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 // NumericDiffCostFunction also supports cost functions with a 99 // runtime-determined number of residuals. For example: 100 // 101 // CostFunction* cost_function 102 // = new NumericDiffCostFunction<MyScalarCostFunctor, CENTRAL, DYNAMIC, 2, 2>( 103 // new CostFunctorWithDynamicNumResiduals(1.0), ^ ^ ^ 104 // TAKE_OWNERSHIP, | | | 105 // runtime_number_of_residuals); <----+ | | | 106 // | | | | 107 // | | | | 108 // Actual number of residuals ------+ | | | 109 // Indicate dynamic number of residuals --------------------+ | | 110 // Dimension of x ------------------------------------------------+ | 111 // Dimension of y ---------------------------------------------------+ 112 // 113 // The framework can currently accommodate cost functions of up to 10 114 // independent variables, and there is no limit on the dimensionality 115 // of each of them. 116 // 117 // The central difference method is considerably more accurate at the cost of 118 // twice as many function evaluations than forward difference. Consider using 119 // central differences begin with, and only after that works, trying forward 120 // difference to improve performance. 121 // 122 // WARNING #1: A common beginner's error when first using 123 // NumericDiffCostFunction is to get the sizing wrong. In particular, 124 // there is a tendency to set the template parameters to (dimension of 125 // residual, number of parameters) instead of passing a dimension 126 // parameter for *every parameter*. In the example above, that would 127 // be <MyScalarCostFunctor, 1, 2>, which is missing the last '2' 128 // argument. Please be careful when setting the size parameters. 129 // 130 //////////////////////////////////////////////////////////////////////////// 131 //////////////////////////////////////////////////////////////////////////// 132 // 133 // ALTERNATE INTERFACE 134 // 135 // For a variety of reason, including compatibility with legacy code, 136 // NumericDiffCostFunction can also take CostFunction objects as 137 // input. The following describes how. 138 // 139 // To get a numerically differentiated cost function, define a 140 // subclass of CostFunction such that the Evaluate() function ignores 141 // the jacobian parameter. The numeric differentiation wrapper will 142 // fill in the jacobian parameter if necessary by repeatedly calling 143 // the Evaluate() function with small changes to the appropriate 144 // parameters, and computing the slope. For performance, the numeric 145 // differentiation wrapper class is templated on the concrete cost 146 // function, even though it could be implemented only in terms of the 147 // virtual CostFunction interface. 148 // 149 // The numerically differentiated version of a cost function for a cost function 150 // can be constructed as follows: 151 // 152 // CostFunction* cost_function 153 // = new NumericDiffCostFunction<MyCostFunction, CENTRAL, 1, 4, 8>( 154 // new MyCostFunction(...), TAKE_OWNERSHIP); 155 // 156 // where MyCostFunction has 1 residual and 2 parameter blocks with sizes 4 and 8 157 // respectively. Look at the tests for a more detailed example. 158 // 159 // TODO(keir): Characterize accuracy; mention pitfalls; provide alternatives. 160 161 #ifndef CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_ 162 #define CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_ 163 164 #include "Eigen/Dense" 165 #include "ceres/cost_function.h" 166 #include "ceres/internal/numeric_diff.h" 167 #include "ceres/internal/scoped_ptr.h" 168 #include "ceres/sized_cost_function.h" 169 #include "ceres/types.h" 170 #include "glog/logging.h" 171 172 namespace ceres { 173 174 template <typename CostFunctor, 175 NumericDiffMethod method = CENTRAL, 176 int kNumResiduals = 0, // Number of residuals, or ceres::DYNAMIC 177 int N0 = 0, // Number of parameters in block 0. 178 int N1 = 0, // Number of parameters in block 1. 179 int N2 = 0, // Number of parameters in block 2. 180 int N3 = 0, // Number of parameters in block 3. 181 int N4 = 0, // Number of parameters in block 4. 182 int N5 = 0, // Number of parameters in block 5. 183 int N6 = 0, // Number of parameters in block 6. 184 int N7 = 0, // Number of parameters in block 7. 185 int N8 = 0, // Number of parameters in block 8. 186 int N9 = 0> // Number of parameters in block 9. 187 class NumericDiffCostFunction 188 : public SizedCostFunction<kNumResiduals, 189 N0, N1, N2, N3, N4, 190 N5, N6, N7, N8, N9> { 191 public: 192 NumericDiffCostFunction(CostFunctor* functor, 193 Ownership ownership = TAKE_OWNERSHIP, 194 int num_residuals = kNumResiduals, 195 const double relative_step_size = 1e-6) 196 :functor_(functor), 197 ownership_(ownership), 198 relative_step_size_(relative_step_size) { 199 if (kNumResiduals == DYNAMIC) { 200 SizedCostFunction<kNumResiduals, 201 N0, N1, N2, N3, N4, 202 N5, N6, N7, N8, N9> 203 ::set_num_residuals(num_residuals); 204 } 205 } 206 207 ~NumericDiffCostFunction() { 208 if (ownership_ != TAKE_OWNERSHIP) { 209 functor_.release(); 210 } 211 } 212 213 virtual bool Evaluate(double const* const* parameters, 214 double* residuals, 215 double** jacobians) const { 216 using internal::FixedArray; 217 using internal::NumericDiff; 218 219 const int kNumParameters = N0 + N1 + N2 + N3 + N4 + N5 + N6 + N7 + N8 + N9; 220 const int kNumParameterBlocks = 221 (N0 > 0) + (N1 > 0) + (N2 > 0) + (N3 > 0) + (N4 > 0) + 222 (N5 > 0) + (N6 > 0) + (N7 > 0) + (N8 > 0) + (N9 > 0); 223 224 // Get the function value (residuals) at the the point to evaluate. 225 if (!internal::EvaluateImpl<CostFunctor, 226 N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>( 227 functor_.get(), 228 parameters, 229 residuals, 230 functor_.get())) { 231 return false; 232 } 233 234 if (jacobians == NULL) { 235 return true; 236 } 237 238 // Create a copy of the parameters which will get mutated. 239 FixedArray<double> parameters_copy(kNumParameters); 240 FixedArray<double*> parameters_reference_copy(kNumParameterBlocks); 241 242 parameters_reference_copy[0] = parameters_copy.get(); 243 if (N1) parameters_reference_copy[1] = parameters_reference_copy[0] + N0; 244 if (N2) parameters_reference_copy[2] = parameters_reference_copy[1] + N1; 245 if (N3) parameters_reference_copy[3] = parameters_reference_copy[2] + N2; 246 if (N4) parameters_reference_copy[4] = parameters_reference_copy[3] + N3; 247 if (N5) parameters_reference_copy[5] = parameters_reference_copy[4] + N4; 248 if (N6) parameters_reference_copy[6] = parameters_reference_copy[5] + N5; 249 if (N7) parameters_reference_copy[7] = parameters_reference_copy[6] + N6; 250 if (N8) parameters_reference_copy[8] = parameters_reference_copy[7] + N7; 251 if (N9) parameters_reference_copy[9] = parameters_reference_copy[8] + N8; 252 253 #define COPY_PARAMETER_BLOCK(block) \ 254 if (N ## block) memcpy(parameters_reference_copy[block], \ 255 parameters[block], \ 256 sizeof(double) * N ## block); // NOLINT 257 258 COPY_PARAMETER_BLOCK(0); 259 COPY_PARAMETER_BLOCK(1); 260 COPY_PARAMETER_BLOCK(2); 261 COPY_PARAMETER_BLOCK(3); 262 COPY_PARAMETER_BLOCK(4); 263 COPY_PARAMETER_BLOCK(5); 264 COPY_PARAMETER_BLOCK(6); 265 COPY_PARAMETER_BLOCK(7); 266 COPY_PARAMETER_BLOCK(8); 267 COPY_PARAMETER_BLOCK(9); 268 269 #undef COPY_PARAMETER_BLOCK 270 271 #define EVALUATE_JACOBIAN_FOR_BLOCK(block) \ 272 if (N ## block && jacobians[block] != NULL) { \ 273 if (!NumericDiff<CostFunctor, \ 274 method, \ 275 kNumResiduals, \ 276 N0, N1, N2, N3, N4, N5, N6, N7, N8, N9, \ 277 block, \ 278 N ## block >::EvaluateJacobianForParameterBlock( \ 279 functor_.get(), \ 280 residuals, \ 281 relative_step_size_, \ 282 SizedCostFunction<kNumResiduals, \ 283 N0, N1, N2, N3, N4, \ 284 N5, N6, N7, N8, N9>::num_residuals(), \ 285 parameters_reference_copy.get(), \ 286 jacobians[block])) { \ 287 return false; \ 288 } \ 289 } 290 291 EVALUATE_JACOBIAN_FOR_BLOCK(0); 292 EVALUATE_JACOBIAN_FOR_BLOCK(1); 293 EVALUATE_JACOBIAN_FOR_BLOCK(2); 294 EVALUATE_JACOBIAN_FOR_BLOCK(3); 295 EVALUATE_JACOBIAN_FOR_BLOCK(4); 296 EVALUATE_JACOBIAN_FOR_BLOCK(5); 297 EVALUATE_JACOBIAN_FOR_BLOCK(6); 298 EVALUATE_JACOBIAN_FOR_BLOCK(7); 299 EVALUATE_JACOBIAN_FOR_BLOCK(8); 300 EVALUATE_JACOBIAN_FOR_BLOCK(9); 301 302 #undef EVALUATE_JACOBIAN_FOR_BLOCK 303 304 return true; 305 } 306 307 private: 308 internal::scoped_ptr<CostFunctor> functor_; 309 Ownership ownership_; 310 const double relative_step_size_; 311 }; 312 313 } // namespace ceres 314 315 #endif // CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_ 316
