A direct sparse LLT Cholesky factorizations. More...

#include <SimplicialCholesky.h>

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

Collaboration 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 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

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<>

See also:: class SimplicialLDLT, class AMDOrdering, class NaturalOrdering

Definition at line 330 of file SimplicialCholesky.h.

Member Typedef Documentation

template<typename _MatrixType , int _UpLo, typename _Ordering >

typedef SimplicialCholeskyBase<SimplicialLLT> Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::Base

Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >.

Definition at line 335 of file SimplicialCholesky.h.

template<typename _MatrixType , int _UpLo, typename _Ordering >

typedef SparseMatrix<Scalar,ColMajor,Index> Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::CholMatrixType

Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >.

Definition at line 339 of file SimplicialCholesky.h.

template<typename _MatrixType , int _UpLo, typename _Ordering >

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

Definition at line 342 of file SimplicialCholesky.h.

template<typename _MatrixType , int _UpLo, typename _Ordering >

typedef _MatrixType Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::MatrixType

Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >.

Definition at line 333 of file SimplicialCholesky.h.

template<typename _MatrixType , int _UpLo, typename _Ordering >

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

Definition at line 343 of file SimplicialCholesky.h.

template<typename _MatrixType , int _UpLo, typename _Ordering >

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

Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >.

Definition at line 337 of file SimplicialCholesky.h.

template<typename _MatrixType , int _UpLo, typename _Ordering >

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

Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >.

Definition at line 336 of file SimplicialCholesky.h.

template<typename _MatrixType , int _UpLo, typename _Ordering >

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

Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >.

Definition at line 338 of file SimplicialCholesky.h.

template<typename _MatrixType , int _UpLo, typename _Ordering >

typedef internal::traits<SimplicialLLT> Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::Traits

Definition at line 341 of file SimplicialCholesky.h.

template<typename _MatrixType , int _UpLo, typename _Ordering >

typedef Matrix<Scalar,Dynamic,1> Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::VectorType

Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >.

Definition at line 340 of file SimplicialCholesky.h.

Member Enumeration Documentation

template<typename _MatrixType , int _UpLo, typename _Ordering >

anonymous enum

Enumerator:

UpLo

Definition at line 334 of file SimplicialCholesky.h.

{ UpLo = _UpLo };

Constructor & Destructor Documentation

template<typename _MatrixType , int _UpLo, typename _Ordering >

Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::SimplicialLLT ( ) [inline]

Default constructor

Definition at line 346 of file SimplicialCholesky.h.

: Base() {}

template<typename _MatrixType , int _UpLo, typename _Ordering >

Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::SimplicialLLT ( const MatrixType & matrix ) [inline, explicit]

Constructs and performs the LLT factorization of matrix

Definition at line 348 of file SimplicialCholesky.h.

        : Base(matrix) {}

Member Function Documentation

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 376 of file SimplicialCholesky.h.

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

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

Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >.

Definition at line 364 of file SimplicialCholesky.h.

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

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 393 of file SimplicialCholesky.h.

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

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()

Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >.

Definition at line 387 of file SimplicialCholesky.h.

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

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 352 of file SimplicialCholesky.h.

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

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 358 of file SimplicialCholesky.h.

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

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

SimplicialCholesky.h

Public Types

Public Member Functions

Detailed Description

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

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

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