LDLT< _MatrixType, _UpLo > Class Template Reference

Robust Cholesky decomposition of a matrix with pivoting. More...

#include <LDLT.h>

List of all members.

Public Types
enum	{   RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, Options = MatrixType::Options & ~RowMajorBit, MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,   MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, UpLo = _UpLo }
typedef _MatrixType	MatrixType
typedef MatrixType::Scalar	Scalar
typedef NumTraits< typename MatrixType::Scalar >::Real	RealScalar
typedef MatrixType::Index	Index
typedef Matrix< Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1 >	TmpMatrixType
typedef Transpositions < RowsAtCompileTime, MaxRowsAtCompileTime >	TranspositionType
typedef PermutationMatrix < RowsAtCompileTime, MaxRowsAtCompileTime >	PermutationType
typedef internal::LDLT_Traits < MatrixType, UpLo >	Traits
Public Member Functions
	LDLT ()
	Default Constructor.
	LDLT (Index size)
	Default Constructor with memory preallocation.
	LDLT (const MatrixType &matrix)
Traits::MatrixU	matrixU () const
Traits::MatrixL	matrixL () const
const TranspositionType &	transpositionsP () const
Diagonal< const MatrixType >	vectorD (void) const
bool	isPositive (void) const
bool	isNegative (void) const
template<typename Rhs >
const internal::solve_retval < LDLT, Rhs >	solve (const MatrixBase< Rhs > &b) const
template<typename Derived >
bool	solveInPlace (MatrixBase< Derived > &bAndX) const
LDLT &	compute (const MatrixType &matrix)
const MatrixType &	matrixLDLT () const
MatrixType	reconstructedMatrix () const
Index	rows () const
Index	cols () const
Protected Attributes
MatrixType	m_matrix
TranspositionType	m_transpositions
TmpMatrixType	m_temporary
int	m_sign
bool	m_isInitialized

---

Detailed Description

template<typename _MatrixType, int _UpLo>
class LDLT< _MatrixType, _UpLo >

Robust Cholesky decomposition of a matrix with pivoting.

Parameters:

MatrixType

the type of the matrix of which to compute the LDL^T Cholesky decomposition

Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite matrix such that , where P is a permutation matrix, L is lower triangular with a unit diagonal and D is a diagonal matrix.

The decomposition uses pivoting to ensure stability, so that L will have zeros in the bottom right rank(A) - n submatrix. Avoiding the square root on D also stabilizes the computation.

Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky decomposition to determine whether a system of equations has a solution.

See also:

MatrixBase::ldlt(), class LLT

---

Member Typedef Documentation

template<typename _MatrixType, int _UpLo>

typedef MatrixType::Index LDLT< _MatrixType, _UpLo >::Index

template<typename _MatrixType, int _UpLo>

typedef _MatrixType LDLT< _MatrixType, _UpLo >::MatrixType

template<typename _MatrixType, int _UpLo>

typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> LDLT< _MatrixType, _UpLo >::PermutationType

template<typename _MatrixType, int _UpLo>

typedef NumTraits<typename MatrixType::Scalar>::Real LDLT< _MatrixType, _UpLo >::RealScalar

template<typename _MatrixType, int _UpLo>

typedef MatrixType::Scalar LDLT< _MatrixType, _UpLo >::Scalar

template<typename _MatrixType, int _UpLo>

typedef Matrix<Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1> LDLT< _MatrixType, _UpLo >::TmpMatrixType

template<typename _MatrixType, int _UpLo>

typedef internal::LDLT_Traits<MatrixType,UpLo> LDLT< _MatrixType, _UpLo >::Traits

template<typename _MatrixType, int _UpLo>

typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> LDLT< _MatrixType, _UpLo >::TranspositionType

---

Member Enumeration Documentation

template<typename _MatrixType, int _UpLo>

anonymous enum

Enumerator:

RowsAtCompileTime
ColsAtCompileTime
Options
MaxRowsAtCompileTime
MaxColsAtCompileTime
UpLo

---

Constructor & Destructor Documentation

template<typename _MatrixType, int _UpLo>

LDLT< _MatrixType, _UpLo >::LDLT

(

)

[inline]

Default Constructor.

The default constructor is useful in cases in which the user intends to perform decompositions via LDLT::compute(const MatrixType&).

template<typename _MatrixType, int _UpLo>

LDLT< _MatrixType, _UpLo >::LDLT

(

Index

size

)

[inline]

Default Constructor with memory preallocation.

Like the default constructor but with preallocation of the internal data according to the specified problem size.

See also:

LDLT()

template<typename _MatrixType, int _UpLo>

LDLT< _MatrixType, _UpLo >::LDLT

(

const MatrixType &

matrix

)

[inline]

---

Member Function Documentation

template<typename _MatrixType, int _UpLo>

Index LDLT< _MatrixType, _UpLo >::cols

(

)

const [inline]

template<typename MatrixType , int _UpLo>

LDLT< MatrixType, _UpLo > & LDLT< MatrixType, _UpLo >::compute

(

const MatrixType &

a

)

Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of matrix

template<typename _MatrixType, int _UpLo>

bool LDLT< _MatrixType, _UpLo >::isNegative

(

void

)

const [inline]

Returns:

true if the matrix is negative (semidefinite)

template<typename _MatrixType, int _UpLo>

bool LDLT< _MatrixType, _UpLo >::isPositive

(

void

)

const [inline]

Returns:

true if the matrix is positive (semidefinite)

template<typename _MatrixType, int _UpLo>

Traits::MatrixL LDLT< _MatrixType, _UpLo >::matrixL

(

)

const [inline]

Returns:

a view of the lower triangular matrix L

template<typename _MatrixType, int _UpLo>

const MatrixType& LDLT< _MatrixType, _UpLo >::matrixLDLT

(

)

const [inline]

Returns:

the internal LDLT decomposition matrix

TODO: document the storage layout

template<typename _MatrixType, int _UpLo>

Traits::MatrixU LDLT< _MatrixType, _UpLo >::matrixU

(

)

const [inline]

Returns:

a view of the upper triangular matrix U

template<typename MatrixType , int _UpLo>

MatrixType LDLT< MatrixType, _UpLo >::reconstructedMatrix

(

)

const

Returns:

the matrix represented by the decomposition, i.e., it returns the product: P^T L D L^* P. This function is provided for debug purpose.

template<typename _MatrixType, int _UpLo>

Index LDLT< _MatrixType, _UpLo >::rows

(

)

const [inline]

template<typename _MatrixType, int _UpLo>

template<typename Rhs >

const internal::solve_retval<LDLT, Rhs> LDLT< _MatrixType, _UpLo >::solve

(

const MatrixBase< Rhs > &

b

)

const [inline]

Returns:

a solution x of using the current decomposition of A.

See also:

solveInPlace(), MatrixBase::ldlt()

template<typename MatrixType , int _UpLo>

template<typename Derived >

bool LDLT< MatrixType, _UpLo >::solveInPlace

(

MatrixBase< Derived > &

bAndX

)

const

template<typename _MatrixType, int _UpLo>

const TranspositionType& LDLT< _MatrixType, _UpLo >::transpositionsP

(

)

const [inline]

Returns:

the permutation matrix P as a transposition sequence.

template<typename _MatrixType, int _UpLo>

Diagonal<const MatrixType> LDLT< _MatrixType, _UpLo >::vectorD

(

void

)

const [inline]

Returns:

the coefficients of the diagonal matrix D

---

Member Data Documentation

template<typename _MatrixType, int _UpLo>

bool LDLT< _MatrixType, _UpLo >::m_isInitialized [protected]

template<typename _MatrixType, int _UpLo>

MatrixType LDLT< _MatrixType, _UpLo >::m_matrix [protected]

template<typename _MatrixType, int _UpLo>

int LDLT< _MatrixType, _UpLo >::m_sign [protected]

template<typename _MatrixType, int _UpLo>

TmpMatrixType LDLT< _MatrixType, _UpLo >::m_temporary [protected]

template<typename _MatrixType, int _UpLo>

TranspositionType LDLT< _MatrixType, _UpLo >::m_transpositions [protected]

---

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

• /home/hauberg/Dokumenter/Capture/humim-tracker-0.1/src/ntk/geometry/Eigen/src/Cholesky/LDLT.h