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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2018 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: alexs.mac@gmail.com (Alex Stewart)
+
+#ifndef CERES_INTERNAL_ACCELERATE_SPARSE_H_
+#define CERES_INTERNAL_ACCELERATE_SPARSE_H_
+
+// This include must come before any #ifndef check on Ceres compile options.
+#include "ceres/internal/port.h"
+
+#ifndef CERES_NO_ACCELERATE_SPARSE
+
+#include <memory>
+#include <string>
+#include <vector>
+
+#include "ceres/linear_solver.h"
+#include "ceres/sparse_cholesky.h"
+#include "Accelerate.h"
+
+namespace ceres {
+namespace internal {
+
+class CompressedRowSparseMatrix;
+class TripletSparseMatrix;
+
+template<typename Scalar>
+struct SparseTypesTrait {
+};
+
+template<>
+struct SparseTypesTrait<double> {
+  typedef DenseVector_Double DenseVector;
+  typedef SparseMatrix_Double SparseMatrix;
+  typedef SparseOpaqueSymbolicFactorization SymbolicFactorization;
+  typedef SparseOpaqueFactorization_Double NumericFactorization;
+};
+
+template<>
+struct SparseTypesTrait<float> {
+  typedef DenseVector_Float DenseVector;
+  typedef SparseMatrix_Float SparseMatrix;
+  typedef SparseOpaqueSymbolicFactorization SymbolicFactorization;
+  typedef SparseOpaqueFactorization_Float NumericFactorization;
+};
+
+template<typename Scalar>
+class AccelerateSparse {
+ public:
+  using DenseVector = typename SparseTypesTrait<Scalar>::DenseVector;
+  // Use ASSparseMatrix to avoid collision with ceres::internal::SparseMatrix.
+  using ASSparseMatrix = typename SparseTypesTrait<Scalar>::SparseMatrix;
+  using SymbolicFactorization = typename SparseTypesTrait<Scalar>::SymbolicFactorization;
+  using NumericFactorization = typename SparseTypesTrait<Scalar>::NumericFactorization;
+
+  // Solves a linear system given its symbolic (reference counted within
+  // NumericFactorization) and numeric factorization.
+  void Solve(NumericFactorization* numeric_factor,
+             DenseVector* rhs_and_solution);
+
+  // Note: Accelerate's API passes/returns its objects by value, but as the
+  //       objects contain pointers to the underlying data these copies are
+  //       all shallow (in some cases Accelerate also reference counts the
+  //       objects internally).
+  ASSparseMatrix CreateSparseMatrixTransposeView(CompressedRowSparseMatrix* A);
+  // Computes a symbolic factorisation of A that can be used in Solve().
+  SymbolicFactorization AnalyzeCholesky(ASSparseMatrix* A);
+  // Compute the numeric Cholesky factorization of A, given its
+  // symbolic factorization.
+  NumericFactorization Cholesky(ASSparseMatrix* A,
+                                SymbolicFactorization* symbolic_factor);
+  // Reuse the NumericFactorization from a previous matrix with the same
+  // symbolic factorization to represent a new numeric factorization.
+  void Cholesky(ASSparseMatrix* A, NumericFactorization* numeric_factor);
+
+ private:
+  std::vector<long> column_starts_;
+  std::vector<uint8_t> solve_workspace_;
+  std::vector<uint8_t> factorization_workspace_;
+  // Storage for the values of A if Scalar != double (necessitating a copy).
+  Eigen::Matrix<Scalar, Eigen::Dynamic, 1> values_;
+};
+
+// An implementation of SparseCholesky interface using Apple's Accelerate
+// framework.
+template<typename Scalar>
+class AppleAccelerateCholesky : public SparseCholesky {
+ public:
+  // Factory
+  static std::unique_ptr<SparseCholesky> Create(OrderingType ordering_type);
+
+  // SparseCholesky interface.
+  virtual ~AppleAccelerateCholesky();
+  CompressedRowSparseMatrix::StorageType StorageType() const;
+  LinearSolverTerminationType Factorize(CompressedRowSparseMatrix* lhs,
+                                        std::string* message) final;
+  LinearSolverTerminationType Solve(const double* rhs,
+                                    double* solution,
+                                    std::string* message) final ;
+
+ private:
+  AppleAccelerateCholesky(const OrderingType ordering_type);
+  void FreeSymbolicFactorization();
+  void FreeNumericFactorization();
+
+  const OrderingType ordering_type_;
+  AccelerateSparse<Scalar> as_;
+  std::unique_ptr<typename AccelerateSparse<Scalar>::SymbolicFactorization>
+  symbolic_factor_;
+  std::unique_ptr<typename AccelerateSparse<Scalar>::NumericFactorization>
+  numeric_factor_;
+  // Copy of rhs/solution if Scalar != double (necessitating a copy).
+  Eigen::Matrix<Scalar, Eigen::Dynamic, 1> scalar_rhs_and_solution_;
+};
+
+}
+}
+
+#endif  // CERES_NO_ACCELERATE_SPARSE
+
+#endif  // CERES_INTERNAL_ACCELERATE_SPARSE_H_