1 // Ceres Solver - A fast non-linear least squares minimizer 2 // Copyright 2010, 2011, 2012 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: keir (at) google.com (Keir Mierle) 30 // sameeragarwal (at) google.com (Sameer Agarwal) 31 // 32 // Create CostFunctions as needed by the least squares framework with jacobians 33 // computed via numeric (a.k.a. finite) differentiation. For more details see 34 // http://en.wikipedia.org/wiki/Numerical_differentiation. 35 // 36 // To get an numerically differentiated cost function, you must define 37 // a class with a operator() (a functor) that computes the residuals. 38 // 39 // The function must write the computed value in the last argument 40 // (the only non-const one) and return true to indicate success. 41 // Please see cost_function.h for details on how the return value 42 // maybe used to impose simple constraints on the parameter block. 43 // 44 // For example, consider a scalar error e = k - x'y, where both x and y are 45 // two-dimensional column vector parameters, the prime sign indicates 46 // transposition, and k is a constant. The form of this error, which is the 47 // difference between a constant and an expression, is a common pattern in least 48 // squares problems. For example, the value x'y might be the model expectation 49 // for a series of measurements, where there is an instance of the cost function 50 // for each measurement k. 51 // 52 // The actual cost added to the total problem is e^2, or (k - x'k)^2; however, 53 // the squaring is implicitly done by the optimization framework. 54 // 55 // To write an numerically-differentiable cost function for the above model, first 56 // define the object 57 // 58 // class MyScalarCostFunctor { 59 // MyScalarCostFunctor(double k): k_(k) {} 60 // 61 // bool operator()(const double* const x, 62 // const double* const y, 63 // double* residuals) const { 64 // residuals[0] = k_ - x[0] * y[0] + x[1] * y[1]; 65 // return true; 66 // } 67 // 68 // private: 69 // double k_; 70 // }; 71 // 72 // Note that in the declaration of operator() the input parameters x 73 // and y come first, and are passed as const pointers to arrays of 74 // doubles. If there were three input parameters, then the third input 75 // parameter would come after y. The output is always the last 76 // parameter, and is also a pointer to an array. In the example above, 77 // the residual is a scalar, so only residuals[0] is set. 78 // 79 // Then given this class definition, the numerically differentiated 80 // cost function with central differences used for computing the 81 // derivative can be constructed as follows. 82 // 83 // CostFunction* cost_function 84 // = new NumericDiffCostFunction<MyScalarCostFunctor, CENTRAL, 1, 2, 2>( 85 // new MyScalarCostFunctor(1.0)); ^ ^ ^ ^ 86 // | | | | 87 // Finite Differencing Scheme -+ | | | 88 // Dimension of residual ------------+ | | 89 // Dimension of x ----------------------+ | 90 // Dimension of y -------------------------+ 91 // 92 // In this example, there is usually an instance for each measurement of k. 93 // 94 // In the instantiation above, the template parameters following 95 // "MyScalarCostFunctor", "1, 2, 2", describe the functor as computing 96 // a 1-dimensional output from two arguments, both 2-dimensional. 97 // 98 // The framework can currently accommodate cost functions of up to 10 99 // independent variables, and there is no limit on the dimensionality 100 // of each of them. 101 // 102 // The central difference method is considerably more accurate at the cost of 103 // twice as many function evaluations than forward difference. Consider using 104 // central differences begin with, and only after that works, trying forward 105 // difference to improve performance. 106 // 107 // TODO(sameeragarwal): Add support for dynamic number of residuals. 108 // 109 // WARNING #1: A common beginner's error when first using 110 // NumericDiffCostFunction is to get the sizing wrong. In particular, 111 // there is a tendency to set the template parameters to (dimension of 112 // residual, number of parameters) instead of passing a dimension 113 // parameter for *every parameter*. In the example above, that would 114 // be <MyScalarCostFunctor, 1, 2>, which is missing the last '2' 115 // argument. Please be careful when setting the size parameters. 116 // 117 //////////////////////////////////////////////////////////////////////////// 118 //////////////////////////////////////////////////////////////////////////// 119 // 120 // ALTERNATE INTERFACE 121 // 122 // For a variety of reason, including compatibility with legacy code, 123 // NumericDiffCostFunction can also take CostFunction objects as 124 // input. The following describes how. 125 // 126 // To get a numerically differentiated cost function, define a 127 // subclass of CostFunction such that the Evaluate() function ignores 128 // the jacobian parameter. The numeric differentiation wrapper will 129 // fill in the jacobian parameter if necessary by repeatedly calling 130 // the Evaluate() function with small changes to the appropriate 131 // parameters, and computing the slope. For performance, the numeric 132 // differentiation wrapper class is templated on the concrete cost 133 // function, even though it could be implemented only in terms of the 134 // virtual CostFunction interface. 135 // 136 // The numerically differentiated version of a cost function for a cost function 137 // can be constructed as follows: 138 // 139 // CostFunction* cost_function 140 // = new NumericDiffCostFunction<MyCostFunction, CENTRAL, 1, 4, 8>( 141 // new MyCostFunction(...), TAKE_OWNERSHIP); 142 // 143 // where MyCostFunction has 1 residual and 2 parameter blocks with sizes 4 and 8 144 // respectively. Look at the tests for a more detailed example. 145 // 146 // TODO(keir): Characterize accuracy; mention pitfalls; provide alternatives. 147 148 #ifndef CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_ 149 #define CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_ 150 151 #include "Eigen/Dense" 152 #include "ceres/cost_function.h" 153 #include "ceres/internal/numeric_diff.h" 154 #include "ceres/internal/scoped_ptr.h" 155 #include "ceres/sized_cost_function.h" 156 #include "ceres/types.h" 157 #include "glog/logging.h" 158 159 namespace ceres { 160 161 template <typename CostFunctor, 162 NumericDiffMethod method = CENTRAL, 163 int kNumResiduals = 0, // Number of residuals, or ceres::DYNAMIC 164 int N0 = 0, // Number of parameters in block 0. 165 int N1 = 0, // Number of parameters in block 1. 166 int N2 = 0, // Number of parameters in block 2. 167 int N3 = 0, // Number of parameters in block 3. 168 int N4 = 0, // Number of parameters in block 4. 169 int N5 = 0, // Number of parameters in block 5. 170 int N6 = 0, // Number of parameters in block 6. 171 int N7 = 0, // Number of parameters in block 7. 172 int N8 = 0, // Number of parameters in block 8. 173 int N9 = 0> // Number of parameters in block 9. 174 class NumericDiffCostFunction 175 : public SizedCostFunction<kNumResiduals, 176 N0, N1, N2, N3, N4, 177 N5, N6, N7, N8, N9> { 178 public: 179 NumericDiffCostFunction(CostFunctor* functor, 180 const double relative_step_size = 1e-6) 181 :functor_(functor), 182 ownership_(TAKE_OWNERSHIP), 183 relative_step_size_(relative_step_size) {} 184 185 NumericDiffCostFunction(CostFunctor* functor, 186 Ownership ownership, 187 const double relative_step_size = 1e-6) 188 : functor_(functor), 189 ownership_(ownership), 190 relative_step_size_(relative_step_size) {} 191 192 ~NumericDiffCostFunction() { 193 if (ownership_ != TAKE_OWNERSHIP) { 194 functor_.release(); 195 } 196 } 197 198 virtual bool Evaluate(double const* const* parameters, 199 double* residuals, 200 double** jacobians) const { 201 using internal::FixedArray; 202 using internal::NumericDiff; 203 204 const int kNumParameters = N0 + N1 + N2 + N3 + N4 + N5 + N6 + N7 + N8 + N9; 205 const int kNumParameterBlocks = 206 (N0 > 0) + (N1 > 0) + (N2 > 0) + (N3 > 0) + (N4 > 0) + 207 (N5 > 0) + (N6 > 0) + (N7 > 0) + (N8 > 0) + (N9 > 0); 208 209 // Get the function value (residuals) at the the point to evaluate. 210 if (!internal::EvaluateImpl<CostFunctor, 211 N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>( 212 functor_.get(), 213 parameters, 214 residuals, 215 functor_.get())) { 216 return false; 217 } 218 219 if (!jacobians) { 220 return true; 221 } 222 223 // Create a copy of the parameters which will get mutated. 224 FixedArray<double> parameters_copy(kNumParameters); 225 FixedArray<double*> parameters_reference_copy(kNumParameterBlocks); 226 227 parameters_reference_copy[0] = parameters_copy.get(); 228 if (N1) parameters_reference_copy[1] = parameters_reference_copy[0] + N0; 229 if (N2) parameters_reference_copy[2] = parameters_reference_copy[1] + N1; 230 if (N3) parameters_reference_copy[3] = parameters_reference_copy[2] + N2; 231 if (N4) parameters_reference_copy[4] = parameters_reference_copy[3] + N3; 232 if (N5) parameters_reference_copy[5] = parameters_reference_copy[4] + N4; 233 if (N6) parameters_reference_copy[6] = parameters_reference_copy[5] + N5; 234 if (N7) parameters_reference_copy[7] = parameters_reference_copy[6] + N6; 235 if (N8) parameters_reference_copy[8] = parameters_reference_copy[7] + N7; 236 if (N9) parameters_reference_copy[9] = parameters_reference_copy[8] + N8; 237 238 #define COPY_PARAMETER_BLOCK(block) \ 239 if (N ## block) memcpy(parameters_reference_copy[block], \ 240 parameters[block], \ 241 sizeof(double) * N ## block); // NOLINT 242 243 COPY_PARAMETER_BLOCK(0); 244 COPY_PARAMETER_BLOCK(1); 245 COPY_PARAMETER_BLOCK(2); 246 COPY_PARAMETER_BLOCK(3); 247 COPY_PARAMETER_BLOCK(4); 248 COPY_PARAMETER_BLOCK(5); 249 COPY_PARAMETER_BLOCK(6); 250 COPY_PARAMETER_BLOCK(7); 251 COPY_PARAMETER_BLOCK(8); 252 COPY_PARAMETER_BLOCK(9); 253 254 #undef COPY_PARAMETER_BLOCK 255 256 #define EVALUATE_JACOBIAN_FOR_BLOCK(block) \ 257 if (N ## block && jacobians[block] != NULL) { \ 258 if (!NumericDiff<CostFunctor, \ 259 method, \ 260 kNumResiduals, \ 261 N0, N1, N2, N3, N4, N5, N6, N7, N8, N9, \ 262 block, \ 263 N ## block >::EvaluateJacobianForParameterBlock( \ 264 functor_.get(), \ 265 residuals, \ 266 relative_step_size_, \ 267 parameters_reference_copy.get(), \ 268 jacobians[block])) { \ 269 return false; \ 270 } \ 271 } 272 273 EVALUATE_JACOBIAN_FOR_BLOCK(0); 274 EVALUATE_JACOBIAN_FOR_BLOCK(1); 275 EVALUATE_JACOBIAN_FOR_BLOCK(2); 276 EVALUATE_JACOBIAN_FOR_BLOCK(3); 277 EVALUATE_JACOBIAN_FOR_BLOCK(4); 278 EVALUATE_JACOBIAN_FOR_BLOCK(5); 279 EVALUATE_JACOBIAN_FOR_BLOCK(6); 280 EVALUATE_JACOBIAN_FOR_BLOCK(7); 281 EVALUATE_JACOBIAN_FOR_BLOCK(8); 282 EVALUATE_JACOBIAN_FOR_BLOCK(9); 283 284 #undef EVALUATE_JACOBIAN_FOR_BLOCK 285 286 return true; 287 } 288 289 private: 290 internal::scoped_ptr<CostFunctor> functor_; 291 Ownership ownership_; 292 const double relative_step_size_; 293 }; 294 295 } // namespace ceres 296 297 #endif // CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_ 298
