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27   * \class LDLT
46 * \sa MatrixBase::ldlt(), class LLT
48 template<typename _MatrixType, int _UpLo> class LDLT
73 * perform decompositions via LDLT::compute(const MatrixType&).
75 LDLT()
86 * \sa LDLT()
88 LDLT(Index size)
99 * \sa LDLT(Index size)
101 LDLT(const MatrixType& matrix)
122 eigen_assert(m_isInitialized && "LDLT is not initialized.");
129 eigen_assert(m_isInitialized && "LDLT is not initialized.");
137 eigen_assert(m_isInitialized && "LDLT is not initialized.");
144 eigen_assert(m_isInitialized && "LDLT is not initialized.");
151 eigen_assert(m_isInitialized && "LDLT is not initialized.");
165 eigen_assert(m_isInitialized && "LDLT is not initialized.");
182 * \sa MatrixBase::ldlt()
185 inline const internal::solve_retval<LDLT, Rhs>
188 eigen_assert(m_isInitialized && "LDLT is not initialized.");
190 && "LDLT::solve(): invalid number of rows of the right hand side matrix b");
191 return internal::solve_retval<LDLT, Rhs>(*this, b.derived());
206 LDLT& compute(const MatrixType& matrix);
209 LDLT& rankUpdate(const MatrixBase<Derived>& w, const RealScalar& alpha=1);
211 /** \returns the internal LDLT decomposition matrix
217 eigen_assert(m_isInitialized && "LDLT is not initialized.");
233 eigen_assert(m_isInitialized && "LDLT is not initialized.");
321 // was smaller than the cutoff value. However, soince LDLT is not rank-revealing
432 /** Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of \a matrix
435 LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const MatrixType& a)
452 /** Update the LDLT decomposition: given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T.
459 LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::rankUpdate(const MatrixBase<Derived>& w, const typename NumTraits<typename MatrixType::Scalar>::Real& sigma)
485 struct solve_retval<LDLT<_MatrixType,_UpLo>, Rhs>
486 : solve_retval_base<LDLT<_MatrixType,_UpLo>, Rhs>
488 typedef LDLT<_MatrixType,_UpLo> LDLTType;
511 // However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the highest
543 * \sa LDLT::solve(), MatrixBase::ldlt()
547 bool LDLT<MatrixType,_UpLo>::solveInPlace(MatrixBase<Derived> &bAndX) const
549 eigen_assert(m_isInitialized && "LDLT is not initialized.");
561 MatrixType LDLT<MatrixType,_UpLo>::reconstructedMatrix() const
563 eigen_assert(m_isInitialized && "LDLT is not initialized.");
586 inline const LDLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
587 SelfAdjointView<MatrixType, UpLo>::ldlt() const
589 return LDLT<PlainObject,UpLo>(m_matrix);
596 inline const LDLT<typename MatrixBase<Derived>::PlainObject>
597 MatrixBase<Derived>::ldlt() const
599 return LDLT<PlainObject>(derived());