Robust Cholesky decomposition of a matrix with pivoting.
- Parameters:
-
| 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.
- See also:
- MatrixBase::ldlt(), class LLT
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 |
using the current decomposition of A.