Public Types | Public Member Functions | Protected Attributes | List of all members
Eigen::LDLT< _MatrixType, _UpLo > Class Template Reference

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, MaxRowsAtCompileTimePermutationType
 
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, UpLoTraits
 
typedef Transpositions< RowsAtCompileTime, MaxRowsAtCompileTimeTranspositionType
 

Public Member Functions

Index cols () const
 
LDLTcompute (const MatrixType &matrix)
 
ComputationInfo info () const
 Reports whether previous computation was successful. More...
 
bool isNegative (void) const
 
bool isPositive () const
 
 LDLT ()
 Default Constructor. More...
 
 LDLT (Index size)
 Default Constructor with memory preallocation. More...
 
 LDLT (const MatrixType &matrix)
 Constructor with decomposition. More...
 
Traits::MatrixL matrixL () const
 
const MatrixTypematrixLDLT () const
 
Traits::MatrixU matrixU () const
 
template<typename Derived >
LDLTrankUpdate (const MatrixBase< Derived > &w, const RealScalar &alpha=1)
 
template<typename Derived >
LDLT< MatrixType, _UpLo > & rankUpdate (const MatrixBase< Derived > &w, const typename NumTraits< typename MatrixType::Scalar >::Real &sigma)
 
MatrixType reconstructedMatrix () const
 
Index rows () const
 
void setZero ()
 
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 TranspositionTypetranspositionsP () const
 
Diagonal< const MatrixTypevectorD () 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 Eigen::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
UpLothe triangular part that will be used for the decompositon: Lower (default) or Upper. The other triangular part won't be read.

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 45 of file LDLT.h.

Member Typedef Documentation

template<typename _MatrixType, int _UpLo>
typedef MatrixType::Index Eigen::LDLT< _MatrixType, _UpLo >::Index

Definition at line 59 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
typedef _MatrixType Eigen::LDLT< _MatrixType, _UpLo >::MatrixType

Definition at line 48 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> Eigen::LDLT< _MatrixType, _UpLo >::PermutationType

Definition at line 63 of file LDLT.h.

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

Definition at line 58 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
typedef MatrixType::Scalar Eigen::LDLT< _MatrixType, _UpLo >::Scalar

Definition at line 57 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
typedef Matrix<Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1> Eigen::LDLT< _MatrixType, _UpLo >::TmpMatrixType

Definition at line 60 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
typedef internal::LDLT_Traits<MatrixType,UpLo> Eigen::LDLT< _MatrixType, _UpLo >::Traits

Definition at line 65 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> Eigen::LDLT< _MatrixType, _UpLo >::TranspositionType

Definition at line 62 of file LDLT.h.

Member Enumeration Documentation

template<typename _MatrixType, int _UpLo>
anonymous enum
Enumerator
RowsAtCompileTime 
ColsAtCompileTime 
Options 
MaxRowsAtCompileTime 
MaxColsAtCompileTime 
UpLo 

Definition at line 49 of file LDLT.h.

Constructor & Destructor Documentation

template<typename _MatrixType, int _UpLo>
Eigen::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 72 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
Eigen::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 80 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
Eigen::LDLT< _MatrixType, _UpLo >::LDLT ( const MatrixType matrix)
inline

Constructor with decomposition.

This calculates the decomposition for the input matrix.

See also
LDLT(Index size)

Definition at line 92 of file LDLT.h.

Member Function Documentation

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

Definition at line 214 of file LDLT.h.

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

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

Definition at line 437 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
ComputationInfo Eigen::LDLT< _MatrixType, _UpLo >::info ( ) const
inline

Reports whether previous computation was successful.

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

Definition at line 221 of file LDLT.h.

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

Definition at line 153 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
bool Eigen::LDLT< _MatrixType, _UpLo >::isPositive ( ) const
inline
Returns
true if the matrix is positive (semidefinite)

Definition at line 139 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
Traits::MatrixL Eigen::LDLT< _MatrixType, _UpLo >::matrixL ( ) const
inline
Returns
a view of the lower triangular matrix L

Definition at line 117 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
const MatrixType& Eigen::LDLT< _MatrixType, _UpLo >::matrixLDLT ( ) const
inline
Returns
the internal LDLT decomposition matrix

TODO: document the storage layout

Definition at line 205 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
Traits::MatrixU Eigen::LDLT< _MatrixType, _UpLo >::matrixU ( ) const
inline
Returns
a view of the upper triangular matrix U

Definition at line 110 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
template<typename Derived >
LDLT& Eigen::LDLT< _MatrixType, _UpLo >::rankUpdate ( const MatrixBase< Derived > &  w,
const RealScalar alpha = 1 
)
template<typename _MatrixType, int _UpLo>
template<typename Derived >
LDLT<MatrixType,_UpLo>& Eigen::LDLT< _MatrixType, _UpLo >::rankUpdate ( const MatrixBase< Derived > &  w,
const typename NumTraits< typename MatrixType::Scalar >::Real &  sigma 
)

Update the LDLT decomposition: given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T.

Parameters
wa vector to be incorporated into the decomposition.
sigmaa scalar, +1 for updates and -1 for "downdates," which correspond to removing previously-added column vectors. Optional; default value is +1.
See also
setZero()

Definition at line 461 of file LDLT.h.

template<typename MatrixType , int _UpLo>
MatrixType Eigen::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 557 of file LDLT.h.

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

Definition at line 213 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
void Eigen::LDLT< _MatrixType, _UpLo >::setZero ( )
inline

Clear any existing decomposition

See also
rankUpdate(w,sigma)

Definition at line 104 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
template<typename Rhs >
const internal::solve_retval<LDLT, Rhs> Eigen::LDLT< _MatrixType, _UpLo >::solve ( const MatrixBase< Rhs > &  b) const
inline
Returns
a solution x of $ A x = b $ using the current decomposition of A.

This function also supports in-place solves using the syntax x = decompositionObject.solve(x) .

More precisely, this method solves $ A x = b $ using the decomposition $ A = P^T L D L^* P $ by solving the systems $ P^T y_1 = b $, $ L y_2 = y_1 $, $ D y_3 = y_2 $, $ L^* y_4 = y_3 $ and $ P x = y_4 $ in succession. If the matrix $ A $ is singular, then $ D $ will also be singular (all the other matrices are invertible). In that case, the least-square solution of $ D y_3 = y_2 $ is computed. This does not mean that this function computes the least-square solution of $ A x = b $ is $ A $ is singular.

See also
MatrixBase::ldlt()

Definition at line 176 of file LDLT.h.

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

Definition at line 543 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
const TranspositionType& Eigen::LDLT< _MatrixType, _UpLo >::transpositionsP ( ) const
inline
Returns
the permutation matrix P as a transposition sequence.

Definition at line 125 of file LDLT.h.

template<typename _MatrixType, int _UpLo>
Diagonal<const MatrixType> Eigen::LDLT< _MatrixType, _UpLo >::vectorD ( ) const
inline
Returns
the coefficients of the diagonal matrix D

Definition at line 132 of file LDLT.h.

Member Data Documentation

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

Definition at line 239 of file LDLT.h.

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

Definition at line 235 of file LDLT.h.

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

Definition at line 238 of file LDLT.h.

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

Definition at line 237 of file LDLT.h.

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

Definition at line 236 of file LDLT.h.


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


acado
Author(s): Milan Vukov, Rien Quirynen
autogenerated on Mon Jun 10 2019 12:35:35