NewtonRaphson.cpp

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// to compile:  g++ -I. -lm NewtonRaphson.cpp<br />

/***************************************************************************
 *   Copyright (C) 2009 by Clark Sims                                      *
 *   http://AcumenSoftwareInc.com/WhoWeAre/Clark_Sims.html                 *
 *   ClarkSims@AcumenSoftwareInc.com                                       *
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 *   it under the terms of the GNU General Public License as published by  *
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 *   This program is distributed in the hope that it will be useful,       *
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 *   GNU General Public License for more details.                          *
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#include "NewtonRaphson.h"
#include <math.h>

class Newton_functor {
public:
  double _offset;
  
  Newton_functor( double offset) : _offset(offset) { }

  double f( double x) {
    return exp( x) - _offset;
  }
  
  double df( double x) {
    return exp( x);
  }
};

int main() {
  Newton_functor functor( 5);

  {
    NewtonRaphsonSolve0< Newton_functor, double > 
      newton( 
             1.2,                  // X0
             1e-8,                 // Epsilon
             true,                 // Twice_df
             100,                  // max_iter
             functor,              // F
             &Newton_functor::f,   // f
             &Newton_functor::df); // df

    cout << "running iteration with f and df defined, over all real numbers" << endl;
    newton.do_iteration( &cout);

    cout << "running iteration with f, df and d2f defined, over all real numbers" << endl;
    newton.set_d2f( &Newton_functor::df);
    newton.do_iteration( &cout);

    cout << "running iteration with f, df and d2f defined, over the interval [1.6, infinity)" << endl;
    newton.set_check_boundary( true);
    newton.set_max_x( 1.6);
    newton.do_iteration( &cout);
  }

  cout << "running a numerically equivalent example, where functor._offset = 0, and newton._fsolve = 5.0" 
       << endl;

  functor._offset = 0;
  {
    NewtonRaphsonSolve0< Newton_functor, double > 
      newton( 
             1.2,                  // X0
             1e-8,                 // Epsilon
             true,                 // Twice_df
             100,                  // max_iter
             functor,              // F
             &Newton_functor::f,   // f
             &Newton_functor::df,  // df
             0,                    // d2f
             5.0);                 // Fsolve

    cout << "running iteration with f and df defined, over all real numbers" << endl;
    newton.do_iteration( &cout);

    cout << "running iteration with f, df and d2f defined, over all real numbers" << endl;
    newton.set_d2f( &Newton_functor::df);
    newton.do_iteration( &cout);

    cout << "running iteration with f, df and d2f defined, over the interval [1.6, infinity)" << endl;
    newton.set_check_boundary( true);
    newton.set_max_x( 1.6);
    newton.do_iteration( &cout);
  }

  return 0;
}

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