Class for computing the matrix exponential. More...

#include <MatrixExponential.h>

Public Member Functions
template<typename ResultType >
void	compute (ResultType &result)
	Computes the matrix exponential. More...

	MatrixExponential (const MatrixType &M)
	Constructor. More...

Private Types
typedef std::complex< RealScalar >	ComplexScalar

typedef NumTraits< Scalar >::Real	RealScalar

typedef internal::traits< MatrixType >::Scalar	Scalar

Private Member Functions
void	computeUV (double)
	Compute Padé approximant to the exponential. More...

void	computeUV (float)
	Compute Padé approximant to the exponential. More...

void	computeUV (long double)
	Compute Padé approximant to the exponential. More...

	MatrixExponential (const MatrixExponential &)

MatrixExponential &	operator= (const MatrixExponential &)

void	pade13 (const MatrixType &A)
	Compute the (13,13)-Padé approximant to the exponential. More...

void	pade17 (const MatrixType &A)
	Compute the (17,17)-Padé approximant to the exponential. More...

void	pade3 (const MatrixType &A)
	Compute the (3,3)-Padé approximant to the exponential. More...

void	pade5 (const MatrixType &A)
	Compute the (5,5)-Padé approximant to the exponential. More...

void	pade7 (const MatrixType &A)
	Compute the (7,7)-Padé approximant to the exponential. More...

void	pade9 (const MatrixType &A)
	Compute the (9,9)-Padé approximant to the exponential. More...

Private Attributes
MatrixType	m_Id
	Identity matrix of the same size as `m_M`. More...

RealScalar	m_l1norm
	L1 norm of m_M. More...

internal::nested< MatrixType >::type	m_M
	Reference to matrix whose exponential is to be computed. More...

int	m_squarings
	Number of squarings required in the last step. More...

MatrixType	m_tmp1
	Used for temporary storage. More...

MatrixType	m_tmp2
	Used for temporary storage. More...

MatrixType	m_U
	Odd-degree terms in numerator of Padé approximant. More...

MatrixType	m_V
	Even-degree terms in numerator of Padé approximant. More...

Detailed Description

template<typename MatrixType>
class Eigen::MatrixExponential< MatrixType >

Class for computing the matrix exponential.

Template Parameters

MatrixType type of the argument of the exponential, expected to be an instantiation of the Matrix class template.

Definition at line 24 of file MatrixExponential.h.

Member Typedef Documentation

template<typename MatrixType>

typedef std::complex<RealScalar> Eigen::MatrixExponential< MatrixType >::ComplexScalar

private

Definition at line 135 of file MatrixExponential.h.

template<typename MatrixType>

typedef NumTraits<Scalar>::Real Eigen::MatrixExponential< MatrixType >::RealScalar

private

Definition at line 134 of file MatrixExponential.h.

template<typename MatrixType>

typedef internal::traits<MatrixType>::Scalar Eigen::MatrixExponential< MatrixType >::Scalar

private

Definition at line 133 of file MatrixExponential.h.

Constructor & Destructor Documentation

template<typename MatrixType >

Eigen::MatrixExponential< MatrixType >::MatrixExponential ( const MatrixType & M )

Constructor.

The class stores a reference to M, so it should not be changed (or destroyed) before compute() is called.

Parameters

[in] M matrix whose exponential is to be computed.

Definition at line 163 of file MatrixExponential.h.

template<typename MatrixType>

Eigen::MatrixExponential< MatrixType >::MatrixExponential ( const MatrixExponential< MatrixType > & )

private

Member Function Documentation

template<typename MatrixType >

template<typename ResultType >

void Eigen::MatrixExponential< MatrixType >::compute ( ResultType & result )

Computes the matrix exponential.

Parameters

[out] result the matrix exponential of M in the constructor.

Definition at line 178 of file MatrixExponential.h.

template<typename MatrixType >

void Eigen::MatrixExponential< MatrixType >::computeUV ( double )

private

Compute Padé approximant to the exponential.

Computes m_U, m_V and m_squarings such that $(V+U)(V-U)^{-1}$ is a Padé of $\exp(2^{-\mbox{squarings}}M)$ around $ M = 0 $ . The degree of the Padé approximant and the value of squarings are chosen such that the approximation error is no more than the round-off error.

The argument of this function should correspond with the (real part of) the entries of m_M. It is used to select the correct implementation using overloading.

Definition at line 302 of file MatrixExponential.h.

template<typename MatrixType >

void Eigen::MatrixExponential< MatrixType >::computeUV ( float )

private

Compute Padé approximant to the exponential.

See also: computeUV(double);

Definition at line 284 of file MatrixExponential.h.

template<typename MatrixType >

void Eigen::MatrixExponential< MatrixType >::computeUV ( long double )

private

Compute Padé approximant to the exponential.

See also: computeUV(double);

Definition at line 324 of file MatrixExponential.h.

template<typename MatrixType>

MatrixExponential& Eigen::MatrixExponential< MatrixType >::operator= ( const MatrixExponential< MatrixType > & )

private

template<typename MatrixType >

EIGEN_STRONG_INLINE void Eigen::MatrixExponential< MatrixType >::pade13 ( const MatrixType & A )

private

Compute the (13,13)-Padé approximant to the exponential.

After exit, $(V+U)(V-U)^{-1}$ is the Padé approximant of $\exp(A)$ around $ A = 0 $ .

Parameters

[in] A Argument of matrix exponential

Definition at line 242 of file MatrixExponential.h.

template<typename MatrixType>

void Eigen::MatrixExponential< MatrixType >::pade17 ( const MatrixType & A )

private

Compute the (17,17)-Padé approximant to the exponential.

After exit, $(V+U)(V-U)^{-1}$ is the Padé approximant of $\exp(A)$ around $ A = 0 $ .

This function activates only if your long double is double-double or quadruple.

Parameters

[in] A Argument of matrix exponential

template<typename MatrixType >

EIGEN_STRONG_INLINE void Eigen::MatrixExponential< MatrixType >::pade3 ( const MatrixType & A )

private

Compute the (3,3)-Padé approximant to the exponential.

After exit, $(V+U)(V-U)^{-1}$ is the Padé approximant of $\exp(A)$ around $ A = 0 $ .

Parameters

[in] A Argument of matrix exponential

Definition at line 195 of file MatrixExponential.h.

template<typename MatrixType >

EIGEN_STRONG_INLINE void Eigen::MatrixExponential< MatrixType >::pade5 ( const MatrixType & A )

private

Compute the (5,5)-Padé approximant to the exponential.

After exit, $(V+U)(V-U)^{-1}$ is the Padé approximant of $\exp(A)$ around $ A = 0 $ .

Parameters

[in] A Argument of matrix exponential

Definition at line 205 of file MatrixExponential.h.

template<typename MatrixType >

EIGEN_STRONG_INLINE void Eigen::MatrixExponential< MatrixType >::pade7 ( const MatrixType & A )

private

Compute the (7,7)-Padé approximant to the exponential.

After exit, $(V+U)(V-U)^{-1}$ is the Padé approximant of $\exp(A)$ around $ A = 0 $ .

Parameters

[in] A Argument of matrix exponential

Definition at line 216 of file MatrixExponential.h.

template<typename MatrixType >

EIGEN_STRONG_INLINE void Eigen::MatrixExponential< MatrixType >::pade9 ( const MatrixType & A )

private

Compute the (9,9)-Padé approximant to the exponential.

After exit, $(V+U)(V-U)^{-1}$ is the Padé approximant of $\exp(A)$ around $ A = 0 $ .

Parameters

[in] A Argument of matrix exponential

Definition at line 228 of file MatrixExponential.h.

Member Data Documentation

template<typename MatrixType>

MatrixType Eigen::MatrixExponential< MatrixType >::m_Id

private

Identity matrix of the same size as m_M.

Definition at line 153 of file MatrixExponential.h.

template<typename MatrixType>

RealScalar Eigen::MatrixExponential< MatrixType >::m_l1norm

private

L1 norm of m_M.

Definition at line 159 of file MatrixExponential.h.

template<typename MatrixType>

internal::nested<MatrixType>::type Eigen::MatrixExponential< MatrixType >::m_M

private

Reference to matrix whose exponential is to be computed.

Definition at line 138 of file MatrixExponential.h.

template<typename MatrixType>

int Eigen::MatrixExponential< MatrixType >::m_squarings

private

Number of squarings required in the last step.

Definition at line 156 of file MatrixExponential.h.

template<typename MatrixType>

MatrixType Eigen::MatrixExponential< MatrixType >::m_tmp1

private

Used for temporary storage.

Definition at line 147 of file MatrixExponential.h.

template<typename MatrixType>

MatrixType Eigen::MatrixExponential< MatrixType >::m_tmp2

private

Used for temporary storage.

Definition at line 150 of file MatrixExponential.h.

template<typename MatrixType>

MatrixType Eigen::MatrixExponential< MatrixType >::m_U

private

Odd-degree terms in numerator of Padé approximant.

Definition at line 141 of file MatrixExponential.h.

template<typename MatrixType>

MatrixType Eigen::MatrixExponential< MatrixType >::m_V

private

Even-degree terms in numerator of Padé approximant.

Definition at line 144 of file MatrixExponential.h.

The documentation for this class was generated from the following file:

MatrixExponential.h

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Detailed Description

template<typename MatrixType> class Eigen::MatrixExponential< MatrixType >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename MatrixType>
class Eigen::MatrixExponential< MatrixType >