Eigen::SimplicialLDLT< MatrixType_, UpLo_, Ordering_ > Class Template Reference

A direct sparse LDLT Cholesky factorizations without square root. More...

#include <SimplicialCholesky.h>

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

Public Types
enum	{ UpLo = UpLo_ }
typedef MatrixType_	MatrixType
typedef SimplicialCholeskyBase< SimplicialLDLT >	Base
typedef MatrixType::Scalar	Scalar
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::StorageIndex	StorageIndex
typedef SparseMatrix< Scalar, ColMajor, StorageIndex >	CholMatrixType
typedef Matrix< Scalar, Dynamic, 1 >	VectorType
typedef internal::traits< SimplicialLDLT >	Traits
typedef Traits::MatrixL	MatrixL
typedef Traits::MatrixU	MatrixU
Public Types inherited from Eigen::SimplicialCholeskyBase< SimplicialLDLT< MatrixType_, UpLo_, Ordering_ > >
enum
enum
typedef internal::traits< SimplicialLDLT< MatrixType_, UpLo_, Ordering_ > >::MatrixType	MatrixType
typedef internal::traits< SimplicialLDLT< MatrixType_, UpLo_, Ordering_ > >::OrderingType	OrderingType
typedef MatrixType::Scalar	Scalar
typedef MatrixType::RealScalar	RealScalar
typedef internal::traits< SimplicialLDLT< 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
	SimplicialLDLT ()
	SimplicialLDLT (const MatrixType &matrix)
const VectorType	vectorD () const
const MatrixL	matrixL () const
const MatrixU	matrixU () const
SimplicialLDLT &	compute (const MatrixType &matrix)
void	analyzePattern (const MatrixType &a)
void	factorize (const MatrixType &a)
Scalar	determinant () const
Public Member Functions inherited from Eigen::SimplicialCholeskyBase< SimplicialLDLT< MatrixType_, UpLo_, Ordering_ > >
	SimplicialCholeskyBase ()
	SimplicialCholeskyBase (const MatrixType &matrix)
	~SimplicialCholeskyBase ()
SimplicialLDLT< MatrixType_, UpLo_, Ordering_ > &	derived ()
const SimplicialLDLT< MatrixType_, UpLo_, Ordering_ > &	derived () const
SimplicialLDLT< MatrixType_, UpLo_, Ordering_ > &	derived ()
const SimplicialLDLT< 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
SimplicialLDLT< 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< SimplicialLDLT< MatrixType_, UpLo_, Ordering_ > >
	SparseSolverBase ()
	SparseSolverBase (SparseSolverBase &&other)
	~SparseSolverBase ()
SimplicialLDLT< MatrixType_, UpLo_, Ordering_ > &	derived ()
const SimplicialLDLT< MatrixType_, UpLo_, Ordering_ > &	derived () const
const Solve< SimplicialLDLT< MatrixType_, UpLo_, Ordering_ >, Rhs >	solve (const MatrixBase< Rhs > &b) const
const Solve< SimplicialLDLT< 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< SimplicialLDLT< 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< SimplicialLDLT< 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< SimplicialLDLT< MatrixType_, UpLo_, Ordering_ > >
bool	m_isInitialized

Detailed Description

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

A direct sparse LDLT Cholesky factorizations without square root.

This class provides a LDL^T Cholesky factorizations without square root 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 SimplicialLLT, class AMDOrdering, class NaturalOrdering

Member Typedef Documentation

Base

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

CholMatrixType

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

typedef SparseMatrix<Scalar, ColMajor, StorageIndex> Eigen::SimplicialLDLT< MatrixType_, UpLo_, Ordering_ >::CholMatrixType

MatrixL

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

MatrixType

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

MatrixU

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

RealScalar

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

Scalar

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

StorageIndex

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

Traits

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

VectorType

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

Member Enumeration Documentation

anonymous enum

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

anonymous enum

Enumerator
UpLo

{ UpLo = UpLo_ };

Constructor & Destructor Documentation

SimplicialLDLT() [1/2]

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

inline

Default constructor

: Base() {}

SimplicialLDLT() [2/2]

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

inlineexplicit

Constructs and performs the LLT factorization of matrix

: Base(matrix) {}

Member Function Documentation

analyzePattern()

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

void Eigen::SimplicialLDLT< 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()

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

References a.

compute()

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

inline

Computes the sparse Cholesky decomposition of matrix

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

References matrix().

determinant()

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

inline

Returns

the determinant of the underlying matrix from the current factorization

{ return Base::m_diag.prod(); }

References Eigen::SimplicialCholeskyBase< Derived >::m_diag.

factorize()

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

void Eigen::SimplicialLDLT< 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()

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

References a.

matrixL()

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

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

inline

Returns

an expression of the factor L

                                       {
    eigen_assert(Base::m_factorizationIsOk && "Simplicial LDLT 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::SimplicialLDLT< MatrixType_, UpLo_, Ordering_ >::matrixU ( ) const

inline

Returns

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

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

References eigen_assert, Eigen::SimplicialCholeskyBase< Derived >::m_factorizationIsOk, and Eigen::SimplicialCholeskyBase< Derived >::m_matrix.

vectorD()

template<typename MatrixType_ , int UpLo_, typename Ordering_ >

const VectorType Eigen::SimplicialLDLT< MatrixType_, UpLo_, Ordering_ >::vectorD ( ) const

inline

Returns

a vector expression of the diagonal D

                                          {
    eigen_assert(Base::m_factorizationIsOk && "Simplicial LDLT not factorized");
    return Base::m_diag;
  }

References eigen_assert, Eigen::SimplicialCholeskyBase< Derived >::m_diag, and Eigen::SimplicialCholeskyBase< Derived >::m_factorizationIsOk.

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

• SimplicialCholesky.h