include/ceres/numeric_diff_first_order_function.h

// Ceres Solver - A fast non-linear least squares minimizer
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// http://ceres-solver.org/
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// Author: sameeragarwal@google.com (Sameer Agarwal)

#ifndef CERES_PUBLIC_NUMERIC_DIFF_FIRST_ORDER_FUNCTION_H_
#define CERES_PUBLIC_NUMERIC_DIFF_FIRST_ORDER_FUNCTION_H_

#include <algorithm>
#include <memory>

#include "ceres/first_order_function.h"
#include "ceres/internal/eigen.h"
#include "ceres/internal/fixed_array.h"
#include "ceres/internal/numeric_diff.h"
#include "ceres/internal/parameter_dims.h"
#include "ceres/internal/variadic_evaluate.h"
#include "ceres/numeric_diff_options.h"
#include "ceres/types.h"

namespace ceres {

// Creates FirstOrderFunctions as needed by the GradientProblem
// framework, with gradients computed via numeric differentiation. For
// more information on numeric differentiation, see the wikipedia
// article at https://en.wikipedia.org/wiki/Numerical_differentiation
//
// To get an numerically differentiated cost function, you must define
// a class with an operator() (a functor) that computes the cost.
//
// The function must write the computed value in the last argument
// (the only non-const one) and return true to indicate success.
//
// For example, consider a scalar error e = x'y - a, where both x and y are
// two-dimensional column vector parameters, the prime sign indicates
// transposition, and a is a constant.
//
// To write an numerically-differentiable cost function for the above model,
// first define the object
//
//  class QuadraticCostFunctor {
//   public:
//    explicit QuadraticCostFunctor(double a) : a_(a) {}
//    bool operator()(const double* const xy, double* cost) const {
//      constexpr int kInputVectorLength = 2;
//      const double* const x = xy;
//      const double* const y = xy + kInputVectorLength;
//      *cost = x[0] * y[0] + x[1] * y[1] - a_;
//      return true;
//    }
//
//   private:
//    double a_;
//  };
//
//
// Note that in the declaration of operator() the input parameters xy
// come first, and are passed as const pointers to array of
// doubles. The output cost is the last parameter.
//
// Then given this class definition, the numerically differentiated
// first order function with central differences used for computing the
// derivative can be constructed as follows.
//
//   FirstOrderFunction* function
//       = new NumericDiffFirstOrderFunction<MyScalarCostFunctor, CENTRAL, 4>(
//           new QuadraticCostFunctor(1.0));                   ^     ^     ^
//                                                             |     |     |
//                                 Finite Differencing Scheme -+     |     |
//                                 Dimension of xy ------------------------+
//
//
// In the instantiation above, the template parameters following
// "QuadraticCostFunctor", "CENTRAL, 4", describe the finite
// differencing scheme as "central differencing" and the functor as
// computing its cost from a 4 dimensional input.
template <typename FirstOrderFunctor,
          NumericDiffMethodType method,
          int kNumParameters>
class NumericDiffFirstOrderFunction final : public FirstOrderFunction {
 public:
  explicit NumericDiffFirstOrderFunction(
      FirstOrderFunctor* functor,
      Ownership ownership = TAKE_OWNERSHIP,
      const NumericDiffOptions& options = NumericDiffOptions())
      : functor_(functor), ownership_(ownership), options_(options) {
    static_assert(kNumParameters > 0, "kNumParameters must be positive");
  }

  ~NumericDiffFirstOrderFunction() override {
    if (ownership_ != TAKE_OWNERSHIP) {
      functor_.release();
    }
  }

  bool Evaluate(const double* const parameters,
                double* cost,
                double* gradient) const override {
    using ParameterDims = internal::StaticParameterDims<kNumParameters>;
    constexpr int kNumResiduals = 1;

    // Get the function value (cost) at the the point to evaluate.
    if (!internal::VariadicEvaluate<ParameterDims>(
            *functor_, &parameters, cost)) {
      return false;
    }

    if (gradient == nullptr) {
      return true;
    }

    // Create a copy of the parameters which will get mutated.
    internal::FixedArray<double, 32> parameters_copy(kNumParameters);
    std::copy_n(parameters, kNumParameters, parameters_copy.data());
    double* parameters_ptr = parameters_copy.data();
    internal::EvaluateJacobianForParameterBlocks<
        ParameterDims>::template Apply<method, kNumResiduals>(functor_.get(),
                                                              cost,
                                                              options_,
                                                              kNumResiduals,
                                                              &parameters_ptr,
                                                              &gradient);
    return true;
  }

  int NumParameters() const override { return kNumParameters; }

  const FirstOrderFunctor& functor() const { return *functor_; }

 private:
  std::unique_ptr<FirstOrderFunctor> functor_;
  Ownership ownership_;
  NumericDiffOptions options_;
};

}  // namespace ceres

#endif  // CERES_PUBLIC_NUMERIC_DIFF_FIRST_ORDER_FUNCTION_H_