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

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

#include <LLT.h>

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
 
LLT & compute (const MatrixType &matrix)
 
ComputationInfo info () const
 Reports whether previous computation was successful. More...
 
 LLT ()
 Default Constructor. More...
 
 LLT (Index size)
 Default Constructor with memory preallocation. More...
 
 LLT (const MatrixType &matrix)
 
Traits::MatrixL matrixL () const
 
const MatrixType & matrixLLT () const
 
Traits::MatrixU matrixU () const
 
template<typename VectorType >
LLT rankUpdate (const VectorType &vec, const RealScalar &sigma=1)
 
template<typename VectorType >
LLT< _MatrixType, _UpLo > rankUpdate (const VectorType &v, const RealScalar &sigma)
 
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 Eigen::LLT< _MatrixType, _UpLo >::rankUpdate 
          (
          const VectorType & 
          vec, 
        

        

          
          
          const RealScalar & 
          sigma = 1 
        

        

          
          )
          
        

      















template<typename _MatrixType, int _UpLo> 



template<typename VectorType > 

      

        

          LLT<_MatrixType,_UpLo> Eigen::LLT< _MatrixType, _UpLo >::rankUpdate 
          (
          const VectorType & 
          v, 
        

        

          
          
          const RealScalar & 
          sigma 
        

        

          
          )
          
        

      




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:







tuw_aruco

Author(s): Lukas Pfeifhofer

autogenerated on Mon Jun 10 2019 15:41:07