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| enum | {
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
UpLo = _UpLo
} |
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typedef _MatrixType | MatrixType |
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typedef MatrixType::Scalar | Scalar |
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typedef NumTraits< typename MatrixType::Scalar >::Real | RealScalar |
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| typedef Eigen::Index | Index |
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typedef MatrixType::StorageIndex | StorageIndex |
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typedef Matrix< Scalar, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime, 1 > | TmpMatrixType |
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typedef Transpositions< RowsAtCompileTime, MaxRowsAtCompileTime > | TranspositionType |
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typedef PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime > | PermutationType |
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typedef internal::LDLT_Traits< MatrixType, UpLo > | Traits |
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| | LDLT () |
| | Default Constructor. More...
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| | LDLT (Index size) |
| | Default Constructor with memory preallocation. More...
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| template<typename InputType > |
| | LDLT (const EigenBase< InputType > &matrix) |
| | Constructor with decomposition. More...
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| template<typename InputType > |
| | LDLT (EigenBase< InputType > &matrix) |
| | Constructs a LDLT factorization from a given matrix. More...
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| void | setZero () |
| | Clear any existing decomposition. More...
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| Traits::MatrixU | matrixU () const |
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| Traits::MatrixL | matrixL () const |
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| const TranspositionType & | transpositionsP () const |
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| Diagonal< const MatrixType > | vectorD () const |
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| bool | isPositive () const |
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| bool | isNegative (void) const |
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| template<typename Rhs > |
| const Solve< LDLT, Rhs > | solve (const MatrixBase< Rhs > &b) const |
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template<typename Derived > |
| bool | solveInPlace (MatrixBase< Derived > &bAndX) const |
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template<typename InputType > |
| LDLT & | compute (const EigenBase< InputType > &matrix) |
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| RealScalar | rcond () const |
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template<typename Derived > |
| LDLT & | rankUpdate (const MatrixBase< Derived > &w, const RealScalar &alpha=1) |
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| const MatrixType & | matrixLDLT () const |
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| MatrixType | reconstructedMatrix () const |
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| const LDLT & | adjoint () const |
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Index | rows () const |
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Index | cols () const |
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| ComputationInfo | info () const |
| | Reports whether previous computation was successful. More...
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template<typename RhsType , typename DstType > |
| EIGEN_DEVICE_FUNC void | _solve_impl (const RhsType &rhs, DstType &dst) const |
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template<typename InputType > |
| LDLT< MatrixType, _UpLo > & | compute (const EigenBase< InputType > &a) |
| | Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of matrix.
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| template<typename Derived > |
| LDLT< MatrixType, _UpLo > & | rankUpdate (const MatrixBase< Derived > &w, const typename LDLT< MatrixType, _UpLo >::RealScalar &sigma) |
| | Update the LDLT decomposition: given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T. More...
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template<typename RhsType , typename DstType > |
| void | _solve_impl (const RhsType &rhs, DstType &dst) const |
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template<typename _MatrixType, int _UpLo>
class Eigen::LDLT< _MatrixType, _UpLo >
Robust Cholesky decomposition of a matrix with pivoting.
- Template Parameters
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| _MatrixType | the type of the matrix of which to compute the LDL^T Cholesky decomposition |
| _UpLo | the triangular part that will be used for the decompositon: Lower (default) or Upper. The other triangular part won't be read. |
Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite matrix \( A \) such that \( A = P^TLDL^*P \), 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.
This class supports the inplace decomposition mechanism.
- See also
- MatrixBase::ldlt(), SelfAdjointView::ldlt(), class LLT
template<typename _MatrixType, int _UpLo>
template<typename Rhs >
- Returns
- a solution x of \( A x = b \) using the current decomposition of A.
This function also supports in-place solves using the syntax x = decompositionObject.solve(x) .
More precisely, this method solves \( A x = b \) using the decomposition \( A = P^T L D L^* P \) by solving the systems \( P^T y_1 = b \), \( L y_2 = y_1 \), \( D y_3 = y_2 \), \( L^* y_4 = y_3 \) and \( P x = y_4 \) in succession. If the matrix \( A \) is singular, then \( D \) will also be singular (all the other matrices are invertible). In that case, the least-square solution of \( D y_3 = y_2 \) is computed. This does not mean that this function computes the least-square solution of \( A x = b \) is \( A \) is singular.
- See also
- MatrixBase::ldlt(), SelfAdjointView::ldlt()
