// 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/.
/** \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;
/** \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:
typedeftypename ExpressionType::Scalar Scalar; typedeftypename ExpressionType::RealScalar RealScalar; typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3 typedeftypename internal::ref_selector<ExpressionType>::non_const_type ExpressionTypeNested; typedeftypename 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;
};
#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 consttypename ReduxReturnType<BinaryOp>::Type
redux(const BinaryOp& func = BinaryOp()) const
{
eigen_assert(redux_length()>0 && "you are using an empty matrix"); returntypename ReduxReturnType<BinaryOp>::Type(_expression(), internal::member_redux<BinaryOp,Scalar>(func));
}
/** \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 consttypename LpNormReturnType<p>::Type lpNorm() const
{ returntypename 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() ); }
/** * \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, consttypename 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, consttypename 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, consttypename 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, consttypename 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, consttypename 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();
}
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