RootFinder.h

#ifndef theplu_yat_utility_root_finder_
#define theplu_yat_utility_root_finder_

// $Id: RootFinder.h 4252 2022-11-18 02:54:04Z peter $

/*
  Copyright (C) 2022 Peter Johansson

  This file is part of the yat library, https://dev.thep.lu.se/yat

  The yat library is free software; you can redistribute it and/or
  modify it under the terms of the GNU General Public License as
  published by the Free Software Foundation; either version 3 of the
  License, or (at your option) any later version.

  The yat library is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
  General Public License for more details.

  You should have received a copy of the GNU General Public License
  along with yat. If not, see <https://www.gnu.org/licenses/>.
*/

#include "univariable/f.h"
#include "yat_assert.h"

#include <gsl/gsl_errno.h>
#include <gsl/gsl_roots.h>

#include <limits>
#include <memory>

namespace theplu {
namespace yat {
namespace utility {

  class RootFinder
  {
  public:
    RootFinder(const RootFinder&) = delete;

    RootFinder& operator=(const RootFinder&) = delete;

    unsigned int epochs(void) const;

    const char* name(void) const;

    class Stopper
    {
    public:
      virtual bool operator()(const gsl_root_fsolver*)=0;
    };

    class Interval : public Stopper
    {
    public:
      Interval(double epsabs, double epsrel);

      bool operator()(const gsl_root_fsolver*);
    private:
      double epsabs_;
      double epsrel_;
    };

    class Delta : public Stopper
    {
    public:
      Delta(double epsabs, double epsrel);

      bool operator()(const gsl_root_fsolver*);
    private:
      double epsabs_;
      double epsrel_;
      std::unique_ptr<double> prev_;
    };

    template<class FUNC>
    class Residual : public Stopper
    {
    public:
      Residual(const FUNC& func, double epsabs)
        : func_(func), epsabs_(epsabs)
      {}

      bool operator()(const gsl_root_fsolver*);
    private:
      const FUNC& func_;
      double epsabs_;
    };

    template<class FUNC>
    double operator()(FUNC& func, double lower, double upper,Stopper&& stopper);

    template<class FUNC>
    double operator()(FUNC& func, double lower, double upper,
                      Stopper&& stopper, unsigned int max_epochs);

  protected:
    RootFinder(const gsl_root_fsolver_type* t);
  private:
    const gsl_root_fsolver_type* type_;
    struct GslFree
    {
      void operator()(gsl_root_fsolver*) const;
    };
    std::unique_ptr<gsl_root_fsolver, GslFree> solver_;
    unsigned int epochs_;
  };


  // template implementation
  template<class FUNC>
  double RootFinder::operator()(FUNC& func, double lower, double upper,
                                RootFinder::Stopper&& stopper)
  {
    unsigned int max_epochs = std::numeric_limits<unsigned int>::max();
    return (*this)(func, lower, upper, std::move(stopper), max_epochs);
  }


  template<class FUNC>
  double
  RootFinder::operator()(FUNC& func, double lower, double upper,
                         RootFinder::Stopper&& stopper,
                         unsigned int max_epochs)
  {
    gsl_function gsl_func;
    gsl_func.function = univariable::f<FUNC>;
    gsl_func.params = &func;
    gsl_root_fsolver_set(solver_.get(), &gsl_func, lower, upper);

    for (epochs_=0; epochs_<max_epochs && !stopper(solver_.get()); ++epochs_) {
      int status = gsl_root_fsolver_iterate(solver_.get());
      if (status) {
        std::ostringstream ss;
        ss << "RootFinder: at x = "
           << gsl_root_fsolver_root(solver_.get());
        throw GSL_error(ss.str(), status);

      }
    }

    return gsl_root_fsolver_root(solver_.get());
  }


  template<class FUNC>
  bool RootFinder::Residual<FUNC>::operator()(const gsl_root_fsolver* s)
  {
    double x = gsl_root_fsolver_root(s);
    double f = func_(x);
    return gsl_root_test_residual(f, epsabs_) == GSL_SUCCESS;
  }

}}}
#endif