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// 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
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
// Helper to cleanup the type of the increment:
template<typename T> struct cleanup_seq_incr {
typedef typename cleanup_index_type<T,DynamicIndex>::type type;
};
} // namespace internal
//--------------------------------------------------------------------------------
// 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:
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);
}
};
/** \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
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));
}
#endif // EIGEN_PARSED_BY_DOXYGEN
namespace placeholders {
/** \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::placeholders::last-(size-fix<1>())*incr, size, incr))
{
return seqN(Eigen::placeholders::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::placeholders::last+fix<1>()-size, size))
{
return seqN(Eigen::placeholders::last+fix<1>()-size, size);
}
} // namespace placeholders
namespace internal {
// Convert a symbolic span into a usable one (i.e., remove last/end "keywords")
template<typename T>
struct make_size_type {
typedef std::conditional_t<symbolic::is_symbolic<T>::value, Index, T> 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::fix;
using Eigen::seq;
using Eigen::seqN;
using Eigen::placeholders::all;
using Eigen::placeholders::last;
using Eigen::placeholders::lastN; // c++11 only
using Eigen::placeholders::lastp1;
\endcode
*/
namespace indexing {
using Eigen::fix;
using Eigen::seq;
using Eigen::seqN;
using Eigen::placeholders::all;
using Eigen::placeholders::last;
using Eigen::placeholders::lastN;
using Eigen::placeholders::lastp1;
}
} // end namespace Eigen
#endif // EIGEN_ARITHMETIC_SEQUENCE_H