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DiagonalMatrix.h
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DiagonalMatrix.h
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// 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
namespace Eigen {
#ifndef EIGEN_PARSED_BY_DOXYGEN
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;
EIGEN_DEVICE_FUNC
inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
EIGEN_DEVICE_FUNC
inline Derived& derived() { return *static_cast<Derived*>(this); }
EIGEN_DEVICE_FUNC
DenseMatrixType toDenseMatrix() const { return derived(); }
EIGEN_DEVICE_FUNC
inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); }
EIGEN_DEVICE_FUNC
inline DiagonalVectorType& diagonal() { return derived().diagonal(); }
EIGEN_DEVICE_FUNC
inline Index rows() const { return diagonal().size(); }
EIGEN_DEVICE_FUNC
inline Index cols() const { return diagonal().size(); }
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());
}
typedef DiagonalWrapper<const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DiagonalVectorType> > InverseReturnType;
EIGEN_DEVICE_FUNC
inline const InverseReturnType
inverse() const
{
return InverseReturnType(diagonal().cwiseInverse());
}
EIGEN_DEVICE_FUNC
inline const DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType,Scalar,product) >
operator*(const Scalar& scalar) const
{
return DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType,Scalar,product) >(diagonal() * scalar);
}
EIGEN_DEVICE_FUNC
friend inline const DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,DiagonalVectorType,product) >
operator*(const Scalar& scalar, const DiagonalBase& other)
{
return DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,DiagonalVectorType,product) >(scalar * other.diagonal());
}
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
#ifdef EIGEN_PARSED_BY_DOXYGEN
inline unspecified_expression_type
#else
inline const DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(DiagonalVectorType,typename OtherDerived::DiagonalVectorType,sum) >
#endif
operator+(const DiagonalBase<OtherDerived>& other) const
{
return (diagonal() + other.diagonal()).asDiagonal();
}
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
#ifdef EIGEN_PARSED_BY_DOXYGEN
inline unspecified_expression_type
#else
inline const DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(DiagonalVectorType,typename OtherDerived::DiagonalVectorType,difference) >
#endif
operator-(const DiagonalBase<OtherDerived>& other) const
{
return (diagonal() - other.diagonal()).asDiagonal();
}
};
#endif
/** \class DiagonalMatrix
* \ingroup Core_Module
*
* \brief Represents a diagonal matrix with its storage
*
* \param _Scalar the type of coefficients
* \param SizeAtCompileTime the dimension of the matrix, or Dynamic
* \param 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 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
};
};
}
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) {}
#if EIGEN_HAS_CXX11
/** \brief Construct a diagonal matrix with fixed size from an arbitrary number of coefficients. \cpp11
*
* There exists C++98 anologue constructors for fixed-size diagonal matrices having 2 or 3 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) {}
#endif // EIGEN_HAS_CXX11
/** 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
/** 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
*
* \param _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

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