Eigen::MatrixLogarithmAtomic< MatrixType > Class Template Reference

Helper class for computing matrix logarithm of atomic matrices. More...

#include <MatrixLogarithm.h>

List of all members.

Public Types
typedef NumTraits< Scalar >::Real	RealScalar
typedef MatrixType::Scalar	Scalar
Public Member Functions
MatrixType	compute (const MatrixType &A)
	Compute matrix logarithm of atomic matrix.
	MatrixLogarithmAtomic ()
	Constructor.
Private Member Functions
void	compute2x2 (const MatrixType &A, MatrixType &result)
	Compute logarithm of 2x2 triangular matrix.
void	computeBig (const MatrixType &A, MatrixType &result)
	Compute logarithm of triangular matrices with size > 2.
void	computePade (MatrixType &result, const MatrixType &T, int degree)
void	computePade10 (MatrixType &result, const MatrixType &T)
void	computePade11 (MatrixType &result, const MatrixType &T)
void	computePade3 (MatrixType &result, const MatrixType &T)
void	computePade4 (MatrixType &result, const MatrixType &T)
void	computePade5 (MatrixType &result, const MatrixType &T)
void	computePade6 (MatrixType &result, const MatrixType &T)
void	computePade7 (MatrixType &result, const MatrixType &T)
void	computePade8 (MatrixType &result, const MatrixType &T)
void	computePade9 (MatrixType &result, const MatrixType &T)
int	getPadeDegree (float normTminusI)
int	getPadeDegree (double normTminusI)
int	getPadeDegree (long double normTminusI)
	MatrixLogarithmAtomic (const MatrixLogarithmAtomic &)
MatrixLogarithmAtomic &	operator= (const MatrixLogarithmAtomic &)
Static Private Member Functions
static Scalar	atanh (Scalar x)
	Compute atanh (inverse hyperbolic tangent).
Static Private Attributes
static const int	maxPadeDegree
static const int	minPadeDegree = 3

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Detailed Description

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

Helper class for computing matrix logarithm of atomic matrices.

Definition at line 31 of file MatrixLogarithm.h.

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Member Typedef Documentation

template<typename MatrixType >

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

Definition at line 37 of file MatrixLogarithm.h.

template<typename MatrixType >

typedef MatrixType::Scalar Eigen::MatrixLogarithmAtomic< MatrixType >::Scalar

Definition at line 35 of file MatrixLogarithm.h.

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Constructor & Destructor Documentation

template<typename MatrixType >

Eigen::MatrixLogarithmAtomic< MatrixType >::MatrixLogarithmAtomic

(

)

[inline]

Constructor.

Definition at line 42 of file MatrixLogarithm.h.

template<typename MatrixType >

Eigen::MatrixLogarithmAtomic< MatrixType >::MatrixLogarithmAtomic

(

const MatrixLogarithmAtomic< MatrixType > &

)

[private]

---

Member Function Documentation

template<typename MatrixType >

MatrixType::Scalar Eigen::MatrixLogarithmAtomic< MatrixType >::atanh

(

typename MatrixType::Scalar

x

)

[static, private]

Compute atanh (inverse hyperbolic tangent).

Definition at line 97 of file MatrixLogarithm.h.

template<typename MatrixType >

MatrixType Eigen::MatrixLogarithmAtomic< MatrixType >::compute

(

const MatrixType &

A

)

Compute matrix logarithm of atomic matrix.

Compute logarithm of triangular matrix with clustered eigenvalues.

Parameters:

[in]

A

argument of matrix logarithm, should be upper triangular and atomic

Returns:

The logarithm of A.

Definition at line 82 of file MatrixLogarithm.h.

template<typename MatrixType >

void Eigen::MatrixLogarithmAtomic< MatrixType >::compute2x2	(	const MatrixType &	A,
		MatrixType &	result
	)		[private]

Compute logarithm of 2x2 triangular matrix.

Definition at line 109 of file MatrixLogarithm.h.

template<typename MatrixType >

void Eigen::MatrixLogarithmAtomic< MatrixType >::computeBig	(	const MatrixType &	A,
		MatrixType &	result
	)		[private]

Compute logarithm of triangular matrices with size > 2.

This uses a inverse scale-and-square algorithm.

Definition at line 138 of file MatrixLogarithm.h.

template<typename MatrixType >

void Eigen::MatrixLogarithmAtomic< MatrixType >::computePade	(	MatrixType &	result,
		const MatrixType &	T,
		int	degree
	)		[private]

Definition at line 225 of file MatrixLogarithm.h.

template<typename MatrixType >

void Eigen::MatrixLogarithmAtomic< MatrixType >::computePade10	(	MatrixType &	result,
		const MatrixType &	T
	)		[private]

Definition at line 372 of file MatrixLogarithm.h.

template<typename MatrixType >

void Eigen::MatrixLogarithmAtomic< MatrixType >::computePade11	(	MatrixType &	result,
		const MatrixType &	T
	)		[private]

Definition at line 394 of file MatrixLogarithm.h.

template<typename MatrixType >

void Eigen::MatrixLogarithmAtomic< MatrixType >::computePade3	(	MatrixType &	result,
		const MatrixType &	T
	)		[private]

Definition at line 242 of file MatrixLogarithm.h.

template<typename MatrixType >

void Eigen::MatrixLogarithmAtomic< MatrixType >::computePade4	(	MatrixType &	result,
		const MatrixType &	T
	)		[private]

Definition at line 258 of file MatrixLogarithm.h.

template<typename MatrixType >

void Eigen::MatrixLogarithmAtomic< MatrixType >::computePade5	(	MatrixType &	result,
		const MatrixType &	T
	)		[private]

Definition at line 274 of file MatrixLogarithm.h.

template<typename MatrixType >

void Eigen::MatrixLogarithmAtomic< MatrixType >::computePade6	(	MatrixType &	result,
		const MatrixType &	T
	)		[private]

Definition at line 292 of file MatrixLogarithm.h.

template<typename MatrixType >

void Eigen::MatrixLogarithmAtomic< MatrixType >::computePade7	(	MatrixType &	result,
		const MatrixType &	T
	)		[private]

Definition at line 310 of file MatrixLogarithm.h.

template<typename MatrixType >

void Eigen::MatrixLogarithmAtomic< MatrixType >::computePade8	(	MatrixType &	result,
		const MatrixType &	T
	)		[private]

Definition at line 330 of file MatrixLogarithm.h.

template<typename MatrixType >

void Eigen::MatrixLogarithmAtomic< MatrixType >::computePade9	(	MatrixType &	result,
		const MatrixType &	T
	)		[private]

Definition at line 350 of file MatrixLogarithm.h.

template<typename MatrixType >

int Eigen::MatrixLogarithmAtomic< MatrixType >::getPadeDegree

(

float

normTminusI

)

[private]

Definition at line 171 of file MatrixLogarithm.h.

template<typename MatrixType >

int Eigen::MatrixLogarithmAtomic< MatrixType >::getPadeDegree

(

double

normTminusI

)

[private]

Definition at line 183 of file MatrixLogarithm.h.

template<typename MatrixType >

int Eigen::MatrixLogarithmAtomic< MatrixType >::getPadeDegree

(

long double

normTminusI

)

[private]

Definition at line 195 of file MatrixLogarithm.h.

template<typename MatrixType >

MatrixLogarithmAtomic& Eigen::MatrixLogarithmAtomic< MatrixType >::operator=

(

const MatrixLogarithmAtomic< MatrixType > &

)

[private]

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Member Data Documentation

template<typename MatrixType >

const int Eigen::MatrixLogarithmAtomic< MatrixType >::maxPadeDegree [static, private]

Initial value:

 std::numeric_limits<RealScalar>::digits<= 24?  5:      
                                   std::numeric_limits<RealScalar>::digits<= 53?  7:      
                                   std::numeric_limits<RealScalar>::digits<= 64?  8:      
                                   std::numeric_limits<RealScalar>::digits<=106? 10: 11

Definition at line 70 of file MatrixLogarithm.h.

template<typename MatrixType >

const int Eigen::MatrixLogarithmAtomic< MatrixType >::minPadeDegree = 3 [static, private]

Definition at line 69 of file MatrixLogarithm.h.

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

• MatrixLogarithm.h