Eigen  3.4.0 (git rev e3e74001f7c4bf95f0dde572e8a08c5b2918a3ab)
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Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering > Class Template Reference
Sparse linear algebra » Reference » SparseCholesky module

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

This class follows the sparse solver concept .

See also
class SimplicialLLT, class AMDOrdering, class NaturalOrdering
+ Inheritance diagram for Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >:

Public Member Functions

void analyzePattern (const MatrixType &a)
 
SimplicialLDLT & compute (const MatrixType &matrix)
 
Scalar determinant () const
 
void factorize (const MatrixType &a)
 
const MatrixL matrixL () const
 
const MatrixU matrixU () const
 
 SimplicialLDLT ()
 
 SimplicialLDLT (const MatrixType &matrix)
 
const VectorType vectorD () const
 
- Public Member Functions inherited from Eigen::SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >
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 RealScalar &offset, const RealScalar &scale=1)
 
 SimplicialCholeskyBase ()
 
- Public Member Functions inherited from Eigen::SparseSolverBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >
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
 
 SparseSolverBase ()
 

Additional Inherited Members

- Protected Member Functions inherited from Eigen::SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >
void compute (const MatrixType &matrix)
 

Constructor & Destructor Documentation

◆ SimplicialLDLT() [1/2]

template<typename _MatrixType , int _UpLo, typename _Ordering >
Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::SimplicialLDLT ( )
inline

Default constructor

◆ 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

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()

◆ 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

◆ 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

◆ 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()

◆ 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

◆ 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^*)

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