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

Inheritance diagram for SimplicialLDLt< _MatrixType, _UpLo >:

Public Types
enum
enum	{ UpLo }
typedef SimplicialCholeskyBase < SimplicialLDLt >	Base
typedef SparseMatrix< Scalar, ColMajor, Index >	CholMatrixType
typedef MatrixType::Index	Index
typedef Traits::MatrixL	MatrixL
typedef _MatrixType	MatrixType
typedef Traits::MatrixU	MatrixU
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::Scalar	Scalar
typedef internal::traits < SimplicialLDLt >	Traits
typedef Matrix< Scalar, Dynamic, 1 >	VectorType
Public Member Functions
void	analyzePattern (const MatrixType &a)
Index	cols () const
SimplicialLDLt< _MatrixType, _UpLo > &	compute (const MatrixType &matrix)
SimplicialLDLt< _MatrixType, _UpLo > &	derived ()
const SimplicialLDLt < _MatrixType, _UpLo > &	derived () const
Scalar	determinant () const
void	factorize (const MatrixType &a)
ComputationInfo	info () const
	Reports whether previous computation was successful.
const MatrixL	matrixL () const
const MatrixU	matrixU () const
const PermutationMatrix < Dynamic, Dynamic, Index > &	permutationP () const
const PermutationMatrix < Dynamic, Dynamic, Index > &	permutationPinv () const
Index	rows () const
SimplicialLDLt< _MatrixType, _UpLo > &	setShift (const RealScalar &offset, const RealScalar &scale=1)
	SimplicialLDLt ()
	SimplicialLDLt (const MatrixType &matrix)
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 VectorType	vectorD () const
Protected Member Functions
void	analyzePattern (const MatrixType &a, bool doLDLt)
Protected Attributes
bool	m_analysisIsOk
VectorType	m_diag
bool	m_factorizationIsOk
ComputationInfo	m_info
bool	m_isInitialized
CholMatrixType	m_matrix
VectorXi	m_nonZerosPerCol
PermutationMatrix< Dynamic, Dynamic, Index >	m_P
VectorXi	m_parent
PermutationMatrix< Dynamic, Dynamic, Index >	m_Pinv
RealScalar	m_shiftOffset
RealScalar	m_shiftScale

Detailed Description

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

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.

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 SimplicialLLt

Member Typedef Documentation

typedef SimplicialCholeskyBase<SimplicialLDLt> Base

typedef SparseMatrix<Scalar,ColMajor,Index> CholMatrixType

Reimplemented from SimplicialCholeskyBase< SimplicialLDLt< _MatrixType, _UpLo > >.

typedef MatrixType::Index Index

Reimplemented from SimplicialCholeskyBase< SimplicialLDLt< _MatrixType, _UpLo > >.

typedef Traits::MatrixL MatrixL

typedef _MatrixType MatrixType

Reimplemented from SimplicialCholeskyBase< SimplicialLDLt< _MatrixType, _UpLo > >.

typedef Traits::MatrixU MatrixU

typedef MatrixType::RealScalar RealScalar

Reimplemented from SimplicialCholeskyBase< SimplicialLDLt< _MatrixType, _UpLo > >.

typedef MatrixType::Scalar Scalar

Reimplemented from SimplicialCholeskyBase< SimplicialLDLt< _MatrixType, _UpLo > >.

typedef internal::traits<SimplicialLDLt> Traits

typedef Matrix<Scalar,Dynamic,1> VectorType

Reimplemented from SimplicialCholeskyBase< SimplicialLDLt< _MatrixType, _UpLo > >.

Member Enumeration Documentation

anonymous enum [inherited]

anonymous enum

Enumerator:

UpLo

Constructor & Destructor Documentation

SimplicialLDLt ( ) [inline]

Default constructor

SimplicialLDLt ( const MatrixType & matrix ) [inline]

Constructs and performs the LLt factorization of matrix

Member Function Documentation

void analyzePattern	(	const MatrixType &	a,
		bool	doLDLt
	)		`[protected, inherited]`

void 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()

Index cols ( void ) const [inline, inherited]

SimplicialLDLt< _MatrixType, _UpLo > & compute ( const MatrixType & matrix ) [inline, inherited]

Computes the sparse Cholesky decomposition of matrix

SimplicialLDLt< _MatrixType, _UpLo > & derived ( ) [inline, inherited]

const SimplicialLDLt< _MatrixType, _UpLo > & derived ( ) const [inline, inherited]

Scalar determinant ( ) const [inline]

Returns:: the determinant of the underlying matrix from the current factorization

void 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 SimplicialCholeskyBase< SimplicialLDLt< _MatrixType, _UpLo > >.

ComputationInfo info ( ) const [inline, inherited]

Reports whether previous computation was successful.

Returns:: Success if computation was succesful, NumericalIssue if the matrix.appears to be negative.

const MatrixL matrixL ( ) const [inline]

Returns:: an expression of the factor L

const MatrixU matrixU ( ) const [inline]

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

const PermutationMatrix<Dynamic,Dynamic,Index>& permutationP ( ) const [inline, inherited]

Returns:: the permutation P

See also:: permutationPinv()

const PermutationMatrix<Dynamic,Dynamic,Index>& permutationPinv ( ) const [inline, inherited]

Returns:: the inverse P^-1 of the permutation P

See also:: permutationP()

Index rows ( void ) const [inline, inherited]

SimplicialLDLt< _MatrixType, _UpLo > & setShift	(	const RealScalar &	offset,
		const RealScalar &	scale = `1`
	)		`[inline, inherited]`

Sets the shift parameters that will be used to adjust the diagonal coefficients during the numerical factorization.

During the numerical factorization, the diagonal coefficients are transformed by the following linear model:
d_ii = offset + scale * d_ii

The default is the identity transformation with offset=0, and scale=1.

Returns:: a reference to *this.

const internal::solve_retval<SimplicialCholeskyBase, Rhs> solve ( const MatrixBase< Rhs > & b ) const [inline, inherited]

Returns:: the solution x of using the current decomposition of A.

See also:: compute()

const internal::sparse_solve_retval<SimplicialCholeskyBase, Rhs> solve ( const SparseMatrixBase< Rhs > & b ) const [inline, inherited]

Returns:: the solution x of using the current decomposition of A.

See also:: compute()

const VectorType vectorD ( ) const [inline]

Returns:: a vector expression of the diagonal D

Member Data Documentation

bool m_analysisIsOk [protected, inherited]

VectorType m_diag [protected, inherited]

bool m_factorizationIsOk [protected, inherited]

ComputationInfo m_info [mutable, protected, inherited]

bool m_isInitialized [protected, inherited]

CholMatrixType m_matrix [protected, inherited]

VectorXi m_nonZerosPerCol [protected, inherited]

PermutationMatrix<Dynamic,Dynamic,Index> m_P [protected, inherited]

VectorXi m_parent [protected, inherited]

PermutationMatrix<Dynamic,Dynamic,Index> m_Pinv [protected, inherited]

RealScalar m_shiftOffset [protected, inherited]

RealScalar m_shiftScale [protected, inherited]

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

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

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

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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