Line data    Source code

       1             : #pragma once
       2             : 
       3             : #include "Functional.h"
       4             : #include "LineSearchMethod.h"
       5             : 
       6             : namespace elsa
       7             : {
       8             :     /**
       9             :      * @brief Newton-Raphson method for optimizing $\frac{\partial}{\partial \alpha}f(x + \alpha
      10             :      * d)$, with $x$ the current guess, $d$ the search direction and $f$ the optimizing function.
      11             :      *
      12             :      * The Newton-Raphson method optimizes the function above, by iteratively applying
      13             :      * $$
      14             :      * \alpha = \frac{\langle f^\prime(x), \, d\rangle}{\langle d, \, f^{\prime \prime} d\rangle}
      15             :      * $$
      16             :      * where $f^{\prime \prime}$ is the Hessian of $f$. Hence, $f$ needs to be
      17             :      * twice continuously differentiable.
      18             :      *
      19             :      * Reference:
      20             :      * - An Introduction to the Conjugate Gradient Method Without the Agonizing Pain, by Jonathan
      21             :      * Richard Shewchuk https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf
      22             :      */
      23             :     template <class data_t>
      24             :     class NewtonRaphson : public LineSearchMethod<data_t>
      25             :     {
      26             :     public:
      27             :         explicit NewtonRaphson(const Functional<data_t>& f, index_t iterations = 5);
      28             : 
      29           2 :         ~NewtonRaphson() override = default;
      30             : 
      31             :         data_t solve(DataContainer<data_t> xi, DataContainer<data_t> di) override;
      32             : 
      33             :         /// implement the polymorphic comparison operation
      34             :         bool isEqual(const LineSearchMethod<data_t>& other) const override;
      35             : 
      36             :     private:
      37             :         /// implement the polymorphic clone operation
      38             :         NewtonRaphson<data_t>* cloneImpl() const override;
      39             : 
      40             :         index_t iters_;
      41             :     };
      42             : } // namespace elsa