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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2015 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// 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 {
+// explicit 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 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 reasons, 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 <array>
+#include <memory>
+
+#include "Eigen/Dense"
+#include "ceres/cost_function.h"
+#include "ceres/internal/numeric_diff.h"
+#include "ceres/internal/parameter_dims.h"
+#include "ceres/numeric_diff_options.h"
+#include "ceres/sized_cost_function.h"
+#include "ceres/types.h"
+#include "glog/logging.h"
+
+namespace ceres {
+
+template <typename CostFunctor,
+ NumericDiffMethodType method = CENTRAL,
+ int kNumResiduals = 0, // Number of residuals, or ceres::DYNAMIC
+ int... Ns> // Parameters dimensions for each block.
+class NumericDiffCostFunction : public SizedCostFunction<kNumResiduals, Ns...> {
+ public:
+ NumericDiffCostFunction(
+ CostFunctor* functor,
+ Ownership ownership = TAKE_OWNERSHIP,
+ int num_residuals = kNumResiduals,
+ const NumericDiffOptions& options = NumericDiffOptions())
+ : functor_(functor),
+ ownership_(ownership),
+ options_(options) {
+ if (kNumResiduals == DYNAMIC) {
+ SizedCostFunction<kNumResiduals, Ns...>::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;
+
+ using ParameterDims =
+ typename SizedCostFunction<kNumResiduals, Ns...>::ParameterDims;
+ using Parameters = typename ParameterDims::Parameters;
+
+ constexpr int kNumParameters = ParameterDims::kNumParameters;
+ constexpr int kNumParameterBlocks = ParameterDims::kNumParameterBlocks;
+
+ // Get the function value (residuals) at the the point to evaluate.
+ if (!internal::VariadicEvaluate<ParameterDims>(*functor_,
+ parameters,
+ residuals)) {
+ return false;
+ }
+
+ if (jacobians == NULL) {
+ return true;
+ }
+
+ // Create a copy of the parameters which will get mutated.
+ FixedArray<double> parameters_copy(kNumParameters);
+ std::array<double*, kNumParameterBlocks> parameters_reference_copy =
+ ParameterDims::GetUnpackedParameters(parameters_copy.get());
+
+ for (int block = 0; block < kNumParameterBlocks; ++block) {
+ memcpy(parameters_reference_copy[block], parameters[block],
+ sizeof(double) * ParameterDims::GetDim(block));
+ }
+
+ internal::EvaluateJacobianForParameterBlocks<ParameterDims>::template Apply<
+ method, kNumResiduals>(
+ functor_.get(),
+ residuals,
+ options_,
+ SizedCostFunction<kNumResiduals, Ns...>::num_residuals(),
+ parameters_reference_copy.data(),
+ jacobians);
+
+ return true;
+ }
+
+ private:
+ std::unique_ptr<CostFunctor> functor_;
+ Ownership ownership_;
+ NumericDiffOptions options_;
+};
+
+} // namespace ceres
+
+#endif // CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_