Public Types |
enum | {
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
Options = MatrixType::Options & ~RowMajorBit,
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
UpLo = _UpLo
} |
typedef MatrixType::Index | Index |
typedef _MatrixType | MatrixType |
typedef PermutationMatrix
< RowsAtCompileTime,
MaxRowsAtCompileTime > | PermutationType |
typedef NumTraits< typename
MatrixType::Scalar >::Real | RealScalar |
typedef MatrixType::Scalar | Scalar |
typedef Matrix< Scalar,
RowsAtCompileTime, 1, Options,
MaxRowsAtCompileTime, 1 > | TmpMatrixType |
typedef internal::LDLT_Traits
< MatrixType, UpLo > | Traits |
typedef Transpositions
< RowsAtCompileTime,
MaxRowsAtCompileTime > | TranspositionType |
Public Member Functions |
Index | cols () const |
LDLT & | compute (const MatrixType &matrix) |
bool | isNegative (void) const |
bool | isPositive (void) const |
| LDLT () |
| Default Constructor.
|
| LDLT (Index size) |
| Default Constructor with memory preallocation.
|
| LDLT (const MatrixType &matrix) |
Traits::MatrixL | matrixL () const |
const MatrixType & | matrixLDLT () const |
Traits::MatrixU | matrixU () const |
MatrixType | reconstructedMatrix () const |
Index | rows () 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 |
const TranspositionType & | transpositionsP () const |
Diagonal< const MatrixType > | vectorD (void) const |
Protected Attributes |
bool | m_isInitialized |
MatrixType | m_matrix |
int | m_sign |
TmpMatrixType | m_temporary |
TranspositionType | m_transpositions |
template<typename _MatrixType, int _UpLo>
class LDLT< _MatrixType, _UpLo >
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
Definition at line 59 of file LDLT.h.