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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2017 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+//   this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+//   this list of conditions and the following disclaimer in the documentation
+//   and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+//   used to endorse or promote products derived from this software without
+//   specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// 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_