# File eigen_sparse_solver.h#

namespace sym
template<typename Scalar, typename EigenSolver>
class EigenSparseSolver
#include <eigen_sparse_solver.h>

A thin wrapper around Eigen’s Sparse Solver interface for use in nonlinear solver classes like sym::LevenbergMarquardtSolver.

Can be specialized with anything satisfying the SparseSolver concept.

For example, can be used like:

```using LinearSolver =
sym::EigenSparseSolver<double, Eigen::CholmodDecomposition<Eigen::SparseMatrix<double>>>;
using NonlinearSolver = sym::LevenbergMarquardtSolver<double, LinearSolver>;
using Optimizer = sym::Optimizer<double, NonlinearSolver>;

Optimizer optimizer{...};
```

Public Types

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

Public Functions

inline bool Factorize(const MatrixType &A)

Factorize A and store internally.

Parameters:

A – 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

Eigen solvers cannot actually solve in place, so this solves, then copies back into the argument.

Pre:

this->Factorize has already been called and succeeded.

inline MatrixType 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 MatrixType 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 Eigen::PermutationMatrix<Eigen::Dynamic> 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.

inline void AnalyzeSparsityPattern(const MatrixType &A)

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

Private Members

EigenSolver solver_#