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Diffstat (limited to 'Eigen/src/Core/ArithmeticSequence.h')
| -rw-r--r-- | Eigen/src/Core/ArithmeticSequence.h | 413 |
1 files changed, 413 insertions, 0 deletions
diff --git a/Eigen/src/Core/ArithmeticSequence.h b/Eigen/src/Core/ArithmeticSequence.h new file mode 100644 index 000000000..b6200fac1 --- /dev/null +++ b/Eigen/src/Core/ArithmeticSequence.h @@ -0,0 +1,413 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// 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_ARITHMETIC_SEQUENCE_H +#define EIGEN_ARITHMETIC_SEQUENCE_H + +namespace Eigen { + +namespace internal { + +#if (!EIGEN_HAS_CXX11) || !((!EIGEN_COMP_GNUC) || EIGEN_COMP_GNUC>=48) +template<typename T> struct aseq_negate {}; + +template<> struct aseq_negate<Index> { + typedef Index type; +}; + +template<int N> struct aseq_negate<FixedInt<N> > { + typedef FixedInt<-N> type; +}; + +// Compilation error in the following case: +template<> struct aseq_negate<FixedInt<DynamicIndex> > {}; + +template<typename FirstType,typename SizeType,typename IncrType, + bool FirstIsSymbolic=symbolic::is_symbolic<FirstType>::value, + bool SizeIsSymbolic =symbolic::is_symbolic<SizeType>::value> +struct aseq_reverse_first_type { + typedef Index type; +}; + +template<typename FirstType,typename SizeType,typename IncrType> +struct aseq_reverse_first_type<FirstType,SizeType,IncrType,true,true> { + typedef symbolic::AddExpr<FirstType, + symbolic::ProductExpr<symbolic::AddExpr<SizeType,symbolic::ValueExpr<FixedInt<-1> > >, + symbolic::ValueExpr<IncrType> > + > type; +}; + +template<typename SizeType,typename IncrType,typename EnableIf = void> +struct aseq_reverse_first_type_aux { + typedef Index type; +}; + +template<typename SizeType,typename IncrType> +struct aseq_reverse_first_type_aux<SizeType,IncrType,typename internal::enable_if<bool((SizeType::value+IncrType::value)|0x1)>::type> { + typedef FixedInt<(SizeType::value-1)*IncrType::value> type; +}; + +template<typename FirstType,typename SizeType,typename IncrType> +struct aseq_reverse_first_type<FirstType,SizeType,IncrType,true,false> { + typedef typename aseq_reverse_first_type_aux<SizeType,IncrType>::type Aux; + typedef symbolic::AddExpr<FirstType,symbolic::ValueExpr<Aux> > type; +}; + +template<typename FirstType,typename SizeType,typename IncrType> +struct aseq_reverse_first_type<FirstType,SizeType,IncrType,false,true> { + typedef symbolic::AddExpr<symbolic::ProductExpr<symbolic::AddExpr<SizeType,symbolic::ValueExpr<FixedInt<-1> > >, + symbolic::ValueExpr<IncrType> >, + symbolic::ValueExpr<> > type; +}; +#endif + +// Helper to cleanup the type of the increment: +template<typename T> struct cleanup_seq_incr { + typedef typename cleanup_index_type<T,DynamicIndex>::type type; +}; + +} + +//-------------------------------------------------------------------------------- +// seq(first,last,incr) and seqN(first,size,incr) +//-------------------------------------------------------------------------------- + +template<typename FirstType=Index,typename SizeType=Index,typename IncrType=internal::FixedInt<1> > +class ArithmeticSequence; + +template<typename FirstType,typename SizeType,typename IncrType> +ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type, + typename internal::cleanup_index_type<SizeType>::type, + typename internal::cleanup_seq_incr<IncrType>::type > +seqN(FirstType first, SizeType size, IncrType incr); + +/** \class ArithmeticSequence + * \ingroup Core_Module + * + * This class represents an arithmetic progression \f$ a_0, a_1, a_2, ..., a_{n-1}\f$ defined by + * its \em first value \f$ a_0 \f$, its \em size (aka length) \em n, and the \em increment (aka stride) + * that is equal to \f$ a_{i+1}-a_{i}\f$ for any \em i. + * + * It is internally used as the return type of the Eigen::seq and Eigen::seqN functions, and as the input arguments + * of DenseBase::operator()(const RowIndices&, const ColIndices&), and most of the time this is the + * only way it is used. + * + * \tparam FirstType type of the first element, usually an Index, + * but internally it can be a symbolic expression + * \tparam SizeType type representing the size of the sequence, usually an Index + * or a compile time integral constant. Internally, it can also be a symbolic expression + * \tparam IncrType type of the increment, can be a runtime Index, or a compile time integral constant (default is compile-time 1) + * + * \sa Eigen::seq, Eigen::seqN, DenseBase::operator()(const RowIndices&, const ColIndices&), class IndexedView + */ +template<typename FirstType,typename SizeType,typename IncrType> +class ArithmeticSequence +{ +public: + ArithmeticSequence(FirstType first, SizeType size) : m_first(first), m_size(size) {} + ArithmeticSequence(FirstType first, SizeType size, IncrType incr) : m_first(first), m_size(size), m_incr(incr) {} + + enum { + SizeAtCompileTime = internal::get_fixed_value<SizeType>::value, + IncrAtCompileTime = internal::get_fixed_value<IncrType,DynamicIndex>::value + }; + + /** \returns the size, i.e., number of elements, of the sequence */ + Index size() const { return m_size; } + + /** \returns the first element \f$ a_0 \f$ in the sequence */ + Index first() const { return m_first; } + + /** \returns the value \f$ a_i \f$ at index \a i in the sequence. */ + Index operator[](Index i) const { return m_first + i * m_incr; } + + const FirstType& firstObject() const { return m_first; } + const SizeType& sizeObject() const { return m_size; } + const IncrType& incrObject() const { return m_incr; } + +protected: + FirstType m_first; + SizeType m_size; + IncrType m_incr; + +public: + +#if EIGEN_HAS_CXX11 && ((!EIGEN_COMP_GNUC) || EIGEN_COMP_GNUC>=48) + auto reverse() const -> decltype(Eigen::seqN(m_first+(m_size+fix<-1>())*m_incr,m_size,-m_incr)) { + return seqN(m_first+(m_size+fix<-1>())*m_incr,m_size,-m_incr); + } +#else +protected: + typedef typename internal::aseq_negate<IncrType>::type ReverseIncrType; + typedef typename internal::aseq_reverse_first_type<FirstType,SizeType,IncrType>::type ReverseFirstType; +public: + ArithmeticSequence<ReverseFirstType,SizeType,ReverseIncrType> + reverse() const { + return seqN(m_first+(m_size+fix<-1>())*m_incr,m_size,-m_incr); + } +#endif +}; + +/** \returns an ArithmeticSequence starting at \a first, of length \a size, and increment \a incr + * + * \sa seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType) */ +template<typename FirstType,typename SizeType,typename IncrType> +ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,typename internal::cleanup_index_type<SizeType>::type,typename internal::cleanup_seq_incr<IncrType>::type > +seqN(FirstType first, SizeType size, IncrType incr) { + return ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,typename internal::cleanup_index_type<SizeType>::type,typename internal::cleanup_seq_incr<IncrType>::type>(first,size,incr); +} + +/** \returns an ArithmeticSequence starting at \a first, of length \a size, and unit increment + * + * \sa seqN(FirstType,SizeType,IncrType), seq(FirstType,LastType) */ +template<typename FirstType,typename SizeType> +ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,typename internal::cleanup_index_type<SizeType>::type > +seqN(FirstType first, SizeType size) { + return ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,typename internal::cleanup_index_type<SizeType>::type>(first,size); +} + +#ifdef EIGEN_PARSED_BY_DOXYGEN + +/** \returns an ArithmeticSequence starting at \a f, up (or down) to \a l, and with positive (or negative) increment \a incr + * + * It is essentially an alias to: + * \code + * seqN(f, (l-f+incr)/incr, incr); + * \endcode + * + * \sa seqN(FirstType,SizeType,IncrType), seq(FirstType,LastType) + */ +template<typename FirstType,typename LastType, typename IncrType> +auto seq(FirstType f, LastType l, IncrType incr); + +/** \returns an ArithmeticSequence starting at \a f, up (or down) to \a l, and unit increment + * + * It is essentially an alias to: + * \code + * seqN(f,l-f+1); + * \endcode + * + * \sa seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType) + */ +template<typename FirstType,typename LastType> +auto seq(FirstType f, LastType l); + +#else // EIGEN_PARSED_BY_DOXYGEN + +#if EIGEN_HAS_CXX11 +template<typename FirstType,typename LastType> +auto seq(FirstType f, LastType l) -> decltype(seqN(typename internal::cleanup_index_type<FirstType>::type(f), + ( typename internal::cleanup_index_type<LastType>::type(l) + - typename internal::cleanup_index_type<FirstType>::type(f)+fix<1>()))) +{ + return seqN(typename internal::cleanup_index_type<FirstType>::type(f), + (typename internal::cleanup_index_type<LastType>::type(l) + -typename internal::cleanup_index_type<FirstType>::type(f)+fix<1>())); +} + +template<typename FirstType,typename LastType, typename IncrType> +auto seq(FirstType f, LastType l, IncrType incr) + -> decltype(seqN(typename internal::cleanup_index_type<FirstType>::type(f), + ( typename internal::cleanup_index_type<LastType>::type(l) + - typename internal::cleanup_index_type<FirstType>::type(f)+typename internal::cleanup_seq_incr<IncrType>::type(incr) + ) / typename internal::cleanup_seq_incr<IncrType>::type(incr), + typename internal::cleanup_seq_incr<IncrType>::type(incr))) +{ + typedef typename internal::cleanup_seq_incr<IncrType>::type CleanedIncrType; + return seqN(typename internal::cleanup_index_type<FirstType>::type(f), + ( typename internal::cleanup_index_type<LastType>::type(l) + -typename internal::cleanup_index_type<FirstType>::type(f)+CleanedIncrType(incr)) / CleanedIncrType(incr), + CleanedIncrType(incr)); +} + +#else // EIGEN_HAS_CXX11 + +template<typename FirstType,typename LastType> +typename internal::enable_if<!(symbolic::is_symbolic<FirstType>::value || symbolic::is_symbolic<LastType>::value), + ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,Index> >::type +seq(FirstType f, LastType l) +{ + return seqN(typename internal::cleanup_index_type<FirstType>::type(f), + Index((typename internal::cleanup_index_type<LastType>::type(l)-typename internal::cleanup_index_type<FirstType>::type(f)+fix<1>()))); +} + +template<typename FirstTypeDerived,typename LastType> +typename internal::enable_if<!symbolic::is_symbolic<LastType>::value, + ArithmeticSequence<FirstTypeDerived, symbolic::AddExpr<symbolic::AddExpr<symbolic::NegateExpr<FirstTypeDerived>,symbolic::ValueExpr<> >, + symbolic::ValueExpr<internal::FixedInt<1> > > > >::type +seq(const symbolic::BaseExpr<FirstTypeDerived> &f, LastType l) +{ + return seqN(f.derived(),(typename internal::cleanup_index_type<LastType>::type(l)-f.derived()+fix<1>())); +} + +template<typename FirstType,typename LastTypeDerived> +typename internal::enable_if<!symbolic::is_symbolic<FirstType>::value, + ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type, + symbolic::AddExpr<symbolic::AddExpr<LastTypeDerived,symbolic::ValueExpr<> >, + symbolic::ValueExpr<internal::FixedInt<1> > > > >::type +seq(FirstType f, const symbolic::BaseExpr<LastTypeDerived> &l) +{ + return seqN(typename internal::cleanup_index_type<FirstType>::type(f),(l.derived()-typename internal::cleanup_index_type<FirstType>::type(f)+fix<1>())); +} + +template<typename FirstTypeDerived,typename LastTypeDerived> +ArithmeticSequence<FirstTypeDerived, + symbolic::AddExpr<symbolic::AddExpr<LastTypeDerived,symbolic::NegateExpr<FirstTypeDerived> >,symbolic::ValueExpr<internal::FixedInt<1> > > > +seq(const symbolic::BaseExpr<FirstTypeDerived> &f, const symbolic::BaseExpr<LastTypeDerived> &l) +{ + return seqN(f.derived(),(l.derived()-f.derived()+fix<1>())); +} + + +template<typename FirstType,typename LastType, typename IncrType> +typename internal::enable_if<!(symbolic::is_symbolic<FirstType>::value || symbolic::is_symbolic<LastType>::value), + ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,Index,typename internal::cleanup_seq_incr<IncrType>::type> >::type +seq(FirstType f, LastType l, IncrType incr) +{ + typedef typename internal::cleanup_seq_incr<IncrType>::type CleanedIncrType; + return seqN(typename internal::cleanup_index_type<FirstType>::type(f), + Index((typename internal::cleanup_index_type<LastType>::type(l)-typename internal::cleanup_index_type<FirstType>::type(f)+CleanedIncrType(incr))/CleanedIncrType(incr)), incr); +} + +template<typename FirstTypeDerived,typename LastType, typename IncrType> +typename internal::enable_if<!symbolic::is_symbolic<LastType>::value, + ArithmeticSequence<FirstTypeDerived, + symbolic::QuotientExpr<symbolic::AddExpr<symbolic::AddExpr<symbolic::NegateExpr<FirstTypeDerived>, + symbolic::ValueExpr<> >, + symbolic::ValueExpr<typename internal::cleanup_seq_incr<IncrType>::type> >, + symbolic::ValueExpr<typename internal::cleanup_seq_incr<IncrType>::type> >, + typename internal::cleanup_seq_incr<IncrType>::type> >::type +seq(const symbolic::BaseExpr<FirstTypeDerived> &f, LastType l, IncrType incr) +{ + typedef typename internal::cleanup_seq_incr<IncrType>::type CleanedIncrType; + return seqN(f.derived(),(typename internal::cleanup_index_type<LastType>::type(l)-f.derived()+CleanedIncrType(incr))/CleanedIncrType(incr), incr); +} + +template<typename FirstType,typename LastTypeDerived, typename IncrType> +typename internal::enable_if<!symbolic::is_symbolic<FirstType>::value, + ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type, + symbolic::QuotientExpr<symbolic::AddExpr<symbolic::AddExpr<LastTypeDerived,symbolic::ValueExpr<> >, + symbolic::ValueExpr<typename internal::cleanup_seq_incr<IncrType>::type> >, + symbolic::ValueExpr<typename internal::cleanup_seq_incr<IncrType>::type> >, + typename internal::cleanup_seq_incr<IncrType>::type> >::type +seq(FirstType f, const symbolic::BaseExpr<LastTypeDerived> &l, IncrType incr) +{ + typedef typename internal::cleanup_seq_incr<IncrType>::type CleanedIncrType; + return seqN(typename internal::cleanup_index_type<FirstType>::type(f), + (l.derived()-typename internal::cleanup_index_type<FirstType>::type(f)+CleanedIncrType(incr))/CleanedIncrType(incr), incr); +} + +template<typename FirstTypeDerived,typename LastTypeDerived, typename IncrType> +ArithmeticSequence<FirstTypeDerived, + symbolic::QuotientExpr<symbolic::AddExpr<symbolic::AddExpr<LastTypeDerived, + symbolic::NegateExpr<FirstTypeDerived> >, + symbolic::ValueExpr<typename internal::cleanup_seq_incr<IncrType>::type> >, + symbolic::ValueExpr<typename internal::cleanup_seq_incr<IncrType>::type> >, + typename internal::cleanup_seq_incr<IncrType>::type> +seq(const symbolic::BaseExpr<FirstTypeDerived> &f, const symbolic::BaseExpr<LastTypeDerived> &l, IncrType incr) +{ + typedef typename internal::cleanup_seq_incr<IncrType>::type CleanedIncrType; + return seqN(f.derived(),(l.derived()-f.derived()+CleanedIncrType(incr))/CleanedIncrType(incr), incr); +} +#endif // EIGEN_HAS_CXX11 + +#endif // EIGEN_PARSED_BY_DOXYGEN + + +#if EIGEN_HAS_CXX11 || defined(EIGEN_PARSED_BY_DOXYGEN) +/** \cpp11 + * \returns a symbolic ArithmeticSequence representing the last \a size elements with increment \a incr. + * + * It is a shortcut for: \code seqN(last-(size-fix<1>)*incr, size, incr) \endcode + * + * \sa lastN(SizeType), seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType) */ +template<typename SizeType,typename IncrType> +auto lastN(SizeType size, IncrType incr) +-> decltype(seqN(Eigen::last-(size-fix<1>())*incr, size, incr)) +{ + return seqN(Eigen::last-(size-fix<1>())*incr, size, incr); +} + +/** \cpp11 + * \returns a symbolic ArithmeticSequence representing the last \a size elements with a unit increment. + * + * It is a shortcut for: \code seq(last+fix<1>-size, last) \endcode + * + * \sa lastN(SizeType,IncrType, seqN(FirstType,SizeType), seq(FirstType,LastType) */ +template<typename SizeType> +auto lastN(SizeType size) +-> decltype(seqN(Eigen::last+fix<1>()-size, size)) +{ + return seqN(Eigen::last+fix<1>()-size, size); +} +#endif + +namespace internal { + +// Convert a symbolic span into a usable one (i.e., remove last/end "keywords") +template<typename T> +struct make_size_type { + typedef typename internal::conditional<symbolic::is_symbolic<T>::value, Index, T>::type type; +}; + +template<typename FirstType,typename SizeType,typename IncrType,int XprSize> +struct IndexedViewCompatibleType<ArithmeticSequence<FirstType,SizeType,IncrType>, XprSize> { + typedef ArithmeticSequence<Index,typename make_size_type<SizeType>::type,IncrType> type; +}; + +template<typename FirstType,typename SizeType,typename IncrType> +ArithmeticSequence<Index,typename make_size_type<SizeType>::type,IncrType> +makeIndexedViewCompatible(const ArithmeticSequence<FirstType,SizeType,IncrType>& ids, Index size,SpecializedType) { + return ArithmeticSequence<Index,typename make_size_type<SizeType>::type,IncrType>( + eval_expr_given_size(ids.firstObject(),size),eval_expr_given_size(ids.sizeObject(),size),ids.incrObject()); +} + +template<typename FirstType,typename SizeType,typename IncrType> +struct get_compile_time_incr<ArithmeticSequence<FirstType,SizeType,IncrType> > { + enum { value = get_fixed_value<IncrType,DynamicIndex>::value }; +}; + +} // end namespace internal + +/** \namespace Eigen::indexing + * \ingroup Core_Module + * + * The sole purpose of this namespace is to be able to import all functions + * and symbols that are expected to be used within operator() for indexing + * and slicing. If you already imported the whole Eigen namespace: + * \code using namespace Eigen; \endcode + * then you are already all set. Otherwise, if you don't want/cannot import + * the whole Eigen namespace, the following line: + * \code using namespace Eigen::indexing; \endcode + * is equivalent to: + * \code + using Eigen::all; + using Eigen::seq; + using Eigen::seqN; + using Eigen::lastN; // c++11 only + using Eigen::last; + using Eigen::lastp1; + using Eigen::fix; + \endcode + */ +namespace indexing { + using Eigen::all; + using Eigen::seq; + using Eigen::seqN; + #if EIGEN_HAS_CXX11 + using Eigen::lastN; + #endif + using Eigen::last; + using Eigen::lastp1; + using Eigen::fix; +} + +} // end namespace Eigen + +#endif // EIGEN_ARITHMETIC_SEQUENCE_H |