Standard Cholesky decomposition (LL^T) of a matrix and associated features. More...

#include </home/runner/work/allwpilib/allwpilib/wpimath/src/main/native/thirdparty/eigen/include/Eigen/src/Cholesky/LLT.h>

Inheritance diagram for Eigen::LLT< _MatrixType, _UpLo >:

Public Types
enum	{ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }

enum	{ PacketSize = internal::packet_traits<Scalar>::size , AlignmentMask = int(PacketSize)-1 , UpLo = _UpLo }

typedef _MatrixType	MatrixType

typedef SolverBase< LLT >	Base

typedef internal::LLT_Traits< MatrixType, UpLo >	Traits

Public Types inherited from Eigen::SolverBase< LLT< _MatrixType, _UpLo > >
enum

typedef EigenBase< LLT< _MatrixType, _UpLo > >	Base

typedef internal::traits< LLT< _MatrixType, _UpLo > >::Scalar	Scalar

typedef Scalar	CoeffReturnType

typedef internal::add_const< Transpose< constDerived > >::type	ConstTransposeReturnType

typedef internal::conditional< NumTraits< Scalar >::IsComplex, CwiseUnaryOp< internal::scalar_conjugate_op< Scalar >, ConstTransposeReturnType >, ConstTransposeReturnType >::type	AdjointReturnType

Public Types inherited from Eigen::EigenBase< LLT< _MatrixType, _UpLo > >
typedef Eigen::Index	Index
	The interface type of indices. More...

typedef internal::traits< LLT< _MatrixType, _UpLo > >::StorageKind	StorageKind

Public Member Functions
	LLT ()
	Default Constructor. More...

	LLT (Index size)
	Default Constructor with memory preallocation. More...

template<typename InputType >
	LLT (const EigenBase< InputType > &matrix)

template<typename InputType >
	LLT (EigenBase< InputType > &matrix)
	Constructs a LLT factorization from a given matrix. More...

Traits::MatrixU	matrixU () const

Traits::MatrixL	matrixL () const

template<typename Derived >
void	solveInPlace (const MatrixBase< Derived > &bAndX) const

template<typename InputType >
LLT &	compute (const EigenBase< InputType > &matrix)

RealScalar	rcond () const

const MatrixType &	matrixLLT () const

MatrixType	reconstructedMatrix () const

ComputationInfo	info () const
	Reports whether previous computation was successful. More...

const LLT &	adjoint () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

template<typename VectorType >
LLT &	rankUpdate (const VectorType &vec, const RealScalar &sigma=1)

template<typename RhsType , typename DstType >
void	_solve_impl (const RhsType &rhs, DstType &dst) const

template<bool Conjugate, typename RhsType , typename DstType >
void	_solve_impl_transposed (const RhsType &rhs, DstType &dst) const

template<typename InputType >
LLT< MatrixType, _UpLo > &	compute (const EigenBase< InputType > &a)
	Computes / recomputes the Cholesky decomposition A = LL^* = U^U of matrix*. More...

template<typename VectorType >
LLT< _MatrixType, _UpLo > &	rankUpdate (const VectorType &v, const RealScalar &sigma)
	Performs a rank one update (or dowdate) of the current decomposition. More...

Public Member Functions inherited from Eigen::SolverBase< LLT< _MatrixType, _UpLo > >
	SolverBase ()
	Default constructor. More...

	~SolverBase ()

const Solve< LLT< _MatrixType, _UpLo >, Rhs >	solve (const MatrixBase< Rhs > &b) const

ConstTransposeReturnType	transpose () const

AdjointReturnType	adjoint () const

EIGEN_DEVICE_FUNC LLT< _MatrixType, _UpLo > &	derived ()

EIGEN_DEVICE_FUNC const LLT< _MatrixType, _UpLo > &	derived () const

Public Member Functions inherited from Eigen::EigenBase< LLT< _MatrixType, _UpLo > >
EIGEN_DEVICE_FUNC LLT< _MatrixType, _UpLo > &	derived ()

EIGEN_DEVICE_FUNC const LLT< _MatrixType, _UpLo > &	derived () const

EIGEN_DEVICE_FUNC LLT< _MatrixType, _UpLo > &	const_cast_derived () const

EIGEN_DEVICE_FUNC const LLT< _MatrixType, _UpLo > &	const_derived () const

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	size () const EIGEN_NOEXCEPT

EIGEN_DEVICE_FUNC void	evalTo (Dest &dst) const

EIGEN_DEVICE_FUNC void	addTo (Dest &dst) const

EIGEN_DEVICE_FUNC void	subTo (Dest &dst) const

EIGEN_DEVICE_FUNC void	applyThisOnTheRight (Dest &dst) const

EIGEN_DEVICE_FUNC void	applyThisOnTheLeft (Dest &dst) const

Static Protected Member Functions
static void	check_template_parameters ()

Protected Attributes
MatrixType	m_matrix

RealScalar	m_l1_norm

bool	m_isInitialized

ComputationInfo	m_info

Friends
class	SolverBase< LLT >

Additional Inherited Members
Protected Member Functions inherited from Eigen::SolverBase< LLT< _MatrixType, _UpLo > >
void	_check_solve_assertion (const Rhs &b) const

Detailed Description

template<typename _MatrixType, int _UpLo>
class Eigen::LLT< _MatrixType, _UpLo >

Standard Cholesky decomposition (LL^T) of a matrix and associated features.

Template Parameters

_MatrixType	the type of the matrix of which we are computing the LL^T Cholesky decomposition
_UpLo	the triangular part that will be used for the decompositon: Lower (default) or Upper. The other triangular part won't be read.

This class performs a LL^T Cholesky decomposition of a symmetric, positive definite matrix A such that A = LL^* = U^*U, where L is lower triangular.

While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b, for that purpose, we recommend the Cholesky decomposition without square root which is more stable and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other situations like generalised eigen problems with hermitian matrices.

Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices, use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations has a solution.

Example:

Output:

Performance: for best performance, it is recommended to use a column-major storage format with the Lower triangular part (the default), or, equivalently, a row-major storage format with the Upper triangular part. Otherwise, you might get a 20% slowdown for the full factorization step, and rank-updates can be up to 3 times slower.

This class supports the inplace decomposition mechanism.

Note that during the decomposition, only the lower (or upper, as defined by _UpLo) triangular part of A is considered. Therefore, the strict lower part does not have to store correct values.

See also: MatrixBase::llt(), SelfAdjointView::llt(), class LDLT

Member Typedef Documentation

◆ Base

template<typename _MatrixType , int _UpLo>

typedef SolverBase<LLT> Eigen::LLT< _MatrixType, _UpLo >::Base

◆ MatrixType

template<typename _MatrixType , int _UpLo>

typedef _MatrixType Eigen::LLT< _MatrixType, _UpLo >::MatrixType

◆ Traits

template<typename _MatrixType , int _UpLo>

typedef internal::LLT_Traits<MatrixType,UpLo> Eigen::LLT< _MatrixType, _UpLo >::Traits

Member Enumeration Documentation

◆ anonymous enum

template<typename _MatrixType , int _UpLo>

anonymous enum

Enumerator
MaxColsAtCompileTime

◆ anonymous enum

template<typename _MatrixType , int _UpLo>

anonymous enum

Enumerator
PacketSize
AlignmentMask
UpLo

Constructor & Destructor Documentation

◆ LLT() [1/4]

template<typename _MatrixType , int _UpLo>

Eigen::LLT< _MatrixType, _UpLo >::LLT ( )

inline

Default Constructor.

The default constructor is useful in cases in which the user intends to perform decompositions via LLT::compute(const MatrixType&).

◆ LLT() [2/4]

template<typename _MatrixType , int _UpLo>

Eigen::LLT< _MatrixType, _UpLo >::LLT ( Index size )

inlineexplicit

Default Constructor with memory preallocation.

Like the default constructor but with preallocation of the internal data according to the specified problem size.

See also: LLT()

◆ LLT() [3/4]

template<typename _MatrixType , int _UpLo>

template<typename InputType >

Eigen::LLT< _MatrixType, _UpLo >::LLT ( const EigenBase< InputType > & matrix )

inlineexplicit

◆ LLT() [4/4]

template<typename _MatrixType , int _UpLo>

template<typename InputType >

Eigen::LLT< _MatrixType, _UpLo >::LLT ( EigenBase< InputType > & matrix )

inlineexplicit

Constructs a LLT factorization from a given matrix.

This overloaded constructor is provided for inplace decomposition when MatrixType is a Eigen::Ref.

See also: LLT(const EigenBase&)

Member Function Documentation

◆ _solve_impl()

template<typename _MatrixType , int _UpLo>

template<typename RhsType , typename DstType >

void Eigen::LLT< _MatrixType, _UpLo >::_solve_impl	(	const RhsType &	rhs,
		DstType &	dst
	)		const

◆ _solve_impl_transposed()

template<typename _MatrixType , int _UpLo>

template<bool Conjugate, typename RhsType , typename DstType >

void Eigen::LLT< _MatrixType, _UpLo >::_solve_impl_transposed	(	const RhsType &	rhs,
		DstType &	dst
	)		const

◆ adjoint()

template<typename _MatrixType , int _UpLo>

const LLT & Eigen::LLT< _MatrixType, _UpLo >::adjoint ( ) const

inline

Returns: the adjoint of *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.

This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:

x = decomposition.adjoint().solve(b)

units::b

b

Definition: data.h:44

◆ check_template_parameters()

template<typename _MatrixType , int _UpLo>

static void Eigen::LLT< _MatrixType, _UpLo >::check_template_parameters ( )

inlinestaticprotected

◆ cols()

template<typename _MatrixType , int _UpLo>

EIGEN_CONSTEXPR Index Eigen::LLT< _MatrixType, _UpLo >::cols ( ) const

inline

◆ compute() [1/2]

template<typename _MatrixType , int _UpLo>

template<typename InputType >

LLT< MatrixType, _UpLo > & Eigen::LLT< _MatrixType, _UpLo >::compute ( const EigenBase< InputType > & a )

Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of matrix.

Returns: a reference to *this

Example:

Output:

◆ compute() [2/2]

template<typename _MatrixType , int _UpLo>

template<typename InputType >

LLT & Eigen::LLT< _MatrixType, _UpLo >::compute ( const EigenBase< InputType > & matrix )

◆ info()

template<typename _MatrixType , int _UpLo>

ComputationInfo Eigen::LLT< _MatrixType, _UpLo >::info ( ) const

inline

Reports whether previous computation was successful.

Returns: Success if computation was successful, NumericalIssue if the matrix.appears not to be positive definite.

◆ matrixL()

template<typename _MatrixType , int _UpLo>

Traits::MatrixL Eigen::LLT< _MatrixType, _UpLo >::matrixL ( ) const

inline

Returns: a view of the lower triangular matrix L

◆ matrixLLT()

template<typename _MatrixType , int _UpLo>

const MatrixType & Eigen::LLT< _MatrixType, _UpLo >::matrixLLT ( ) const

inline

Returns: the LLT decomposition matrix

TODO: document the storage layout

◆ matrixU()

template<typename _MatrixType , int _UpLo>

Traits::MatrixU Eigen::LLT< _MatrixType, _UpLo >::matrixU ( ) const

inline

Returns: a view of the upper triangular matrix U

◆ rankUpdate() [1/2]

template<typename _MatrixType , int _UpLo>

template<typename VectorType >

LLT< _MatrixType, _UpLo > & Eigen::LLT< _MatrixType, _UpLo >::rankUpdate	(	const VectorType &	v,
		const RealScalar &	sigma
	)

Performs a rank one update (or dowdate) of the current decomposition.

If A = LL^* before the rank one update, then after it we have LL^* = A + sigma * v v^* where v must be a vector of same dimension.

◆ rankUpdate() [2/2]

template<typename _MatrixType , int _UpLo>

template<typename VectorType >

LLT & Eigen::LLT< _MatrixType, _UpLo >::rankUpdate	(	const VectorType &	vec,
		const RealScalar &	sigma = `1`
	)

◆ rcond()

template<typename _MatrixType , int _UpLo>

RealScalar Eigen::LLT< _MatrixType, _UpLo >::rcond ( ) const

inline

Returns: an estimate of the reciprocal condition number of the matrix of which *this is the Cholesky decomposition.

◆ reconstructedMatrix()

template<typename MatrixType , int _UpLo>

MatrixType Eigen::LLT< MatrixType, _UpLo >::reconstructedMatrix

Returns: the matrix represented by the decomposition, i.e., it returns the product: L L^*. This function is provided for debug purpose.

◆ rows()

template<typename _MatrixType , int _UpLo>

EIGEN_CONSTEXPR Index Eigen::LLT< _MatrixType, _UpLo >::rows ( ) const

inline

◆ solveInPlace()

template<typename MatrixType , int _UpLo>

template<typename Derived >

void Eigen::LLT< MatrixType, _UpLo >::solveInPlace ( const MatrixBase< Derived > & bAndX ) const

Friends And Related Function Documentation

◆ SolverBase< LLT >

template<typename _MatrixType , int _UpLo>

friend class SolverBase< LLT >

friend

Member Data Documentation

◆ m_info

template<typename _MatrixType , int _UpLo>

ComputationInfo Eigen::LLT< _MatrixType, _UpLo >::m_info

protected

◆ m_isInitialized

template<typename _MatrixType , int _UpLo>

bool Eigen::LLT< _MatrixType, _UpLo >::m_isInitialized

protected

◆ m_l1_norm

template<typename _MatrixType , int _UpLo>

RealScalar Eigen::LLT< _MatrixType, _UpLo >::m_l1_norm

protected

◆ m_matrix

template<typename _MatrixType , int _UpLo>

MatrixType Eigen::LLT< _MatrixType, _UpLo >::m_matrix

protected

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

/home/runner/work/allwpilib/allwpilib/wpimath/src/main/native/thirdparty/eigen/include/Eigen/src/Cholesky/LLT.h

Public Types

Public Member Functions

Static Protected Member Functions

Protected Attributes

Friends

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Base

◆ MatrixType

◆ Traits

Member Enumeration Documentation

◆ anonymous enum

◆ anonymous enum

Constructor & Destructor Documentation

◆ LLT() [1/4]

◆ LLT() [2/4]

◆ LLT() [3/4]

◆ LLT() [4/4]

Member Function Documentation

◆ _solve_impl()

◆ _solve_impl_transposed()

◆ adjoint()

◆ check_template_parameters()

◆ cols()

◆ compute() [1/2]

◆ compute() [2/2]

◆ info()

◆ matrixL()

◆ matrixLLT()

◆ matrixU()

◆ rankUpdate() [1/2]

◆ rankUpdate() [2/2]

◆ rcond()

◆ reconstructedMatrix()

◆ rows()

◆ solveInPlace()

Friends And Related Function Documentation

◆ SolverBase< LLT >

Member Data Documentation

◆ m_info

◆ m_isInitialized

◆ m_l1_norm

◆ m_matrix