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 MatrixPowerParenthesesReturnValue< MatrixType >	operator() (RealScalar p)
	Returns the matrix power. More...

Index	rows () const

Private Types
typedef Matrix< ComplexScalar, Dynamic, Dynamic, 0, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime >	ComplexMatrix

typedef std::complex< RealScalar >	ComplexScalar

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::Scalar	Scalar

Private Member Functions
template<typename ResultType >
void	computeFracPower (ResultType &res, RealScalar p)

template<typename ResultType >
void	computeIntPower (ResultType &res, RealScalar p)

void	initialize ()
	Perform Schur decomposition for fractional power. More...

void	split (RealScalar &p, RealScalar &intpart)
	Split p into integral part and fractional part. More...

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
	Reference to the base of matrix power. More...

RealScalar	m_conditionNumber
	Condition number of m_A. More...

ComplexMatrix	m_fT
	Store fractional power of m_T. More...

Index	m_nulls
	Rank deficiency of m_A. More...

Index	m_rank
	Rank of m_A. More...

ComplexMatrix	m_T
	Store the result of Schur decomposition. More...

MatrixType	m_tmp
	Temporary storage. More...

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:

#include <unsupported/Eigen/MatrixFunctions>
#include <iostream>
 
using namespace Eigen;
 
int main()
{
  Matrix4cd A = Matrix4cd::Random();
  MatrixPower<Matrix4cd> Apow(A);
 
  std::cout << "The matrix A is:\n" << A << "\n\n"
               "A^3.1 is:\n" << Apow(3.1) << "\n\n"
               "A^3.3 is:\n" << Apow(3.3) << "\n\n"
               "A^3.7 is:\n" << Apow(3.7) << "\n\n"
               "A^3.9 is:\n" << Apow(3.9) << std::endl;
  return 0;
}

Output:

Definition at line 15 of file MatrixPower.h.

Member Typedef Documentation

◆ ComplexMatrix

template<typename MatrixType >

typedef Matrix<ComplexScalar, Dynamic, Dynamic, 0, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime> Eigen::MatrixPower< MatrixType >::ComplexMatrix

private

Definition at line 385 of file MatrixPower.h.

◆ ComplexScalar

template<typename MatrixType >

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

private

Definition at line 383 of file MatrixPower.h.

◆ RealScalar

template<typename MatrixType >

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

private

Definition at line 341 of file MatrixPower.h.

◆ Scalar

template<typename MatrixType >

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

private

Definition at line 340 of file MatrixPower.h.

Constructor & Destructor Documentation

◆ MatrixPower()

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 352 of file MatrixPower.h.

Member Function Documentation

◆ cols()

template<typename MatrixType >

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

inline

Definition at line 380 of file MatrixPower.h.

◆ compute()

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 448 of file MatrixPower.h.

◆ computeFracPower()

template<typename MatrixType >

template<typename ResultType >

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

private

Definition at line 551 of file MatrixPower.h.

◆ computeIntPower()

template<typename MatrixType >

template<typename ResultType >

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

private

Definition at line 528 of file MatrixPower.h.

◆ initialize()

template<typename MatrixType >

void Eigen::MatrixPower< MatrixType >::initialize

private

Perform Schur decomposition for fractional power.

Definition at line 489 of file MatrixPower.h.

◆ operator()()

template<typename MatrixType >

const MatrixPowerParenthesesReturnValue<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 366 of file MatrixPower.h.

◆ revertSchur() [1/2]

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 568 of file MatrixPower.h.

◆ revertSchur() [2/2]

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 576 of file MatrixPower.h.

◆ rows()

template<typename MatrixType >

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

inline

Definition at line 379 of file MatrixPower.h.

◆ split()

template<typename MatrixType >

void Eigen::MatrixPower< MatrixType >::split	(	RealScalar &	p,
		RealScalar &	intpart
	)

private

Split p into integral part and fractional part.

Parameters

[in]	p	The exponent.
[out]	p	The fractional part ranging in .
[out]	intpart	The integral part.

Only if the fractional part is nonzero, it calls initialize().

Definition at line 468 of file MatrixPower.h.

Member Data Documentation

◆ m_A

template<typename MatrixType >

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

private

Reference to the base of matrix power.

Definition at line 388 of file MatrixPower.h.

◆ m_conditionNumber

template<typename MatrixType >

RealScalar Eigen::MatrixPower< MatrixType >::m_conditionNumber

private

Condition number of m_A.

It is initialized as 0 to avoid performing unnecessary Schur decomposition, which is the bottleneck.

Definition at line 405 of file MatrixPower.h.

◆ m_fT

template<typename MatrixType >

ComplexMatrix Eigen::MatrixPower< MatrixType >::m_fT

private

Store fractional power of m_T.

Definition at line 397 of file MatrixPower.h.

◆ m_nulls

template<typename MatrixType >

Index Eigen::MatrixPower< MatrixType >::m_nulls

private

Rank deficiency of m_A.

Definition at line 411 of file MatrixPower.h.

◆ m_rank

template<typename MatrixType >

Index Eigen::MatrixPower< MatrixType >::m_rank

private

Rank of m_A.

Definition at line 408 of file MatrixPower.h.

◆ m_T

template<typename MatrixType >

ComplexMatrix Eigen::MatrixPower< MatrixType >::m_T

private

Store the result of Schur decomposition.

Definition at line 394 of file MatrixPower.h.

◆ m_tmp

template<typename MatrixType >

MatrixType Eigen::MatrixPower< MatrixType >::m_tmp

private

Temporary storage.

Definition at line 391 of file MatrixPower.h.

◆ m_U

template<typename MatrixType >

ComplexMatrix Eigen::MatrixPower< MatrixType >::m_U

private

Definition at line 394 of file MatrixPower.h.

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

MatrixPower.h

Public Member Functions

Private Types

Private Member Functions

Static Private Member Functions

Private Attributes

Detailed Description

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

Member Typedef Documentation

◆ ComplexMatrix

◆ ComplexScalar

◆ RealScalar

◆ Scalar

Constructor & Destructor Documentation

◆ MatrixPower()

Member Function Documentation

◆ cols()

◆ compute()

◆ computeFracPower()

◆ computeIntPower()

◆ initialize()

◆ operator()()

◆ revertSchur() [1/2]

◆ revertSchur() [2/2]

◆ rows()

◆ split()

Member Data Documentation

◆ m_A

◆ m_conditionNumber

◆ m_fT

◆ m_nulls

◆ m_rank

◆ m_T

◆ m_tmp

◆ m_U

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