// Ceres Solver - A fast non-linear least squares minimizer // Copyright 2010, 2011, 2012 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: keir@google.com (Keir Mierle) // sameeragarwal@google.com (Sameer Agarwal) // // Create CostFunctions as needed by the least squares framework with jacobians // computed via numeric (a.k.a. finite) differentiation. For more details see // http://en.wikipedia.org/wiki/Numerical_differentiation. // // To get an numerically differentiated cost function, you must define // a class with a operator() (a functor) that computes the residuals. // // The function must write the computed value in the last argument // (the only non-const one) and return true to indicate success. // Please see cost_function.h for details on how the return value // maybe used to impose simple constraints on the parameter block. // // For example, consider a scalar error e = k - x'y, where both x and y are // two-dimensional column vector parameters, the prime sign indicates // transposition, and k is a constant. The form of this error, which is the // difference between a constant and an expression, is a common pattern in least // squares problems. For example, the value x'y might be the model expectation // for a series of measurements, where there is an instance of the cost function // for each measurement k. // // The actual cost added to the total problem is e^2, or (k - x'k)^2; however, // the squaring is implicitly done by the optimization framework. // // To write an numerically-differentiable cost function for the above model, first // define the object // // class MyScalarCostFunctor { // MyScalarCostFunctor(double k): k_(k) {} // // bool operator()(const double* const x, // const double* const y, // double* residuals) const { // residuals[0] = k_ - x[0] * y[0] + x[1] * y[1]; // return true; // } // // private: // double k_; // }; // // Note that in the declaration of operator() the input parameters x // and y come first, and are passed as const pointers to arrays of // doubles. If there were three input parameters, then the third input // parameter would come after y. The output is always the last // parameter, and is also a pointer to an array. In the example above, // the residual is a scalar, so only residuals[0] is set. // // Then given this class definition, the numerically differentiated // cost function with central differences used for computing the // derivative can be constructed as follows. // // CostFunction* cost_function // = new NumericDiffCostFunction<MyScalarCostFunctor, CENTRAL, 1, 2, 2>( // new MyScalarCostFunctor(1.0)); ^ ^ ^ ^ // | | | | // Finite Differencing Scheme -+ | | | // Dimension of residual ------------+ | | // Dimension of x ----------------------+ | // Dimension of y -------------------------+ // // In this example, there is usually an instance for each measurement of k. // // In the instantiation above, the template parameters following // "MyScalarCostFunctor", "1, 2, 2", describe the functor as computing // a 1-dimensional output from two arguments, both 2-dimensional. // // The framework can currently accommodate cost functions of up to 10 // independent variables, and there is no limit on the dimensionality // of each of them. // // The central difference method is considerably more accurate at the cost of // twice as many function evaluations than forward difference. Consider using // central differences begin with, and only after that works, trying forward // difference to improve performance. // // TODO(sameeragarwal): Add support for dynamic number of residuals. // // WARNING #1: A common beginner's error when first using // NumericDiffCostFunction is to get the sizing wrong. In particular, // there is a tendency to set the template parameters to (dimension of // residual, number of parameters) instead of passing a dimension // parameter for *every parameter*. In the example above, that would // be <MyScalarCostFunctor, 1, 2>, which is missing the last '2' // argument. Please be careful when setting the size parameters. // //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// // // ALTERNATE INTERFACE // // For a variety of reason, including compatibility with legacy code, // NumericDiffCostFunction can also take CostFunction objects as // input. The following describes how. // // To get a numerically differentiated cost function, define a // subclass of CostFunction such that the Evaluate() function ignores // the jacobian parameter. The numeric differentiation wrapper will // fill in the jacobian parameter if necessary by repeatedly calling // the Evaluate() function with small changes to the appropriate // parameters, and computing the slope. For performance, the numeric // differentiation wrapper class is templated on the concrete cost // function, even though it could be implemented only in terms of the // virtual CostFunction interface. // // The numerically differentiated version of a cost function for a cost function // can be constructed as follows: // // CostFunction* cost_function // = new NumericDiffCostFunction<MyCostFunction, CENTRAL, 1, 4, 8>( // new MyCostFunction(...), TAKE_OWNERSHIP); // // where MyCostFunction has 1 residual and 2 parameter blocks with sizes 4 and 8 // respectively. Look at the tests for a more detailed example. // // TODO(keir): Characterize accuracy; mention pitfalls; provide alternatives. #ifndef CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_ #define CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_ #include "Eigen/Dense" #include "ceres/cost_function.h" #include "ceres/internal/numeric_diff.h" #include "ceres/internal/scoped_ptr.h" #include "ceres/sized_cost_function.h" #include "ceres/types.h" #include "glog/logging.h" namespace ceres { template <typename CostFunctor, NumericDiffMethod method = CENTRAL, int kNumResiduals = 0, // Number of residuals, or ceres::DYNAMIC int N0 = 0, // Number of parameters in block 0. int N1 = 0, // Number of parameters in block 1. int N2 = 0, // Number of parameters in block 2. int N3 = 0, // Number of parameters in block 3. int N4 = 0, // Number of parameters in block 4. int N5 = 0, // Number of parameters in block 5. int N6 = 0, // Number of parameters in block 6. int N7 = 0, // Number of parameters in block 7. int N8 = 0, // Number of parameters in block 8. int N9 = 0> // Number of parameters in block 9. class NumericDiffCostFunction : public SizedCostFunction<kNumResiduals, N0, N1, N2, N3, N4, N5, N6, N7, N8, N9> { public: NumericDiffCostFunction(CostFunctor* functor, const double relative_step_size = 1e-6) :functor_(functor), ownership_(TAKE_OWNERSHIP), relative_step_size_(relative_step_size) {} NumericDiffCostFunction(CostFunctor* functor, Ownership ownership, const double relative_step_size = 1e-6) : functor_(functor), ownership_(ownership), relative_step_size_(relative_step_size) {} ~NumericDiffCostFunction() { if (ownership_ != TAKE_OWNERSHIP) { functor_.release(); } } virtual bool Evaluate(double const* const* parameters, double* residuals, double** jacobians) const { using internal::FixedArray; using internal::NumericDiff; const int kNumParameters = N0 + N1 + N2 + N3 + N4 + N5 + N6 + N7 + N8 + N9; const int kNumParameterBlocks = (N0 > 0) + (N1 > 0) + (N2 > 0) + (N3 > 0) + (N4 > 0) + (N5 > 0) + (N6 > 0) + (N7 > 0) + (N8 > 0) + (N9 > 0); // Get the function value (residuals) at the the point to evaluate. if (!internal::EvaluateImpl<CostFunctor, N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>( functor_.get(), parameters, residuals, functor_.get())) { return false; } if (!jacobians) { return true; } // Create a copy of the parameters which will get mutated. FixedArray<double> parameters_copy(kNumParameters); FixedArray<double*> parameters_reference_copy(kNumParameterBlocks); parameters_reference_copy[0] = parameters_copy.get(); if (N1) parameters_reference_copy[1] = parameters_reference_copy[0] + N0; if (N2) parameters_reference_copy[2] = parameters_reference_copy[1] + N1; if (N3) parameters_reference_copy[3] = parameters_reference_copy[2] + N2; if (N4) parameters_reference_copy[4] = parameters_reference_copy[3] + N3; if (N5) parameters_reference_copy[5] = parameters_reference_copy[4] + N4; if (N6) parameters_reference_copy[6] = parameters_reference_copy[5] + N5; if (N7) parameters_reference_copy[7] = parameters_reference_copy[6] + N6; if (N8) parameters_reference_copy[8] = parameters_reference_copy[7] + N7; if (N9) parameters_reference_copy[9] = parameters_reference_copy[8] + N8; #define COPY_PARAMETER_BLOCK(block) \ if (N ## block) memcpy(parameters_reference_copy[block], \ parameters[block], \ sizeof(double) * N ## block); // NOLINT COPY_PARAMETER_BLOCK(0); COPY_PARAMETER_BLOCK(1); COPY_PARAMETER_BLOCK(2); COPY_PARAMETER_BLOCK(3); COPY_PARAMETER_BLOCK(4); COPY_PARAMETER_BLOCK(5); COPY_PARAMETER_BLOCK(6); COPY_PARAMETER_BLOCK(7); COPY_PARAMETER_BLOCK(8); COPY_PARAMETER_BLOCK(9); #undef COPY_PARAMETER_BLOCK #define EVALUATE_JACOBIAN_FOR_BLOCK(block) \ if (N ## block && jacobians[block] != NULL) { \ if (!NumericDiff<CostFunctor, \ method, \ kNumResiduals, \ N0, N1, N2, N3, N4, N5, N6, N7, N8, N9, \ block, \ N ## block >::EvaluateJacobianForParameterBlock( \ functor_.get(), \ residuals, \ relative_step_size_, \ parameters_reference_copy.get(), \ jacobians[block])) { \ return false; \ } \ } EVALUATE_JACOBIAN_FOR_BLOCK(0); EVALUATE_JACOBIAN_FOR_BLOCK(1); EVALUATE_JACOBIAN_FOR_BLOCK(2); EVALUATE_JACOBIAN_FOR_BLOCK(3); EVALUATE_JACOBIAN_FOR_BLOCK(4); EVALUATE_JACOBIAN_FOR_BLOCK(5); EVALUATE_JACOBIAN_FOR_BLOCK(6); EVALUATE_JACOBIAN_FOR_BLOCK(7); EVALUATE_JACOBIAN_FOR_BLOCK(8); EVALUATE_JACOBIAN_FOR_BLOCK(9); #undef EVALUATE_JACOBIAN_FOR_BLOCK return true; } private: internal::scoped_ptr<CostFunctor> functor_; Ownership ownership_; const double relative_step_size_; }; } // namespace ceres #endif // CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_