Eigen::SparseLDLT< _MatrixType, Backend > Class Template Reference

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Detailed Description

template<typename _MatrixType, typename Backend = DefaultBackend>
class Eigen::SparseLDLT< _MatrixType, Backend >

LDLT Cholesky decomposition of a sparse matrix and associated features.

Parameters:

MatrixType

the type of the matrix of which we are computing the LDLT Cholesky decomposition

Warning:

the upper triangular part has to be specified. The rest of the matrix is not used. The input matrix must be column major.

See also:

class LDLT, class LDLT

Definition at line 80 of file SparseExtra.

Inheritance diagram for Eigen::SparseLDLT< _MatrixType, Backend >:

List of all members.

Public Types
typedef SparseMatrix< Scalar >	CholMatrixType
typedef _MatrixType	MatrixType
typedef MatrixType::Index	Index
Public Member Functions
	SparseLDLT (int flags=0)
	Creates a dummy LDLT factorization object with flags flags.
	SparseLDLT (const MatrixType &matrix, int flags=0)
	Creates a LDLT object and compute the respective factorization of matrix using flags flags.
void	setPrecision (RealScalar v)
	Sets the relative threshold value used to prune zero coefficients during the decomposition.
RealScalar	precision () const
void	settags (int f)
	Sets the flags.
int	flags () const
void	compute (const MatrixType &matrix)
	Computes/re-computes the LDLT factorization.
void	_symbolic (const MatrixType &matrix)
	Perform a symbolic factorization.
bool	_numeric (const MatrixType &matrix)
	Perform the actual factorization using the previously computed symbolic factorization.
const CholMatrixType &	matrixL (void) const
VectorType	vectorD (void) const
template<typename Derived >
bool	solveInPlace (MatrixBase< Derived > &b) const
	Computes b = L^-T D^-1 L^-1 b.
template<typename Rhs >
const internal::solve_retval < SparseLDLT< MatrixType > , Rhs >	solve (const MatrixBase< Rhs > &b) const
Index	cols () const
Index	rows () const
const VectorType &	diag () const
bool	succeeded (void) const
Protected Types
enum	{ SupernodalFactorIsDirty = 0x10000, MatrixLIsDirty = 0x20000 }
typedef _MatrixType::Scalar	Scalar
typedef NumTraits< typename _MatrixType::Scalar >::Real	RealScalar
typedef Matrix< Scalar, _MatrixType::ColsAtCompileTime, 1 >	VectorType
Protected Attributes
CholMatrixType	m_matrix
VectorType	m_diag
VectorXi	m_parent
VectorXi	m_nonZerosPerCol
PermutationMatrix< Dynamic >	m_P
PermutationMatrix< Dynamic >	m_Pinv
RealScalar	m_precision
int	m_flags
int	m_status
bool	m_succeeded

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Member Typedef Documentation

template<typename _MatrixType, typename Backend = DefaultBackend>

typedef SparseMatrix<Scalar> Eigen::SparseLDLT< _MatrixType, Backend >::CholMatrixType

Definition at line 94 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

typedef MatrixType::Index Eigen::SparseLDLT< _MatrixType, Backend >::Index

Reimplemented in Eigen::SparseLDLT< _MatrixType, Cholmod >.

Definition at line 96 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

typedef _MatrixType Eigen::SparseLDLT< _MatrixType, Backend >::MatrixType

Reimplemented in Eigen::SparseLDLT< _MatrixType, Cholmod >.

Definition at line 95 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

typedef NumTraits<typename _MatrixType::Scalar>::Real Eigen::SparseLDLT< _MatrixType, Backend >::RealScalar [protected]

Reimplemented in Eigen::SparseLDLT< _MatrixType, Cholmod >.

Definition at line 84 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

typedef _MatrixType::Scalar Eigen::SparseLDLT< _MatrixType, Backend >::Scalar [protected]

Reimplemented in Eigen::SparseLDLT< _MatrixType, Cholmod >.

Definition at line 83 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

typedef Matrix<Scalar,_MatrixType::ColsAtCompileTime,1> Eigen::SparseLDLT< _MatrixType, Backend >::VectorType [protected]

Definition at line 86 of file SparseExtra.

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Member Enumeration Documentation

template<typename _MatrixType, typename Backend = DefaultBackend>

anonymous enum [protected]

Enumerator:

SupernodalFactorIsDirty
MatrixLIsDirty

Definition at line 88 of file SparseExtra.

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Constructor & Destructor Documentation

template<typename _MatrixType, typename Backend = DefaultBackend>

Eigen::SparseLDLT< _MatrixType, Backend >::SparseLDLT

(

int

flags = 0

)

[inline]

Creates a dummy LDLT factorization object with flags flags.

Reimplemented in Eigen::SparseLDLT< _MatrixType, Cholmod >.

Definition at line 100 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

Eigen::SparseLDLT< _MatrixType, Backend >::SparseLDLT	(	const MatrixType &	matrix,
		int	flags = 0
	)		[inline]

Creates a LDLT object and compute the respective factorization of matrix using flags flags.

Reimplemented in Eigen::SparseLDLT< _MatrixType, Cholmod >.

Definition at line 109 of file SparseExtra.

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Member Function Documentation

template<typename _MatrixType , typename Backend >

bool Eigen::SparseLDLT< _MatrixType, Backend >::_numeric

(

const MatrixType &

matrix

)

Perform the actual factorization using the previously computed symbolic factorization.

Definition at line 306 of file SparseExtra.

template<typename _MatrixType , typename Backend >

void Eigen::SparseLDLT< _MatrixType, Backend >::_symbolic

(

const MatrixType &

matrix

)

Perform a symbolic factorization.

Definition at line 242 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

Index Eigen::SparseLDLT< _MatrixType, Backend >::cols

(

void

)

const [inline]

Reimplemented in Eigen::SparseLDLT< _MatrixType, Cholmod >.

Definition at line 177 of file SparseExtra.

template<typename _MatrixType , typename Backend >

void Eigen::SparseLDLT< _MatrixType, Backend >::compute

(

const MatrixType &

matrix

)

Computes/re-computes the LDLT factorization.

Computes / recomputes the LDLT decomposition of matrix a using the default algorithm.

Reimplemented in Eigen::SparseLDLT< _MatrixType, Cholmod >.

Definition at line 235 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

const VectorType& Eigen::SparseLDLT< _MatrixType, Backend >::diag

(

)

const [inline]

Definition at line 180 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

int Eigen::SparseLDLT< _MatrixType, Backend >::flags

(

)

const [inline]

Returns:

the current flags

Definition at line 149 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

const CholMatrixType& Eigen::SparseLDLT< _MatrixType, Backend >::matrixL

(

void

)

const [inline]

Returns:

the lower triangular matrix L

Reimplemented in Eigen::SparseLDLT< _MatrixType, Cholmod >.

Definition at line 161 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

RealScalar Eigen::SparseLDLT< _MatrixType, Backend >::precision

(

)

const [inline]

Returns:

the current precision.

See also:

setPrecision()

Definition at line 135 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

Index Eigen::SparseLDLT< _MatrixType, Backend >::rows

(

void

)

const [inline]

Reimplemented in Eigen::SparseLDLT< _MatrixType, Cholmod >.

Definition at line 178 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

void Eigen::SparseLDLT< _MatrixType, Backend >::setPrecision

(

RealScalar

v

)

[inline]

Sets the relative threshold value used to prune zero coefficients during the decomposition.

Setting a value greater than zero speeds up computation, and yields to an imcomplete factorization with fewer non zero coefficients. Such approximate factors are especially useful to initialize an iterative solver.

Warning:

if precision is greater that zero, the LDLT factorization is not guaranteed to succeed even if the matrix is positive definite.

Note that the exact meaning of this parameter might depends on the actual backend. Moreover, not all backends support this feature.

See also:

precision()

Definition at line 130 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

void Eigen::SparseLDLT< _MatrixType, Backend >::settags

(

int

f

)

[inline]

Sets the flags.

Possible values are:

• CompleteFactorization
• IncompleteFactorization
• MemoryEfficient (hint to use the memory most efficient method offered by the backend)
• SupernodalMultifrontal (implies a complete factorization if supported by the backend, overloads the MemoryEfficient flags)
• SupernodalLeftLooking (implies a complete factorization if supported by the backend, overloads the MemoryEfficient flags)

See also:

flags()

Definition at line 147 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

template<typename Rhs >

const internal::solve_retval<SparseLDLT<MatrixType>, Rhs> Eigen::SparseLDLT< _MatrixType, Backend >::solve

(

const MatrixBase< Rhs > &

b

)

const [inline]

Reimplemented in Eigen::SparseLDLT< _MatrixType, Cholmod >.

Definition at line 171 of file SparseExtra.

template<typename _MatrixType , typename Backend >

template<typename Derived >

bool Eigen::SparseLDLT< _MatrixType, Backend >::solveInPlace

(

MatrixBase< Derived > &

b

)

const

Computes b = L^-T D^-1 L^-1 b.

Reimplemented in Eigen::SparseLDLT< _MatrixType, Cholmod >.

Definition at line 393 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

bool Eigen::SparseLDLT< _MatrixType, Backend >::succeeded

(

void

)

const [inline]

Returns:

true if the factorization succeeded

Reimplemented in Eigen::SparseLDLT< _MatrixType, Cholmod >.

Definition at line 183 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

VectorType Eigen::SparseLDLT< _MatrixType, Backend >::vectorD

(

void

)

const [inline]

Returns:

the coefficients of the diagonal matrix D

Definition at line 164 of file SparseExtra.

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Member Data Documentation

template<typename _MatrixType, typename Backend = DefaultBackend>

VectorType Eigen::SparseLDLT< _MatrixType, Backend >::m_diag [protected]

Definition at line 187 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

int Eigen::SparseLDLT< _MatrixType, Backend >::m_flags [protected]

Definition at line 194 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

CholMatrixType Eigen::SparseLDLT< _MatrixType, Backend >::m_matrix [protected]

Definition at line 186 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

VectorXi Eigen::SparseLDLT< _MatrixType, Backend >::m_nonZerosPerCol [protected]

Definition at line 189 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

PermutationMatrix<Dynamic> Eigen::SparseLDLT< _MatrixType, Backend >::m_P [protected]

Definition at line 191 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

VectorXi Eigen::SparseLDLT< _MatrixType, Backend >::m_parent [protected]

Definition at line 188 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

PermutationMatrix<Dynamic> Eigen::SparseLDLT< _MatrixType, Backend >::m_Pinv [protected]

Definition at line 192 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

RealScalar Eigen::SparseLDLT< _MatrixType, Backend >::m_precision [protected]

Definition at line 193 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

int Eigen::SparseLDLT< _MatrixType, Backend >::m_status [mutable, protected]

Definition at line 195 of file SparseExtra.

template<typename _MatrixType, typename Backend = DefaultBackend>

bool Eigen::SparseLDLT< _MatrixType, Backend >::m_succeeded [protected]

Definition at line 196 of file SparseExtra.