include/ceres/autodiff_cost_function.h

// Ceres Solver - A fast non-linear least squares minimizer
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// Author: sameeragarwal@google.com (Sameer Agarwal)
//
// Create CostFunctions as needed by the least squares framework, with
// Jacobians computed via automatic differentiation. For more
// information on automatic differentiation, see the wikipedia article
// at http://en.wikipedia.org/wiki/Automatic_differentiation
//
// To get an auto differentiated cost function, you must define a class with a
// templated operator() (a functor) that computes the cost function in terms of
// the template parameter T. The autodiff framework substitutes appropriate
// "jet" objects for T in order to compute the derivative when necessary, but
// this is hidden, and you should write the function as if T were a scalar type
// (e.g. a double-precision floating point number).
//
// 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 auto-differentiable cost function for the above model, first
// define the object
//
//   class MyScalarCostFunctor {
//     MyScalarCostFunctor(double k): k_(k) {}
//
//     template <typename T>
//     bool operator()(const T* const x , const T* const y, T* e) const {
//       e[0] = T(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 T. 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, e is a scalar, so only e[0] is set.
//
// Then given this class definition, the auto differentiated cost function for
// it can be constructed as follows.
//
//   CostFunction* cost_function
//       = new AutoDiffCostFunction<MyScalarCostFunctor, 1, 2, 2>(
//            new MyScalarCostFunctor(1.0));             ^  ^  ^
//                                                       |  |  |
//                            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.
//
// AutoDiffCostFunction also supports cost functions with a
// runtime-determined number of residuals. For example:
//
//   CostFunction* cost_function
//       = new AutoDiffCostFunction<MyScalarCostFunctor, DYNAMIC, 2, 2>(
//           new CostFunctorWithDynamicNumResiduals(1.0),   ^     ^  ^
//           runtime_number_of_residuals); <----+           |     |  |
//                                              |           |     |  |
//                                              |           |     |  |
//             Actual number of residuals ------+           |     |  |
//             Indicate dynamic number of residuals --------+     |  |
//             Dimension of x ------------------------------------+  |
//             Dimension of y ---------------------------------------+
//
// WARNING #1: Since the functor will get instantiated with different types for
// T, you must convert from other numeric types to T before mixing
// computations with other variables of type T. In the example above, this is
// seen where instead of using k_ directly, k_ is wrapped with T(k_).
//
// WARNING #2: A common beginner's error when first using autodiff cost
// functions 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.

#ifndef CERES_PUBLIC_AUTODIFF_COST_FUNCTION_H_
#define CERES_PUBLIC_AUTODIFF_COST_FUNCTION_H_

#include <memory>
#include "ceres/internal/autodiff.h"
#include "ceres/sized_cost_function.h"
#include "ceres/types.h"
#include "glog/logging.h"

namespace ceres {

// A cost function which computes the derivative of the cost with respect to
// the parameters (a.k.a. the jacobian) using an auto differentiation framework.
// The first template argument is the functor object, described in the header
// comment. The second argument is the dimension of the residual (or
// ceres::DYNAMIC to indicate it will be set at runtime), and subsequent
// arguments describe the size of the Nth parameter, one per parameter.
//
// The constructors take ownership of the cost functor.
//
// If the number of residuals (argument kNumResiduals below) is
// ceres::DYNAMIC, then the two-argument constructor must be used. The
// second constructor takes a number of residuals (in addition to the
// templated number of residuals). This allows for varying the number
// of residuals for a single autodiff cost function at runtime.
template <typename CostFunctor,
          int kNumResiduals,  // Number of residuals, or ceres::DYNAMIC.
          int... Ns>          // Number of parameters in each parameter block.
class AutoDiffCostFunction : public SizedCostFunction<kNumResiduals, Ns...> {
 public:
  // Takes ownership of functor. Uses the template-provided value for the
  // number of residuals ("kNumResiduals").
  explicit AutoDiffCostFunction(CostFunctor* functor)
      : functor_(functor) {
    static_assert(kNumResiduals != DYNAMIC,
                  "Can't run the fixed-size constructor if the number of "
                  "residuals is set to ceres::DYNAMIC.");
  }

  // Takes ownership of functor. Ignores the template-provided
  // kNumResiduals in favor of the "num_residuals" argument provided.
  //
  // This allows for having autodiff cost functions which return varying
  // numbers of residuals at runtime.
  AutoDiffCostFunction(CostFunctor* functor, int num_residuals)
      : functor_(functor) {
    static_assert(kNumResiduals == DYNAMIC,
                  "Can't run the dynamic-size constructor if the number of "
                  "residuals is not ceres::DYNAMIC.");
    SizedCostFunction<kNumResiduals, Ns...>::set_num_residuals(num_residuals);
  }

  virtual ~AutoDiffCostFunction() {}

  // Implementation details follow; clients of the autodiff cost function should
  // not have to examine below here.
  //
  // To handle variadic cost functions, some template magic is needed. It's
  // mostly hidden inside autodiff.h.
  virtual bool Evaluate(double const* const* parameters,
                        double* residuals,
                        double** jacobians) const {
    using ParameterDims =
        typename SizedCostFunction<kNumResiduals, Ns...>::ParameterDims;

    if (!jacobians) {
      return internal::VariadicEvaluate<ParameterDims>(*functor_,
                                                       parameters,
                                                       residuals);
    }
    return internal::AutoDifferentiate<ParameterDims>(
        *functor_,
        parameters,
        SizedCostFunction<kNumResiduals, Ns...>::num_residuals(),
        residuals,
        jacobians);
  }

 private:
  std::unique_ptr<CostFunctor> functor_;
};

}  // namespace ceres

#endif  // CERES_PUBLIC_AUTODIFF_COST_FUNCTION_H_