# Class sym::DenseCholeskySolver#

template<typename Scalar>
class DenseCholeskySolver#

A thin wrapper around Eigen::LDLT for use in nonlinear solver classes like sym::LevenbergMarquardtSolver.

Public Types

using MatrixType = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>#
using RhsType = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>#

Public Functions

inline bool Factorize(const MatrixType &A)#

Decompose A into A = P^T * L * D * L^T * P and store internally.

Pre:

A is a symmetric positive definite matrix.

Returns:

true if factorization succeeded, and false if failed.

template<typename Rhs>
inline RhsType Solve(const Eigen::MatrixBase<Rhs> &b) const#
Returns:

x for A x = b, where x and b are dense

Pre:

this->Factorize has already been called and succeeded.

template<typename Rhs>
inline void SolveInPlace(Eigen::MatrixBase<Rhs> &b) const#

Solves in place for x in A x = b, where x and b are dense

Pre:

this->Factorize has already been called and succeeded.

inline auto L() const#
Returns:

the lower triangular matrix L such that P^T * L * D * L^T * P = A, where A is the last matrix to have been factorized with this->Factorize and D is a diagonal matrix with positive diagonal entries, and P is a permutation matrix.

Pre:

this->Factorize has already been called and succeeded.

inline auto D() const#
Returns:

the diagonal matrix D such that P^T * L * D * L^T * P = A, where A is the last matrix to have been factorized with this->Factorize, L is lower triangular with unit diagonal, and P is a permutation matrix

Pre:

this->Factorize has already been called and succeeded.

inline auto Permutation() const#
Returns:

the permutation matrix P such that P^T * L * D * L^T * P = A, where A is the last matrix to have been factorized with this->Factorize, L is lower triangular with unit diagonal, and D is a diagonal matrix

Pre:

this->Factorize has already been called and succeeded.

template<typename Derived>
inline void AnalyzeSparsityPattern(const Eigen::EigenBase<Derived>&)#

Defined to satisfy interface. No analysis is needed so is a no-op.