1 // Ceres Solver - A fast non-linear least squares minimizer 2 // Copyright 2013 Google Inc. All rights reserved. 3 // http://code.google.com/p/ceres-solver/ 4 // 5 // Redistribution and use in source and binary forms, with or without 6 // modification, are permitted provided that the following conditions are met: 7 // 8 // * Redistributions of source code must retain the above copyright notice, 9 // this list of conditions and the following disclaimer. 10 // * Redistributions in binary form must reproduce the above copyright notice, 11 // this list of conditions and the following disclaimer in the documentation 12 // and/or other materials provided with the distribution. 13 // * Neither the name of Google Inc. nor the names of its contributors may be 14 // used to endorse or promote products derived from this software without 15 // specific prior written permission. 16 // 17 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 18 // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 19 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 20 // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 21 // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 22 // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 23 // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 24 // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 25 // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 26 // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 27 // POSSIBILITY OF SUCH DAMAGE. 28 // 29 // Author: sergey.vfx (at) gmail.com (Sergey Sharybin) 30 // mierle (at) gmail.com (Keir Mierle) 31 // sameeragarwal (at) google.com (Sameer Agarwal) 32 33 #ifndef CERES_PUBLIC_AUTODIFF_LOCAL_PARAMETERIZATION_H_ 34 #define CERES_PUBLIC_AUTODIFF_LOCAL_PARAMETERIZATION_H_ 35 36 #include "ceres/internal/autodiff.h" 37 #include "ceres/internal/scoped_ptr.h" 38 #include "ceres/local_parameterization.h" 39 40 namespace ceres { 41 42 // Create local parameterization with Jacobians computed via automatic 43 // differentiation. For more information on local parameterizations, 44 // see include/ceres/local_parameterization.h 45 // 46 // To get an auto differentiated local parameterization, you must define 47 // a class with a templated operator() (a functor) that computes 48 // 49 // x_plus_delta = Plus(x, delta); 50 // 51 // the template parameter T. The autodiff framework substitutes appropriate 52 // "Jet" objects for T in order to compute the derivative when necessary, but 53 // this is hidden, and you should write the function as if T were a scalar type 54 // (e.g. a double-precision floating point number). 55 // 56 // The function must write the computed value in the last argument (the only 57 // non-const one) and return true to indicate success. 58 // 59 // For example, Quaternions have a three dimensional local 60 // parameterization. It's plus operation can be implemented as (taken 61 // from internal/ceres/auto_diff_local_parameterization_test.cc) 62 // 63 // struct QuaternionPlus { 64 // template<typename T> 65 // bool operator()(const T* x, const T* delta, T* x_plus_delta) const { 66 // const T squared_norm_delta = 67 // delta[0] * delta[0] + delta[1] * delta[1] + delta[2] * delta[2]; 68 // 69 // T q_delta[4]; 70 // if (squared_norm_delta > T(0.0)) { 71 // T norm_delta = sqrt(squared_norm_delta); 72 // const T sin_delta_by_delta = sin(norm_delta) / norm_delta; 73 // q_delta[0] = cos(norm_delta); 74 // q_delta[1] = sin_delta_by_delta * delta[0]; 75 // q_delta[2] = sin_delta_by_delta * delta[1]; 76 // q_delta[3] = sin_delta_by_delta * delta[2]; 77 // } else { 78 // // We do not just use q_delta = [1,0,0,0] here because that is a 79 // // constant and when used for automatic differentiation will 80 // // lead to a zero derivative. Instead we take a first order 81 // // approximation and evaluate it at zero. 82 // q_delta[0] = T(1.0); 83 // q_delta[1] = delta[0]; 84 // q_delta[2] = delta[1]; 85 // q_delta[3] = delta[2]; 86 // } 87 // 88 // QuaternionProduct(q_delta, x, x_plus_delta); 89 // return true; 90 // } 91 // }; 92 // 93 // Then given this struct, the auto differentiated local 94 // parameterization can now be constructed as 95 // 96 // LocalParameterization* local_parameterization = 97 // new AutoDiffLocalParameterization<QuaternionPlus, 4, 3>; 98 // | | 99 // Global Size ---------------+ | 100 // Local Size -------------------+ 101 // 102 // WARNING: Since the functor will get instantiated with different types for 103 // T, you must to convert from other numeric types to T before mixing 104 // computations with other variables of type T. In the example above, this is 105 // seen where instead of using k_ directly, k_ is wrapped with T(k_). 106 107 template <typename Functor, int kGlobalSize, int kLocalSize> 108 class AutoDiffLocalParameterization : public LocalParameterization { 109 public: 110 virtual ~AutoDiffLocalParameterization() {} 111 virtual bool Plus(const double* x, 112 const double* delta, 113 double* x_plus_delta) const { 114 return Functor()(x, delta, x_plus_delta); 115 } 116 117 virtual bool ComputeJacobian(const double* x, double* jacobian) const { 118 double zero_delta[kLocalSize]; 119 for (int i = 0; i < kLocalSize; ++i) { 120 zero_delta[i] = 0.0; 121 } 122 123 double x_plus_delta[kGlobalSize]; 124 for (int i = 0; i < kGlobalSize; ++i) { 125 x_plus_delta[i] = 0.0; 126 } 127 128 const double* parameter_ptrs[2] = {x, zero_delta}; 129 double* jacobian_ptrs[2] = { NULL, jacobian }; 130 return internal::AutoDiff<Functor, double, kGlobalSize, kLocalSize> 131 ::Differentiate(Functor(), 132 parameter_ptrs, 133 kGlobalSize, 134 x_plus_delta, 135 jacobian_ptrs); 136 } 137 138 virtual int GlobalSize() const { return kGlobalSize; } 139 virtual int LocalSize() const { return kLocalSize; } 140 }; 141 142 } // namespace ceres 143 144 #endif // CERES_PUBLIC_AUTODIFF_LOCAL_PARAMETERIZATION_H_ 145
