A direct sparse LLT Cholesky factorizations. More...

#include <SimplicialCholesky.h>

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

Public Types
enum	{ UpLo = UpLo_ }

typedef MatrixType_	MatrixType

typedef SimplicialCholeskyBase< SimplicialLLT >	Base

typedef MatrixType::Scalar	Scalar

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::StorageIndex	StorageIndex

typedef SparseMatrix< Scalar, ColMajor, Index >	CholMatrixType

typedef Matrix< Scalar, Dynamic, 1 >	VectorType

typedef internal::traits< SimplicialLLT >	Traits

typedef Traits::MatrixL	MatrixL

typedef Traits::MatrixU	MatrixU

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

enum

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

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

typedef MatrixType::Scalar	Scalar

typedef MatrixType::RealScalar	RealScalar

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

typedef MatrixType::StorageIndex	StorageIndex

typedef SparseMatrix< Scalar, ColMajor, StorageIndex >	CholMatrixType

typedef CholMatrixType const *	ConstCholMatrixPtr

typedef Matrix< Scalar, Dynamic, 1 >	VectorType

typedef Matrix< StorageIndex, Dynamic, 1 >	VectorI

Public Member Functions
	SimplicialLLT ()

	SimplicialLLT (const MatrixType &matrix)

const MatrixL	matrixL () const

const MatrixU	matrixU () const

SimplicialLLT &	compute (const MatrixType &matrix)

void	analyzePattern (const MatrixType &a)

void	factorize (const MatrixType &a)

Scalar	determinant () const

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

	SimplicialCholeskyBase (const MatrixType &matrix)

	~SimplicialCholeskyBase ()

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

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

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

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

Index	cols () const

Index	rows () 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

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

void	dumpMemory (Stream &s)

void	_solve_impl (const MatrixBase< Rhs > &b, MatrixBase< Dest > &dest) const

void	_solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const

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

	SparseSolverBase (SparseSolverBase &&other)

	~SparseSolverBase ()

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

void	_solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const

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

void	factorize (const MatrixType &a)

void	factorize_preordered (const CholMatrixType &a)

void	analyzePattern (const MatrixType &a)

void	analyzePattern_preordered (const CholMatrixType &a, bool doLDLT)

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

DiagonalScalar	getDiag (Scalar x)

Scalar	getSymm (Scalar x)

Protected Attributes inherited from Eigen::SimplicialCholeskyBase< SimplicialLLT< MatrixType_, UpLo_, Ordering_ > >
ComputationInfo	m_info

bool	m_factorizationIsOk

bool	m_analysisIsOk

CholMatrixType	m_matrix

VectorType	m_diag

VectorI	m_parent

VectorI	m_workSpace

PermutationMatrix< Dynamic, Dynamic, StorageIndex >	m_P

PermutationMatrix< Dynamic, Dynamic, StorageIndex >	m_Pinv

DiagonalScalar	m_shiftOffset

DiagonalScalar	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<>

\implsparsesolverconcept

See also: class SimplicialLDLT, class AMDOrdering, class NaturalOrdering

Member Typedef Documentation

◆ Base

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

◆ CholMatrixType

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

◆ MatrixL

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

◆ MatrixType

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

◆ MatrixU

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

◆ RealScalar

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

◆ Scalar

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

◆ StorageIndex

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

◆ Traits

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

◆ VectorType

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

Member Enumeration Documentation

◆ anonymous enum

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

anonymous enum

Enumerator
UpLo

374 { UpLo = UpLo_ };

Eigen::SimplicialLLT::UpLo

@ UpLo

Definition: SimplicialCholesky.h:374

Constructor & Destructor Documentation

◆ SimplicialLLT() [1/2]

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

inline

Default constructor

387 : Base() {}

Eigen::SimplicialLLT::Base

SimplicialCholeskyBase< SimplicialLLT > Base

Definition: SimplicialCholesky.h:375

◆ 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

389 : Base(matrix) {}

matrix

Eigen::Map< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic, Eigen::ColMajor >, 0, Eigen::OuterStride<> > matrix(T *data, int rows, int cols, int stride)

Definition: common.h:85

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()

415 { Base::template analyzePattern<false, false>(a); }

a

const Scalar * a

Definition: level2_cplx_impl.h:32

References a.

◆ 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

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

References matrix().

◆ 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

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

References Eigen::numext::abs2(), Eigen::SparseMatrix< Scalar_, Options_, StorageIndex_ >::diagonal(), and Eigen::SimplicialCholeskyBase< Derived >::m_matrix.

◆ 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()

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

References 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

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

References eigen_assert, Eigen::SimplicialCholeskyBase< Derived >::m_factorizationIsOk, and Eigen::SimplicialCholeskyBase< Derived >::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^*)

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

References eigen_assert, Eigen::SimplicialCholeskyBase< Derived >::m_factorizationIsOk, and Eigen::SimplicialCholeskyBase< Derived >::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_ >