// 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) | |
// | |
// 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'y)^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. | |
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 final | |
: public SizedCostFunction<kNumResiduals, Ns...> { | |
public: | |
// Takes ownership of functor by default. Uses the template-provided | |
// value for the number of residuals ("kNumResiduals"). | |
explicit AutoDiffCostFunction(CostFunctor* functor, | |
Ownership ownership = TAKE_OWNERSHIP) | |
: functor_(functor), ownership_(ownership) { | |
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 by default. 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, | |
Ownership ownership = TAKE_OWNERSHIP) | |
: functor_(functor), ownership_(ownership) { | |
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); | |
} | |
AutoDiffCostFunction(AutoDiffCostFunction&& other) | |
: functor_(std::move(other.functor_)), ownership_(other.ownership_) {} | |
virtual ~AutoDiffCostFunction() { | |
// Manually release pointer if configured to not take ownership rather than | |
// deleting only if ownership is taken. | |
// This is to stay maximally compatible to old user code which may have | |
// forgotten to implement a virtual destructor, from when the | |
// AutoDiffCostFunction always took ownership. | |
if (ownership_ == DO_NOT_TAKE_OWNERSHIP) { | |
functor_.release(); | |
} | |
} | |
// 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. | |
bool Evaluate(double const* const* parameters, | |
double* residuals, | |
double** jacobians) const override { | |
using ParameterDims = | |
typename SizedCostFunction<kNumResiduals, Ns...>::ParameterDims; | |
if (!jacobians) { | |
return internal::VariadicEvaluate<ParameterDims>( | |
*functor_, parameters, residuals); | |
} | |
return internal::AutoDifferentiate<kNumResiduals, ParameterDims>( | |
*functor_, | |
parameters, | |
SizedCostFunction<kNumResiduals, Ns...>::num_residuals(), | |
residuals, | |
jacobians); | |
}; | |
const CostFunctor& functor() const { return *functor_; } | |
private: | |
std::unique_ptr<CostFunctor> functor_; | |
Ownership ownership_; | |
}; | |
} // namespace ceres | |