Compute the largest eigenvalues and the associated principle eigenvector via power iteration. More...

#include <lanczos-decomposition.hpp>

Public Types
enum	{ Options = _Matrix::Options }

typedef _Matrix::Scalar	Scalar

typedef TridiagonalSymmetricMatrixTpl< Scalar, Options >	TridiagonalMatrix

Public Member Functions
template<typename MatrixLikeType >
void	compute (const MatrixLikeType &A)
	Computes the Lanczos decomposition of the input matrix A. More...

template<typename MatrixLikeType >
PlainMatrix	computeDecompositionResidual (const MatrixLikeType &A) const
	Computes the residual associated with the decomposition, namely, the quantity . More...

template<typename MatrixLikeType >
	LanczosDecompositionTpl (const MatrixLikeType &mat, const Eigen::DenseIndex decomposition_size)
	Default constructor for the Lanczos decomposition from an input matrix. More...

bool	operator!= (const LanczosDecompositionTpl &other) const

bool	operator== (const LanczosDecompositionTpl &other) const

EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef	PINOCCHIO_EIGEN_PLAIN_TYPE (_Matrix) PlainMatrix

typedef	PINOCCHIO_EIGEN_PLAIN_TYPE (typename PlainMatrix::ColXpr) Vector

PlainMatrix &	Qs ()
	Returns the orthogonal basis associated with the Lanczos decomposition. More...

const PlainMatrix &	Qs () const
	Returns the orthogonal basis associated with the Lanczos decomposition. More...

Eigen::DenseIndex	rank () const
	Returns the rank of the decomposition. More...

TridiagonalMatrix &	Ts ()
	Returns the tridiagonal matrix associated with the Lanczos decomposition. More...

const TridiagonalMatrix &	Ts () const
	Returns the tridiagonal matrix associated with the Lanczos decomposition. More...

Protected Attributes
Vector	m_A_times_q

PlainMatrix	m_Qs

Eigen::DenseIndex	m_rank

TridiagonalMatrix	m_Ts

Detailed Description

template<typename _Matrix>
struct pinocchio::LanczosDecompositionTpl< _Matrix >

Compute the largest eigenvalues and the associated principle eigenvector via power iteration.

Definition at line 18 of file math/lanczos-decomposition.hpp.

Member Typedef Documentation

◆ Scalar

template<typename _Matrix >

typedef _Matrix::Scalar pinocchio::LanczosDecompositionTpl< _Matrix >::Scalar

Definition at line 24 of file math/lanczos-decomposition.hpp.

◆ TridiagonalMatrix

template<typename _Matrix >

typedef TridiagonalSymmetricMatrixTpl<Scalar, Options> pinocchio::LanczosDecompositionTpl< _Matrix >::TridiagonalMatrix

Definition at line 29 of file math/lanczos-decomposition.hpp.

Member Enumeration Documentation

◆ anonymous enum

template<typename _Matrix >

anonymous enum

Enumerator
Options

Definition at line 25 of file math/lanczos-decomposition.hpp.

Constructor & Destructor Documentation

◆ LanczosDecompositionTpl()

template<typename _Matrix >

template<typename MatrixLikeType >

pinocchio::LanczosDecompositionTpl< _Matrix >::LanczosDecompositionTpl	(	const MatrixLikeType &	mat,
		const Eigen::DenseIndex	decomposition_size
	)

inline

Default constructor for the Lanczos decomposition from an input matrix.

Definition at line 33 of file math/lanczos-decomposition.hpp.

Member Function Documentation

◆ compute()

template<typename _Matrix >

template<typename MatrixLikeType >

void pinocchio::LanczosDecompositionTpl< _Matrix >::compute ( const MatrixLikeType & A )

inline

Computes the Lanczos decomposition of the input matrix A.

Parameters

[in] A The matrix to decompose

Definition at line 67 of file math/lanczos-decomposition.hpp.

◆ computeDecompositionResidual()

template<typename _Matrix >

template<typename MatrixLikeType >

PlainMatrix pinocchio::LanczosDecompositionTpl< _Matrix >::computeDecompositionResidual ( const MatrixLikeType & A ) const

inline

Computes the residual associated with the decomposition, namely, the quantity $ A Q_s - Q_s T_s $ .

Parameters

[in] A the matrix that have been decomposed.

Returns: The residual of the decomposition

Definition at line 123 of file math/lanczos-decomposition.hpp.

◆ operator!=()

template<typename _Matrix >

bool pinocchio::LanczosDecompositionTpl< _Matrix >::operator!= ( const LanczosDecompositionTpl< _Matrix > & other ) const

inline

Definition at line 56 of file math/lanczos-decomposition.hpp.

◆ operator==()

template<typename _Matrix >

bool pinocchio::LanczosDecompositionTpl< _Matrix >::operator== ( const LanczosDecompositionTpl< _Matrix > & other ) const

inline

Definition at line 49 of file math/lanczos-decomposition.hpp.

◆ PINOCCHIO_EIGEN_PLAIN_TYPE() [1/2]

template<typename _Matrix >

EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef pinocchio::LanczosDecompositionTpl< _Matrix >::PINOCCHIO_EIGEN_PLAIN_TYPE ( _Matrix )

◆ PINOCCHIO_EIGEN_PLAIN_TYPE() [2/2]

template<typename _Matrix >

typedef pinocchio::LanczosDecompositionTpl< _Matrix >::PINOCCHIO_EIGEN_PLAIN_TYPE ( typename PlainMatrix::ColXpr )

◆ Qs() [1/2]

template<typename _Matrix >

PlainMatrix& pinocchio::LanczosDecompositionTpl< _Matrix >::Qs ( )

inline

Returns the orthogonal basis associated with the Lanczos decomposition.

Definition at line 162 of file math/lanczos-decomposition.hpp.

◆ Qs() [2/2]

template<typename _Matrix >

const PlainMatrix& pinocchio::LanczosDecompositionTpl< _Matrix >::Qs ( ) const

inline

Returns the orthogonal basis associated with the Lanczos decomposition.

Definition at line 157 of file math/lanczos-decomposition.hpp.

◆ rank()

template<typename _Matrix >

Eigen::DenseIndex pinocchio::LanczosDecompositionTpl< _Matrix >::rank ( ) const

inline

Returns the rank of the decomposition.

Definition at line 168 of file math/lanczos-decomposition.hpp.

◆ Ts() [1/2]

template<typename _Matrix >

TridiagonalMatrix& pinocchio::LanczosDecompositionTpl< _Matrix >::Ts ( )

inline

Returns the tridiagonal matrix associated with the Lanczos decomposition.

Definition at line 151 of file math/lanczos-decomposition.hpp.

◆ Ts() [2/2]

template<typename _Matrix >

const TridiagonalMatrix& pinocchio::LanczosDecompositionTpl< _Matrix >::Ts ( ) const

inline

Returns the tridiagonal matrix associated with the Lanczos decomposition.

Definition at line 146 of file math/lanczos-decomposition.hpp.

Member Data Documentation

◆ m_A_times_q

template<typename _Matrix >

Vector pinocchio::LanczosDecompositionTpl< _Matrix >::m_A_times_q

mutableprotected

Definition at line 176 of file math/lanczos-decomposition.hpp.

◆ m_Qs

template<typename _Matrix >

PlainMatrix pinocchio::LanczosDecompositionTpl< _Matrix >::m_Qs

protected

Definition at line 174 of file math/lanczos-decomposition.hpp.

◆ m_rank

template<typename _Matrix >

Eigen::DenseIndex pinocchio::LanczosDecompositionTpl< _Matrix >::m_rank

protected

Definition at line 177 of file math/lanczos-decomposition.hpp.

◆ m_Ts

template<typename _Matrix >

TridiagonalMatrix pinocchio::LanczosDecompositionTpl< _Matrix >::m_Ts

protected

Definition at line 175 of file math/lanczos-decomposition.hpp.

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

math/lanczos-decomposition.hpp

Public Types

Public Member Functions

Protected Attributes

Detailed Description

template<typename _Matrix> struct pinocchio::LanczosDecompositionTpl< _Matrix >

Member Typedef Documentation

◆ Scalar

◆ TridiagonalMatrix

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ LanczosDecompositionTpl()

Member Function Documentation

◆ compute()

◆ computeDecompositionResidual()

◆ operator!=()

◆ operator==()

◆ PINOCCHIO_EIGEN_PLAIN_TYPE() [1/2]

◆ PINOCCHIO_EIGEN_PLAIN_TYPE() [2/2]

◆ Qs() [1/2]

◆ Qs() [2/2]

◆ rank()

◆ Ts() [1/2]

◆ Ts() [2/2]

Member Data Documentation

◆ m_A_times_q

◆ m_Qs

◆ m_rank

◆ m_Ts

template<typename _Matrix>
struct pinocchio::LanczosDecompositionTpl< _Matrix >