Public Types | Public Member Functions | List of all members
Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering > Class Template Reference

A direct sparse LLT Cholesky factorizations. More...

#include <SimplicialCholesky.h>

Inheritance diagram for Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >:
Inheritance graph
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Public Types

enum  { UpLo = _UpLo }
 
typedef SimplicialCholeskyBase< SimplicialLLTBase
 
typedef SparseMatrix< Scalar, ColMajor, IndexCholMatrixType
 
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< SimplicialLLTTraits
 
typedef Matrix< Scalar, Dynamic, 1 > VectorType
 
- Public Types inherited from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >
enum  
 
enum  
 
typedef SparseMatrix< Scalar, ColMajor, StorageIndexCholMatrixType
 
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)
 
SimplicialLLTcompute (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 > >
void _solve_impl (const MatrixBase< Rhs > &b, MatrixBase< Dest > &dest) const
 
void _solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const
 
Index cols () const
 
SimplicialLLT< _MatrixType, _UpLo, _Ordering > & derived ()
 
const SimplicialLLT< _MatrixType, _UpLo, _Ordering > & derived () const
 
void dumpMemory (Stream &s)
 
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 > >
void _solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const
 
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 ()
 

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, StorageIndexm_P
 
VectorI m_parent
 
PermutationMatrix< Dynamic, Dynamic, StorageIndexm_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
_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<>
See also
class SimplicialLDLT, class AMDOrdering, class NaturalOrdering

Definition at line 274 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 343 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 347 of file SimplicialCholesky.h.

◆ MatrixL

template<typename _MatrixType, int _UpLo, typename _Ordering>
typedef Traits::MatrixL Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::MatrixL

Definition at line 350 of file SimplicialCholesky.h.

◆ MatrixType

template<typename _MatrixType, int _UpLo, typename _Ordering>
typedef _MatrixType Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::MatrixType

Definition at line 341 of file SimplicialCholesky.h.

◆ MatrixU

template<typename _MatrixType, int _UpLo, typename _Ordering>
typedef Traits::MatrixU Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::MatrixU

Definition at line 351 of file SimplicialCholesky.h.

◆ RealScalar

template<typename _MatrixType, int _UpLo, typename _Ordering>
typedef MatrixType::RealScalar Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::RealScalar

Definition at line 345 of file SimplicialCholesky.h.

◆ Scalar

template<typename _MatrixType, int _UpLo, typename _Ordering>
typedef MatrixType::Scalar Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::Scalar

Definition at line 344 of file SimplicialCholesky.h.

◆ StorageIndex

template<typename _MatrixType, int _UpLo, typename _Ordering>
typedef MatrixType::StorageIndex Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::StorageIndex

Definition at line 346 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 349 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 348 of file SimplicialCholesky.h.

Member Enumeration Documentation

◆ anonymous enum

template<typename _MatrixType, int _UpLo, typename _Ordering>
anonymous enum
Enumerator
UpLo 

Definition at line 342 of file SimplicialCholesky.h.

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 354 of file SimplicialCholesky.h.

◆ 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 356 of file SimplicialCholesky.h.

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 384 of file SimplicialCholesky.h.

◆ 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 372 of file SimplicialCholesky.h.

◆ 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 401 of file SimplicialCholesky.h.

◆ 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 395 of file SimplicialCholesky.h.

◆ 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 360 of file SimplicialCholesky.h.

◆ 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 366 of file SimplicialCholesky.h.


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


gtsam
Author(s):
autogenerated on Tue Jul 4 2023 02:43:12