Eigen::MatrixPower< MatrixType > Class Template Reference

Class for computing matrix powers. More...

#include <MatrixPower.h>

Public Member Functions
Index	cols () const
template<typename ResultType >
void	compute (ResultType &res, RealScalar p)
	Compute the matrix power. More...
	MatrixPower (const MatrixType &A)
	Constructor. More...
const MatrixPowerRetval< MatrixType >	operator() (RealScalar p)
	Returns the matrix power. More...
Index	rows () const

Private Types
enum	{ RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }
typedef Matrix< ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, MatrixType::Options, MaxRowsAtCompileTime, MaxColsAtCompileTime >	ComplexMatrix
typedef std::complex< RealScalar >	ComplexScalar
typedef MatrixType::Index	Index
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::Scalar	Scalar

Private Member Functions
template<typename ResultType >
void	computeFracPower (ResultType &, RealScalar)
template<typename ResultType >
void	computeIntPower (ResultType &, RealScalar)
RealScalar	modfAndInit (RealScalar, RealScalar *)

Static Private Member Functions
template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>
static void	revertSchur (Matrix< ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols > &res, const ComplexMatrix &T, const ComplexMatrix &U)
template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>
static void	revertSchur (Matrix< RealScalar, Rows, Cols, Options, MaxRows, MaxCols > &res, const ComplexMatrix &T, const ComplexMatrix &U)

Private Attributes
MatrixType::Nested	m_A
RealScalar	m_conditionNumber
ComplexMatrix	m_fT
ComplexMatrix	m_T
MatrixType	m_tmp
ComplexMatrix	m_U

Detailed Description

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

Class for computing matrix powers.

Template Parameters

MatrixType

type of the base, expected to be an instantiation of the Matrix class template.

This class is capable of computing real/complex matrices raised to an arbitrary real power. Meanwhile, it saves the result of Schur decomposition if an non-integral power has even been calculated. Therefore, if you want to compute multiple (>= 2) matrix powers for the same matrix, using the class directly is more efficient than calling MatrixBase::pow().

Example:

Output:

Definition at line 15 of file MatrixPower.h.

Member Typedef Documentation

template<typename MatrixType>

typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, MatrixType::Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> Eigen::MatrixPower< MatrixType >::ComplexMatrix

private

Definition at line 326 of file MatrixPower.h.

template<typename MatrixType>

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

private

Definition at line 324 of file MatrixPower.h.

template<typename MatrixType>

typedef MatrixType::Index Eigen::MatrixPower< MatrixType >::Index

private

Definition at line 286 of file MatrixPower.h.

template<typename MatrixType>

typedef MatrixType::RealScalar Eigen::MatrixPower< MatrixType >::RealScalar

private

Definition at line 285 of file MatrixPower.h.

template<typename MatrixType>

typedef MatrixType::Scalar Eigen::MatrixPower< MatrixType >::Scalar

private

Definition at line 284 of file MatrixPower.h.

Member Enumeration Documentation

template<typename MatrixType>

anonymous enum

private

Enumerator
RowsAtCompileTime
ColsAtCompileTime
MaxRowsAtCompileTime
MaxColsAtCompileTime

Definition at line 278 of file MatrixPower.h.

Constructor & Destructor Documentation

template<typename MatrixType>

Eigen::MatrixPower< MatrixType >::MatrixPower ( const MatrixType &  A )

inlineexplicit

Constructor.

Parameters

[in]

A

the base of the matrix power.

The class stores a reference to A, so it should not be changed (or destroyed) before evaluation.

Definition at line 297 of file MatrixPower.h.

Member Function Documentation

template<typename MatrixType>

Index Eigen::MatrixPower< MatrixType >::cols ( void  ) const

inline

Definition at line 321 of file MatrixPower.h.

template<typename MatrixType >

template<typename ResultType >

void Eigen::MatrixPower< MatrixType >::compute	(	ResultType &	res,
		RealScalar	p
	)

Compute the matrix power.

Parameters

[in]	p	exponent, a real scalar.
[out]	res	where A is specified in the constructor.

Definition at line 356 of file MatrixPower.h.

template<typename MatrixType >

template<typename ResultType >

void Eigen::MatrixPower< MatrixType >::computeFracPower ( ResultType &  res, RealScalar  p  )

private

Definition at line 416 of file MatrixPower.h.

template<typename MatrixType >

template<typename ResultType >

void Eigen::MatrixPower< MatrixType >::computeIntPower ( ResultType &  res, RealScalar  p  )

private

Definition at line 398 of file MatrixPower.h.

template<typename MatrixType >

MatrixPower< MatrixType >::RealScalar Eigen::MatrixPower< MatrixType >::modfAndInit ( RealScalar  x, RealScalar *  intpart  )

private

Definition at line 373 of file MatrixPower.h.

template<typename MatrixType>

const MatrixPowerRetval<MatrixType> Eigen::MatrixPower< MatrixType >::operator() ( RealScalar  p )

inline

Returns the matrix power.

Parameters

[in]

p

exponent, a real scalar.

Returns

The expression , where A is specified in the constructor.

Definition at line 307 of file MatrixPower.h.

template<typename MatrixType >

template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>

void Eigen::MatrixPower< MatrixType >::revertSchur ( Matrix< ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols > &  res, const ComplexMatrix &  T, const ComplexMatrix &  U  )

inlinestaticprivate

Definition at line 428 of file MatrixPower.h.

template<typename MatrixType >

template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>

void Eigen::MatrixPower< MatrixType >::revertSchur ( Matrix< RealScalar, Rows, Cols, Options, MaxRows, MaxCols > &  res, const ComplexMatrix &  T, const ComplexMatrix &  U  )

inlinestaticprivate

Definition at line 436 of file MatrixPower.h.

template<typename MatrixType>

Index Eigen::MatrixPower< MatrixType >::rows ( void  ) const

inline

Definition at line 320 of file MatrixPower.h.

Member Data Documentation

template<typename MatrixType>

MatrixType::Nested Eigen::MatrixPower< MatrixType >::m_A

private

Definition at line 328 of file MatrixPower.h.

template<typename MatrixType>

RealScalar Eigen::MatrixPower< MatrixType >::m_conditionNumber

private

Definition at line 331 of file MatrixPower.h.

template<typename MatrixType>

ComplexMatrix Eigen::MatrixPower< MatrixType >::m_fT

private

Definition at line 330 of file MatrixPower.h.

template<typename MatrixType>

ComplexMatrix Eigen::MatrixPower< MatrixType >::m_T

private

Definition at line 330 of file MatrixPower.h.

template<typename MatrixType>

MatrixType Eigen::MatrixPower< MatrixType >::m_tmp

private

Definition at line 329 of file MatrixPower.h.

template<typename MatrixType>

ComplexMatrix Eigen::MatrixPower< MatrixType >::m_U

private

Definition at line 330 of file MatrixPower.h.

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

• MatrixPower.h