// Ceres Solver - A fast non-linear least squares minimizer
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// http://ceres-solver.org/
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// Author: sameeragarwal@google.com (Sameer Agarwal)
//
// Preconditioned Conjugate Gradients based solver for positive
// semidefinite linear systems.

#ifndef CERES_INTERNAL_CONJUGATE_GRADIENTS_SOLVER_H_
#define CERES_INTERNAL_CONJUGATE_GRADIENTS_SOLVER_H_

#include "ceres/linear_solver.h"

namespace ceres {
namespace internal {

class LinearOperator;

// This class implements the now classical Conjugate Gradients
// algorithm of Hestenes & Stiefel for solving postive semidefinite
// linear sytems. Optionally it can use a preconditioner also to
// reduce the condition number of the linear system and improve the
// convergence rate. Modern references for Conjugate Gradients are the
// books by Yousef Saad and Trefethen & Bau. This implementation of CG
// has been augmented with additional termination tests that are
// needed for forcing early termination when used as part of an
// inexact Newton solver.
//
// For more details see the documentation for
// LinearSolver::PerSolveOptions::r_tolerance and
// LinearSolver::PerSolveOptions::q_tolerance in linear_solver.h.
class ConjugateGradientsSolver : public LinearSolver {
 public:
  explicit ConjugateGradientsSolver(const LinearSolver::Options& options);
  Summary Solve(LinearOperator* A,
                const double* b,
                const LinearSolver::PerSolveOptions& per_solve_options,
                double* x) final;

 private:
  const LinearSolver::Options options_;
};

}  // namespace internal
}  // namespace ceres

#endif  // CERES_INTERNAL_CONJUGATE_GRADIENTS_SOLVER_H_