1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
5// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
6//
7// This Source Code Form is subject to the terms of the Mozilla
8// Public License v. 2.0. If a copy of the MPL was not distributed
9// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10
11#ifndef EIGEN_PARTIAL_REDUX_H
12#define EIGEN_PARTIAL_REDUX_H
13
14namespace Eigen {
15
16/** \class PartialReduxExpr
17  * \ingroup Core_Module
18  *
19  * \brief Generic expression of a partially reduxed matrix
20  *
21  * \tparam MatrixType the type of the matrix we are applying the redux operation
22  * \tparam MemberOp type of the member functor
23  * \tparam Direction indicates the direction of the redux (#Vertical or #Horizontal)
24  *
25  * This class represents an expression of a partial redux operator of a matrix.
26  * It is the return type of some VectorwiseOp functions,
27  * and most of the time this is the only way it is used.
28  *
29  * \sa class VectorwiseOp
30  */
31
32template< typename MatrixType, typename MemberOp, int Direction>
33class PartialReduxExpr;
34
35namespace internal {
36template<typename MatrixType, typename MemberOp, int Direction>
37struct traits<PartialReduxExpr<MatrixType, MemberOp, Direction> >
38 : traits<MatrixType>
39{
40  typedef typename MemberOp::result_type Scalar;
41  typedef typename traits<MatrixType>::StorageKind StorageKind;
42  typedef typename traits<MatrixType>::XprKind XprKind;
43  typedef typename MatrixType::Scalar InputScalar;
44  enum {
45    RowsAtCompileTime = Direction==Vertical   ? 1 : MatrixType::RowsAtCompileTime,
46    ColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::ColsAtCompileTime,
47    MaxRowsAtCompileTime = Direction==Vertical   ? 1 : MatrixType::MaxRowsAtCompileTime,
48    MaxColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::MaxColsAtCompileTime,
49    Flags = RowsAtCompileTime == 1 ? RowMajorBit : 0,
50    TraversalSize = Direction==Vertical ? MatrixType::RowsAtCompileTime :  MatrixType::ColsAtCompileTime
51  };
52};
53}
54
55template< typename MatrixType, typename MemberOp, int Direction>
56class PartialReduxExpr : public internal::dense_xpr_base< PartialReduxExpr<MatrixType, MemberOp, Direction> >::type,
57                         internal::no_assignment_operator
58{
59  public:
60
61    typedef typename internal::dense_xpr_base<PartialReduxExpr>::type Base;
62    EIGEN_DENSE_PUBLIC_INTERFACE(PartialReduxExpr)
63
64    EIGEN_DEVICE_FUNC
65    explicit PartialReduxExpr(const MatrixType& mat, const MemberOp& func = MemberOp())
66      : m_matrix(mat), m_functor(func) {}
67
68    EIGEN_DEVICE_FUNC
69    Index rows() const { return (Direction==Vertical   ? 1 : m_matrix.rows()); }
70    EIGEN_DEVICE_FUNC
71    Index cols() const { return (Direction==Horizontal ? 1 : m_matrix.cols()); }
72
73    EIGEN_DEVICE_FUNC
74    typename MatrixType::Nested nestedExpression() const { return m_matrix; }
75
76    EIGEN_DEVICE_FUNC
77    const MemberOp& functor() const { return m_functor; }
78
79  protected:
80    typename MatrixType::Nested m_matrix;
81    const MemberOp m_functor;
82};
83
84#define EIGEN_MEMBER_FUNCTOR(MEMBER,COST)                               \
85  template <typename ResultType>                                        \
86  struct member_##MEMBER {                                              \
87    EIGEN_EMPTY_STRUCT_CTOR(member_##MEMBER)                            \
88    typedef ResultType result_type;                                     \
89    template<typename Scalar, int Size> struct Cost                     \
90    { enum { value = COST }; };                                         \
91    template<typename XprType>                                          \
92    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                               \
93    ResultType operator()(const XprType& mat) const                     \
94    { return mat.MEMBER(); } \
95  }
96
97namespace internal {
98
99EIGEN_MEMBER_FUNCTOR(squaredNorm, Size * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
100EIGEN_MEMBER_FUNCTOR(norm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
101EIGEN_MEMBER_FUNCTOR(stableNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
102EIGEN_MEMBER_FUNCTOR(blueNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
103EIGEN_MEMBER_FUNCTOR(hypotNorm, (Size-1) * functor_traits<scalar_hypot_op<Scalar> >::Cost );
104EIGEN_MEMBER_FUNCTOR(sum, (Size-1)*NumTraits<Scalar>::AddCost);
105EIGEN_MEMBER_FUNCTOR(mean, (Size-1)*NumTraits<Scalar>::AddCost + NumTraits<Scalar>::MulCost);
106EIGEN_MEMBER_FUNCTOR(minCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
107EIGEN_MEMBER_FUNCTOR(maxCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
108EIGEN_MEMBER_FUNCTOR(all, (Size-1)*NumTraits<Scalar>::AddCost);
109EIGEN_MEMBER_FUNCTOR(any, (Size-1)*NumTraits<Scalar>::AddCost);
110EIGEN_MEMBER_FUNCTOR(count, (Size-1)*NumTraits<Scalar>::AddCost);
111EIGEN_MEMBER_FUNCTOR(prod, (Size-1)*NumTraits<Scalar>::MulCost);
112
113template <int p, typename ResultType>
114struct member_lpnorm {
115  typedef ResultType result_type;
116  template<typename Scalar, int Size> struct Cost
117  { enum { value = (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost }; };
118  EIGEN_DEVICE_FUNC member_lpnorm() {}
119  template<typename XprType>
120  EIGEN_DEVICE_FUNC inline ResultType operator()(const XprType& mat) const
121  { return mat.template lpNorm<p>(); }
122};
123
124template <typename BinaryOp, typename Scalar>
125struct member_redux {
126  typedef typename result_of<
127                     BinaryOp(const Scalar&,const Scalar&)
128                   >::type  result_type;
129  template<typename _Scalar, int Size> struct Cost
130  { enum { value = (Size-1) * functor_traits<BinaryOp>::Cost }; };
131  EIGEN_DEVICE_FUNC explicit member_redux(const BinaryOp func) : m_functor(func) {}
132  template<typename Derived>
133  EIGEN_DEVICE_FUNC inline result_type operator()(const DenseBase<Derived>& mat) const
134  { return mat.redux(m_functor); }
135  const BinaryOp m_functor;
136};
137}
138
139/** \class VectorwiseOp
140  * \ingroup Core_Module
141  *
142  * \brief Pseudo expression providing partial reduction operations
143  *
144  * \tparam ExpressionType the type of the object on which to do partial reductions
145  * \tparam Direction indicates the direction of the redux (#Vertical or #Horizontal)
146  *
147  * This class represents a pseudo expression with partial reduction features.
148  * It is the return type of DenseBase::colwise() and DenseBase::rowwise()
149  * and most of the time this is the only way it is used.
150  *
151  * Example: \include MatrixBase_colwise.cpp
152  * Output: \verbinclude MatrixBase_colwise.out
153  *
154  * \sa DenseBase::colwise(), DenseBase::rowwise(), class PartialReduxExpr
155  */
156template<typename ExpressionType, int Direction> class VectorwiseOp
157{
158  public:
159
160    typedef typename ExpressionType::Scalar Scalar;
161    typedef typename ExpressionType::RealScalar RealScalar;
162    typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
163    typedef typename internal::ref_selector<ExpressionType>::non_const_type ExpressionTypeNested;
164    typedef typename internal::remove_all<ExpressionTypeNested>::type ExpressionTypeNestedCleaned;
165
166    template<template<typename _Scalar> class Functor,
167                      typename Scalar_=Scalar> struct ReturnType
168    {
169      typedef PartialReduxExpr<ExpressionType,
170                               Functor<Scalar_>,
171                               Direction
172                              > Type;
173    };
174
175    template<typename BinaryOp> struct ReduxReturnType
176    {
177      typedef PartialReduxExpr<ExpressionType,
178                               internal::member_redux<BinaryOp,Scalar>,
179                               Direction
180                              > Type;
181    };
182
183    enum {
184      isVertical   = (Direction==Vertical) ? 1 : 0,
185      isHorizontal = (Direction==Horizontal) ? 1 : 0
186    };
187
188  protected:
189
190    typedef typename internal::conditional<isVertical,
191                               typename ExpressionType::ColXpr,
192                               typename ExpressionType::RowXpr>::type SubVector;
193    /** \internal
194      * \returns the i-th subvector according to the \c Direction */
195    EIGEN_DEVICE_FUNC
196    SubVector subVector(Index i)
197    {
198      return SubVector(m_matrix.derived(),i);
199    }
200
201    /** \internal
202      * \returns the number of subvectors in the direction \c Direction */
203    EIGEN_DEVICE_FUNC
204    Index subVectors() const
205    { return isVertical?m_matrix.cols():m_matrix.rows(); }
206
207    template<typename OtherDerived> struct ExtendedType {
208      typedef Replicate<OtherDerived,
209                        isVertical   ? 1 : ExpressionType::RowsAtCompileTime,
210                        isHorizontal ? 1 : ExpressionType::ColsAtCompileTime> Type;
211    };
212
213    /** \internal
214      * Replicates a vector to match the size of \c *this */
215    template<typename OtherDerived>
216    EIGEN_DEVICE_FUNC
217    typename ExtendedType<OtherDerived>::Type
218    extendedTo(const DenseBase<OtherDerived>& other) const
219    {
220      EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(isVertical, OtherDerived::MaxColsAtCompileTime==1),
221                          YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED)
222      EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(isHorizontal, OtherDerived::MaxRowsAtCompileTime==1),
223                          YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED)
224      return typename ExtendedType<OtherDerived>::Type
225                      (other.derived(),
226                       isVertical   ? 1 : m_matrix.rows(),
227                       isHorizontal ? 1 : m_matrix.cols());
228    }
229
230    template<typename OtherDerived> struct OppositeExtendedType {
231      typedef Replicate<OtherDerived,
232                        isHorizontal ? 1 : ExpressionType::RowsAtCompileTime,
233                        isVertical   ? 1 : ExpressionType::ColsAtCompileTime> Type;
234    };
235
236    /** \internal
237      * Replicates a vector in the opposite direction to match the size of \c *this */
238    template<typename OtherDerived>
239    EIGEN_DEVICE_FUNC
240    typename OppositeExtendedType<OtherDerived>::Type
241    extendedToOpposite(const DenseBase<OtherDerived>& other) const
242    {
243      EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(isHorizontal, OtherDerived::MaxColsAtCompileTime==1),
244                          YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED)
245      EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(isVertical, OtherDerived::MaxRowsAtCompileTime==1),
246                          YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED)
247      return typename OppositeExtendedType<OtherDerived>::Type
248                      (other.derived(),
249                       isHorizontal  ? 1 : m_matrix.rows(),
250                       isVertical    ? 1 : m_matrix.cols());
251    }
252
253  public:
254    EIGEN_DEVICE_FUNC
255    explicit inline VectorwiseOp(ExpressionType& matrix) : m_matrix(matrix) {}
256
257    /** \internal */
258    EIGEN_DEVICE_FUNC
259    inline const ExpressionType& _expression() const { return m_matrix; }
260
261    /** \returns a row or column vector expression of \c *this reduxed by \a func
262      *
263      * The template parameter \a BinaryOp is the type of the functor
264      * of the custom redux operator. Note that func must be an associative operator.
265      *
266      * \sa class VectorwiseOp, DenseBase::colwise(), DenseBase::rowwise()
267      */
268    template<typename BinaryOp>
269    EIGEN_DEVICE_FUNC
270    const typename ReduxReturnType<BinaryOp>::Type
271    redux(const BinaryOp& func = BinaryOp()) const
272    { return typename ReduxReturnType<BinaryOp>::Type(_expression(), internal::member_redux<BinaryOp,Scalar>(func)); }
273
274    typedef typename ReturnType<internal::member_minCoeff>::Type MinCoeffReturnType;
275    typedef typename ReturnType<internal::member_maxCoeff>::Type MaxCoeffReturnType;
276    typedef typename ReturnType<internal::member_squaredNorm,RealScalar>::Type SquaredNormReturnType;
277    typedef typename ReturnType<internal::member_norm,RealScalar>::Type NormReturnType;
278    typedef typename ReturnType<internal::member_blueNorm,RealScalar>::Type BlueNormReturnType;
279    typedef typename ReturnType<internal::member_stableNorm,RealScalar>::Type StableNormReturnType;
280    typedef typename ReturnType<internal::member_hypotNorm,RealScalar>::Type HypotNormReturnType;
281    typedef typename ReturnType<internal::member_sum>::Type SumReturnType;
282    typedef typename ReturnType<internal::member_mean>::Type MeanReturnType;
283    typedef typename ReturnType<internal::member_all>::Type AllReturnType;
284    typedef typename ReturnType<internal::member_any>::Type AnyReturnType;
285    typedef PartialReduxExpr<ExpressionType, internal::member_count<Index>, Direction> CountReturnType;
286    typedef typename ReturnType<internal::member_prod>::Type ProdReturnType;
287    typedef Reverse<const ExpressionType, Direction> ConstReverseReturnType;
288    typedef Reverse<ExpressionType, Direction> ReverseReturnType;
289
290    template<int p> struct LpNormReturnType {
291      typedef PartialReduxExpr<ExpressionType, internal::member_lpnorm<p,RealScalar>,Direction> Type;
292    };
293
294    /** \returns a row (or column) vector expression of the smallest coefficient
295      * of each column (or row) of the referenced expression.
296      *
297      * \warning the result is undefined if \c *this contains NaN.
298      *
299      * Example: \include PartialRedux_minCoeff.cpp
300      * Output: \verbinclude PartialRedux_minCoeff.out
301      *
302      * \sa DenseBase::minCoeff() */
303    EIGEN_DEVICE_FUNC
304    const MinCoeffReturnType minCoeff() const
305    { return MinCoeffReturnType(_expression()); }
306
307    /** \returns a row (or column) vector expression of the largest coefficient
308      * of each column (or row) of the referenced expression.
309      *
310      * \warning the result is undefined if \c *this contains NaN.
311      *
312      * Example: \include PartialRedux_maxCoeff.cpp
313      * Output: \verbinclude PartialRedux_maxCoeff.out
314      *
315      * \sa DenseBase::maxCoeff() */
316    EIGEN_DEVICE_FUNC
317    const MaxCoeffReturnType maxCoeff() const
318    { return MaxCoeffReturnType(_expression()); }
319
320    /** \returns a row (or column) vector expression of the squared norm
321      * of each column (or row) of the referenced expression.
322      * This is a vector with real entries, even if the original matrix has complex entries.
323      *
324      * Example: \include PartialRedux_squaredNorm.cpp
325      * Output: \verbinclude PartialRedux_squaredNorm.out
326      *
327      * \sa DenseBase::squaredNorm() */
328    EIGEN_DEVICE_FUNC
329    const SquaredNormReturnType squaredNorm() const
330    { return SquaredNormReturnType(_expression()); }
331
332    /** \returns a row (or column) vector expression of the norm
333      * of each column (or row) of the referenced expression.
334      * This is a vector with real entries, even if the original matrix has complex entries.
335      *
336      * Example: \include PartialRedux_norm.cpp
337      * Output: \verbinclude PartialRedux_norm.out
338      *
339      * \sa DenseBase::norm() */
340    EIGEN_DEVICE_FUNC
341    const NormReturnType norm() const
342    { return NormReturnType(_expression()); }
343
344    /** \returns a row (or column) vector expression of the norm
345      * of each column (or row) of the referenced expression.
346      * This is a vector with real entries, even if the original matrix has complex entries.
347      *
348      * Example: \include PartialRedux_norm.cpp
349      * Output: \verbinclude PartialRedux_norm.out
350      *
351      * \sa DenseBase::norm() */
352    template<int p>
353    EIGEN_DEVICE_FUNC
354    const typename LpNormReturnType<p>::Type lpNorm() const
355    { return typename LpNormReturnType<p>::Type(_expression()); }
356
357
358    /** \returns a row (or column) vector expression of the norm
359      * of each column (or row) of the referenced expression, using
360      * Blue's algorithm.
361      * This is a vector with real entries, even if the original matrix has complex entries.
362      *
363      * \sa DenseBase::blueNorm() */
364    EIGEN_DEVICE_FUNC
365    const BlueNormReturnType blueNorm() const
366    { return BlueNormReturnType(_expression()); }
367
368
369    /** \returns a row (or column) vector expression of the norm
370      * of each column (or row) of the referenced expression, avoiding
371      * underflow and overflow.
372      * This is a vector with real entries, even if the original matrix has complex entries.
373      *
374      * \sa DenseBase::stableNorm() */
375    EIGEN_DEVICE_FUNC
376    const StableNormReturnType stableNorm() const
377    { return StableNormReturnType(_expression()); }
378
379
380    /** \returns a row (or column) vector expression of the norm
381      * of each column (or row) of the referenced expression, avoiding
382      * underflow and overflow using a concatenation of hypot() calls.
383      * This is a vector with real entries, even if the original matrix has complex entries.
384      *
385      * \sa DenseBase::hypotNorm() */
386    EIGEN_DEVICE_FUNC
387    const HypotNormReturnType hypotNorm() const
388    { return HypotNormReturnType(_expression()); }
389
390    /** \returns a row (or column) vector expression of the sum
391      * of each column (or row) of the referenced expression.
392      *
393      * Example: \include PartialRedux_sum.cpp
394      * Output: \verbinclude PartialRedux_sum.out
395      *
396      * \sa DenseBase::sum() */
397    EIGEN_DEVICE_FUNC
398    const SumReturnType sum() const
399    { return SumReturnType(_expression()); }
400
401    /** \returns a row (or column) vector expression of the mean
402    * of each column (or row) of the referenced expression.
403    *
404    * \sa DenseBase::mean() */
405    EIGEN_DEVICE_FUNC
406    const MeanReturnType mean() const
407    { return MeanReturnType(_expression()); }
408
409    /** \returns a row (or column) vector expression representing
410      * whether \b all coefficients of each respective column (or row) are \c true.
411      * This expression can be assigned to a vector with entries of type \c bool.
412      *
413      * \sa DenseBase::all() */
414    EIGEN_DEVICE_FUNC
415    const AllReturnType all() const
416    { return AllReturnType(_expression()); }
417
418    /** \returns a row (or column) vector expression representing
419      * whether \b at \b least one coefficient of each respective column (or row) is \c true.
420      * This expression can be assigned to a vector with entries of type \c bool.
421      *
422      * \sa DenseBase::any() */
423    EIGEN_DEVICE_FUNC
424    const AnyReturnType any() const
425    { return AnyReturnType(_expression()); }
426
427    /** \returns a row (or column) vector expression representing
428      * the number of \c true coefficients of each respective column (or row).
429      * This expression can be assigned to a vector whose entries have the same type as is used to
430      * index entries of the original matrix; for dense matrices, this is \c std::ptrdiff_t .
431      *
432      * Example: \include PartialRedux_count.cpp
433      * Output: \verbinclude PartialRedux_count.out
434      *
435      * \sa DenseBase::count() */
436    EIGEN_DEVICE_FUNC
437    const CountReturnType count() const
438    { return CountReturnType(_expression()); }
439
440    /** \returns a row (or column) vector expression of the product
441      * of each column (or row) of the referenced expression.
442      *
443      * Example: \include PartialRedux_prod.cpp
444      * Output: \verbinclude PartialRedux_prod.out
445      *
446      * \sa DenseBase::prod() */
447    EIGEN_DEVICE_FUNC
448    const ProdReturnType prod() const
449    { return ProdReturnType(_expression()); }
450
451
452    /** \returns a matrix expression
453      * where each column (or row) are reversed.
454      *
455      * Example: \include Vectorwise_reverse.cpp
456      * Output: \verbinclude Vectorwise_reverse.out
457      *
458      * \sa DenseBase::reverse() */
459    EIGEN_DEVICE_FUNC
460    const ConstReverseReturnType reverse() const
461    { return ConstReverseReturnType( _expression() ); }
462
463    /** \returns a writable matrix expression
464      * where each column (or row) are reversed.
465      *
466      * \sa reverse() const */
467    EIGEN_DEVICE_FUNC
468    ReverseReturnType reverse()
469    { return ReverseReturnType( _expression() ); }
470
471    typedef Replicate<ExpressionType,(isVertical?Dynamic:1),(isHorizontal?Dynamic:1)> ReplicateReturnType;
472    EIGEN_DEVICE_FUNC
473    const ReplicateReturnType replicate(Index factor) const;
474
475    /**
476      * \return an expression of the replication of each column (or row) of \c *this
477      *
478      * Example: \include DirectionWise_replicate.cpp
479      * Output: \verbinclude DirectionWise_replicate.out
480      *
481      * \sa VectorwiseOp::replicate(Index), DenseBase::replicate(), class Replicate
482      */
483    // NOTE implemented here because of sunstudio's compilation errors
484    // isVertical*Factor+isHorizontal instead of (isVertical?Factor:1) to handle CUDA bug with ternary operator
485    template<int Factor> const Replicate<ExpressionType,isVertical*Factor+isHorizontal,isHorizontal*Factor+isVertical>
486    EIGEN_DEVICE_FUNC
487    replicate(Index factor = Factor) const
488    {
489      return Replicate<ExpressionType,(isVertical?Factor:1),(isHorizontal?Factor:1)>
490          (_expression(),isVertical?factor:1,isHorizontal?factor:1);
491    }
492
493/////////// Artithmetic operators ///////////
494
495    /** Copies the vector \a other to each subvector of \c *this */
496    template<typename OtherDerived>
497    EIGEN_DEVICE_FUNC
498    ExpressionType& operator=(const DenseBase<OtherDerived>& other)
499    {
500      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
501      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
502      //eigen_assert((m_matrix.isNull()) == (other.isNull())); FIXME
503      return const_cast<ExpressionType&>(m_matrix = extendedTo(other.derived()));
504    }
505
506    /** Adds the vector \a other to each subvector of \c *this */
507    template<typename OtherDerived>
508    EIGEN_DEVICE_FUNC
509    ExpressionType& operator+=(const DenseBase<OtherDerived>& other)
510    {
511      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
512      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
513      return const_cast<ExpressionType&>(m_matrix += extendedTo(other.derived()));
514    }
515
516    /** Substracts the vector \a other to each subvector of \c *this */
517    template<typename OtherDerived>
518    EIGEN_DEVICE_FUNC
519    ExpressionType& operator-=(const DenseBase<OtherDerived>& other)
520    {
521      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
522      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
523      return const_cast<ExpressionType&>(m_matrix -= extendedTo(other.derived()));
524    }
525
526    /** Multiples each subvector of \c *this by the vector \a other */
527    template<typename OtherDerived>
528    EIGEN_DEVICE_FUNC
529    ExpressionType& operator*=(const DenseBase<OtherDerived>& other)
530    {
531      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
532      EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
533      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
534      m_matrix *= extendedTo(other.derived());
535      return const_cast<ExpressionType&>(m_matrix);
536    }
537
538    /** Divides each subvector of \c *this by the vector \a other */
539    template<typename OtherDerived>
540    EIGEN_DEVICE_FUNC
541    ExpressionType& operator/=(const DenseBase<OtherDerived>& other)
542    {
543      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
544      EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
545      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
546      m_matrix /= extendedTo(other.derived());
547      return const_cast<ExpressionType&>(m_matrix);
548    }
549
550    /** Returns the expression of the sum of the vector \a other to each subvector of \c *this */
551    template<typename OtherDerived> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
552    CwiseBinaryOp<internal::scalar_sum_op<Scalar,typename OtherDerived::Scalar>,
553                  const ExpressionTypeNestedCleaned,
554                  const typename ExtendedType<OtherDerived>::Type>
555    operator+(const DenseBase<OtherDerived>& other) const
556    {
557      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
558      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
559      return m_matrix + extendedTo(other.derived());
560    }
561
562    /** Returns the expression of the difference between each subvector of \c *this and the vector \a other */
563    template<typename OtherDerived>
564    EIGEN_DEVICE_FUNC
565    CwiseBinaryOp<internal::scalar_difference_op<Scalar,typename OtherDerived::Scalar>,
566                  const ExpressionTypeNestedCleaned,
567                  const typename ExtendedType<OtherDerived>::Type>
568    operator-(const DenseBase<OtherDerived>& other) const
569    {
570      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
571      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
572      return m_matrix - extendedTo(other.derived());
573    }
574
575    /** Returns the expression where each subvector is the product of the vector \a other
576      * by the corresponding subvector of \c *this */
577    template<typename OtherDerived> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
578    CwiseBinaryOp<internal::scalar_product_op<Scalar>,
579                  const ExpressionTypeNestedCleaned,
580                  const typename ExtendedType<OtherDerived>::Type>
581    EIGEN_DEVICE_FUNC
582    operator*(const DenseBase<OtherDerived>& other) const
583    {
584      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
585      EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
586      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
587      return m_matrix * extendedTo(other.derived());
588    }
589
590    /** Returns the expression where each subvector is the quotient of the corresponding
591      * subvector of \c *this by the vector \a other */
592    template<typename OtherDerived>
593    EIGEN_DEVICE_FUNC
594    CwiseBinaryOp<internal::scalar_quotient_op<Scalar>,
595                  const ExpressionTypeNestedCleaned,
596                  const typename ExtendedType<OtherDerived>::Type>
597    operator/(const DenseBase<OtherDerived>& other) const
598    {
599      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
600      EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
601      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
602      return m_matrix / extendedTo(other.derived());
603    }
604
605    /** \returns an expression where each column (or row) of the referenced matrix are normalized.
606      * The referenced matrix is \b not modified.
607      * \sa MatrixBase::normalized(), normalize()
608      */
609    EIGEN_DEVICE_FUNC
610    CwiseBinaryOp<internal::scalar_quotient_op<Scalar>,
611                  const ExpressionTypeNestedCleaned,
612                  const typename OppositeExtendedType<typename ReturnType<internal::member_norm,RealScalar>::Type>::Type>
613    normalized() const { return m_matrix.cwiseQuotient(extendedToOpposite(this->norm())); }
614
615
616    /** Normalize in-place each row or columns of the referenced matrix.
617      * \sa MatrixBase::normalize(), normalized()
618      */
619    EIGEN_DEVICE_FUNC void normalize() {
620      m_matrix = this->normalized();
621    }
622
623    EIGEN_DEVICE_FUNC inline void reverseInPlace();
624
625/////////// Geometry module ///////////
626
627    typedef Homogeneous<ExpressionType,Direction> HomogeneousReturnType;
628    EIGEN_DEVICE_FUNC
629    HomogeneousReturnType homogeneous() const;
630
631    typedef typename ExpressionType::PlainObject CrossReturnType;
632    template<typename OtherDerived>
633    EIGEN_DEVICE_FUNC
634    const CrossReturnType cross(const MatrixBase<OtherDerived>& other) const;
635
636    enum {
637      HNormalized_Size = Direction==Vertical ? internal::traits<ExpressionType>::RowsAtCompileTime
638                                             : internal::traits<ExpressionType>::ColsAtCompileTime,
639      HNormalized_SizeMinusOne = HNormalized_Size==Dynamic ? Dynamic : HNormalized_Size-1
640    };
641    typedef Block<const ExpressionType,
642                  Direction==Vertical   ? int(HNormalized_SizeMinusOne)
643                                        : int(internal::traits<ExpressionType>::RowsAtCompileTime),
644                  Direction==Horizontal ? int(HNormalized_SizeMinusOne)
645                                        : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
646            HNormalized_Block;
647    typedef Block<const ExpressionType,
648                  Direction==Vertical   ? 1 : int(internal::traits<ExpressionType>::RowsAtCompileTime),
649                  Direction==Horizontal ? 1 : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
650            HNormalized_Factors;
651    typedef CwiseBinaryOp<internal::scalar_quotient_op<typename internal::traits<ExpressionType>::Scalar>,
652                const HNormalized_Block,
653                const Replicate<HNormalized_Factors,
654                  Direction==Vertical   ? HNormalized_SizeMinusOne : 1,
655                  Direction==Horizontal ? HNormalized_SizeMinusOne : 1> >
656            HNormalizedReturnType;
657
658    EIGEN_DEVICE_FUNC
659    const HNormalizedReturnType hnormalized() const;
660
661  protected:
662    ExpressionTypeNested m_matrix;
663};
664
665//const colwise moved to DenseBase.h due to CUDA compiler bug
666
667
668/** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
669  *
670  * \sa rowwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
671  */
672template<typename Derived>
673inline typename DenseBase<Derived>::ColwiseReturnType
674DenseBase<Derived>::colwise()
675{
676  return ColwiseReturnType(derived());
677}
678
679//const rowwise moved to DenseBase.h due to CUDA compiler bug
680
681
682/** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
683  *
684  * \sa colwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
685  */
686template<typename Derived>
687inline typename DenseBase<Derived>::RowwiseReturnType
688DenseBase<Derived>::rowwise()
689{
690  return RowwiseReturnType(derived());
691}
692
693} // end namespace Eigen
694
695#endif // EIGEN_PARTIAL_REDUX_H
696