Eigen::SimplicialLLT< _MatrixType, _UpLo > Class Template Reference

A direct sparse LLT Cholesky factorizations. More...

#include <SimplicialCholesky.h>

Inheritance diagram for Eigen::SimplicialLLT< _MatrixType, _UpLo >:

Collaboration diagram for Eigen::SimplicialLLT< _MatrixType, _UpLo >:

Public Types
enum	{ UpLo = _UpLo }
typedef _MatrixType	MatrixType
typedef SimplicialCholeskyBase< SimplicialLLT >	Base
typedef MatrixType::Scalar	Scalar
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::Index	Index
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 > >
enum
typedef internal::traits< SimplicialLLT< _MatrixType, _UpLo > >::MatrixType	MatrixType
typedef MatrixType::Scalar	Scalar
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::Index	Index
typedef SparseMatrix< Scalar, ColMajor, Index >	CholMatrixType
typedef Matrix< Scalar, Dynamic, 1 >	VectorType

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 > >
	SimplicialCholeskyBase ()
	SimplicialCholeskyBase (const MatrixType &matrix)
SimplicialLLT< _MatrixType, _UpLo > &	derived ()
const SimplicialLLT< _MatrixType, _UpLo > &	derived () const
Index	cols () const
Index	rows () const
ComputationInfo	info () const
	Reports whether previous computation was successful. More...
const internal::solve_retval< SimplicialCholeskyBase, Rhs >	solve (const MatrixBase< Rhs > &b) const
const internal::sparse_solve_retval< SimplicialCholeskyBase, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const
const PermutationMatrix< Dynamic, Dynamic, Index > &	permutationP () const
const PermutationMatrix< Dynamic, Dynamic, Index > &	permutationPinv () const
SimplicialLLT< _MatrixType, _UpLo > &	setShift (const RealScalar &offset, const RealScalar &scale=1)
void	dumpMemory (Stream &s)
void	_solve (const MatrixBase< Rhs > &b, MatrixBase< Dest > &dest) const

Additional Inherited Members
Protected Member Functions inherited from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo > >
void	compute (const MatrixType &matrix)
void	factorize (const MatrixType &a)
void	factorize_preordered (const CholMatrixType &a)
void	analyzePattern (const MatrixType &a, bool doLDLT)
void	analyzePattern_preordered (const CholMatrixType &a, bool doLDLT)
void	ordering (const MatrixType &a, CholMatrixType &ap)
Protected Attributes inherited from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo > >
ComputationInfo	m_info
bool	m_isInitialized
bool	m_factorizationIsOk
bool	m_analysisIsOk
CholMatrixType	m_matrix
VectorType	m_diag
VectorXi	m_parent
VectorXi	m_nonZerosPerCol
PermutationMatrix< Dynamic, Dynamic, Index >	m_P
PermutationMatrix< Dynamic, Dynamic, Index >	m_Pinv
RealScalar	m_shiftOffset
RealScalar	m_shiftScale

Detailed Description

template<typename _MatrixType, int _UpLo>
class Eigen::SimplicialLLT< _MatrixType, _UpLo >

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.

See also

class SimplicialLDLT

Definition at line 243 of file SimplicialCholesky.h.

Constructor & Destructor Documentation

template<typename _MatrixType , int _UpLo>

Eigen::SimplicialLLT< _MatrixType, _UpLo >::SimplicialLLT ( )

inline

Default constructor

Definition at line 317 of file SimplicialCholesky.h.

: Base() {}

template<typename _MatrixType , int _UpLo>

Eigen::SimplicialLLT< _MatrixType, _UpLo >::SimplicialLLT ( const MatrixType &  matrix )

inline

Constructs and performs the LLT factorization of matrix

Definition at line 319 of file SimplicialCholesky.h.

        : Base(matrix) {}

Member Function Documentation

template<typename _MatrixType , int _UpLo>

void Eigen::SimplicialLLT< _MatrixType, _UpLo >::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 347 of file SimplicialCholesky.h.

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

template<typename _MatrixType , int _UpLo>

SimplicialLLT& Eigen::SimplicialLLT< _MatrixType, _UpLo >::compute ( const MatrixType &  matrix )

inline

Computes the sparse Cholesky decomposition of matrix

Definition at line 335 of file SimplicialCholesky.h.

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

template<typename _MatrixType , int _UpLo>

Scalar Eigen::SimplicialLLT< _MatrixType, _UpLo >::determinant ( ) const

inline

Returns

the determinant of the underlying matrix from the current factorization

Definition at line 364 of file SimplicialCholesky.h.

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

template<typename _MatrixType , int _UpLo>

void Eigen::SimplicialLLT< _MatrixType, _UpLo >::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 358 of file SimplicialCholesky.h.

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

template<typename _MatrixType , int _UpLo>

const MatrixL Eigen::SimplicialLLT< _MatrixType, _UpLo >::matrixL ( ) const

inline

Returns

an expression of the factor L

Definition at line 323 of file SimplicialCholesky.h.

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

template<typename _MatrixType , int _UpLo>

const MatrixU Eigen::SimplicialLLT< _MatrixType, _UpLo >::matrixU ( ) const

inline

Returns

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

Definition at line 329 of file SimplicialCholesky.h.

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

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

• C:/Users/Brig/Documents/ShapeWorksStudio/src/Surfworks/Eigen/src/SparseCholesky/SimplicialCholesky.h