Eigen/src/Core/ArithmeticSequence.h

// 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:
  constexpr ArithmeticSequence() = default;
  constexpr ArithmeticSequence(FirstType first, SizeType size) : m_first(first), m_size(size) {}
  constexpr 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 */
  constexpr Index size() const { return m_size; }

  /** \returns the first element \f$ a_0 \f$ in the sequence */
  constexpr Index first() const { return m_first; }

  /** \returns the value \f$ a_i \f$ at index \a i in the sequence. */
  constexpr Index operator[](Index i) const { return m_first + i * m_incr; }

  constexpr const FirstType& firstObject() const { return m_first; }
  constexpr const SizeType& sizeObject() const { return m_size; }
  constexpr const IncrType& incrObject() const { return m_incr; }

 protected:
  FirstType m_first;
  SizeType m_size;
  IncrType m_incr;

 public:
  constexpr 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 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;
}  // namespace indexing

}  // end namespace Eigen

#endif  // EIGEN_ARITHMETIC_SEQUENCE_H