internal/ceres/iterative_refiner.h

// 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)

#ifndef CERES_INTERNAL_ITERATIVE_REFINER_H_
#define CERES_INTERNAL_ITERATIVE_REFINER_H_

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

#include "ceres/internal/eigen.h"
#include "ceres/internal/export.h"

namespace ceres::internal {

class DenseCholesky;
class SparseCholesky;
class SparseMatrix;

// Iterative refinement
// (https://en.wikipedia.org/wiki/Iterative_refinement) is the process
// of improving the solution to a linear system, by using the
// following iteration.
//
// r_i = b - Ax_i
// Ad_i = r_i
// x_{i+1} = x_i + d_i
//
// IterativeRefiner implements this process for Symmetric Positive
// Definite linear systems.
//
// The above iterative loop is run until max_num_iterations is reached.
class CERES_NO_EXPORT SparseIterativeRefiner {
 public:
  // max_num_iterations is the number of refinement iterations to
  // perform.
  explicit SparseIterativeRefiner(int max_num_iterations);

  // Needed for mocking.
  virtual ~SparseIterativeRefiner();

  // Given an initial estimate of the solution of lhs * x = rhs, use
  // max_num_iterations rounds of iterative refinement to improve it.
  //
  // cholesky is assumed to contain an already computed factorization (or
  // an approximation thereof) of lhs.
  //
  // solution is expected to contain a approximation to the solution
  // to lhs * x = rhs. It can be zero.
  //
  // This method is virtual to facilitate mocking.
  virtual void Refine(const SparseMatrix& lhs,
                      const double* rhs,
                      SparseCholesky* cholesky,
                      double* solution);

 private:
  void Allocate(int num_cols);

  int max_num_iterations_;
  Vector residual_;
  Vector correction_;
  Vector lhs_x_solution_;
};

class CERES_NO_EXPORT DenseIterativeRefiner {
 public:
  // max_num_iterations is the number of refinement iterations to
  // perform.
  explicit DenseIterativeRefiner(int max_num_iterations);

  // Needed for mocking.
  virtual ~DenseIterativeRefiner();

  // Given an initial estimate of the solution of lhs * x = rhs, use
  // max_num_iterations rounds of iterative refinement to improve it.
  //
  // cholesky is assumed to contain an already computed factorization (or
  // an approximation thereof) of lhs.
  //
  // solution is expected to contain a approximation to the solution
  // to lhs * x = rhs. It can be zero.
  //
  // This method is virtual to facilitate mocking.
  virtual void Refine(int num_cols,
                      const double* lhs,
                      const double* rhs,
                      DenseCholesky* cholesky,
                      double* solution);

 private:
  void Allocate(int num_cols);

  int max_num_iterations_;
  Vector residual_;
  Vector correction_;
};

}  // namespace ceres::internal

#endif  // CERES_INTERNAL_ITERATIVE_REFINER_H_