<
typename Rhs>
90 template<
typename Lhs>
friend
94 eigen_assert(
int(Direction)==
Vertical);
98 template<
typename Scalar,
int Dim,
int Mode,
int Options>
friend
102 eigen_assert(
int(Direction)==
Vertical);
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
110 return func(m_matrix.redux(func),
Scalar(1));
114 typename MatrixType::Nested m_matrix;
130template<
typename Derived>
134 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
148template<
typename ExpressionType,
int Direction>
172template<
typename Derived>
176 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
178 ColsAtCompileTime==1?size()-1:1,
179 ColsAtCompileTime==1?1:size()-1) / coeff(size()-1);
196template<
typename ExpressionType,
int Direction>
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>
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));
217template<
typename MatrixOrTransformType>
218struct take_matrix_for_product
220 typedef MatrixOrTransformType type;
221 EIGEN_DEVICE_FUNC
static const type& run(
const type &x) {
return x; }
224template<
typename Scalar,
int Dim,
int Mode,
int Options>
225struct take_matrix_for_product<Transform<Scalar, Dim, Mode, Options> >
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(); }
232template<
typename Scalar,
int Dim,
int Options>
233struct take_matrix_for_product<Transform<Scalar, Dim,
Projective, Options> >
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(); }
240template<
typename MatrixType,
typename Lhs>
241struct traits<homogeneous_left_product_impl<Homogeneous<MatrixType,
Vertical>,Lhs> >
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;
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> >
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)),
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(); }
272 template<
typename Dest> EIGEN_DEVICE_FUNC
void evalTo(Dest& dst)
const
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());
283 typename LhsMatrixTypeCleaned::Nested m_lhs;
284 typename MatrixType::Nested m_rhs;
287template<
typename MatrixType,
typename Rhs>
288struct traits<homogeneous_right_product_impl<Homogeneous<MatrixType,
Horizontal>,Rhs> >
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;
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> >
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)
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(); }
310 template<
typename Dest> EIGEN_DEVICE_FUNC
void evalTo(Dest& dst)
const
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());
321 typename MatrixType::Nested m_lhs;
322 typename Rhs::Nested m_rhs;
325template<
typename ArgType,
int Direction>
326struct evaluator_traits<Homogeneous<ArgType,Direction> >
328 typedef typename storage_kind_to_evaluator_kind<typename ArgType::StorageKind>::Kind Kind;
329 typedef HomogeneousShape Shape;
332template<>
struct AssignmentKind<DenseShape,HomogeneousShape> {
typedef Dense2Dense Kind; };
335template<
typename ArgType,
int Direction>
336struct unary_evaluator<Homogeneous<ArgType,Direction>, IndexBased>
337 : evaluator<typename Homogeneous<ArgType,Direction>::PlainObject >
339 typedef Homogeneous<ArgType,Direction> XprType;
340 typedef typename XprType::PlainObject PlainObject;
341 typedef evaluator<PlainObject> Base;
343 EIGEN_DEVICE_FUNC
explicit unary_evaluator(
const XprType& op)
346 ::new (
static_cast<Base*
>(
this)) Base(m_temp);
354template< typename DstXprType, typename ArgType, typename Scalar>
355struct Assignment<DstXprType, Homogeneous<ArgType,
Vertical>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
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> &)
360 Index dstRows = src.rows();
361 Index dstCols = src.cols();
362 if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
363 dst.resize(dstRows, dstCols);
365 dst.template topRows<ArgType::RowsAtCompileTime>(src.nestedExpression().rows()) = src.nestedExpression();
366 dst.row(dst.rows()-1).setOnes();
371template<
typename DstXprType,
typename ArgType,
typename Scalar>
372struct Assignment<DstXprType, Homogeneous<ArgType,
Horizontal>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
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> &)
377 Index dstRows = src.rows();
378 Index dstCols = src.cols();
379 if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
380 dst.resize(dstRows, dstCols);
382 dst.template leftCols<ArgType::ColsAtCompileTime>(src.nestedExpression().cols()) = src.nestedExpression();
383 dst.col(dst.cols()-1).setOnes();
387template<
typename LhsArg,
typename Rhs,
int ProductTag>
388struct generic_product_impl<Homogeneous<LhsArg,
Horizontal>, Rhs, HomogeneousShape, DenseShape, ProductTag>
390 template<
typename Dest>
391 EIGEN_DEVICE_FUNC
static void evalTo(Dest& dst,
const Homogeneous<LhsArg,Horizontal>& lhs,
const Rhs& rhs)
393 homogeneous_right_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs>(lhs.nestedExpression(), rhs).evalTo(dst);
397template<
typename Lhs,
typename Rhs>
398struct homogeneous_right_product_refactoring_helper
401 Dim = Lhs::ColsAtCompileTime,
402 Rows = Lhs::RowsAtCompileTime
404 typedef typename Rhs::template ConstNRowsBlockXpr<Dim>::Type LinearBlockConst;
405 typedef typename remove_const<LinearBlockConst>::type LinearBlock;
406 typedef typename Rhs::ConstRowXpr ConstantColumn;
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>
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;
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) )
428template<
typename Lhs,
typename RhsArg,
int ProductTag>
429struct generic_product_impl<Lhs, Homogeneous<RhsArg,
Vertical>, DenseShape, HomogeneousShape, ProductTag>
431 template<
typename Dest>
432 EIGEN_DEVICE_FUNC
static void evalTo(Dest& dst,
const Lhs& lhs,
const Homogeneous<RhsArg,Vertical>& rhs)
434 homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, Lhs>(lhs, rhs.nestedExpression()).evalTo(dst);
440template<
typename Lhs,
typename RhsArg,
int ProductTag>
441struct generic_product_impl<Lhs, Homogeneous<RhsArg,
Vertical>, TriangularShape, HomogeneousShape, ProductTag>
443 template<
typename Dest>
444 static void evalTo(Dest& dst,
const Lhs& lhs,
const Homogeneous<RhsArg,Vertical>& rhs)
446 dst.noalias() = lhs * rhs.eval();
450template<
typename Lhs,
typename Rhs>
451struct homogeneous_left_product_refactoring_helper
454 Dim = Rhs::RowsAtCompileTime,
455 Cols = Rhs::ColsAtCompileTime
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;
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>
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;
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()) )
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>
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)
488 homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, TransformType>(lhs, rhs.nestedExpression()).evalTo(dst);
492template<
typename ExpressionType,
int S
ide,
bool Transposed>
493struct permutation_matrix_product<ExpressionType, Side, Transposed, HomogeneousShape>
494 :
public permutation_matrix_product<ExpressionType, Side, Transposed, DenseShape>
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
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