internal/ceres/sparse_cholesky.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_SPARSE_CHOLESKY_H_
#define CERES_INTERNAL_SPARSE_CHOLESKY_H_

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

#include <memory>
#include "ceres/linear_solver.h"
#include "glog/logging.h"

namespace ceres {
namespace internal {

// An interface that abstracts away the internal details of various
// sparse linear algebra libraries and offers a simple API for solving
// symmetric positive definite linear systems using a sparse Cholesky
// factorization.
//
// Instances of SparseCholesky are expected to cache the symbolic
// factorization of the linear system. They do this on the first call
// to Factorize or FactorAndSolve. Subsequent calls to Factorize and
// FactorAndSolve are expected to have the same sparsity structure.
//
// Example usage:
//
//  std::unique_ptr<SparseCholesky>
//  sparse_cholesky(SparseCholesky::Create(SUITE_SPARSE, AMD));
//
//  CompressedRowSparseMatrix lhs = ...;
//  std::string message;
//  CHECK_EQ(sparse_cholesky->Factorize(&lhs, &message), LINEAR_SOLVER_SUCCESS);
//  Vector rhs = ...;
//  Vector solution = ...;
//  CHECK_EQ(sparse_cholesky->Solve(rhs.data(), solution.data(), &message),
//           LINEAR_SOLVER_SUCCESS);

class SparseCholesky {
 public:
  static std::unique_ptr<SparseCholesky> Create(
      const LinearSolver::Options& options);

  virtual ~SparseCholesky();

  // Due to the symmetry of the linear system, sparse linear algebra
  // libraries only use one half of the input matrix. Whether it is
  // the upper or the lower triangular part of the matrix depends on
  // the library and the re-ordering strategy being used. This
  // function tells the user the storage type expected of the input
  // matrix for the sparse linear algebra library and reordering
  // strategy used.
  virtual CompressedRowSparseMatrix::StorageType StorageType() const = 0;

  // Computes the numeric factorization of the given matrix.  If this
  // is the first call to Factorize, first the symbolic factorization
  // will be computed and cached and the numeric factorization will be
  // computed based on that.
  //
  // Subsequent calls to Factorize will use that symbolic
  // factorization assuming that the sparsity of the matrix has
  // remained constant.
  virtual LinearSolverTerminationType Factorize(
      CompressedRowSparseMatrix* lhs, std::string* message) = 0;

  // Computes the solution to the equation
  //
  // lhs * solution = rhs
  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.
  virtual LinearSolverTerminationType FactorAndSolve(
      CompressedRowSparseMatrix* lhs,
      const double* rhs,
      double* solution,
      std::string* message);

};

class IterativeRefiner;

// Computes an initial solution using the given instance of
// SparseCholesky, and then refines it using the IterativeRefiner.
class RefinedSparseCholesky : public SparseCholesky {
 public:
  RefinedSparseCholesky(std::unique_ptr<SparseCholesky> sparse_cholesky,
                        std::unique_ptr<IterativeRefiner> iterative_refiner);
  virtual ~RefinedSparseCholesky();

  virtual CompressedRowSparseMatrix::StorageType StorageType() const;
  virtual LinearSolverTerminationType Factorize(
      CompressedRowSparseMatrix* lhs, std::string* message);
  virtual LinearSolverTerminationType Solve(const double* rhs,
                                            double* solution,
                                            std::string* message);

 private:
  std::unique_ptr<SparseCholesky> sparse_cholesky_;
  std::unique_ptr<IterativeRefiner> iterative_refiner_;
  CompressedRowSparseMatrix* lhs_ = nullptr;
};

}  // namespace internal
}  // namespace ceres

#endif  // CERES_INTERNAL_SPARSE_CHOLESKY_H_