| // 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. |
| // |
| // NumericDiffCostFunction also supports cost functions with a |
| // runtime-determined number of residuals. For example: |
| // |
| // CostFunction* cost_function |
| // = new NumericDiffCostFunction<MyScalarCostFunctor, CENTRAL, DYNAMIC, 2, 2>( |
| // new CostFunctorWithDynamicNumResiduals(1.0), ^ ^ ^ |
| // TAKE_OWNERSHIP, | | | |
| // runtime_number_of_residuals); <----+ | | | |
| // | | | | |
| // | | | | |
| // Actual number of residuals ------+ | | | |
| // Indicate dynamic number of residuals --------------------+ | | |
| // Dimension of x ------------------------------------------------+ | |
| // Dimension of y ---------------------------------------------------+ |
| // |
| // 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. |
| // |
| // 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, |
| Ownership ownership = TAKE_OWNERSHIP, |
| int num_residuals = kNumResiduals, |
| const double relative_step_size = 1e-6) |
| :functor_(functor), |
| ownership_(ownership), |
| relative_step_size_(relative_step_size) { |
| if (kNumResiduals == DYNAMIC) { |
| SizedCostFunction<kNumResiduals, |
| N0, N1, N2, N3, N4, |
| N5, N6, N7, N8, N9> |
| ::set_num_residuals(num_residuals); |
| } |
| } |
| |
| ~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 == NULL) { |
| 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_, \ |
| SizedCostFunction<kNumResiduals, \ |
| N0, N1, N2, N3, N4, \ |
| N5, N6, N7, N8, N9>::num_residuals(), \ |
| 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_ |
