LanczosDecompositionTpl< _Matrix > Struct Template Reference

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

#include <pinocchio/math/lanczos-decomposition.hpp>

Collaboration diagram for LanczosDecompositionTpl< _Matrix >:

Public Types
enum	{ Options = _Matrix::Options }
typedef _Matrix	PlainMatrix
typedef _Matrix::Scalar	Scalar
typedef TridiagonalSymmetricMatrixTpl< Scalar, Options >	TridiagonalMatrix
typedef PlainMatrix::ColXpr	Vector

Public Member Functions
template<typename MatrixLikeType >
	LanczosDecompositionTpl (const MatrixLikeType &mat, const Eigen::DenseIndex decomposition_size)
	Default constructor for the Lanczos decomposition from an input matrix.
template<typename MatrixLikeType >
void	compute (const MatrixLikeType &A)
	Computes the Lanczos decomposition of the input matrix A.
template<typename MatrixLikeType >
PlainMatrix	computeDecompositionResidual (const MatrixLikeType &A) const
	Computes the residual associated with the decomposition, namely, the quantity \( A Q_s - Q_s T_s \).
bool	operator!= (const LanczosDecompositionTpl &other) const
bool	operator== (const LanczosDecompositionTpl &other) const
PlainMatrix &	Qs ()
	Returns the orthogonal basis associated with the Lanczos decomposition.
const PlainMatrix &	Qs () const
	Returns the orthogonal basis associated with the Lanczos decomposition.
Eigen::DenseIndex	rank () const
	Returns the rank of the decomposition.
TridiagonalMatrix &	Ts ()
	Returns the tridiagonal matrix associated with the Lanczos decomposition.
const TridiagonalMatrix &	Ts () const
	Returns the tridiagonal matrix associated with the Lanczos decomposition.

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 lanczos-decomposition.hpp.

Member Typedef Documentation

PlainMatrix

template<typename _Matrix >

typedef _Matrix PlainMatrix

Definition at line 22 of file lanczos-decomposition.hpp.

Scalar

template<typename _Matrix >

typedef _Matrix::Scalar Scalar

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

TridiagonalMatrix

template<typename _Matrix >

typedef TridiagonalSymmetricMatrixTpl<Scalar, Options> TridiagonalMatrix

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

Vector

template<typename _Matrix >

typedef PlainMatrix::ColXpr Vector

Definition at line 23 of file lanczos-decomposition.hpp.

Member Enumeration Documentation

anonymous enum

template<typename _Matrix >

anonymous enum

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

Constructor & Destructor Documentation

LanczosDecompositionTpl()

template<typename _Matrix >

template<typename MatrixLikeType >

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 lanczos-decomposition.hpp.

Member Function Documentation

compute()

template<typename _Matrix >

template<typename MatrixLikeType >

void 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 lanczos-decomposition.hpp.

computeDecompositionResidual()

template<typename _Matrix >

template<typename MatrixLikeType >

PlainMatrix 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 lanczos-decomposition.hpp.

operator!=()

template<typename _Matrix >

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

inline

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

operator==()

template<typename _Matrix >

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

inline

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

Qs() [1/2]

template<typename _Matrix >

PlainMatrix & Qs ( )

inline

Returns the orthogonal basis associated with the Lanczos decomposition.

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

Qs() [2/2]

template<typename _Matrix >

const PlainMatrix & Qs ( ) const

inline

Returns the orthogonal basis associated with the Lanczos decomposition.

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

rank()

template<typename _Matrix >

Eigen::DenseIndex rank ( ) const

inline

Returns the rank of the decomposition.

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

Ts() [1/2]

template<typename _Matrix >

TridiagonalMatrix & Ts ( )

inline

Returns the tridiagonal matrix associated with the Lanczos decomposition.

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

Ts() [2/2]

template<typename _Matrix >

const TridiagonalMatrix & Ts ( ) const

inline

Returns the tridiagonal matrix associated with the Lanczos decomposition.

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

Member Data Documentation

m_A_times_q

template<typename _Matrix >

Vector m_A_times_q

mutableprotected

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

m_Qs

template<typename _Matrix >

PlainMatrix m_Qs

protected

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

m_rank

template<typename _Matrix >

Eigen::DenseIndex m_rank

protected

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

m_Ts

template<typename _Matrix >

TridiagonalMatrix m_Ts

protected

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

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

• include/pinocchio/math/lanczos-decomposition.hpp