A direct sparse LDLT Cholesky factorizations without square root. More...
#include <SimplicialCholesky.h>
Public Types | |
| enum | { UpLo = _UpLo } |
| typedef SimplicialCholeskyBase < SimplicialLDLT > | Base |
| typedef SparseMatrix< Scalar, ColMajor, Index > | CholMatrixType |
| typedef MatrixType::Index | Index |
| typedef Traits::MatrixL | MatrixL |
| typedef _MatrixType | MatrixType |
| typedef Traits::MatrixU | MatrixU |
| typedef MatrixType::RealScalar | RealScalar |
| typedef MatrixType::Scalar | Scalar |
| typedef internal::traits < SimplicialLDLT > | Traits |
| typedef Matrix< Scalar, Dynamic, 1 > | VectorType |
Public Member Functions | |
| void | analyzePattern (const MatrixType &a) |
| SimplicialLDLT & | compute (const MatrixType &matrix) |
| Scalar | determinant () const |
| void | factorize (const MatrixType &a) |
| const MatrixL | matrixL () const |
| const MatrixU | matrixU () const |
| SimplicialLDLT () | |
| SimplicialLDLT (const MatrixType &matrix) | |
| const VectorType | vectorD () const |
Detailed Description
template<typename _MatrixType, int _UpLo, typename _Ordering>
class Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >
A direct sparse LDLT Cholesky factorizations without square root.
This class provides a LDL^T Cholesky factorizations without square root of sparse matrices that are selfadjoint and positive definite. The factorization allows for solving A.X = B where X and B can be either dense or sparse.
In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization such that the factorized matrix is P A P^-1.
- Template Parameters:
-
_MatrixType the type of the sparse matrix A, it must be a SparseMatrix<> _UpLo the triangular part that will be used for the computations. It can be Lower or Upper. Default is Lower. _Ordering The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<>
- See also:
- class SimplicialLLT, class AMDOrdering, class NaturalOrdering
Definition at line 395 of file SimplicialCholesky.h.
Member Typedef Documentation
| typedef SimplicialCholeskyBase<SimplicialLDLT> Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::Base |
Definition at line 400 of file SimplicialCholesky.h.
| typedef SparseMatrix<Scalar,ColMajor,Index> Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::CholMatrixType |
Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >.
Definition at line 404 of file SimplicialCholesky.h.
| typedef MatrixType::Index Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::Index |
Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >.
Definition at line 403 of file SimplicialCholesky.h.
| typedef Traits::MatrixL Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::MatrixL |
Definition at line 407 of file SimplicialCholesky.h.
| typedef _MatrixType Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::MatrixType |
Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >.
Definition at line 398 of file SimplicialCholesky.h.
| typedef Traits::MatrixU Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::MatrixU |
Definition at line 408 of file SimplicialCholesky.h.
| typedef MatrixType::RealScalar Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::RealScalar |
Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >.
Definition at line 402 of file SimplicialCholesky.h.
| typedef MatrixType::Scalar Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::Scalar |
Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >.
Definition at line 401 of file SimplicialCholesky.h.
| typedef internal::traits<SimplicialLDLT> Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::Traits |
Definition at line 406 of file SimplicialCholesky.h.
| typedef Matrix<Scalar,Dynamic,1> Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::VectorType |
Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >.
Definition at line 405 of file SimplicialCholesky.h.
Member Enumeration Documentation
| anonymous enum |
Definition at line 399 of file SimplicialCholesky.h.
Constructor & Destructor Documentation
| Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::SimplicialLDLT | ( | ) | [inline] |
Default constructor
Definition at line 411 of file SimplicialCholesky.h.
| Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::SimplicialLDLT | ( | const MatrixType & | matrix | ) | [inline] |
Constructs and performs the LLT factorization of matrix
Definition at line 414 of file SimplicialCholesky.h.
Member Function Documentation
| void Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::analyzePattern | ( | const MatrixType & | a | ) | [inline] |
Performs a symbolic decomposition on the sparcity of matrix.
This function is particularly useful when solving for several problems having the same structure.
- See also:
- factorize()
Definition at line 447 of file SimplicialCholesky.h.
| SimplicialLDLT& Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::compute | ( | const MatrixType & | matrix | ) | [inline] |
Computes the sparse Cholesky decomposition of matrix
Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >.
Definition at line 435 of file SimplicialCholesky.h.
| Scalar Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::determinant | ( | ) | const [inline] |
- Returns:
- the determinant of the underlying matrix from the current factorization
Definition at line 464 of file SimplicialCholesky.h.
| void Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::factorize | ( | const MatrixType & | a | ) | [inline] |
Performs a numeric decomposition of matrix
The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
- See also:
- analyzePattern()
Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >.
Definition at line 458 of file SimplicialCholesky.h.
| const MatrixL Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::matrixL | ( | ) | const [inline] |
- Returns:
- an expression of the factor L
Definition at line 423 of file SimplicialCholesky.h.
| const MatrixU Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::matrixU | ( | ) | const [inline] |
- Returns:
- an expression of the factor U (= L^*)
Definition at line 429 of file SimplicialCholesky.h.
| const VectorType Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::vectorD | ( | ) | const [inline] |
- Returns:
- a vector expression of the diagonal D
Definition at line 418 of file SimplicialCholesky.h.
The documentation for this class was generated from the following file: