A direct sparse LLT Cholesky factorizations. More...

Inheritance diagram for Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >:

Public Types
enum	{ UpLo }

typedef SimplicialCholeskyBase< SimplicialLLT >	Base

typedef SparseMatrix< Scalar, ColMajor, Index >	CholMatrixType

typedef Traits::MatrixL	MatrixL

typedef MatrixType_	MatrixType

typedef Traits::MatrixU	MatrixU

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::Scalar	Scalar

typedef MatrixType::StorageIndex	StorageIndex

typedef internal::traits< SimplicialLLT >	Traits

typedef Matrix< Scalar, Dynamic, 1 >	VectorType

Public Types inherited from Eigen::SimplicialCholeskyBase< SimplicialLLT< MatrixType_, UpLo_, Ordering_ > >
enum

enum

typedef SparseMatrix< Scalar, ColMajor, StorageIndex >	CholMatrixType

typedef CholMatrixType const *	ConstCholMatrixPtr

typedef internal::traits< SimplicialLLT< MatrixType_, UpLo_, Ordering_ > >::MatrixType	MatrixType

typedef internal::traits< SimplicialLLT< MatrixType_, UpLo_, Ordering_ > >::OrderingType	OrderingType

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::Scalar	Scalar

typedef MatrixType::StorageIndex	StorageIndex

typedef Matrix< StorageIndex, Dynamic, 1 >	VectorI

typedef Matrix< Scalar, Dynamic, 1 >	VectorType

Public Member Functions
void	analyzePattern (const MatrixType &a)

SimplicialLLT &	compute (const MatrixType &matrix)

Scalar	determinant () const

void	factorize (const MatrixType &a)

const MatrixL	matrixL () const

const MatrixU	matrixU () const

	SimplicialLLT ()

	SimplicialLLT (const MatrixType &matrix)

Public Member Functions inherited from Eigen::SimplicialCholeskyBase< SimplicialLLT< MatrixType_, UpLo_, Ordering_ > >
Index	cols () const

SimplicialLLT< MatrixType_, UpLo_, Ordering_ > &	derived ()

SimplicialLLT< MatrixType_, UpLo_, Ordering_ > &	derived ()

const SimplicialLLT< MatrixType_, UpLo_, Ordering_ > &	derived () const

const SimplicialLLT< MatrixType_, UpLo_, Ordering_ > &	derived () const

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

const PermutationMatrix< Dynamic, Dynamic, StorageIndex > &	permutationP () const

const PermutationMatrix< Dynamic, Dynamic, StorageIndex > &	permutationPinv () const

Index	rows () const

SimplicialLLT< MatrixType_, UpLo_, Ordering_ > &	setShift (const RealScalar &offset, const RealScalar &scale=1)

	SimplicialCholeskyBase ()

	SimplicialCholeskyBase (const MatrixType &matrix)

	~SimplicialCholeskyBase ()

Public Member Functions inherited from Eigen::SparseSolverBase< SimplicialLLT< MatrixType_, UpLo_, Ordering_ > >
SimplicialLLT< MatrixType_, UpLo_, Ordering_ > &	derived ()

const SimplicialLLT< MatrixType_, UpLo_, Ordering_ > &	derived () const

const Solve< SimplicialLLT< MatrixType_, UpLo_, Ordering_ >, Rhs >	solve (const MatrixBase< Rhs > &b) const

const Solve< SimplicialLLT< MatrixType_, UpLo_, Ordering_ >, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const

	SparseSolverBase ()

	SparseSolverBase (SparseSolverBase &&other)

	~SparseSolverBase ()

Additional Inherited Members
Protected Member Functions inherited from Eigen::SimplicialCholeskyBase< SimplicialLLT< MatrixType_, UpLo_, Ordering_ > >
void	analyzePattern (const MatrixType &a, bool doLDLT)

void	analyzePattern_preordered (const CholMatrixType &a, bool doLDLT)

void	compute (const MatrixType &matrix)

void	factorize (const MatrixType &a)

void	factorize_preordered (const CholMatrixType &a)

void	ordering (const MatrixType &a, ConstCholMatrixPtr &pmat, CholMatrixType &ap)

Protected Attributes inherited from Eigen::SimplicialCholeskyBase< SimplicialLLT< MatrixType_, UpLo_, Ordering_ > >
bool	m_analysisIsOk

VectorType	m_diag

bool	m_factorizationIsOk

ComputationInfo	m_info

CholMatrixType	m_matrix

VectorI	m_nonZerosPerCol

PermutationMatrix< Dynamic, Dynamic, StorageIndex >	m_P

VectorI	m_parent

PermutationMatrix< Dynamic, Dynamic, StorageIndex >	m_Pinv

RealScalar	m_shiftOffset

RealScalar	m_shiftScale

Protected Attributes inherited from Eigen::SparseSolverBase< SimplicialLLT< MatrixType_, UpLo_, Ordering_ > >
bool	m_isInitialized

Detailed Description

template<typename MatrixType_, int UpLo_, typename Ordering_>
class Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >

A direct sparse LLT Cholesky factorizations.

This class provides a LL^T Cholesky factorizations of sparse matrices that are selfadjoint and positive definite. The factorization allows for solving A.X = B where X and B can be either dense or sparse.

In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization such that the factorized matrix is P A P^-1.

Template Parameters

MatrixType_	the type of the sparse matrix A, it must be a SparseMatrix<>
UpLo_	the triangular part that will be used for the computations. It can be Lower or Upper. Default is Lower.
Ordering_	The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<>

This class follows the sparse solver concept .

See also: class SimplicialLDLT, class AMDOrdering, class NaturalOrdering

Definition at line 340 of file SimplicialCholesky.h.

Member Typedef Documentation

◆ Base

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

typedef SimplicialCholeskyBase<SimplicialLLT> Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::Base

Definition at line 345 of file SimplicialCholesky.h.

◆ CholMatrixType

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

typedef SparseMatrix<Scalar,ColMajor,Index> Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::CholMatrixType

Definition at line 349 of file SimplicialCholesky.h.

◆ MatrixL

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

typedef Traits::MatrixL Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::MatrixL

Definition at line 352 of file SimplicialCholesky.h.

◆ MatrixType

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

typedef MatrixType_ Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::MatrixType

Definition at line 343 of file SimplicialCholesky.h.

◆ MatrixU

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

typedef Traits::MatrixU Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::MatrixU

Definition at line 353 of file SimplicialCholesky.h.

◆ RealScalar

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

typedef MatrixType::RealScalar Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::RealScalar

Definition at line 347 of file SimplicialCholesky.h.

◆ Scalar

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

typedef MatrixType::Scalar Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::Scalar

Definition at line 346 of file SimplicialCholesky.h.

◆ StorageIndex

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

typedef MatrixType::StorageIndex Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::StorageIndex

Definition at line 348 of file SimplicialCholesky.h.

◆ Traits

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

typedef internal::traits<SimplicialLLT> Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::Traits

Definition at line 351 of file SimplicialCholesky.h.

◆ VectorType

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

typedef Matrix<Scalar,Dynamic,1> Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::VectorType

Definition at line 350 of file SimplicialCholesky.h.

Member Enumeration Documentation

◆ anonymous enum

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

anonymous enum

Enumerator
UpLo

Definition at line 344 of file SimplicialCholesky.h.

344 { UpLo = UpLo_ };

Eigen::SimplicialLLT::UpLo

@ UpLo

Definition: SimplicialCholesky.h:344

Constructor & Destructor Documentation

◆ SimplicialLLT() [1/2]

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::SimplicialLLT ( )

inline

Default constructor

Definition at line 356 of file SimplicialCholesky.h.

356 : Base() {}

Eigen::SimplicialLLT::Base

SimplicialCholeskyBase< SimplicialLLT > Base

Definition: SimplicialCholesky.h:345

◆ SimplicialLLT() [2/2]

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::SimplicialLLT ( const MatrixType & matrix )

inlineexplicit

Constructs and performs the LLT factorization of matrix

Definition at line 358 of file SimplicialCholesky.h.

359 : Base(matrix) {}

Member Function Documentation

◆ analyzePattern()

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

void Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::analyzePattern ( const MatrixType & a )

inline

Performs a symbolic decomposition on the sparcity of matrix.

This function is particularly useful when solving for several problems having the same structure.

See also: factorize()

Definition at line 386 of file SimplicialCholesky.h.

     {
       Base::analyzePattern(a, false);
     }

◆ compute()

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

SimplicialLLT& Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::compute ( const MatrixType & matrix )

inline

Computes the sparse Cholesky decomposition of matrix

Definition at line 374 of file SimplicialCholesky.h.

     {
       Base::template compute<false>(matrix);
       return *this;
     }

◆ determinant()

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

Scalar Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::determinant ( ) const

inline

Returns: the determinant of the underlying matrix from the current factorization

Definition at line 403 of file SimplicialCholesky.h.

     {
       Scalar detL = Base::m_matrix.diagonal().prod();
       return numext::abs2(detL);
     }

◆ factorize()

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

void Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::factorize ( const MatrixType & a )

inline

Performs a numeric decomposition of matrix

The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.

See also: analyzePattern()

Definition at line 397 of file SimplicialCholesky.h.

     {
       Base::template factorize<false>(a);
     }

◆ matrixL()

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

const MatrixL Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::matrixL ( ) const

inline

Returns: an expression of the factor L

Definition at line 362 of file SimplicialCholesky.h.

                                          {
         eigen_assert(Base::m_factorizationIsOk && "Simplicial LLT not factorized");
         return Traits::getL(Base::m_matrix);
     }

◆ matrixU()

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

const MatrixU Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::matrixU ( ) const

inline

Returns: an expression of the factor U (= L^*)

Definition at line 368 of file SimplicialCholesky.h.

                                          {
         eigen_assert(Base::m_factorizationIsOk && "Simplicial LLT not factorized");
         return Traits::getU(Base::m_matrix);
     }

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

SimplicialCholesky.h

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

template<typename MatrixType_, int UpLo_, typename Ordering_> class Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >

Member Typedef Documentation

◆ Base

◆ CholMatrixType

◆ MatrixL

◆ MatrixType

◆ MatrixU

◆ RealScalar

◆ Scalar

◆ StorageIndex

◆ Traits

◆ VectorType

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ SimplicialLLT() [1/2]

◆ SimplicialLLT() [2/2]

Member Function Documentation

◆ analyzePattern()

◆ compute()

◆ determinant()

◆ factorize()

◆ matrixL()

◆ matrixU()

template<typename MatrixType_, int UpLo_, typename Ordering_>
class Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >