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

#include <LDLT.h>

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

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 $ A $ such that $ A = P^TLDL^*P $ , 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

Definition at line 59 of file LDLT.h.

Member Typedef Documentation

template<typename _MatrixType, int _UpLo>

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

Definition at line 73 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

typedef _MatrixType LDLT< _MatrixType, _UpLo >::MatrixType

Definition at line 62 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

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

Definition at line 77 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

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

Definition at line 72 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

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

Definition at line 71 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

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

Definition at line 74 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

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

Definition at line 79 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

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

Definition at line 76 of file LDLT.h.

Member Enumeration Documentation

template<typename _MatrixType, int _UpLo>

anonymous enum

Enumerator:

RowsAtCompileTime
ColsAtCompileTime
Options
MaxRowsAtCompileTime
MaxColsAtCompileTime
UpLo

Definition at line 63 of file LDLT.h.

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&).

Definition at line 86 of file LDLT.h.

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()

Definition at line 94 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

LDLT< _MatrixType, _UpLo >::LDLT ( const MatrixType & matrix ) [inline]

Definition at line 101 of file LDLT.h.

Member Function Documentation

template<typename _MatrixType, int _UpLo>

Index LDLT< _MatrixType, _UpLo >::cols ( ) const [inline]

Definition at line 203 of file LDLT.h.

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

Definition at line 344 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

bool LDLT< _MatrixType, _UpLo >::isNegative ( void ) const [inline]

Returns:: true if the matrix is negative (semidefinite)

Definition at line 154 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

bool LDLT< _MatrixType, _UpLo >::isPositive ( void ) const [inline]

Returns:: true if the matrix is positive (semidefinite)

Definition at line 140 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

Traits::MatrixL LDLT< _MatrixType, _UpLo >::matrixL ( ) const [inline]

Returns:: a view of the lower triangular matrix L

Definition at line 118 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

const MatrixType& LDLT< _MatrixType, _UpLo >::matrixLDLT ( ) const [inline]

Returns:: the internal LDLT decomposition matrix

TODO: document the storage layout

Definition at line 194 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

Traits::MatrixU LDLT< _MatrixType, _UpLo >::matrixU ( ) const [inline]

Returns:: a view of the upper triangular matrix U

Definition at line 111 of file LDLT.h.

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.

Definition at line 420 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

Index LDLT< _MatrixType, _UpLo >::rows ( ) const [inline]

Definition at line 202 of file LDLT.h.

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()

Definition at line 168 of file LDLT.h.

template<typename MatrixType , int _UpLo>

template<typename Derived >

bool LDLT< MatrixType, _UpLo >::solveInPlace ( MatrixBase< Derived > & bAndX ) const

Definition at line 405 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

const TranspositionType& LDLT< _MatrixType, _UpLo >::transpositionsP ( ) const [inline]

Returns:: the permutation matrix P as a transposition sequence.

Definition at line 126 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

Diagonal<const MatrixType> LDLT< _MatrixType, _UpLo >::vectorD ( void ) const [inline]

Returns:: the coefficients of the diagonal matrix D

Definition at line 133 of file LDLT.h.

Member Data Documentation

template<typename _MatrixType, int _UpLo>

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

Definition at line 217 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

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

Definition at line 213 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

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

Definition at line 216 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

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

Definition at line 215 of file LDLT.h.

template<typename _MatrixType, int _UpLo>

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

Definition at line 214 of file LDLT.h.

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

LDLT.h

Public Types

Public Member Functions

Protected Attributes

Detailed Description

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

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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