Eigen::MatrixSquareRootQuasiTriangular< MatrixType > Class Template Reference

Class for computing matrix square roots of upper quasi-triangular matrices. More...

#include <MatrixSquareRoot.h>

List of all members.

Public Member Functions
template<typename ResultType >
void	compute (ResultType &result)
	Compute the matrix square root.
	MatrixSquareRootQuasiTriangular (const MatrixType &A)
	Constructor.
Private Types
typedef MatrixType::Index	Index
typedef MatrixType::Scalar	Scalar
Private Member Functions
void	compute1x1offDiagonalBlock (MatrixType &sqrtT, const MatrixType &T, typename MatrixType::Index i, typename MatrixType::Index j)
void	compute1x2offDiagonalBlock (MatrixType &sqrtT, const MatrixType &T, typename MatrixType::Index i, typename MatrixType::Index j)
void	compute2x1offDiagonalBlock (MatrixType &sqrtT, const MatrixType &T, typename MatrixType::Index i, typename MatrixType::Index j)
void	compute2x2diagonalBlock (MatrixType &sqrtT, const MatrixType &T, typename MatrixType::Index i)
void	compute2x2offDiagonalBlock (MatrixType &sqrtT, const MatrixType &T, typename MatrixType::Index i, typename MatrixType::Index j)
void	computeDiagonalPartOfSqrt (MatrixType &sqrtT, const MatrixType &T)
void	computeOffDiagonalPartOfSqrt (MatrixType &sqrtT, const MatrixType &T)
Static Private Member Functions
template<typename SmallMatrixType >
static void	solveAuxiliaryEquation (SmallMatrixType &X, const SmallMatrixType &A, const SmallMatrixType &B, const SmallMatrixType &C)
Private Attributes
const MatrixType &	m_A

---

Detailed Description

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

Class for computing matrix square roots of upper quasi-triangular matrices.

Template Parameters:

MatrixType

type of the argument of the matrix square root, expected to be an instantiation of the Matrix class template.

This class computes the square root of the upper quasi-triangular matrix stored in the upper Hessenberg part of the matrix passed to the constructor.

See also:

MatrixSquareRoot, MatrixSquareRootTriangular

Definition at line 27 of file MatrixSquareRoot.h.

---

Member Typedef Documentation

template<typename MatrixType >

typedef MatrixType::Index Eigen::MatrixSquareRootQuasiTriangular< MatrixType >::Index [private]

Definition at line 56 of file MatrixSquareRoot.h.

template<typename MatrixType >

typedef MatrixType::Scalar Eigen::MatrixSquareRootQuasiTriangular< MatrixType >::Scalar [private]

Definition at line 57 of file MatrixSquareRoot.h.

---

Constructor & Destructor Documentation

template<typename MatrixType >

Eigen::MatrixSquareRootQuasiTriangular< MatrixType >::MatrixSquareRootQuasiTriangular

(

const MatrixType &

A

)

[inline]

Constructor.

Parameters:

[in]

A

upper quasi-triangular matrix whose square root is to be computed.

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

Definition at line 39 of file MatrixSquareRoot.h.

---

Member Function Documentation

template<typename MatrixType >

template<typename ResultType >

void Eigen::MatrixSquareRootQuasiTriangular< MatrixType >::compute

(

ResultType &

result

)

Compute the matrix square root.

Parameters:

[out]

result

square root of A, as specified in the constructor.

Only the upper Hessenberg part of result is updated, the rest is not touched. See MatrixBase::sqrt() for details on how this computation is implemented.

Definition at line 80 of file MatrixSquareRoot.h.

template<typename MatrixType >

void Eigen::MatrixSquareRootQuasiTriangular< MatrixType >::compute1x1offDiagonalBlock	(	MatrixType &	sqrtT,
		const MatrixType &	T,
		typename MatrixType::Index	i,
		typename MatrixType::Index	j
	)		[private]

Definition at line 153 of file MatrixSquareRoot.h.

template<typename MatrixType >

void Eigen::MatrixSquareRootQuasiTriangular< MatrixType >::compute1x2offDiagonalBlock	(	MatrixType &	sqrtT,
		const MatrixType &	T,
		typename MatrixType::Index	i,
		typename MatrixType::Index	j
	)		[private]

Definition at line 163 of file MatrixSquareRoot.h.

template<typename MatrixType >

void Eigen::MatrixSquareRootQuasiTriangular< MatrixType >::compute2x1offDiagonalBlock	(	MatrixType &	sqrtT,
		const MatrixType &	T,
		typename MatrixType::Index	i,
		typename MatrixType::Index	j
	)		[private]

Definition at line 177 of file MatrixSquareRoot.h.

template<typename MatrixType >

void Eigen::MatrixSquareRootQuasiTriangular< MatrixType >::compute2x2diagonalBlock	(	MatrixType &	sqrtT,
		const MatrixType &	T,
		typename MatrixType::Index	i
	)		[private]

Definition at line 138 of file MatrixSquareRoot.h.

template<typename MatrixType >

void Eigen::MatrixSquareRootQuasiTriangular< MatrixType >::compute2x2offDiagonalBlock	(	MatrixType &	sqrtT,
		const MatrixType &	T,
		typename MatrixType::Index	i,
		typename MatrixType::Index	j
	)		[private]

Definition at line 191 of file MatrixSquareRoot.h.

template<typename MatrixType >

void Eigen::MatrixSquareRootQuasiTriangular< MatrixType >::computeDiagonalPartOfSqrt	(	MatrixType &	sqrtT,
		const MatrixType &	T
	)		[private]

Definition at line 90 of file MatrixSquareRoot.h.

template<typename MatrixType >

void Eigen::MatrixSquareRootQuasiTriangular< MatrixType >::computeOffDiagonalPartOfSqrt	(	MatrixType &	sqrtT,
		const MatrixType &	T
	)		[private]

Definition at line 110 of file MatrixSquareRoot.h.

template<typename MatrixType >

template<typename SmallMatrixType >

void Eigen::MatrixSquareRootQuasiTriangular< MatrixType >::solveAuxiliaryEquation	(	SmallMatrixType &	X,
		const SmallMatrixType &	A,
		const SmallMatrixType &	B,
		const SmallMatrixType &	C
	)		[static, private]

Definition at line 208 of file MatrixSquareRoot.h.

---

Member Data Documentation

template<typename MatrixType >

const MatrixType& Eigen::MatrixSquareRootQuasiTriangular< MatrixType >::m_A [private]

Definition at line 75 of file MatrixSquareRoot.h.

---

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

• MatrixSquareRoot.h