314 lines
11 KiB
C
314 lines
11 KiB
C
|
// 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>::Index Index;
|
||
|
|
|
||
|
|
enum {
|
||
|
|
RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
|
||
|
|
ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
|
||
|
|
MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
|
||
|
|
MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
|
||
|
|
IsVectorAtCompileTime = 0,
|
||
|
|
Flags = 0
|
||
|
|
};
|
||
|
|
|
||
|
|
typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime> DenseMatrixType;
|
||
|
|
typedef DenseMatrixType DenseType;
|
||
|
|
typedef DiagonalMatrix<Scalar,DiagonalVectorType::SizeAtCompileTime,DiagonalVectorType::MaxSizeAtCompileTime> PlainObject;
|
||
|
|
|
||
|
|
inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
|
||
|
|
inline Derived& derived() { return *static_cast<Derived*>(this); }
|
||
|
|
|
||
|
|
DenseMatrixType toDenseMatrix() const { return derived(); }
|
||
|
|
template<typename DenseDerived>
|
||
|
|
void evalTo(MatrixBase<DenseDerived> &other) const;
|
||
|
|
template<typename DenseDerived>
|
||
|
|
inline void addTo(MatrixBase<DenseDerived> &other) const
|
||
|
|
{ other.diagonal() += diagonal(); }
|
||
|
|
template<typename DenseDerived>
|
||
|
|
inline void subTo(MatrixBase<DenseDerived> &other) const
|
||
|
|
{ other.diagonal() -= diagonal(); }
|
||
|
|
|
||
|
|
inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); }
|
||
|
|
inline DiagonalVectorType& diagonal() { return derived().diagonal(); }
|
||
|
|
|
||
|
|
inline Index rows() const { return diagonal().size(); }
|
||
|
|
inline Index cols() const { return diagonal().size(); }
|
||
|
|
|
||
|
|
/** \returns the diagonal matrix product of \c *this by the matrix \a matrix.
|
||
|
|
*/
|
||
|
|
template<typename MatrixDerived>
|
||
|
|
const DiagonalProduct<MatrixDerived, Derived, OnTheLeft>
|
||
|
|
operator*(const MatrixBase<MatrixDerived> &matrix) const
|
||
|
|
{
|
||
|
|
return DiagonalProduct<MatrixDerived, Derived, OnTheLeft>(matrix.derived(), derived());
|
||
|
|
}
|
||
|
|
|
||
|
|
inline const DiagonalWrapper<const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DiagonalVectorType> >
|
||
|
|
inverse() const
|
||
|
|
{
|
||
|
|
return diagonal().cwiseInverse();
|
||
|
|
}
|
||
|
|
|
||
|
|
inline const DiagonalWrapper<const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DiagonalVectorType> >
|
||
|
|
operator*(const Scalar& scalar) const
|
||
|
|
{
|
||
|
|
return diagonal() * scalar;
|
||
|
|
}
|
||
|
|
friend inline const DiagonalWrapper<const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DiagonalVectorType> >
|
||
|
|
operator*(const Scalar& scalar, const DiagonalBase& other)
|
||
|
|
{
|
||
|
|
return other.diagonal() * scalar;
|
||
|
|
}
|
||
|
|
|
||
|
|
#ifdef EIGEN2_SUPPORT
|
||
|
|
template<typename OtherDerived>
|
||
|
|
bool isApprox(const DiagonalBase<OtherDerived>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
|
||
|
|
{
|
||
|
|
return diagonal().isApprox(other.diagonal(), precision);
|
||
|
|
}
|
||
|
|
template<typename OtherDerived>
|
||
|
|
bool isApprox(const MatrixBase<OtherDerived>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
|
||
|
|
{
|
||
|
|
return toDenseMatrix().isApprox(other, precision);
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
};
|
||
|
|
|
||
|
|
template<typename Derived>
|
||
|
|
template<typename DenseDerived>
|
||
|
|
inline void DiagonalBase<Derived>::evalTo(MatrixBase<DenseDerived> &other) const
|
||
|
|
{
|
||
|
|
other.setZero();
|
||
|
|
other.diagonal() = diagonal();
|
||
|
|
}
|
||
|
|
#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 Dense StorageKind;
|
||
|
|
typedef DenseIndex Index;
|
||
|
|
enum {
|
||
|
|
Flags = LvalueBit
|
||
|
|
};
|
||
|
|
};
|
||
|
|
}
|
||
|
|
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>::Index Index;
|
||
|
|
#endif
|
||
|
|
|
||
|
|
protected:
|
||
|
|
|
||
|
|
DiagonalVectorType m_diagonal;
|
||
|
|
|
||
|
|
public:
|
||
|
|
|
||
|
|
/** const version of diagonal(). */
|
||
|
|
inline const DiagonalVectorType& diagonal() const { return m_diagonal; }
|
||
|
|
/** \returns a reference to the stored vector of diagonal coefficients. */
|
||
|
|
inline DiagonalVectorType& diagonal() { return m_diagonal; }
|
||
|
|
|
||
|
|
/** Default constructor without initialization */
|
||
|
|
inline DiagonalMatrix() {}
|
||
|
|
|
||
|
|
/** Constructs a diagonal matrix with given dimension */
|
||
|
|
inline DiagonalMatrix(Index dim) : m_diagonal(dim) {}
|
||
|
|
|
||
|
|
/** 2D constructor. */
|
||
|
|
inline DiagonalMatrix(const Scalar& x, const Scalar& y) : m_diagonal(x,y) {}
|
||
|
|
|
||
|
|
/** 3D constructor. */
|
||
|
|
inline DiagonalMatrix(const Scalar& x, const Scalar& y, const Scalar& z) : m_diagonal(x,y,z) {}
|
||
|
|
|
||
|
|
/** Copy constructor. */
|
||
|
|
template<typename OtherDerived>
|
||
|
|
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>
|
||
|
|
explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : m_diagonal(other)
|
||
|
|
{}
|
||
|
|
|
||
|
|
/** Copy operator. */
|
||
|
|
template<typename OtherDerived>
|
||
|
|
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=.
|
||
|
|
*/
|
||
|
|
DiagonalMatrix& operator=(const DiagonalMatrix& other)
|
||
|
|
{
|
||
|
|
m_diagonal = other.diagonal();
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
|
||
|
|
/** Resizes to given size. */
|
||
|
|
inline void resize(Index size) { m_diagonal.resize(size); }
|
||
|
|
/** Sets all coefficients to zero. */
|
||
|
|
inline void setZero() { m_diagonal.setZero(); }
|
||
|
|
/** Resizes and sets all coefficients to zero. */
|
||
|
|
inline void setZero(Index size) { m_diagonal.setZero(size); }
|
||
|
|
/** Sets this matrix to be the identity matrix of the current size. */
|
||
|
|
inline void setIdentity() { m_diagonal.setOnes(); }
|
||
|
|
/** Sets this matrix to be the identity matrix of the given size. */
|
||
|
|
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::Index Index;
|
||
|
|
typedef typename DiagonalVectorType::StorageKind StorageKind;
|
||
|
|
enum {
|
||
|
|
RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
|
||
|
|
ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
|
||
|
|
MaxRowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
|
||
|
|
MaxColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
|
||
|
|
Flags = traits<DiagonalVectorType>::Flags & LvalueBit
|
||
|
|
};
|
||
|
|
};
|
||
|
|
}
|
||
|
|
|
||
|
|
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. */
|
||
|
|
inline DiagonalWrapper(DiagonalVectorType& a_diagonal) : m_diagonal(a_diagonal) {}
|
||
|
|
|
||
|
|
/** \returns a const reference to the wrapped expression of diagonal coefficients. */
|
||
|
|
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>
|
||
|
|
inline const DiagonalWrapper<const Derived>
|
||
|
|
MatrixBase<Derived>::asDiagonal() const
|
||
|
|
{
|
||
|
|
return 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
|
||
|
|
{
|
||
|
|
using std::abs;
|
||
|
|
if(cols() != rows()) return false;
|
||
|
|
RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
|
||
|
|
for(Index j = 0; j < cols(); ++j)
|
||
|
|
{
|
||
|
|
RealScalar absOnDiagonal = 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;
|
||
|
|
}
|
||
|
|
|
||
|
|
} // end namespace Eigen
|
||
|
|
|
||
|
|
#endif // EIGEN_DIAGONALMATRIX_H
|