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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2013 Google Inc. All rights reserved.
+// http://code.google.com/p/ceres-solver/
+//
+// 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: sergey.vfx@gmail.com (Sergey Sharybin)
+//         mierle@gmail.com (Keir Mierle)
+//         sameeragarwal@google.com (Sameer Agarwal)
+
+#ifndef CERES_PUBLIC_AUTODIFF_LOCAL_PARAMETERIZATION_H_
+#define CERES_PUBLIC_AUTODIFF_LOCAL_PARAMETERIZATION_H_
+
+#include "ceres/internal/autodiff.h"
+#include "ceres/internal/scoped_ptr.h"
+#include "ceres/local_parameterization.h"
+
+namespace ceres {
+
+// Create local parameterization with Jacobians computed via automatic
+// differentiation. For more information on local parameterizations,
+// see include/ceres/local_parameterization.h
+//
+// To get an auto differentiated local parameterization, you must define
+// a class with a templated operator() (a functor) that computes
+//
+//   x_plus_delta = Plus(x, delta);
+//
+// the template parameter T. The autodiff framework substitutes appropriate
+// "Jet" objects for T in order to compute the derivative when necessary, but
+// this is hidden, and you should write the function as if T were a scalar type
+// (e.g. a double-precision floating point number).
+//
+// The function must write the computed value in the last argument (the only
+// non-const one) and return true to indicate success.
+//
+// For example, Quaternions have a three dimensional local
+// parameterization. It's plus operation can be implemented as (taken
+// from interncal/ceres/auto_diff_local_parameterization_test.cc)
+//
+//   struct QuaternionPlus {
+//     template<typename T>
+//     bool operator()(const T* x, const T* delta, T* x_plus_delta) const {
+//       const T squared_norm_delta =
+//           delta[0] * delta[0] + delta[1] * delta[1] + delta[2] * delta[2];
+//
+//       T q_delta[4];
+//       if (squared_norm_delta > T(0.0)) {
+//         T norm_delta = sqrt(squared_norm_delta);
+//         const T sin_delta_by_delta = sin(norm_delta) / norm_delta;
+//         q_delta[0] = cos(norm_delta);
+//         q_delta[1] = sin_delta_by_delta * delta[0];
+//         q_delta[2] = sin_delta_by_delta * delta[1];
+//         q_delta[3] = sin_delta_by_delta * delta[2];
+//       } else {
+//         // We do not just use q_delta = [1,0,0,0] here because that is a
+//         // constant and when used for automatic differentiation will
+//         // lead to a zero derivative. Instead we take a first order
+//         // approximation and evaluate it at zero.
+//         q_delta[0] = T(1.0);
+//         q_delta[1] = delta[0];
+//         q_delta[2] = delta[1];
+//         q_delta[3] = delta[2];
+//       }
+//
+//       QuaternionProduct(q_delta, x, x_plus_delta);
+//       return true;
+//     }
+//   };
+//
+// Then given this struct, the auto differentiated local
+// parameterization can now be constructed as
+//
+//   LocalParameterization* local_parameterization =
+//     new AutoDiffLocalParameterization<QuaternionPlus, 4, 3>;
+//                                                       |  |
+//                            Global Size ---------------+  |
+//                            Local Size -------------------+
+//
+// WARNING: Since the functor will get instantiated with different types for
+// T, you must to convert from other numeric types to T before mixing
+// computations with other variables of type T. In the example above, this is
+// seen where instead of using k_ directly, k_ is wrapped with T(k_).
+
+template <typename Functor, int kGlobalSize, int kLocalSize>
+class AutoDiffLocalParameterization : public LocalParameterization {
+ public:
+  virtual ~AutoDiffLocalParameterization() {}
+  virtual bool Plus(const double* x,
+                    const double* delta,
+                    double* x_plus_delta) const {
+    return Functor()(x, delta, x_plus_delta);
+  }
+
+  virtual bool ComputeJacobian(const double* x, double* jacobian) const {
+    double zero_delta[kLocalSize];
+    for (int i = 0; i < kLocalSize; ++i) {
+      zero_delta[i] = 0.0;
+    }
+
+    double x_plus_delta[kGlobalSize];
+    for (int i = 0; i < kGlobalSize; ++i) {
+      x_plus_delta[i] = 0.0;
+    }
+
+    const double* parameter_ptrs[2] = {x, zero_delta};
+    double* jacobian_ptrs[2] = { NULL, jacobian };
+    return internal::AutoDiff<Functor, double, kGlobalSize, kLocalSize>
+        ::Differentiate(Functor(),
+                        parameter_ptrs,
+                        kGlobalSize,
+                        x_plus_delta,
+                        jacobian_ptrs);
+  }
+
+  virtual int GlobalSize() const { return kGlobalSize; }
+  virtual int LocalSize() const { return kLocalSize; }
+};
+
+}  // namespace ceres
+
+#endif  // CERES_PUBLIC_AUTODIFF_LOCAL_PARAMETERIZATION_H_