Eigen/src/Core/Diagonal.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009-2010 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_DIAGONAL_H
#define EIGEN_DIAGONAL_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

/** \class Diagonal
 * \ingroup Core_Module
 *
 * \brief Expression of a diagonal/subdiagonal/superdiagonal in a matrix
 *
 * \tparam MatrixType the type of the object in which we are taking a sub/main/super diagonal
 * \tparam DiagIndex the index of the sub/super diagonal. The default is 0 and it means the main diagonal.
 *              A positive value means a superdiagonal, a negative value means a subdiagonal.
 *              You can also use DynamicIndex so the index can be set at runtime.
 *
 * The matrix is not required to be square.
 *
 * This class represents an expression of the main diagonal, or any sub/super diagonal
 * of a square matrix. It is the return type of MatrixBase::diagonal() and MatrixBase::diagonal(Index) and most of the
 * time this is the only way it is used.
 *
 * \sa MatrixBase::diagonal(), MatrixBase::diagonal(Index)
 */

namespace internal {
template <typename MatrixType, int DiagIndex>
struct traits<Diagonal<MatrixType, DiagIndex> > : traits<MatrixType> {
  typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
  typedef std::remove_reference_t<MatrixTypeNested> MatrixTypeNested_;
  typedef typename MatrixType::StorageKind StorageKind;
  enum {
    RowsAtCompileTime = (int(DiagIndex) == DynamicIndex || int(MatrixType::SizeAtCompileTime) == Dynamic)
                            ? Dynamic
                            : (plain_enum_min(MatrixType::RowsAtCompileTime - plain_enum_max(-DiagIndex, 0),
                                              MatrixType::ColsAtCompileTime - plain_enum_max(DiagIndex, 0))),
    ColsAtCompileTime = 1,
    MaxRowsAtCompileTime =
        int(MatrixType::MaxSizeAtCompileTime) == Dynamic ? Dynamic
        : DiagIndex == DynamicIndex
            ? min_size_prefer_fixed(MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime)
            : (plain_enum_min(MatrixType::MaxRowsAtCompileTime - plain_enum_max(-DiagIndex, 0),
                              MatrixType::MaxColsAtCompileTime - plain_enum_max(DiagIndex, 0))),
    MaxColsAtCompileTime = 1,
    MaskLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
    Flags = (unsigned int)MatrixTypeNested_::Flags & (RowMajorBit | MaskLvalueBit | DirectAccessBit) &
            ~RowMajorBit,  // FIXME DirectAccessBit should not be handled by expressions
    MatrixTypeOuterStride = outer_stride_at_compile_time<MatrixType>::ret,
    InnerStrideAtCompileTime = MatrixTypeOuterStride == Dynamic ? Dynamic : MatrixTypeOuterStride + 1,
    OuterStrideAtCompileTime = 0
  };
};
}  // namespace internal

template <typename MatrixType, int DiagIndex_>
class Diagonal : public internal::dense_xpr_base<Diagonal<MatrixType, DiagIndex_> >::type {
 public:
  enum { DiagIndex = DiagIndex_ };
  typedef typename internal::dense_xpr_base<Diagonal>::type Base;
  EIGEN_DENSE_PUBLIC_INTERFACE(Diagonal)

  EIGEN_DEVICE_FUNC constexpr explicit inline Diagonal(MatrixType& matrix, Index a_index = DiagIndex)
      : m_matrix(matrix), m_index(a_index) {
    eigen_assert(a_index <= m_matrix.cols() && -a_index <= m_matrix.rows());
  }

  EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Diagonal)

  EIGEN_DEVICE_FUNC constexpr inline Index rows() const {
    return m_index.value() < 0 ? numext::mini<Index>(m_matrix.cols(), m_matrix.rows() + m_index.value())
                               : numext::mini<Index>(m_matrix.rows(), m_matrix.cols() - m_index.value());
  }

  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return 1; }

  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_matrix.outerStride() + 1; }

  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return 0; }

  typedef std::conditional_t<internal::is_lvalue<MatrixType>::value, Scalar, const Scalar> ScalarWithConstIfNotLvalue;

  EIGEN_DEVICE_FUNC inline ScalarWithConstIfNotLvalue* data() {
    return rows() > 0 ? &(m_matrix.coeffRef(rowOffset(), colOffset())) : nullptr;
  }
  EIGEN_DEVICE_FUNC inline const Scalar* data() const {
    return rows() > 0 ? &(m_matrix.coeffRef(rowOffset(), colOffset())) : nullptr;
  }

  EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index row, Index) {
    EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
    return m_matrix.coeffRef(row + rowOffset(), row + colOffset());
  }

  EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index row, Index) const {
    return m_matrix.coeffRef(row + rowOffset(), row + colOffset());
  }

  EIGEN_DEVICE_FUNC inline CoeffReturnType coeff(Index row, Index) const {
    return m_matrix.coeff(row + rowOffset(), row + colOffset());
  }

  EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index idx) {
    EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
    return m_matrix.coeffRef(idx + rowOffset(), idx + colOffset());
  }

  EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index idx) const {
    return m_matrix.coeffRef(idx + rowOffset(), idx + colOffset());
  }

  EIGEN_DEVICE_FUNC inline CoeffReturnType coeff(Index idx) const {
    return m_matrix.coeff(idx + rowOffset(), idx + colOffset());
  }

  EIGEN_DEVICE_FUNC constexpr inline const internal::remove_all_t<typename MatrixType::Nested>& nestedExpression()
      const {
    return m_matrix;
  }

  EIGEN_DEVICE_FUNC constexpr inline Index index() const { return m_index.value(); }

 protected:
  typename internal::ref_selector<MatrixType>::non_const_type m_matrix;
  const internal::variable_if_dynamicindex<Index, DiagIndex> m_index;

 private:
  // some compilers may fail to optimize std::max etc in case of compile-time constants...
  EIGEN_DEVICE_FUNC constexpr Index absDiagIndex() const noexcept {
    return m_index.value() > 0 ? m_index.value() : -m_index.value();
  }
  EIGEN_DEVICE_FUNC constexpr Index rowOffset() const noexcept { return m_index.value() > 0 ? 0 : -m_index.value(); }
  EIGEN_DEVICE_FUNC constexpr Index colOffset() const noexcept { return m_index.value() > 0 ? m_index.value() : 0; }
  // trigger a compile-time error if someone try to call packet
  template <int LoadMode>
  typename MatrixType::PacketReturnType packet(Index) const;
  template <int LoadMode>
  typename MatrixType::PacketReturnType packet(Index, Index) const;
};

/** \returns an expression of the main diagonal of the matrix \c *this
 *
 * \c *this is not required to be square.
 *
 * Example: \include MatrixBase_diagonal.cpp
 * Output: \verbinclude MatrixBase_diagonal.out
 *
 * \sa class Diagonal */
template <typename Derived>
EIGEN_DEVICE_FUNC constexpr typename MatrixBase<Derived>::DiagonalReturnType MatrixBase<Derived>::diagonal() {
  return DiagonalReturnType(derived());
}

/** This is the const version of diagonal(). */
template <typename Derived>
EIGEN_DEVICE_FUNC constexpr const typename MatrixBase<Derived>::ConstDiagonalReturnType MatrixBase<Derived>::diagonal()
    const {
  return ConstDiagonalReturnType(derived());
}

/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
 *
 * \c *this is not required to be square.
 *
 * The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
 * and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
 *
 * Example: \include MatrixBase_diagonal_int.cpp
 * Output: \verbinclude MatrixBase_diagonal_int.out
 *
 * \sa MatrixBase::diagonal(), class Diagonal */
template <typename Derived>
EIGEN_DEVICE_FUNC constexpr Diagonal<Derived, DynamicIndex> MatrixBase<Derived>::diagonal(Index index) {
  return Diagonal<Derived, DynamicIndex>(derived(), index);
}

/** This is the const version of diagonal(Index). */
template <typename Derived>
EIGEN_DEVICE_FUNC constexpr const Diagonal<const Derived, DynamicIndex> MatrixBase<Derived>::diagonal(
    Index index) const {
  return Diagonal<const Derived, DynamicIndex>(derived(), index);
}

/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
 *
 * \c *this is not required to be square.
 *
 * The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
 * and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
 *
 * Example: \include MatrixBase_diagonal_template_int.cpp
 * Output: \verbinclude MatrixBase_diagonal_template_int.out
 *
 * \sa MatrixBase::diagonal(), class Diagonal */
template <typename Derived>
template <int Index_>
EIGEN_DEVICE_FUNC constexpr Diagonal<Derived, Index_> MatrixBase<Derived>::diagonal() {
  return Diagonal<Derived, Index_>(derived());
}

/** This is the const version of diagonal<int>(). */
template <typename Derived>
template <int Index_>
EIGEN_DEVICE_FUNC constexpr const Diagonal<const Derived, Index_> MatrixBase<Derived>::diagonal() const {
  return Diagonal<const Derived, Index_>(derived());
}

}  // end namespace Eigen

#endif  // EIGEN_DIAGONAL_H