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enum | { MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
UpLo = _UpLo
} |
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typedef SolverBase< LDLT > | Base |
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typedef _MatrixType | MatrixType |
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typedef PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime > | PermutationType |
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typedef Matrix< Scalar, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime, 1 > | TmpMatrixType |
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typedef internal::LDLT_Traits< MatrixType, UpLo > | Traits |
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typedef Transpositions< RowsAtCompileTime, MaxRowsAtCompileTime > | TranspositionType |
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enum | |
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typedef internal::conditional< NumTraits< Scalar >::IsComplex, CwiseUnaryOp< internal::scalar_conjugate_op< Scalar >, ConstTransposeReturnType >, ConstTransposeReturnType >::type | AdjointReturnType |
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typedef EigenBase< LDLT< _MatrixType, _UpLo > > | Base |
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typedef Scalar | CoeffReturnType |
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typedef internal::add_const< Transpose< const LDLT< _MatrixType, _UpLo > > >::type | ConstTransposeReturnType |
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typedef internal::traits< LDLT< _MatrixType, _UpLo > >::Scalar | Scalar |
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typedef Eigen::Index | Index |
| The interface type of indices. More...
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typedef internal::traits< LDLT< _MatrixType, _UpLo > >::StorageKind | StorageKind |
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template<typename RhsType , typename DstType > |
void | _solve_impl (const RhsType &rhs, DstType &dst) const |
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template<bool Conjugate, typename RhsType , typename DstType > |
void | _solve_impl_transposed (const RhsType &rhs, DstType &dst) const |
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const LDLT & | adjoint () const |
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EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index | cols () const EIGEN_NOEXCEPT |
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template<typename InputType > |
LDLT< MatrixType, _UpLo > & | compute (const EigenBase< InputType > &a) |
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template<typename InputType > |
LDLT & | compute (const EigenBase< InputType > &matrix) |
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ComputationInfo | info () const |
| Reports whether previous computation was successful. More...
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bool | isNegative (void) const |
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bool | isPositive () const |
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| LDLT () |
| Default Constructor. 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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| LDLT (Index size) |
| Default Constructor with memory preallocation. More...
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Traits::MatrixL | matrixL () const |
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const MatrixType & | matrixLDLT () const |
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Traits::MatrixU | matrixU () const |
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template<typename Derived > |
LDLT & | rankUpdate (const MatrixBase< Derived > &w, const RealScalar &alpha=1) |
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template<typename Derived > |
LDLT< MatrixType, _UpLo > & | rankUpdate (const MatrixBase< Derived > &w, const typename LDLT< MatrixType, _UpLo >::RealScalar &sigma) |
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RealScalar | rcond () const |
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MatrixType | reconstructedMatrix () const |
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EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index | rows () const EIGEN_NOEXCEPT |
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void | setZero () |
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template<typename Derived > |
bool | solveInPlace (MatrixBase< Derived > &bAndX) const |
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const TranspositionType & | transpositionsP () const |
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Diagonal< const MatrixType > | vectorD () const |
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AdjointReturnType | adjoint () const |
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EIGEN_DEVICE_FUNC LDLT< _MatrixType, _UpLo > & | derived () |
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const EIGEN_DEVICE_FUNC LDLT< _MatrixType, _UpLo > & | derived () const |
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const Solve< LDLT< _MatrixType, _UpLo >, Rhs > | solve (const MatrixBase< Rhs > &b) const |
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| SolverBase () |
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ConstTransposeReturnType | transpose () const |
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| ~SolverBase () |
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EIGEN_DEVICE_FUNC void | addTo (Dest &dst) const |
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EIGEN_DEVICE_FUNC void | applyThisOnTheLeft (Dest &dst) const |
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EIGEN_DEVICE_FUNC void | applyThisOnTheRight (Dest &dst) const |
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EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index | cols () const EIGEN_NOEXCEPT |
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EIGEN_DEVICE_FUNC LDLT< _MatrixType, _UpLo > & | const_cast_derived () const |
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const EIGEN_DEVICE_FUNC LDLT< _MatrixType, _UpLo > & | const_derived () const |
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EIGEN_DEVICE_FUNC LDLT< _MatrixType, _UpLo > & | derived () |
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const EIGEN_DEVICE_FUNC LDLT< _MatrixType, _UpLo > & | derived () const |
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EIGEN_DEVICE_FUNC void | evalTo (Dest &dst) const |
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EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index | rows () const EIGEN_NOEXCEPT |
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EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index | size () const EIGEN_NOEXCEPT |
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EIGEN_DEVICE_FUNC void | subTo (Dest &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 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 D 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
Definition at line 59 of file LDLT.h.