Eigen/src/Core/DiagonalMatrix.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2007-2009 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/.

#ifndef EIGEN_DIAGONALMATRIX_H
#define EIGEN_DIAGONALMATRIX_H

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

namespace Eigen {

/** \class DiagonalBase
 * \ingroup Core_Module
 *
 * \brief Base class for diagonal matrices and expressions
 *
 * This is the base class that is inherited by diagonal matrix and related expression
 * types, which internally use a vector for storing the diagonal entries. Diagonal
 * types always represent square matrices.
 *
 * \tparam Derived is the derived type, a DiagonalMatrix or DiagonalWrapper.
 *
 * \sa class DiagonalMatrix, class DiagonalWrapper
 */
template<typename Derived>
class DiagonalBase : public EigenBase<Derived>
{
  public:
    typedef typename internal::traits<Derived>::DiagonalVectorType DiagonalVectorType;
    typedef typename DiagonalVectorType::Scalar Scalar;
    typedef typename DiagonalVectorType::RealScalar RealScalar;
    typedef typename internal::traits<Derived>::StorageKind StorageKind;
    typedef typename internal::traits<Derived>::StorageIndex StorageIndex;

    enum {
      RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
      ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
      MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
      MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
      IsVectorAtCompileTime = 0,
      Flags = NoPreferredStorageOrderBit
    };

    typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime> DenseMatrixType;
    typedef DenseMatrixType DenseType;
    typedef DiagonalMatrix<Scalar,DiagonalVectorType::SizeAtCompileTime,DiagonalVectorType::MaxSizeAtCompileTime> PlainObject;

    /** \returns a reference to the derived object. */
    EIGEN_DEVICE_FUNC
    inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
    /** \returns a const reference to the derived object. */
    EIGEN_DEVICE_FUNC
    inline Derived& derived() { return *static_cast<Derived*>(this); }

    /**
     * Constructs a dense matrix from \c *this. Note, this directly returns a dense matrix type,
     * not an expression.
     * \returns A dense matrix, with its diagonal entries set from the the derived object. */
    EIGEN_DEVICE_FUNC
    DenseMatrixType toDenseMatrix() const { return derived(); }

    /** \returns a reference to the derived object's vector of diagonal coefficients. */
    EIGEN_DEVICE_FUNC
    inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); }
    /** \returns a const reference to the derived object's vector of diagonal coefficients. */
    EIGEN_DEVICE_FUNC
    inline DiagonalVectorType& diagonal() { return derived().diagonal(); }

    /** \returns the value of the coefficient as if \c *this was a dense matrix. */
    EIGEN_DEVICE_FUNC
    inline Scalar coeff(Index row, Index col) const {
      eigen_assert(row >= 0 && col >= 0 && row < rows() && col <= cols());
      return row == col ? diagonal().coeff(row) : Scalar(0);
    }

    /** \returns the number of rows. */
    EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR 
    inline Index rows() const { return diagonal().size(); }
    /** \returns the number of columns. */
    EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR 
    inline Index cols() const { return diagonal().size(); }

    /** \returns the diagonal matrix product of \c *this by the dense matrix, \a matrix */
    template<typename MatrixDerived>
    EIGEN_DEVICE_FUNC
    const Product<Derived,MatrixDerived,LazyProduct>
    operator*(const MatrixBase<MatrixDerived> &matrix) const
    {
      return Product<Derived, MatrixDerived, LazyProduct>(derived(),matrix.derived());
    }

    template <typename OtherDerived>
    using DiagonalProductReturnType = DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(
        DiagonalVectorType, typename OtherDerived::DiagonalVectorType, product)>;

    /** \returns the diagonal matrix product of \c *this by the diagonal matrix \a other */
    template <typename OtherDerived>
    EIGEN_DEVICE_FUNC const DiagonalProductReturnType<OtherDerived> operator*(
        const DiagonalBase<OtherDerived>& other) const {
      return diagonal().cwiseProduct(other.diagonal()).asDiagonal();
    }

    using DiagonalInverseReturnType =
        DiagonalWrapper<const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DiagonalVectorType>>;

    /** \returns the inverse \c *this. Computed as the coefficient-wise inverse of the diagonal. */
    EIGEN_DEVICE_FUNC
    inline const DiagonalInverseReturnType inverse() const { return diagonal().cwiseInverse().asDiagonal(); }

    using DiagonalScaleReturnType =
        DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType, Scalar, product)>;

    /** \returns the product of \c *this by the scalar \a scalar */
    EIGEN_DEVICE_FUNC
    inline const DiagonalScaleReturnType operator*(const Scalar& scalar) const {
      return (diagonal() * scalar).asDiagonal();
    }

    using ScaleDiagonalReturnType =
        DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar, DiagonalVectorType, product)>;

    /** \returns the product of a scalar and the diagonal matrix \a other */
    EIGEN_DEVICE_FUNC
    friend inline const ScaleDiagonalReturnType operator*(const Scalar& scalar, const DiagonalBase& other) {
      return (scalar * other.diagonal()).asDiagonal();
    }

    template <typename OtherDerived>
    using DiagonalSumReturnType = DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(
        DiagonalVectorType, typename OtherDerived::DiagonalVectorType, sum)>;

    /** \returns the sum of \c *this and the diagonal matrix \a other */
    template <typename OtherDerived>
    EIGEN_DEVICE_FUNC inline const DiagonalSumReturnType<OtherDerived> operator+(
        const DiagonalBase<OtherDerived>& other) const {
      return (diagonal() + other.diagonal()).asDiagonal();
    }

    template <typename OtherDerived>
    using DiagonalDifferenceReturnType = DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(
        DiagonalVectorType, typename OtherDerived::DiagonalVectorType, difference)>;

    /** \returns the difference of \c *this and the diagonal matrix \a other */
    template <typename OtherDerived>
    EIGEN_DEVICE_FUNC inline const DiagonalDifferenceReturnType<OtherDerived> operator-(
        const DiagonalBase<OtherDerived>& other) const {
      return (diagonal() - other.diagonal()).asDiagonal();
    }
};

/** \class DiagonalMatrix
 * \ingroup Core_Module
 *
 * \brief Represents a diagonal matrix with its storage
 *
 * \tparam Scalar_ the type of coefficients
 * \tparam SizeAtCompileTime the dimension of the matrix, or Dynamic
 * \tparam MaxSizeAtCompileTime the dimension of the matrix, or Dynamic. This parameter is optional and defaults
 *        to SizeAtCompileTime. Most of the time, you do not need to specify it.
 *
 * \sa class DiagonalBase, class DiagonalWrapper
 */

namespace internal {
template<typename Scalar_, int SizeAtCompileTime, int MaxSizeAtCompileTime>
struct traits<DiagonalMatrix<Scalar_,SizeAtCompileTime,MaxSizeAtCompileTime> >
 : traits<Matrix<Scalar_,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
{
  typedef Matrix<Scalar_,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1> DiagonalVectorType;
  typedef DiagonalShape StorageKind;
  enum {
    Flags = LvalueBit | NoPreferredStorageOrderBit | NestByRefBit
  };
};
}
template<typename Scalar_, int SizeAtCompileTime, int MaxSizeAtCompileTime>
class DiagonalMatrix
  : public DiagonalBase<DiagonalMatrix<Scalar_,SizeAtCompileTime,MaxSizeAtCompileTime> >
{
  public:
    #ifndef EIGEN_PARSED_BY_DOXYGEN
    typedef typename internal::traits<DiagonalMatrix>::DiagonalVectorType DiagonalVectorType;
    typedef const DiagonalMatrix& Nested;
    typedef Scalar_ Scalar;
    typedef typename internal::traits<DiagonalMatrix>::StorageKind StorageKind;
    typedef typename internal::traits<DiagonalMatrix>::StorageIndex StorageIndex;
    #endif

  protected:

    DiagonalVectorType m_diagonal;

  public:

    /** const version of diagonal(). */
    EIGEN_DEVICE_FUNC
    inline const DiagonalVectorType& diagonal() const { return m_diagonal; }
    /** \returns a reference to the stored vector of diagonal coefficients. */
    EIGEN_DEVICE_FUNC
    inline DiagonalVectorType& diagonal() { return m_diagonal; }

    /** Default constructor without initialization */
    EIGEN_DEVICE_FUNC
    inline DiagonalMatrix() {}

    /** Constructs a diagonal matrix with given dimension  */
    EIGEN_DEVICE_FUNC
    explicit inline DiagonalMatrix(Index dim) : m_diagonal(dim) {}

    /** 2D constructor. */
    EIGEN_DEVICE_FUNC
    inline DiagonalMatrix(const Scalar& x, const Scalar& y) : m_diagonal(x,y) {}

    /** 3D constructor. */
    EIGEN_DEVICE_FUNC
    inline DiagonalMatrix(const Scalar& x, const Scalar& y, const Scalar& z) : m_diagonal(x,y,z) {}

    /** \brief Construct a diagonal matrix with fixed size from an arbitrary number of coefficients.
      * 
      * \warning To construct a diagonal matrix of fixed size, the number of values passed to this 
      * constructor must match the fixed dimension of \c *this.
      * 
      * \sa DiagonalMatrix(const Scalar&, const Scalar&)
      * \sa DiagonalMatrix(const Scalar&, const Scalar&, const Scalar&)
      */
    template <typename... ArgTypes>
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
    DiagonalMatrix(const Scalar& a0, const Scalar& a1, const Scalar& a2, const ArgTypes&... args)
      : m_diagonal(a0, a1, a2, args...) {}

    /** \brief Constructs a DiagonalMatrix and initializes it by elements given by an initializer list of initializer
      * lists \cpp11
      */
    EIGEN_DEVICE_FUNC
    explicit EIGEN_STRONG_INLINE DiagonalMatrix(const std::initializer_list<std::initializer_list<Scalar>>& list)
      : m_diagonal(list) {}

    /** \brief Constructs a DiagonalMatrix from an r-value diagonal vector type */
    EIGEN_DEVICE_FUNC
    explicit inline DiagonalMatrix(DiagonalVectorType&& diag) : m_diagonal(std::move(diag)) {}

    /** Copy constructor. */
    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    inline DiagonalMatrix(const DiagonalBase<OtherDerived>& other) : m_diagonal(other.diagonal()) {}

    #ifndef EIGEN_PARSED_BY_DOXYGEN
    /** copy constructor. prevent a default copy constructor from hiding the other templated constructor */
    inline DiagonalMatrix(const DiagonalMatrix& other) : m_diagonal(other.diagonal()) {}
    #endif

    /** generic constructor from expression of the diagonal coefficients */
    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : m_diagonal(other)
    {}

    /** Copy operator. */
    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    DiagonalMatrix& operator=(const DiagonalBase<OtherDerived>& other)
    {
      m_diagonal = other.diagonal();
      return *this;
    }

    #ifndef EIGEN_PARSED_BY_DOXYGEN
    /** This is a special case of the templated operator=. Its purpose is to
      * prevent a default operator= from hiding the templated operator=.
      */
    EIGEN_DEVICE_FUNC
    DiagonalMatrix& operator=(const DiagonalMatrix& other)
    {
      m_diagonal = other.diagonal();
      return *this;
    }
    #endif

    typedef DiagonalWrapper<const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, DiagonalVectorType>>
        InitializeReturnType;

    /** Initializes a diagonal matrix of size SizeAtCompileTime with coefficients set to zero */
    EIGEN_DEVICE_FUNC
    static const InitializeReturnType Zero() { return DiagonalVectorType::Zero().asDiagonal(); }
    /** Initializes a diagonal matrix of size dim with coefficients set to zero */
    EIGEN_DEVICE_FUNC
    static const InitializeReturnType Zero(Index size) { return DiagonalVectorType::Zero(size).asDiagonal(); }
    /** Initializes a identity matrix of size SizeAtCompileTime */
    EIGEN_DEVICE_FUNC
    static const InitializeReturnType Identity() { return DiagonalVectorType::Ones().asDiagonal(); }
    /** Initializes a identity matrix of size dim */
    EIGEN_DEVICE_FUNC
    static const InitializeReturnType Identity(Index size) { return DiagonalVectorType::Ones(size).asDiagonal(); }

    /** Resizes to given size. */
    EIGEN_DEVICE_FUNC
    inline void resize(Index size) { m_diagonal.resize(size); }
    /** Sets all coefficients to zero. */
    EIGEN_DEVICE_FUNC
    inline void setZero() { m_diagonal.setZero(); }
    /** Resizes and sets all coefficients to zero. */
    EIGEN_DEVICE_FUNC
    inline void setZero(Index size) { m_diagonal.setZero(size); }
    /** Sets this matrix to be the identity matrix of the current size. */
    EIGEN_DEVICE_FUNC
    inline void setIdentity() { m_diagonal.setOnes(); }
    /** Sets this matrix to be the identity matrix of the given size. */
    EIGEN_DEVICE_FUNC
    inline void setIdentity(Index size) { m_diagonal.setOnes(size); }
};

/** \class DiagonalWrapper
  * \ingroup Core_Module
  *
  * \brief Expression of a diagonal matrix
  *
  * \tparam DiagonalVectorType_ the type of the vector of diagonal coefficients
  *
  * This class is an expression of a diagonal matrix, but not storing its own vector of diagonal coefficients,
  * instead wrapping an existing vector expression. It is the return type of MatrixBase::asDiagonal()
  * and most of the time this is the only way that it is used.
  *
  * \sa class DiagonalMatrix, class DiagonalBase, MatrixBase::asDiagonal()
  */

namespace internal {
template<typename DiagonalVectorType_>
struct traits<DiagonalWrapper<DiagonalVectorType_> >
{
  typedef DiagonalVectorType_ DiagonalVectorType;
  typedef typename DiagonalVectorType::Scalar Scalar;
  typedef typename DiagonalVectorType::StorageIndex StorageIndex;
  typedef DiagonalShape StorageKind;
  typedef typename traits<DiagonalVectorType>::XprKind XprKind;
  enum {
    RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
    ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
    MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
    MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
    Flags =  (traits<DiagonalVectorType>::Flags & LvalueBit) | NoPreferredStorageOrderBit
  };
};
}

template<typename DiagonalVectorType_>
class DiagonalWrapper
  : public DiagonalBase<DiagonalWrapper<DiagonalVectorType_> >, internal::no_assignment_operator
{
  public:
    #ifndef EIGEN_PARSED_BY_DOXYGEN
    typedef DiagonalVectorType_ DiagonalVectorType;
    typedef DiagonalWrapper Nested;
    #endif

    /** Constructor from expression of diagonal coefficients to wrap. */
    EIGEN_DEVICE_FUNC
    explicit inline DiagonalWrapper(DiagonalVectorType& a_diagonal) : m_diagonal(a_diagonal) {}

    /** \returns a const reference to the wrapped expression of diagonal coefficients. */
    EIGEN_DEVICE_FUNC
    const DiagonalVectorType& diagonal() const { return m_diagonal; }

  protected:
    typename DiagonalVectorType::Nested m_diagonal;
};

/** \returns a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients
  *
  * \only_for_vectors
  *
  * Example: \include MatrixBase_asDiagonal.cpp
  * Output: \verbinclude MatrixBase_asDiagonal.out
  *
  * \sa class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()
  **/
template<typename Derived>
EIGEN_DEVICE_FUNC inline const DiagonalWrapper<const Derived>
MatrixBase<Derived>::asDiagonal() const
{
  return DiagonalWrapper<const Derived>(derived());
}

/** \returns true if *this is approximately equal to a diagonal matrix,
  *          within the precision given by \a prec.
  *
  * Example: \include MatrixBase_isDiagonal.cpp
  * Output: \verbinclude MatrixBase_isDiagonal.out
  *
  * \sa asDiagonal()
  */
template<typename Derived>
bool MatrixBase<Derived>::isDiagonal(const RealScalar& prec) const
{
  if(cols() != rows()) return false;
  RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
  for(Index j = 0; j < cols(); ++j)
  {
    RealScalar absOnDiagonal = numext::abs(coeff(j,j));
    if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
  }
  for(Index j = 0; j < cols(); ++j)
    for(Index i = 0; i < j; ++i)
    {
      if(!internal::isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;
      if(!internal::isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;
    }
  return true;
}

namespace internal {

template<> struct storage_kind_to_shape<DiagonalShape> { typedef DiagonalShape Shape; };

struct Diagonal2Dense {};

template<> struct AssignmentKind<DenseShape,DiagonalShape> { typedef Diagonal2Dense Kind; };

// Diagonal matrix to Dense assignment
template< typename DstXprType, typename SrcXprType, typename Functor>
struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Dense>
{
  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
  {
    Index dstRows = src.rows();
    Index dstCols = src.cols();
    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
      dst.resize(dstRows, dstCols);
    
    dst.setZero();
    dst.diagonal() = src.diagonal();
  }
  
  static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
  { dst.diagonal() += src.diagonal(); }
  
  static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
  { dst.diagonal() -= src.diagonal(); }
};

} // namespace internal

}  // end namespace Eigen

#endif // EIGEN_DIAGONALMATRIX_H