Quelle VectorwiseOp.h Sprache: C

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2019 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_PARTIAL_REDUX_H
#define EIGEN_PARTIAL_REDUX_H

namespace Eigen {

/** \class PartialReduxExpr
  * \ingroup Core_Module
  *
  * \brief Generic expression of a partially reduxed matrix
  *
  * \tparam MatrixType the type of the matrix we are applying the redux operation
  * \tparam MemberOp type of the member functor
  * \tparam Direction indicates the direction of the redux (#Vertical or #Horizontal)
  *
  * This class represents an expression of a partial redux operator of a matrix.
  * It is the return type of some VectorwiseOp functions,
  * and most of the time this is the only way it is used.
  *
  * \sa class VectorwiseOp
  */

template< typename MatrixType, typename MemberOp, int Direction>
class PartialReduxExpr;

namespace internal {
template<typename MatrixType, typename MemberOp, int Direction>
struct traits<PartialReduxExpr<MatrixType, MemberOp, Direction> >
: traits<MatrixType>
{
  typedef typename MemberOp::result_type Scalar;
  typedef typename traits<MatrixType>::StorageKind StorageKind;
  typedef typename traits<MatrixType>::XprKind XprKind;
  typedef typename MatrixType::Scalar InputScalar;
  enum {
    RowsAtCompileTime = Direction==Vertical   ? 1 : MatrixType::RowsAtCompileTime,
    ColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::ColsAtCompileTime,
    MaxRowsAtCompileTime = Direction==Vertical   ? 1 : MatrixType::MaxRowsAtCompileTime,
    MaxColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::MaxColsAtCompileTime,
    Flags = RowsAtCompileTime == 1 ? RowMajorBit : 0,
    TraversalSize = Direction==Vertical ? MatrixType::RowsAtCompileTime :  MatrixType::ColsAtCompileTime
  };
};
}

template< typename MatrixType, typename MemberOp, int Direction>
class PartialReduxExpr : public internal::dense_xpr_base< PartialReduxExpr<MatrixType, MemberOp, Direction> >::type,
                         internal::no_assignment_operator
{
  public:

    typedef typename internal::dense_xpr_base<PartialReduxExpr>::type Base;
    EIGEN_DENSE_PUBLIC_INTERFACE(PartialReduxExpr)

    EIGEN_DEVICE_FUNC
    explicit PartialReduxExpr(const MatrixType& mat, const MemberOp& func = MemberOp())
      : m_matrix(mat), m_functor(func) {}

    EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
    Index rows() const EIGEN_NOEXCEPT { return (Direction==Vertical   ? 1 : m_matrix.rows()); }
    EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
    Index cols() const EIGEN_NOEXCEPT { return (Direction==Horizontal ? 1 : m_matrix.cols()); }

    EIGEN_DEVICE_FUNC
    typename MatrixType::Nested nestedExpression() const { return m_matrix; }

    EIGEN_DEVICE_FUNC
    const MemberOp& functor() const { return m_functor; }

  protected:
    typename MatrixType::Nested m_matrix;
    const MemberOp m_functor;
};

template<typename A,typename B> struct partial_redux_dummy_func;

#define EIGEN_MAKE_PARTIAL_REDUX_FUNCTOR(MEMBER,COST,VECTORIZABLE,BINARYOP)                \
  template <typename ResultType,typename Scalar>                                                            \
  struct member_##MEMBER {                                                                  \
    EIGEN_EMPTY_STRUCT_CTOR(member_##MEMBER)                                                \
    typedef ResultType result_type;                                                         \
    typedef BINARYOP<Scalar,Scalar> BinaryOp;   \
    template<int Size> struct Cost { enum { value = COST }; };             \
    enum { Vectorizable = VECTORIZABLE };                                                   \
    template<typename XprType>                                                              \
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                   \
    ResultType operator()(const XprType& mat) const                                         \
    { return mat.MEMBER(); }                                                                \
    BinaryOp binaryFunc() const { return BinaryOp(); }                                      \
  }

#define EIGEN_MEMBER_FUNCTOR(MEMBER,COST) \
  EIGEN_MAKE_PARTIAL_REDUX_FUNCTOR(MEMBER,COST,0,partial_redux_dummy_func)

namespace internal {

EIGEN_MEMBER_FUNCTOR(norm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
EIGEN_MEMBER_FUNCTOR(stableNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
EIGEN_MEMBER_FUNCTOR(blueNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
EIGEN_MEMBER_FUNCTOR(hypotNorm, (Size-1) * functor_traits<scalar_hypot_op<Scalar> >::Cost );
EIGEN_MEMBER_FUNCTOR(all, (Size-1)*NumTraits<Scalar>::AddCost);
EIGEN_MEMBER_FUNCTOR(any, (Size-1)*NumTraits<Scalar>::AddCost);
EIGEN_MEMBER_FUNCTOR(count, (Size-1)*NumTraits<Scalar>::AddCost);

EIGEN_MAKE_PARTIAL_REDUX_FUNCTOR(sum, (Size-1)*NumTraits<Scalar>::AddCost, 1, internal::scalar_sum_op);
EIGEN_MAKE_PARTIAL_REDUX_FUNCTOR(minCoeff, (Size-1)*NumTraits<Scalar>::AddCost, 1, internal::scalar_min_op);
EIGEN_MAKE_PARTIAL_REDUX_FUNCTOR(maxCoeff, (Size-1)*NumTraits<Scalar>::AddCost, 1, internal::scalar_max_op);
EIGEN_MAKE_PARTIAL_REDUX_FUNCTOR(prod, (Size-1)*NumTraits<Scalar>::MulCost, 1, internal::scalar_product_op);

template <int p, typename ResultType,typename Scalar>
struct member_lpnorm {
  typedef ResultType result_type;
  enum { Vectorizable = 0 };
  template<int Size> struct Cost
  { enum { value = (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost }; };
  EIGEN_DEVICE_FUNC member_lpnorm() {}
  template<typename XprType>
  EIGEN_DEVICE_FUNC inline ResultType operator()(const XprType& mat) const
  { return mat.template lpNorm<p>(); }
};

template <typename BinaryOpT, typename Scalar>
struct member_redux {
  typedef BinaryOpT BinaryOp;
  typedef typename result_of<
                     BinaryOp(const Scalar&,const Scalar&)
                   >::type  result_type;

  enum { Vectorizable = functor_traits<BinaryOp>::PacketAccess };
  template<int Size> struct Cost { enum { value = (Size-1) * functor_traits<BinaryOp>::Cost }; };
  EIGEN_DEVICE_FUNC explicit member_redux(const BinaryOp func) : m_functor(func) {}
  template<typename Derived>
  EIGEN_DEVICE_FUNC inline result_type operator()(const DenseBase<Derived>& mat) const
  { return mat.redux(m_functor); }
  const BinaryOp& binaryFunc() const { return m_functor; }
  const BinaryOp m_functor;
};
}

/** \class VectorwiseOp
  * \ingroup Core_Module
  *
  * \brief Pseudo expression providing broadcasting and partial reduction operations
  *
  * \tparam ExpressionType the type of the object on which to do partial reductions
  * \tparam Direction indicates whether to operate on columns (#Vertical) or rows (#Horizontal)
  *
  * This class represents a pseudo expression with broadcasting and partial reduction features.
  * It is the return type of DenseBase::colwise() and DenseBase::rowwise()
  * and most of the time this is the only way it is explicitly used.
  *
  * To understand the logic of rowwise/colwise expression, let's consider a generic case `A.colwise().foo()`
  * where `foo` is any method of `VectorwiseOp`. This expression is equivalent to applying `foo()` to each
  * column of `A` and then re-assemble the outputs in a matrix expression:
  * \code [A.col(0).foo(), A.col(1).foo(), ..., A.col(A.cols()-1).foo()] \endcode
  *
  * Example: \include MatrixBase_colwise.cpp
  * Output: \verbinclude MatrixBase_colwise.out
  *
  * The begin() and end() methods are obviously exceptions to the previous rule as they
  * return STL-compatible begin/end iterators to the rows or columns of the nested expression.
  * Typical use cases include for-range-loop and calls to STL algorithms:
  *
  * Example: \include MatrixBase_colwise_iterator_cxx11.cpp
  * Output: \verbinclude MatrixBase_colwise_iterator_cxx11.out
  *
  * For a partial reduction on an empty input, some rules apply.
  * For the sake of clarity, let's consider a vertical reduction:
  *   - If the number of columns is zero, then a 1x0 row-major vector expression is returned.
  *   - Otherwise, if the number of rows is zero, then
  *       - a row vector of zeros is returned for sum-like reductions (sum, squaredNorm, norm, etc.)
  *       - a row vector of ones is returned for a product reduction (e.g., <code>MatrixXd(n,0).colwise().prod()</code>)
  *       - an assert is triggered for all other reductions (minCoeff,maxCoeff,redux(bin_op))
  *
  * \sa DenseBase::colwise(), DenseBase::rowwise(), class PartialReduxExpr
  */
template<typename ExpressionType, int Direction> class VectorwiseOp
{
  public:

    typedef typename ExpressionType::Scalar Scalar;
    typedef typename ExpressionType::RealScalar RealScalar;
    typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
    typedef typename internal::ref_selector<ExpressionType>::non_const_type ExpressionTypeNested;
    typedef typename internal::remove_all<ExpressionTypeNested>::type ExpressionTypeNestedCleaned;

    template<template<typename OutScalar,typename InputScalar> class Functor,
                      typename ReturnScalar=Scalar> struct ReturnType
    {
      typedef PartialReduxExpr<ExpressionType,
                               Functor<ReturnScalar,Scalar>,
                               Direction
                              > Type;
    };

    template<typename BinaryOp> struct ReduxReturnType
    {
      typedef PartialReduxExpr<ExpressionType,
                               internal::member_redux<BinaryOp,Scalar>,
                               Direction
                              > Type;
    };

    enum {
      isVertical   = (Direction==Vertical) ? 1 : 0,
      isHorizontal = (Direction==Horizontal) ? 1 : 0
    };

  protected:

    template<typename OtherDerived> struct ExtendedType {
      typedef Replicate<OtherDerived,
                        isVertical   ? 1 : ExpressionType::RowsAtCompileTime,
                        isHorizontal ? 1 : ExpressionType::ColsAtCompileTime> Type;
    };

    /** \internal
      * Replicates a vector to match the size of \c *this */
    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    typename ExtendedType<OtherDerived>::Type
    extendedTo(const DenseBase<OtherDerived>& other) const
    {
      EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(isVertical, OtherDerived::MaxColsAtCompileTime==1),
                          YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED)
      EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(isHorizontal, OtherDerived::MaxRowsAtCompileTime==1),
                          YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED)
      return typename ExtendedType<OtherDerived>::Type
                      (other.derived(),
                       isVertical   ? 1 : m_matrix.rows(),
                       isHorizontal ? 1 : m_matrix.cols());
    }

    template<typename OtherDerived> struct OppositeExtendedType {
      typedef Replicate<OtherDerived,
                        isHorizontal ? 1 : ExpressionType::RowsAtCompileTime,
                        isVertical   ? 1 : ExpressionType::ColsAtCompileTime> Type;
    };

    /** \internal
      * Replicates a vector in the opposite direction to match the size of \c *this */
    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    typename OppositeExtendedType<OtherDerived>::Type
    extendedToOpposite(const DenseBase<OtherDerived>& other) const
    {
      EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(isHorizontal, OtherDerived::MaxColsAtCompileTime==1),
                          YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED)
      EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(isVertical, OtherDerived::MaxRowsAtCompileTime==1),
                          YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED)
      return typename OppositeExtendedType<OtherDerived>::Type
                      (other.derived(),
                       isHorizontal  ? 1 : m_matrix.rows(),
                       isVertical    ? 1 : m_matrix.cols());
    }

  public:
    EIGEN_DEVICE_FUNC
    explicit inline VectorwiseOp(ExpressionType& matrix) : m_matrix(matrix) {}

    /** \internal */
    EIGEN_DEVICE_FUNC
    inline const ExpressionType& _expression() const { return m_matrix; }

    #ifdef EIGEN_PARSED_BY_DOXYGEN
    /** STL-like <a href="https://en.cppreference.com/w/cpp/named_req/RandomAccessIterator">RandomAccessIterator</a>
      * iterator type over the columns or rows as returned by the begin() and end() methods.
      */
    random_access_iterator_type iterator;
    /** This is the const version of iterator (aka read-only) */
    random_access_iterator_type const_iterator;
    #else
    typedef internal::subvector_stl_iterator<ExpressionType,               DirectionType(Direction)> iterator;
    typedef internal::subvector_stl_iterator<const ExpressionType,         DirectionType(Direction)> const_iterator;
    typedef internal::subvector_stl_reverse_iterator<ExpressionType,       DirectionType(Direction)> reverse_iterator;
    typedef internal::subvector_stl_reverse_iterator<const ExpressionType, DirectionType(Direction)> const_reverse_iterator;
    #endif

    /** returns an iterator to the first row (rowwise) or column (colwise) of the nested expression.
      * \sa end(), cbegin()
      */
    iterator                 begin()       { return iterator      (m_matrix, 0); }
    /** const version of begin() */
    const_iterator           begin() const { return const_iterator(m_matrix, 0); }
    /** const version of begin() */
    const_iterator          cbegin() const { return const_iterator(m_matrix, 0); }

    /** returns a reverse iterator to the last row (rowwise) or column (colwise) of the nested expression.
      * \sa rend(), crbegin()
      */
    reverse_iterator        rbegin()       { return reverse_iterator       (m_matrix, m_matrix.template subVectors<DirectionType(Direction)>()-1); }
/** const version of rbegin() */
    const_reverse_iterator  rbegin() const { return const_reverse_iterator (m_matrix, m_matrix.template subVectors<DirectionType(Direction)>()-1); }
/** const version of rbegin() */
const_reverse_iterator crbegin() const { return const_reverse_iterator (m_matrix, m_matrix.template subVectors<DirectionType(Direction)>()-1); }

    /** returns an iterator to the row (resp. column) following the last row (resp. column) of the nested expression
      * \sa begin(), cend()
      */
    iterator                 end()         { return iterator      (m_matrix, m_matrix.template subVectors<DirectionType(Direction)>()); }
    /** const version of end() */
    const_iterator           end()  const  { return const_iterator(m_matrix, m_matrix.template subVectors<DirectionType(Direction)>()); }
    /** const version of end() */
    const_iterator          cend()  const  { return const_iterator(m_matrix, m_matrix.template subVectors<DirectionType(Direction)>()); }

    /** returns a reverse iterator to the row (resp. column) before the first row (resp. column) of the nested expression
      * \sa begin(), cend()
      */
    reverse_iterator        rend()         { return reverse_iterator       (m_matrix, -1); }
    /** const version of rend() */
    const_reverse_iterator  rend()  const  { return const_reverse_iterator (m_matrix, -1); }
    /** const version of rend() */
    const_reverse_iterator crend()  const  { return const_reverse_iterator (m_matrix, -1); }

    /** \returns a row or column vector expression of \c *this reduxed by \a func
      *
      * The template parameter \a BinaryOp is the type of the functor
      * of the custom redux operator. Note that func must be an associative operator.
      *
      * \warning the size along the reduction direction must be strictly positive,
      *          otherwise an assertion is triggered.
      *
      * \sa class VectorwiseOp, DenseBase::colwise(), DenseBase::rowwise()
      */
    template<typename BinaryOp>
    EIGEN_DEVICE_FUNC
    const typename ReduxReturnType<BinaryOp>::Type
    redux(const BinaryOp& func = BinaryOp()) const
    {
      eigen_assert(redux_length()>0 && "you are using an empty matrix");
      return typename ReduxReturnType<BinaryOp>::Type(_expression(), internal::member_redux<BinaryOp,Scalar>(func));
    }

    typedef typename ReturnType<internal::member_minCoeff>::Type MinCoeffReturnType;
    typedef typename ReturnType<internal::member_maxCoeff>::Type MaxCoeffReturnType;
    typedef PartialReduxExpr<const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const ExpressionTypeNestedCleaned>,internal::member_sum<RealScalar,RealScalar>,Direction> SquaredNormReturnType;
    typedef CwiseUnaryOp<internal::scalar_sqrt_op<RealScalar>, const SquaredNormReturnType> NormReturnType;
    typedef typename ReturnType<internal::member_blueNorm,RealScalar>::Type BlueNormReturnType;
    typedef typename ReturnType<internal::member_stableNorm,RealScalar>::Type StableNormReturnType;
    typedef typename ReturnType<internal::member_hypotNorm,RealScalar>::Type HypotNormReturnType;
    typedef typename ReturnType<internal::member_sum>::Type SumReturnType;
    typedef EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(SumReturnType,Scalar,quotient) MeanReturnType;
    typedef typename ReturnType<internal::member_all>::Type AllReturnType;
    typedef typename ReturnType<internal::member_any>::Type AnyReturnType;
    typedef PartialReduxExpr<ExpressionType, internal::member_count<Index,Scalar>, Direction> CountReturnType;
    typedef typename ReturnType<internal::member_prod>::Type ProdReturnType;
    typedef Reverse<const ExpressionType, Direction> ConstReverseReturnType;
    typedef Reverse<ExpressionType, Direction> ReverseReturnType;

    template<int p> struct LpNormReturnType {
      typedef PartialReduxExpr<ExpressionType, internal::member_lpnorm<p,RealScalar,Scalar>,Direction> Type;
    };

    /** \returns a row (or column) vector expression of the smallest coefficient
      * of each column (or row) of the referenced expression.
      *
      * \warning the size along the reduction direction must be strictly positive,
      *          otherwise an assertion is triggered.
      *
      * \warning the result is undefined if \c *this contains NaN.
      *
      * Example: \include PartialRedux_minCoeff.cpp
      * Output: \verbinclude PartialRedux_minCoeff.out
      *
      * \sa DenseBase::minCoeff() */
    EIGEN_DEVICE_FUNC
    const MinCoeffReturnType minCoeff() const
    {
      eigen_assert(redux_length()>0 && "you are using an empty matrix");
      return MinCoeffReturnType(_expression());
    }

    /** \returns a row (or column) vector expression of the largest coefficient
      * of each column (or row) of the referenced expression.
      *
      * \warning the size along the reduction direction must be strictly positive,
      *          otherwise an assertion is triggered.
      *
      * \warning the result is undefined if \c *this contains NaN.
      *
      * Example: \include PartialRedux_maxCoeff.cpp
      * Output: \verbinclude PartialRedux_maxCoeff.out
      *
      * \sa DenseBase::maxCoeff() */
    EIGEN_DEVICE_FUNC
    const MaxCoeffReturnType maxCoeff() const
    {
      eigen_assert(redux_length()>0 && "you are using an empty matrix");
      return MaxCoeffReturnType(_expression());
    }

    /** \returns a row (or column) vector expression of the squared norm
      * of each column (or row) of the referenced expression.
      * This is a vector with real entries, even if the original matrix has complex entries.
      *
      * Example: \include PartialRedux_squaredNorm.cpp
      * Output: \verbinclude PartialRedux_squaredNorm.out
      *
      * \sa DenseBase::squaredNorm() */
    EIGEN_DEVICE_FUNC
    const SquaredNormReturnType squaredNorm() const
    { return SquaredNormReturnType(m_matrix.cwiseAbs2()); }

    /** \returns a row (or column) vector expression of the norm
      * of each column (or row) of the referenced expression.
      * This is a vector with real entries, even if the original matrix has complex entries.
      *
      * Example: \include PartialRedux_norm.cpp
      * Output: \verbinclude PartialRedux_norm.out
      *
      * \sa DenseBase::norm() */
    EIGEN_DEVICE_FUNC
    const NormReturnType norm() const
    { return NormReturnType(squaredNorm()); }

    /** \returns a row (or column) vector expression of the norm
      * of each column (or row) of the referenced expression.
      * This is a vector with real entries, even if the original matrix has complex entries.
      *
      * Example: \include PartialRedux_norm.cpp
      * Output: \verbinclude PartialRedux_norm.out
      *
      * \sa DenseBase::norm() */
    template<int p>
    EIGEN_DEVICE_FUNC
    const typename LpNormReturnType<p>::Type lpNorm() const
    { return typename LpNormReturnType<p>::Type(_expression()); }

    /** \returns a row (or column) vector expression of the norm
      * of each column (or row) of the referenced expression, using
      * Blue's algorithm.
      * This is a vector with real entries, even if the original matrix has complex entries.
      *
      * \sa DenseBase::blueNorm() */
    EIGEN_DEVICE_FUNC
    const BlueNormReturnType blueNorm() const
    { return BlueNormReturnType(_expression()); }

    /** \returns a row (or column) vector expression of the norm
      * of each column (or row) of the referenced expression, avoiding
      * underflow and overflow.
      * This is a vector with real entries, even if the original matrix has complex entries.
      *
      * \sa DenseBase::stableNorm() */
    EIGEN_DEVICE_FUNC
    const StableNormReturnType stableNorm() const
    { return StableNormReturnType(_expression()); }

    /** \returns a row (or column) vector expression of the norm
      * of each column (or row) of the referenced expression, avoiding
      * underflow and overflow using a concatenation of hypot() calls.
      * This is a vector with real entries, even if the original matrix has complex entries.
      *
      * \sa DenseBase::hypotNorm() */
    EIGEN_DEVICE_FUNC
    const HypotNormReturnType hypotNorm() const
    { return HypotNormReturnType(_expression()); }

    /** \returns a row (or column) vector expression of the sum
      * of each column (or row) of the referenced expression.
      *
      * Example: \include PartialRedux_sum.cpp
      * Output: \verbinclude PartialRedux_sum.out
      *
      * \sa DenseBase::sum() */
    EIGEN_DEVICE_FUNC
    const SumReturnType sum() const
    { return SumReturnType(_expression()); }

    /** \returns a row (or column) vector expression of the mean
    * of each column (or row) of the referenced expression.
    *
    * \sa DenseBase::mean() */
    EIGEN_DEVICE_FUNC
    const MeanReturnType mean() const
    { return sum() / Scalar(Direction==Vertical?m_matrix.rows():m_matrix.cols()); }

    /** \returns a row (or column) vector expression representing
      * whether \b all coefficients of each respective column (or row) are \c true.
      * This expression can be assigned to a vector with entries of type \c bool.
      *
      * \sa DenseBase::all() */
    EIGEN_DEVICE_FUNC
    const AllReturnType all() const
    { return AllReturnType(_expression()); }

    /** \returns a row (or column) vector expression representing
      * whether \b at \b least one coefficient of each respective column (or row) is \c true.
      * This expression can be assigned to a vector with entries of type \c bool.
      *
      * \sa DenseBase::any() */
    EIGEN_DEVICE_FUNC
    const AnyReturnType any() const
    { return AnyReturnType(_expression()); }

    /** \returns a row (or column) vector expression representing
      * the number of \c true coefficients of each respective column (or row).
      * This expression can be assigned to a vector whose entries have the same type as is used to
      * index entries of the original matrix; for dense matrices, this is \c std::ptrdiff_t .
      *
      * Example: \include PartialRedux_count.cpp
      * Output: \verbinclude PartialRedux_count.out
      *
      * \sa DenseBase::count() */
    EIGEN_DEVICE_FUNC
    const CountReturnType count() const
    { return CountReturnType(_expression()); }

    /** \returns a row (or column) vector expression of the product
      * of each column (or row) of the referenced expression.
      *
      * Example: \include PartialRedux_prod.cpp
      * Output: \verbinclude PartialRedux_prod.out
      *
      * \sa DenseBase::prod() */
    EIGEN_DEVICE_FUNC
    const ProdReturnType prod() const
    { return ProdReturnType(_expression()); }

    /** \returns a matrix expression
      * where each column (or row) are reversed.
      *
      * Example: \include Vectorwise_reverse.cpp
      * Output: \verbinclude Vectorwise_reverse.out
      *
      * \sa DenseBase::reverse() */
    EIGEN_DEVICE_FUNC
    const ConstReverseReturnType reverse() const
    { return ConstReverseReturnType( _expression() ); }

    /** \returns a writable matrix expression
      * where each column (or row) are reversed.
      *
      * \sa reverse() const */
    EIGEN_DEVICE_FUNC
    ReverseReturnType reverse()
    { return ReverseReturnType( _expression() ); }

    typedef Replicate<ExpressionType,(isVertical?Dynamic:1),(isHorizontal?Dynamic:1)> ReplicateReturnType;
    EIGEN_DEVICE_FUNC
    const ReplicateReturnType replicate(Index factor) const;

    /**
      * \return an expression of the replication of each column (or row) of \c *this
      *
      * Example: \include DirectionWise_replicate.cpp
      * Output: \verbinclude DirectionWise_replicate.out
      *
      * \sa VectorwiseOp::replicate(Index), DenseBase::replicate(), class Replicate
      */
    // NOTE implemented here because of sunstudio's compilation errors
    // isVertical*Factor+isHorizontal instead of (isVertical?Factor:1) to handle CUDA bug with ternary operator
    template<int Factor> const Replicate<ExpressionType,isVertical*Factor+isHorizontal,isHorizontal*Factor+isVertical>
    EIGEN_DEVICE_FUNC
    replicate(Index factor = Factor) const
    {
      return Replicate<ExpressionType,(isVertical?Factor:1),(isHorizontal?Factor:1)>
          (_expression(),isVertical?factor:1,isHorizontal?factor:1);
    }

/////////// Artithmetic operators ///////////

    /** Copies the vector \a other to each subvector of \c *this */
    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    ExpressionType& operator=(const DenseBase<OtherDerived>& other)
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
      //eigen_assert((m_matrix.isNull()) == (other.isNull())); FIXME
      return m_matrix = extendedTo(other.derived());
    }

    /** Adds the vector \a other to each subvector of \c *this */
    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    ExpressionType& operator+=(const DenseBase<OtherDerived>& other)
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
      return m_matrix += extendedTo(other.derived());
    }

    /** Substracts the vector \a other to each subvector of \c *this */
    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    ExpressionType& operator-=(const DenseBase<OtherDerived>& other)
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
      return m_matrix -= extendedTo(other.derived());
    }

    /** Multiples each subvector of \c *this by the vector \a other */
    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    ExpressionType& operator*=(const DenseBase<OtherDerived>& other)
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
      EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
      m_matrix *= extendedTo(other.derived());
      return m_matrix;
    }

    /** Divides each subvector of \c *this by the vector \a other */
    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    ExpressionType& operator/=(const DenseBase<OtherDerived>& other)
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
      EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
      m_matrix /= extendedTo(other.derived());
      return m_matrix;
    }

    /** Returns the expression of the sum of the vector \a other to each subvector of \c *this */
    template<typename OtherDerived> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
    CwiseBinaryOp<internal::scalar_sum_op<Scalar,typename OtherDerived::Scalar>,
                  const ExpressionTypeNestedCleaned,
                  const typename ExtendedType<OtherDerived>::Type>
    operator+(const DenseBase<OtherDerived>& other) const
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
      return m_matrix + extendedTo(other.derived());
    }

    /** Returns the expression of the difference between each subvector of \c *this and the vector \a other */
    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    CwiseBinaryOp<internal::scalar_difference_op<Scalar,typename OtherDerived::Scalar>,
                  const ExpressionTypeNestedCleaned,
                  const typename ExtendedType<OtherDerived>::Type>
    operator-(const DenseBase<OtherDerived>& other) const
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
      return m_matrix - extendedTo(other.derived());
    }

    /** Returns the expression where each subvector is the product of the vector \a other
      * by the corresponding subvector of \c *this */
    template<typename OtherDerived> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
    CwiseBinaryOp<internal::scalar_product_op<Scalar>,
                  const ExpressionTypeNestedCleaned,
                  const typename ExtendedType<OtherDerived>::Type>
    EIGEN_DEVICE_FUNC
    operator*(const DenseBase<OtherDerived>& other) const
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
      EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
      return m_matrix * extendedTo(other.derived());
    }

    /** Returns the expression where each subvector is the quotient of the corresponding
      * subvector of \c *this by the vector \a other */
    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    CwiseBinaryOp<internal::scalar_quotient_op<Scalar>,
                  const ExpressionTypeNestedCleaned,
                  const typename ExtendedType<OtherDerived>::Type>
    operator/(const DenseBase<OtherDerived>& other) const
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
      EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
      return m_matrix / extendedTo(other.derived());
    }

    /** \returns an expression where each column (or row) of the referenced matrix are normalized.
      * The referenced matrix is \b not modified.
      * \sa MatrixBase::normalized(), normalize()
      */
    EIGEN_DEVICE_FUNC
    CwiseBinaryOp<internal::scalar_quotient_op<Scalar>,
                  const ExpressionTypeNestedCleaned,
                  const typename OppositeExtendedType<NormReturnType>::Type>
    normalized() const { return m_matrix.cwiseQuotient(extendedToOpposite(this->norm())); }

    /** Normalize in-place each row or columns of the referenced matrix.
      * \sa MatrixBase::normalize(), normalized()
      */
    EIGEN_DEVICE_FUNC void normalize() {
      m_matrix = this->normalized();
    }

    EIGEN_DEVICE_FUNC inline void reverseInPlace();

/////////// Geometry module ///////////

    typedef Homogeneous<ExpressionType,Direction> HomogeneousReturnType;
    EIGEN_DEVICE_FUNC
    HomogeneousReturnType homogeneous() const;

    typedef typename ExpressionType::PlainObject CrossReturnType;
    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    const CrossReturnType cross(const MatrixBase<OtherDerived>& other) const;

    enum {
      HNormalized_Size = Direction==Vertical ? internal::traits<ExpressionType>::RowsAtCompileTime
                                             : internal::traits<ExpressionType>::ColsAtCompileTime,
      HNormalized_SizeMinusOne = HNormalized_Size==Dynamic ? Dynamic : HNormalized_Size-1
    };
    typedef Block<const ExpressionType,
                  Direction==Vertical   ? int(HNormalized_SizeMinusOne)
                                        : int(internal::traits<ExpressionType>::RowsAtCompileTime),
                  Direction==Horizontal ? int(HNormalized_SizeMinusOne)
                                        : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
            HNormalized_Block;
    typedef Block<const ExpressionType,
                  Direction==Vertical   ? 1 : int(internal::traits<ExpressionType>::RowsAtCompileTime),
                  Direction==Horizontal ? 1 : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
            HNormalized_Factors;
    typedef CwiseBinaryOp<internal::scalar_quotient_op<typename internal::traits<ExpressionType>::Scalar>,
                const HNormalized_Block,
                const Replicate<HNormalized_Factors,
                  Direction==Vertical   ? HNormalized_SizeMinusOne : 1,
                  Direction==Horizontal ? HNormalized_SizeMinusOne : 1> >
            HNormalizedReturnType;

    EIGEN_DEVICE_FUNC
    const HNormalizedReturnType hnormalized() const;

#   ifdef EIGEN_VECTORWISEOP_PLUGIN
#     include EIGEN_VECTORWISEOP_PLUGIN
#   endif

  protected:
    Index redux_length() const
    {
      return Direction==Vertical ? m_matrix.rows() : m_matrix.cols();
    }
    ExpressionTypeNested m_matrix;
};

//const colwise moved to DenseBase.h due to CUDA compiler bug

/** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
  *
  * \sa rowwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
  */
template<typename Derived>
EIGEN_DEVICE_FUNC inline typename DenseBase<Derived>::ColwiseReturnType
DenseBase<Derived>::colwise()
{
  return ColwiseReturnType(derived());
}

//const rowwise moved to DenseBase.h due to CUDA compiler bug

/** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
  *
  * \sa colwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
  */
template<typename Derived>
EIGEN_DEVICE_FUNC inline typename DenseBase<Derived>::RowwiseReturnType
DenseBase<Derived>::rowwise()
{
  return RowwiseReturnType(derived());
}

} // end namespace Eigen

#endif // EIGEN_PARTIAL_REDUX_H

quality100%

¤ Dauer der Verarbeitung: 0.38 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.