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LDLT< _MatrixType, _UpLo > Class Template Reference

Detailed Description

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

Robust Cholesky decomposition of a matrix with pivoting.

Parameters:
MatrixTypethe 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.

#include <src/Cholesky/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)
 Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of 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

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.

References LDLT< _MatrixType, _UpLo >::compute().

Member Function Documentation

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

Definition at line 187 of file LDLT.h.

References LDLT< _MatrixType, _UpLo >::m_matrix.

template<typename MatrixType , int _UpLo>
LDLT< MatrixType, _UpLo > & LDLT< MatrixType, _UpLo >::compute ( const MatrixType &  matrix )

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

Definition at line 328 of file LDLT.h.

References eigen_assert, and mrpt::math::size().

Referenced by LDLT< _MatrixType, _UpLo >::LDLT().

template<typename _MatrixType, int _UpLo>
bool LDLT< _MatrixType, _UpLo >::isNegative ( void   ) const [inline]
Returns:
true if the matrix is negative (semidefinite)

Definition at line 147 of file LDLT.h.

References eigen_assert, LDLT< _MatrixType, _UpLo >::m_isInitialized, and LDLT< _MatrixType, _UpLo >::m_sign.

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.

References eigen_assert, LDLT< _MatrixType, _UpLo >::m_isInitialized, and LDLT< _MatrixType, _UpLo >::m_sign.

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.

References eigen_assert, LDLT< _MatrixType, _UpLo >::m_isInitialized, and LDLT< _MatrixType, _UpLo >::m_matrix.

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 178 of file LDLT.h.

References eigen_assert, LDLT< _MatrixType, _UpLo >::m_isInitialized, and LDLT< _MatrixType, _UpLo >::m_matrix.

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.

References eigen_assert, LDLT< _MatrixType, _UpLo >::m_isInitialized, and LDLT< _MatrixType, _UpLo >::m_matrix.

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 404 of file LDLT.h.

References eigen_assert, and mrpt::math::size().

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

Definition at line 186 of file LDLT.h.

References LDLT< _MatrixType, _UpLo >::m_matrix.

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 $ A x = b $ using the current decomposition of A.
See also:
solveInPlace(), MatrixBase::ldlt()

Definition at line 161 of file LDLT.h.

References eigen_assert, LDLT< _MatrixType, _UpLo >::m_isInitialized, and LDLT< _MatrixType, _UpLo >::m_matrix.

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

Definition at line 389 of file LDLT.h.

References eigen_assert, and mrpt::math::size().

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.

References eigen_assert, LDLT< _MatrixType, _UpLo >::m_isInitialized, and LDLT< _MatrixType, _UpLo >::m_transpositions.

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.

References eigen_assert, LDLT< _MatrixType, _UpLo >::m_isInitialized, and LDLT< _MatrixType, _UpLo >::m_matrix.

Member Data Documentation

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

Definition at line 201 of file LDLT.h.

Referenced by LDLT< _MatrixType, _UpLo >::isNegative(), LDLT< _MatrixType, _UpLo >::isPositive(), LDLT< _MatrixType, _UpLo >::matrixL(), LDLT< _MatrixType, _UpLo >::matrixLDLT(), LDLT< _MatrixType, _UpLo >::matrixU(), LDLT< _MatrixType, _UpLo >::solve(), LDLT< _MatrixType, _UpLo >::transpositionsP(), and LDLT< _MatrixType, _UpLo >::vectorD().

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

Definition at line 197 of file LDLT.h.

Referenced by LDLT< _MatrixType, _UpLo >::cols(), LDLT< _MatrixType, _UpLo >::matrixL(), LDLT< _MatrixType, _UpLo >::matrixLDLT(), LDLT< _MatrixType, _UpLo >::matrixU(), LDLT< _MatrixType, _UpLo >::rows(), LDLT< _MatrixType, _UpLo >::solve(), and LDLT< _MatrixType, _UpLo >::vectorD().

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

Definition at line 200 of file LDLT.h.

Referenced by LDLT< _MatrixType, _UpLo >::isNegative(), and LDLT< _MatrixType, _UpLo >::isPositive().

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

Definition at line 199 of file LDLT.h.

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

Definition at line 198 of file LDLT.h.

Referenced by LDLT< _MatrixType, _UpLo >::transpositionsP().



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