Public Types | Public Member Functions | Protected Attributes
Eigen::LLT< _MatrixType, _UpLo > Class Template Reference

Standard Cholesky decomposition (LL^T) of a matrix and associated features. More...

#include <LLT.h>

List of all members.

Public Types

enum  { RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, Options = MatrixType::Options, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }
enum  { PacketSize = internal::packet_traits<Scalar>::size, AlignmentMask = int(PacketSize)-1, UpLo = _UpLo }
typedef MatrixType::Index Index
typedef _MatrixType MatrixType
typedef NumTraits< typename
MatrixType::Scalar >::Real 
RealScalar
typedef MatrixType::Scalar Scalar
typedef internal::LLT_Traits
< MatrixType, UpLo
Traits

Public Member Functions

Index cols () const
LLTcompute (const MatrixType &matrix)
ComputationInfo info () const
 Reports whether previous computation was successful.
 LLT ()
 Default Constructor.
 LLT (Index size)
 Default Constructor with memory preallocation.
 LLT (const MatrixType &matrix)
Traits::MatrixL matrixL () const
const MatrixTypematrixLLT () const
Traits::MatrixU matrixU () const
template<typename VectorType >
LLT rankUpdate (const VectorType &vec, const RealScalar &sigma=1)
MatrixType reconstructedMatrix () const
Index rows () const
template<typename Rhs >
const internal::solve_retval
< LLT, Rhs > 
solve (const MatrixBase< Rhs > &b) const
template<typename Derived >
void solveInPlace (MatrixBase< Derived > &bAndX) const

Protected Attributes

ComputationInfo m_info
bool m_isInitialized
MatrixType m_matrix

Detailed Description

template<typename _MatrixType, int _UpLo>
class Eigen::LLT< _MatrixType, _UpLo >

Standard Cholesky decomposition (LL^T) of a matrix and associated features.

Parameters:
MatrixTypethe type of the matrix of which we are computing the LL^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.

This class performs a LL^T Cholesky decomposition of a symmetric, positive definite matrix A such that A = LL^* = U^*U, where L is lower triangular.

While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b, for that purpose, we recommend the Cholesky decomposition without square root which is more stable and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other situations like generalised eigen problems with hermitian matrices.

Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices, use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations has a solution.

Example:

Output:

See also:
MatrixBase::llt(), class LDLT

Definition at line 50 of file LLT.h.


Member Typedef Documentation

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

Definition at line 62 of file LLT.h.

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

Definition at line 53 of file LLT.h.

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

Definition at line 61 of file LLT.h.

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

Definition at line 60 of file LLT.h.

template<typename _MatrixType, int _UpLo>
typedef internal::LLT_Traits<MatrixType,UpLo> Eigen::LLT< _MatrixType, _UpLo >::Traits

Definition at line 70 of file LLT.h.


Member Enumeration Documentation

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

Definition at line 54 of file LLT.h.

template<typename _MatrixType, int _UpLo>
anonymous enum
Enumerator:
PacketSize 
AlignmentMask 
UpLo 

Definition at line 64 of file LLT.h.


Constructor & Destructor Documentation

template<typename _MatrixType, int _UpLo>
Eigen::LLT< _MatrixType, _UpLo >::LLT ( ) [inline]

Default Constructor.

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

Definition at line 78 of file LLT.h.

template<typename _MatrixType, int _UpLo>
Eigen::LLT< _MatrixType, _UpLo >::LLT ( 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:
LLT()

Definition at line 86 of file LLT.h.

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

Definition at line 89 of file LLT.h.


Member Function Documentation

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

Definition at line 171 of file LLT.h.

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

Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of matrix

Returns:
a reference to *this

Example:

Output:

Definition at line 385 of file LLT.h.

template<typename _MatrixType, int _UpLo>
ComputationInfo Eigen::LLT< _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 164 of file LLT.h.

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

Definition at line 104 of file LLT.h.

template<typename _MatrixType, int _UpLo>
const MatrixType& Eigen::LLT< _MatrixType, _UpLo >::matrixLLT ( ) const [inline]
Returns:
the LLT decomposition matrix

TODO: document the storage layout

Definition at line 150 of file LLT.h.

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

Definition at line 97 of file LLT.h.

template<typename _MatrixType , int _UpLo>
template<typename VectorType >
LLT< _MatrixType, _UpLo > Eigen::LLT< _MatrixType, _UpLo >::rankUpdate ( const VectorType &  v,
const RealScalar sigma = 1 
)

Performs a rank one update (or dowdate) of the current decomposition. If A = LL^* before the rank one update, then after it we have LL^* = A + sigma * v v^* where v must be a vector of same dimension.

Definition at line 406 of file LLT.h.

template<typename MatrixType , int _UpLo>
MatrixType Eigen::LLT< MatrixType, _UpLo >::reconstructedMatrix ( ) const
Returns:
the matrix represented by the decomposition, i.e., it returns the product: L L^*. This function is provided for debug purpose.

Definition at line 462 of file LLT.h.

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

Definition at line 170 of file LLT.h.

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

Since this LLT class assumes anyway that the matrix A is invertible, the solution theoretically exists and is unique regardless of b.

Example:

Output:

See also:
solveInPlace(), MatrixBase::llt()

Definition at line 122 of file LLT.h.

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

Definition at line 450 of file LLT.h.


Member Data Documentation

template<typename _MatrixType, int _UpLo>
ComputationInfo Eigen::LLT< _MatrixType, _UpLo >::m_info [protected]

Definition at line 183 of file LLT.h.

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

Definition at line 182 of file LLT.h.

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

Definition at line 181 of file LLT.h.


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


acado
Author(s): Milan Vukov, Rien Quirynen
autogenerated on Sat Jun 8 2019 19:40:47