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 | MatrixType |
| typedef MatrixType::Scalar | Scalar |
| typedef NumTraits< typename MatrixType::Scalar >::Real | RealScalar |
| typedef MatrixType::Index | Index |
| typedef internal::LLT_Traits < MatrixType, UpLo > | Traits |
Public Member Functions | |
| LLT () | |
| Default Constructor. | |
| LLT (Index size) | |
| Default Constructor with memory preallocation. | |
| LLT (const MatrixType &matrix) | |
| Traits::MatrixU | matrixU () const |
| Traits::MatrixL | matrixL () 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 |
| LLT & | compute (const MatrixType &matrix) |
| const MatrixType & | matrixLLT () const |
| MatrixType | reconstructedMatrix () const |
| ComputationInfo | info () const |
| Reports whether previous computation was successful. | |
| Index | rows () const |
| Index | cols () const |
Protected Attributes | |
| MatrixType | m_matrix |
| bool | m_isInitialized |
| ComputationInfo | m_info |
Detailed Description
template<typename _MatrixType, int _UpLo>
class LLT< _MatrixType, _UpLo >
Standard Cholesky decomposition (LL^T) of a matrix and associated features.
- Parameters:
-
MatrixType the type of the matrix of which we are computing the LL^T Cholesky decomposition
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.
- See also:
- MatrixBase::llt(), class LDLT
Member Typedef Documentation
| typedef MatrixType::Index LLT< _MatrixType, _UpLo >::Index |
| typedef _MatrixType LLT< _MatrixType, _UpLo >::MatrixType |
| typedef NumTraits<typename MatrixType::Scalar>::Real LLT< _MatrixType, _UpLo >::RealScalar |
| typedef MatrixType::Scalar LLT< _MatrixType, _UpLo >::Scalar |
| typedef internal::LLT_Traits<MatrixType,UpLo> LLT< _MatrixType, _UpLo >::Traits |
Member Enumeration Documentation
| anonymous enum |
Constructor & Destructor Documentation
Default Constructor.
The default constructor is useful in cases in which the user intends to perform decompositions via LLT::compute(const MatrixType&).
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()
| LLT< _MatrixType, _UpLo >::LLT | ( | const MatrixType & | matrix | ) | [inline] |
Member Function Documentation
| LLT< MatrixType, _UpLo > & LLT< MatrixType, _UpLo >::compute | ( | const MatrixType & | a | ) |
Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of matrix
- Returns:
- a reference to *this
| ComputationInfo LLT< _MatrixType, _UpLo >::info | ( | ) | const [inline] |
Reports whether previous computation was successful.
- Returns:
Successif computation was succesful,NumericalIssueif the matrix.appears to be negative.
| Traits::MatrixL LLT< _MatrixType, _UpLo >::matrixL | ( | ) | const [inline] |
- Returns:
- a view of the lower triangular matrix L
| const MatrixType& LLT< _MatrixType, _UpLo >::matrixLLT | ( | ) | const [inline] |
- Returns:
- the LLT decomposition matrix
TODO: document the storage layout
| Traits::MatrixU LLT< _MatrixType, _UpLo >::matrixU | ( | ) | const [inline] |
- Returns:
- a view of the upper triangular matrix U
| MatrixType 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.
| const internal::solve_retval<LLT, Rhs> LLT< _MatrixType, _UpLo >::solve | ( | const MatrixBase< Rhs > & | b | ) | const [inline] |
- Returns:
- the solution x of
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()
| void LLT< MatrixType, _UpLo >::solveInPlace | ( | MatrixBase< Derived > & | bAndX | ) | const |
Member Data Documentation
ComputationInfo LLT< _MatrixType, _UpLo >::m_info [protected] |
bool LLT< _MatrixType, _UpLo >::m_isInitialized [protected] |
MatrixType LLT< _MatrixType, _UpLo >::m_matrix [protected] |
The documentation for this class was generated from the following file:
- /home/hauberg/Dokumenter/Capture/humim-tracker-0.1/src/ntk/geometry/Eigen/src/Cholesky/LLT.h
