internal/ceres/dense_cholesky.h

// Ceres Solver - A fast non-linear least squares minimizer
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// Author: sameeragarwal@google.com (Sameer Agarwal)

#ifndef CERES_INTERNAL_DENSE_CHOLESKY_H_
#define CERES_INTERNAL_DENSE_CHOLESKY_H_

// This include must come before any #ifndef check on Ceres compile options.
// clang-format off
#include "ceres/internal/port.h"
// clang-format on

#include <memory>

#include "Eigen/Dense"
#include "ceres/linear_solver.h"
#include "glog/logging.h"

namespace ceres {
namespace internal {

// An interface that abstracts away the internal details of various dense linear
// algebra libraries and offers a simple API for solving dense symmetric
// positive definite linear systems using a Cholesky factorization.
class CERES_EXPORT_INTERNAL DenseCholesky {
 public:
  static std::unique_ptr<DenseCholesky> Create(
      const LinearSolver::Options& options);

  virtual ~DenseCholesky() = default;

  // Computes the Cholesky factorization of the given matrix.
  //
  // The input matrix lhs is assumed to be a column-major num_cols x num_cols
  // matrix, that is symmetric positive definite with its lower triangular part
  // containing the left hand side of the linear system being solved.
  //
  // The input matrix lhs may be modified by the implementation to store the
  // factorization, irrespective of whether the factorization succeeds or not.
  // As a result it is the user's responsibility to ensure that lhs is valid
  // when Solve is called.
  virtual LinearSolverTerminationType Factorize(int num_cols,
                                                double* lhs,
                                                std::string* message) = 0;

  // Computes the solution to the equation
  //
  // lhs * solution = rhs
  //
  // Calling Solve without calling Factorize is undefined behaviour. It is the
  // user's responsibility to ensure that the input matrix lhs passed to
  // Factorize has not been freed/modified when Solve is called.
  virtual LinearSolverTerminationType Solve(const double* rhs,
                                            double* solution,
                                            std::string* message) = 0;

  // Convenience method which combines a call to Factorize and Solve. Solve is
  // only called if Factorize returns LINEAR_SOLVER_SUCCESS.
  //
  // The input matrix lhs may be modified by the implementation to store the
  // factorization, irrespective of whether the method succeeds or not. It is
  // the user's responsibility to ensure that lhs is valid if and when Solve is
  // called again after this call.
  LinearSolverTerminationType FactorAndSolve(int num_cols,
                                             double* lhs,
                                             const double* rhs,
                                             double* solution,
                                             std::string* message);
};

class CERES_EXPORT_INTERNAL EigenDenseCholesky : public DenseCholesky {
 public:
  ~EigenDenseCholesky() override = default;

  LinearSolverTerminationType Factorize(int num_cols,
                                        double* lhs,
                                        std::string* message) override;
  LinearSolverTerminationType Solve(const double* rhs,
                                    double* solution,
                                    std::string* message) override;

 private:
  using LLTType = Eigen::LLT<Eigen::Ref<Eigen::MatrixXd>, Eigen::Lower>;
  std::unique_ptr<LLTType> llt_;
};

class CERES_EXPORT_INTERNAL LAPACKDenseCholesky : public DenseCholesky {
 public:
  ~LAPACKDenseCholesky() override = default;

  LinearSolverTerminationType Factorize(int num_cols,
                                        double* lhs,
                                        std::string* message) override;
  LinearSolverTerminationType Solve(const double* rhs,
                                    double* solution,
                                    std::string* message) override;

 private:
  double* lhs_ = nullptr;
  int num_cols_ = -1;
  LinearSolverTerminationType termination_type_ = LINEAR_SOLVER_FATAL_ERROR;
};

}  // namespace internal
}  // namespace ceres

#endif  // CERES_INTERNAL_DENSE_CHOLESKY_H_