Robust Cholesky decomposition of a matrix with pivoting.
| MatrixType | the 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 
such that 
, 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.
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 |
| typedef MatrixType::Index Eigen::LDLT< _MatrixType, _UpLo >::Index |
| typedef _MatrixType Eigen::LDLT< _MatrixType, _UpLo >::MatrixType |
| typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> Eigen::LDLT< _MatrixType, _UpLo >::PermutationType |
| typedef NumTraits<typename MatrixType::Scalar>::Real Eigen::LDLT< _MatrixType, _UpLo >::RealScalar |
| typedef MatrixType::Scalar Eigen::LDLT< _MatrixType, _UpLo >::Scalar |
| typedef Matrix<Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1> Eigen::LDLT< _MatrixType, _UpLo >::TmpMatrixType |
| typedef internal::LDLT_Traits<MatrixType,UpLo> Eigen::LDLT< _MatrixType, _UpLo >::Traits |
| typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> Eigen::LDLT< _MatrixType, _UpLo >::TranspositionType |
| anonymous enum |
| 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&).
| Eigen::LDLT< _MatrixType, _UpLo >::LDLT | ( | Index | size | ) | [inline] |
| Eigen::LDLT< _MatrixType, _UpLo >::LDLT | ( | const MatrixType & | matrix | ) | [inline] |
| Index Eigen::LDLT< _MatrixType, _UpLo >::cols | ( | void | ) | const [inline] |
| LDLT< MatrixType, _UpLo > & LDLT< MatrixType, _UpLo >::compute | ( | const MatrixType & | matrix | ) |
| bool Eigen::LDLT< _MatrixType, _UpLo >::isNegative | ( | void | ) | const [inline] |
| bool Eigen::LDLT< _MatrixType, _UpLo >::isPositive | ( | void | ) | const [inline] |
| Traits::MatrixL Eigen::LDLT< _MatrixType, _UpLo >::matrixL | ( | ) | const [inline] |
| const MatrixType& Eigen::LDLT< _MatrixType, _UpLo >::matrixLDLT | ( | ) | const [inline] |
| Traits::MatrixU Eigen::LDLT< _MatrixType, _UpLo >::matrixU | ( | ) | const [inline] |
| MatrixType LDLT< MatrixType, _UpLo >::reconstructedMatrix | ( | ) | const |
| Index Eigen::LDLT< _MatrixType, _UpLo >::rows | ( | void | ) | const [inline] |
| const internal::solve_retval<LDLT, Rhs> Eigen::LDLT< _MatrixType, _UpLo >::solve | ( | const MatrixBase< Rhs > & | b | ) | const [inline] |
using the current decomposition of A.| bool LDLT< MatrixType, _UpLo >::solveInPlace | ( | MatrixBase< Derived > & | bAndX | ) | const |
| const TranspositionType& Eigen::LDLT< _MatrixType, _UpLo >::transpositionsP | ( | ) | const [inline] |
| Diagonal<const MatrixType> Eigen::LDLT< _MatrixType, _UpLo >::vectorD | ( | void | ) | const [inline] |
bool Eigen::LDLT< _MatrixType, _UpLo >::m_isInitialized [protected] |
MatrixType Eigen::LDLT< _MatrixType, _UpLo >::m_matrix [protected] |
int Eigen::LDLT< _MatrixType, _UpLo >::m_sign [protected] |
TmpMatrixType Eigen::LDLT< _MatrixType, _UpLo >::m_temporary [protected] |
TranspositionType Eigen::LDLT< _MatrixType, _UpLo >::m_transpositions [protected] |
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