Detailed Description
template<typename _MatrixType, int _UpLo>
class Eigen::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 60 of file Cholesky.
List of all members.
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 |
Member Typedef Documentation
template<typename _MatrixType , int _UpLo>
template<typename _MatrixType , int _UpLo>
template<typename _MatrixType , int _UpLo>
template<typename _MatrixType , int _UpLo>
template<typename _MatrixType , int _UpLo>
template<typename _MatrixType , int _UpLo>
template<typename _MatrixType , int _UpLo>
template<typename _MatrixType , int _UpLo>
Member Enumeration Documentation
template<typename _MatrixType , int _UpLo>
- Enumerator:
RowsAtCompileTime |
|
ColsAtCompileTime |
|
Options |
|
MaxRowsAtCompileTime |
|
MaxColsAtCompileTime |
|
UpLo |
|
Definition at line 64 of file Cholesky.
Constructor & Destructor Documentation
template<typename _MatrixType , int _UpLo>
template<typename _MatrixType , int _UpLo>
Default Constructor with memory preallocation.
Like the default constructor but with preallocation of the internal data according to the specified problem size.
- See also:
- LDLT()
Definition at line 95 of file Cholesky.
template<typename _MatrixType , int _UpLo>
Member Function Documentation
template<typename _MatrixType , int _UpLo>
template<typename MatrixType , int _UpLo>
Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of matrix.
Definition at line 329 of file Cholesky.
template<typename _MatrixType , int _UpLo>
bool Eigen::LDLT< _MatrixType, _UpLo >::isNegative |
( |
void |
) |
const [inline] |
- Returns:
- true if the matrix is negative (semidefinite)
Definition at line 148 of file Cholesky.
template<typename _MatrixType , int _UpLo>
bool Eigen::LDLT< _MatrixType, _UpLo >::isPositive |
( |
void |
) |
const [inline] |
- Returns:
- true if the matrix is positive (semidefinite)
Definition at line 141 of file Cholesky.
template<typename _MatrixType , int _UpLo>
Traits::MatrixL Eigen::LDLT< _MatrixType, _UpLo >::matrixL |
( |
) |
const [inline] |
- Returns:
- a view of the lower triangular matrix L
Definition at line 119 of file Cholesky.
template<typename _MatrixType , int _UpLo>
- Returns:
- the internal LDLT decomposition matrix
TODO: document the storage layout
Definition at line 179 of file Cholesky.
template<typename _MatrixType , int _UpLo>
Traits::MatrixU Eigen::LDLT< _MatrixType, _UpLo >::matrixU |
( |
) |
const [inline] |
- Returns:
- a view of the upper triangular matrix U
Definition at line 112 of file Cholesky.
template<typename MatrixType , int _UpLo>
- Returns:
- the matrix represented by the decomposition, i.e., it returns the product: P^T L D L^* P. This function is provided for debug purpose.
Definition at line 405 of file Cholesky.
template<typename _MatrixType , int _UpLo>
template<typename _MatrixType , int _UpLo>
template<typename Rhs >
const internal::solve_retval<LDLT, Rhs> Eigen::LDLT< _MatrixType, _UpLo >::solve |
( |
const MatrixBase< Rhs > & |
b ) |
const [inline] |
template<typename MatrixType , int _UpLo>
template<typename Derived >
template<typename _MatrixType , int _UpLo>
- Returns:
- the permutation matrix P as a transposition sequence.
Definition at line 127 of file Cholesky.
template<typename _MatrixType , int _UpLo>
- Returns:
- the coefficients of the diagonal matrix D
Definition at line 134 of file Cholesky.
Member Data Documentation
template<typename _MatrixType , int _UpLo>
template<typename _MatrixType , int _UpLo>
template<typename _MatrixType , int _UpLo>
template<typename _MatrixType , int _UpLo>
template<typename _MatrixType , int _UpLo>