newton_method.cpp

/****************************************************************************************************************/
/*                                                                                                              */
/*   OpenNN: Open Neural Networks Library                                                                       */
/*   www.artelnics.com/opennn                                                                                   */
/*                                                                                                              */
/*   N E W T O N   M E T H O D   C L A S S                                                                      */
/*                                                                                                              */
/*   Roberto Lopez                                                                                              */
/*   Artelnics - Making intelligent use of data                                                                 */
/*   [email protected]                                                                                 */
/*                                                                                                              */ 
/****************************************************************************************************************/

// OpenNN includes

#include "newton_method.h"

namespace OpenNN
{

// DEFAULT CONSTRUCTOR


NewtonMethod::NewtonMethod(void) 
 : TrainingAlgorithm()
{
   set_default();
}


// PERFORMANCE FUNCTIONAL CONSTRUCTOR 


NewtonMethod::NewtonMethod(PerformanceFunctional* new_performance_functional_pointer)
: TrainingAlgorithm(new_performance_functional_pointer)
{
   training_rate_algorithm.set_performance_functional_pointer(new_performance_functional_pointer);

   set_default();
}


// XML CONSTRUCTOR


NewtonMethod::NewtonMethod(const tinyxml2::XMLDocument& document)
 : TrainingAlgorithm(document)
{
   set_default();

   from_XML(document);
}


// DESTRUCTOR


NewtonMethod::~NewtonMethod(void)
{
}


// METHODS

// const TrainingRateAlgorithm& get_training_rate_algorithm(void) const method


const TrainingRateAlgorithm& NewtonMethod::get_training_rate_algorithm(void) const
{
   return(training_rate_algorithm);
}


// TrainingRateAlgorithm* get_training_rate_algorithm_pointer(void) method


TrainingRateAlgorithm* NewtonMethod::get_training_rate_algorithm_pointer(void)
{
   return(&training_rate_algorithm);
}


// const double& get_warning_parameters_norm(void) const method


const double& NewtonMethod::get_warning_parameters_norm(void) const
{
   return(warning_parameters_norm);       
}


// const double& get_warning_gradient_norm(void) const method


const double& NewtonMethod::get_warning_gradient_norm(void) const
{
   return(warning_gradient_norm);       
}


// const double& get_warning_training_rate(void) const method


const double& NewtonMethod::get_warning_training_rate(void) const
{
   return(warning_training_rate);
}


// const double& get_error_parameters_norm(void) const method


const double& NewtonMethod::get_error_parameters_norm(void) const
{
   return(error_parameters_norm);
}


// const double& get_error_gradient_norm(void) const method


const double& NewtonMethod::get_error_gradient_norm(void) const
{
   return(error_gradient_norm);
}


// const double& get_error_training_rate(void) const method


const double& NewtonMethod::get_error_training_rate(void) const
{
   return(error_training_rate);
}


// const double& get_minimum_parameters_increment_norm(void) const method


const double& NewtonMethod::get_minimum_parameters_increment_norm(void) const
{
   return(minimum_parameters_increment_norm);
}


// const double& get_minimum_performance_increase(void) const method


const double& NewtonMethod::get_minimum_performance_increase(void) const
{
   return(minimum_performance_increase);
}


// const double& get_performance_goal(void) const method


const double& NewtonMethod::get_performance_goal(void) const
{
   return(performance_goal);
}


// const double& get_gradient_norm_goal(void) const method


const double& NewtonMethod::get_gradient_norm_goal(void) const
{
   return(gradient_norm_goal);
}


// const size_t& get_maximum_generalization_performance_decreases(void) const method


const size_t& NewtonMethod::get_maximum_generalization_performance_decreases(void) const
{
   return(maximum_generalization_performance_decreases);
}


// const size_t& get_maximum_iterations_number(void) const method


const size_t& NewtonMethod::get_maximum_iterations_number(void) const
{
   return(maximum_iterations_number);
}


// const double& get_maximum_time(void) const method


const double& NewtonMethod::get_maximum_time(void) const
{
   return(maximum_time);
}


// const bool& get_reserve_parameters_history(void) const method


const bool& NewtonMethod::get_reserve_parameters_history(void) const
{
   return(reserve_parameters_history);     
}


// const bool& get_reserve_parameters_norm_history(void) const method 


const bool& NewtonMethod::get_reserve_parameters_norm_history(void) const
{
   return(reserve_parameters_norm_history);     
}


// const bool& get_reserve_performance_history(void) const method


const bool& NewtonMethod::get_reserve_performance_history(void) const
{
   return(reserve_performance_history);     
}


// const bool& get_reserve_gradient_history(void) const method


const bool& NewtonMethod::get_reserve_gradient_history(void) const
{
   return(reserve_gradient_history);     
}


// const bool& get_reserve_gradient_norm_history(void) const method


const bool& NewtonMethod::get_reserve_gradient_norm_history(void) const
{
   return(reserve_gradient_norm_history);     
}


// const bool& get_reserve_inverse_Hessian_history(void) const method


const bool& NewtonMethod::get_reserve_inverse_Hessian_history(void) const
{
   return(reserve_inverse_Hessian_history);
}


// const bool& get_reserve_training_direction_history(void) const method


const bool& NewtonMethod::get_reserve_training_direction_history(void) const
{
   return(reserve_training_direction_history);     
}


// const bool& get_reserve_training_rate_history(void) const method


const bool& NewtonMethod::get_reserve_training_rate_history(void) const
{
   return(reserve_training_rate_history);     
}


// const bool& get_reserve_elapsed_time_history(void) const method


const bool& NewtonMethod::get_reserve_elapsed_time_history(void) const
{
   return(reserve_elapsed_time_history);     
}


// const bool& get_reserve_generalization_performance_history(void) const method


const bool& NewtonMethod::get_reserve_generalization_performance_history(void) const
{
   return(reserve_generalization_performance_history);
}


// void set_performance_functional_pointer(PerformanceFunctional*) method


void NewtonMethod::set_performance_functional_pointer(PerformanceFunctional* new_performance_functional_pointer)
{
   performance_functional_pointer = new_performance_functional_pointer;

   training_rate_algorithm.set_performance_functional_pointer(new_performance_functional_pointer);
}


// void set_default(void) method

void NewtonMethod::set_default(void)
{
   // TRAINING PARAMETERS

   warning_parameters_norm = 1.0e6;
   warning_gradient_norm = 1.0e6;   
   warning_training_rate = 1.0e6;

   error_parameters_norm = 1.0e9;
   error_gradient_norm = 1.0e9;
   error_training_rate = 1.0e9;

   // STOPPING CRITERIA

   minimum_parameters_increment_norm = 0.0;

   minimum_performance_increase = 0.0;
   performance_goal = -1.0e99;
   gradient_norm_goal = 0.0;
   maximum_generalization_performance_decreases = 1000000;

   maximum_iterations_number = 1000;
   maximum_time = 1000.0;

   // TRAINING HISTORY

   reserve_parameters_history = false;
   reserve_parameters_norm_history = false;

   reserve_performance_history = true;
   reserve_gradient_history = false;
   reserve_gradient_norm_history = false;
   reserve_generalization_performance_history = false;

   reserve_training_direction_history = false;
   reserve_training_rate_history = false;
   reserve_elapsed_time_history = false;

   // UTILITIES

   display = true;
   display_period = 10;

}


// void set_warning_parameters_norm(const double&) method


void NewtonMethod::set_warning_parameters_norm(const double& new_warning_parameters_norm)
{
   // Control sentence (if debug)

   #ifndef NDEBUG 

   if(new_warning_parameters_norm < 0.0)
   {
      std::ostringstream buffer;

      buffer << "OpenNN Exception: NewtonMethod class.\n"
             << "void set_warning_parameters_norm(const double&) method.\n"
             << "Warning parameters norm must be equal or greater than 0.\n";

      throw std::logic_error(buffer.str());   
   }

   #endif

   // Set warning parameters norm

   warning_parameters_norm = new_warning_parameters_norm;     
}


// void set_warning_gradient_norm(const double&) method


void NewtonMethod::set_warning_gradient_norm(const double& new_warning_gradient_norm)
{
   // Control sentence (if debug)

   #ifndef NDEBUG 

   if(new_warning_gradient_norm < 0.0)
   {
      std::ostringstream buffer;

      buffer << "OpenNN Exception: NewtonMethod class.\n"
             << "void set_warning_gradient_norm(const double&) method.\n"
             << "Warning gradient norm must be equal or greater than 0.\n";

      throw std::logic_error(buffer.str());   
   }

   #endif

   // Set warning gradient norm

   warning_gradient_norm = new_warning_gradient_norm;     
}


// void set_warning_training_rate(const double&) method


void NewtonMethod::set_warning_training_rate(const double& new_warning_training_rate)
{
   // Control sentence (if debug)

   #ifndef NDEBUG 

   if(new_warning_training_rate < 0.0)
   {
      std::ostringstream buffer;

      buffer << "OpenNN Exception: NewtonMethod class.\n" 
             << "void set_warning_training_rate(const double&) method.\n"
             << "Warning training rate must be equal or greater than 0.\n";

      throw std::logic_error(buffer.str());   
   }

   #endif

   warning_training_rate = new_warning_training_rate;
}


// void set_error_parameters_norm(const double&) method


void NewtonMethod::set_error_parameters_norm(const double& new_error_parameters_norm)
{
   // Control sentence (if debug)

   #ifndef NDEBUG 

   if(new_error_parameters_norm < 0.0)
   {
      std::ostringstream buffer;

      buffer << "OpenNN Exception: NewtonMethod class.\n"
             << "void set_error_parameters_norm(const double&) method.\n"
             << "Error parameters norm must be equal or greater than 0.\n";

      throw std::logic_error(buffer.str());   
   }

   #endif

   // Set error parameters norm

   error_parameters_norm = new_error_parameters_norm;
}


// void set_error_gradient_norm(const double&) method


void NewtonMethod::set_error_gradient_norm(const double& new_error_gradient_norm)
{
   // Control sentence (if debug)

   #ifndef NDEBUG 

   if(new_error_gradient_norm < 0.0)
   {
      std::ostringstream buffer;

      buffer << "OpenNN Exception: NewtonMethod class.\n"
             << "void set_error_gradient_norm(const double&) method.\n"
             << "Error gradient norm must be equal or greater than 0.\n";

      throw std::logic_error(buffer.str());   
   }

   #endif

   // Set error gradient norm

   error_gradient_norm = new_error_gradient_norm;
}


// void set_error_training_rate(const double&) method


void NewtonMethod::set_error_training_rate(const double& new_error_training_rate)
{
   // Control sentence (if debug)

   #ifndef NDEBUG 

   if(new_error_training_rate < 0.0)
   {
      std::ostringstream buffer;

      buffer << "OpenNN Exception: NewtonMethod class.\n"
             << "void set_error_training_rate(const double&) method.\n"
             << "Error training rate must be equal or greater than 0.\n";

      throw std::logic_error(buffer.str());   
   }

   #endif

   // Set error training rate

   error_training_rate = new_error_training_rate;
}


// void set_minimum_parameters_increment_norm(const double&) method


void NewtonMethod::set_minimum_parameters_increment_norm(const double& new_minimum_parameters_increment_norm)
{
   // Control sentence (if debug)

   #ifndef NDEBUG 

   if(new_minimum_parameters_increment_norm < 0.0)
   {
      std::ostringstream buffer;

      buffer << "OpenNN Exception: NewtonMethod class.\n"
             << "void new_minimum_parameters_increment_norm(const double&) method.\n"
             << "Minimum parameters increment norm must be equal or greater than 0.\n";

      throw std::logic_error(buffer.str());   
   }

   #endif

   // Set error training rate

   minimum_parameters_increment_norm = new_minimum_parameters_increment_norm;
}


// void set_minimum_performance_increase(const double&) method


void NewtonMethod::set_minimum_performance_increase(const double& new_minimum_performance_increase)
{
   // Control sentence (if debug)

   #ifndef NDEBUG 

   if(new_minimum_performance_increase < 0.0)
   {
      std::ostringstream buffer;

      buffer << "OpenNN Exception: NewtonMethod class.\n"
             << "void set_minimum_performance_increase(const double&) method.\n"
             << "Minimum performance improvement must be equal or greater than 0.\n";

      throw std::logic_error(buffer.str());   
   }

   #endif

   // Set minimum performance improvement

   minimum_performance_increase = new_minimum_performance_increase;
}


// void set_performance_goal(const double&) method


void NewtonMethod::set_performance_goal(const double& new_performance_goal)
{
   performance_goal = new_performance_goal;
}


// void set_gradient_norm_goal(const double&) method


void NewtonMethod::set_gradient_norm_goal(const double& new_gradient_norm_goal)
{
   // Control sentence (if debug)

   #ifndef NDEBUG 

   if(new_gradient_norm_goal < 0.0)
   {
      std::ostringstream buffer;

      buffer << "OpenNN Exception: NewtonMethod class.\n"
             << "void set_gradient_norm_goal(const double&) method.\n"
             << "Gradient norm goal must be equal or greater than 0.\n";

      throw std::logic_error(buffer.str());   
   }

   #endif

   // Set gradient norm goal

   gradient_norm_goal = new_gradient_norm_goal;
}


// void set_maximum_generalization_performance_decreases(const size_t&) method


void NewtonMethod::set_maximum_generalization_performance_decreases(const size_t& new_maximum_generalization_performance_decreases)
{
   maximum_generalization_performance_decreases = new_maximum_generalization_performance_decreases;
}


// void set_maximum_iterations_number(size_t) method


void NewtonMethod::set_maximum_iterations_number(const size_t& new_maximum_iterations_number)
{
   maximum_iterations_number = new_maximum_iterations_number;
}


// void set_maximum_time(const double&) method


void NewtonMethod::set_maximum_time(const double& new_maximum_time)
{
   // Control sentence (if debug)

   #ifndef NDEBUG 

   if(new_maximum_time < 0.0)
   {
      std::ostringstream buffer;

      buffer << "OpenNN Exception: NewtonMethod class.\n"
             << "void set_maximum_time(const double&) method.\n"
             << "Maximum time must be equal or greater than 0.\n";

      throw std::logic_error(buffer.str());   
   }
   
   #endif

   // Set maximum time

   maximum_time = new_maximum_time;
}


// void set_reserve_parameters_history(bool) method


void NewtonMethod::set_reserve_parameters_history(const bool& new_reserve_parameters_history)
{
   reserve_parameters_history = new_reserve_parameters_history;     
}


// void set_reserve_parameters_norm_history(bool) method


void NewtonMethod::set_reserve_parameters_norm_history(const bool& new_reserve_parameters_norm_history)
{
   reserve_parameters_norm_history = new_reserve_parameters_norm_history;     
}


// void set_reserve_performance_history(bool) method


void NewtonMethod::set_reserve_performance_history(const bool& new_reserve_performance_history)
{
   reserve_performance_history = new_reserve_performance_history;     
}


// void set_reserve_gradient_history(bool) method


void NewtonMethod::set_reserve_gradient_history(const bool& new_reserve_gradient_history)
{
   reserve_gradient_history = new_reserve_gradient_history;    
}


// void set_reserve_gradient_norm_history(bool) method


void NewtonMethod::set_reserve_gradient_norm_history(const bool& new_reserve_gradient_norm_history)
{
   reserve_gradient_norm_history = new_reserve_gradient_norm_history;     
}


// void set_reserve_inverse_Hessian_history(bool) method


void NewtonMethod::set_reserve_inverse_Hessian_history(const bool& new_reserve_inverse_Hessian_history)
{
   reserve_inverse_Hessian_history = new_reserve_inverse_Hessian_history;
}


// void set_reserve_training_direction_history(bool) method


void NewtonMethod::set_reserve_training_direction_history(const bool& new_reserve_training_direction_history)
{
   reserve_training_direction_history = new_reserve_training_direction_history;          
}


// void set_reserve_training_rate_history(bool) method


void NewtonMethod::set_reserve_training_rate_history(const bool& new_reserve_training_rate_history)
{
   reserve_training_rate_history = new_reserve_training_rate_history;          
}


// void set_reserve_elapsed_time_history(bool) method


void NewtonMethod::set_reserve_elapsed_time_history(const bool& new_reserve_elapsed_time_history)
{
   reserve_elapsed_time_history = new_reserve_elapsed_time_history;     
}


// void set_reserve_generalization_performance_history(bool) method


void NewtonMethod::set_reserve_generalization_performance_history(const bool& new_reserve_generalization_performance_history)  
{
   reserve_generalization_performance_history = new_reserve_generalization_performance_history;
}


// void set_display_period(size_t) method


void NewtonMethod::set_display_period(const size_t& new_display_period)
{
   // Control sentence (if debug)

   #ifndef NDEBUG 
     
   if(new_display_period <= 0)
   {
      std::ostringstream buffer;

      buffer << "OpenNN Exception: NewtonMethod class.\n"
             << "void set_display_period(const double&) method.\n"
             << "First training rate must be greater than 0.\n";

      throw std::logic_error(buffer.str());   
   }

   #endif

   display_period = new_display_period;
}



// Vector<double> calculate_gradient_descent_training_direction(const Vector<double>&) const method


Vector<double> NewtonMethod::calculate_gradient_descent_training_direction(const Vector<double>& gradient) const
{
    // Control sentence (if debug)

    #ifndef NDEBUG

    std::ostringstream buffer;

    if(!performance_functional_pointer)
    {
       buffer << "OpenNN Exception: NewtonMethod class.\n"
              << "Vector<double> calculate_gradient_descent_training_direction(const Vector<double>&) const method.\n"
              << "Performance functional pointer is NULL.\n";

       throw std::logic_error(buffer.str());
    }

    const NeuralNetwork* neural_network_pointer = performance_functional_pointer->get_neural_network_pointer();

    const size_t parameters_number = neural_network_pointer->count_parameters_number();

    const size_t gradient_size = gradient.size();

    if(gradient_size != parameters_number)
    {
       buffer << "OpenNN Exception: NewtonMethod class.\n"
              << "Vector<double> calculate_gradient_descent_training_direction(const Vector<double>&) const method.\n"
              << "Size of gradient (" << gradient_size << ") is not equal to number of parameters (" << parameters_number << ").\n";

       throw std::logic_error(buffer.str());
    }

    #endif

    return(gradient.calculate_normalized()*(-1.0));
}


// Vector<double> calculate_training_direction(const Vector<double>&, const Matrix<double>&) const method


Vector<double> NewtonMethod::calculate_training_direction
(const Vector<double>& gradient, const Matrix<double>& inverse_Hessian) const
{
   return((inverse_Hessian.dot(gradient)*(-1.0)).calculate_normalized());
}


// void resize_training_history(const size_t&) method


void NewtonMethod::NewtonMethodResults::resize_training_history(const size_t& new_size)
{
    // Control sentence (if debug)

    #ifndef NDEBUG

    if(Newton_method_pointer == NULL)
    {
       std::ostringstream buffer;

       buffer << "OpenNN Exception: NewtonMethodResults structure.\n"
              << "void resize_training_history(const size_t&) method.\n"
              << "NewtonMethod pointer is NULL.\n";

       throw std::logic_error(buffer.str());
    }

    #endif

    if(Newton_method_pointer->get_reserve_parameters_history())
    {
        parameters_history.resize(new_size);
    }

    if(Newton_method_pointer->get_reserve_parameters_norm_history())
    {
        parameters_norm_history.resize(new_size);
    }

    if(Newton_method_pointer->get_reserve_performance_history())
    {
        performance_history.resize(new_size);
    }

    if(Newton_method_pointer->get_reserve_generalization_performance_history())
    {
        generalization_performance_history.resize(new_size);
    }

    if(Newton_method_pointer->get_reserve_gradient_history())
    {
        gradient_history.resize(new_size);
    }

    if(Newton_method_pointer->get_reserve_gradient_norm_history())
    {
        gradient_norm_history.resize(new_size);
    }

    if(Newton_method_pointer->get_reserve_inverse_Hessian_history())
    {
        inverse_Hessian_history.resize(new_size);
    }

    if(Newton_method_pointer->get_reserve_training_direction_history())
    {
        training_direction_history.resize(new_size);
    }

    if(Newton_method_pointer->get_reserve_training_rate_history())
    {
        training_rate_history.resize(new_size);
    }

    if(Newton_method_pointer->get_reserve_elapsed_time_history())
    {
        elapsed_time_history.resize(new_size);
    }
}


// std::string to_string(void) const method


std::string NewtonMethod::NewtonMethodResults::to_string(void) const
{
   std::ostringstream buffer;

   // Parameters history

   if(!parameters_history.empty())
   {
      if(!parameters_history[0].empty())
      {
          buffer << "% Parameters history:\n"
                 << parameters_history << "\n"; 
      }
   }

   // Parameters norm history

   if(!parameters_norm_history.empty())
   {
       buffer << "% Parameters norm history:\n"
              << parameters_norm_history << "\n"; 
   }
   
   // performance history   

   if(!performance_history.empty())
   {
       buffer << "% performance history:\n"
              << performance_history << "\n"; 
   }

   // Generalization performance history

   if(!generalization_performance_history.empty())
   {
       buffer << "% Generalization performance history:\n"
              << generalization_performance_history << "\n"; 
   }

   // Gradient history 

   if(!gradient_history.empty())
   {
      if(!gradient_history[0].empty())
      {
          buffer << "% Gradient history:\n"
                 << gradient_history << "\n"; 
      }
   }

   // Gradient norm history

   if(!gradient_norm_history.empty())
   {
       buffer << "% Gradient norm history:\n"
              << gradient_norm_history << "\n"; 
   }

   // Inverse Hessian history

   if(!inverse_Hessian_history.empty())
   {
      if(!inverse_Hessian_history[0].empty())
      {
          buffer << "% Inverse Hessian history:\n"
                 << inverse_Hessian_history << "\n"; 
      }
   }

   // Training direction history

   if(!training_direction_history.empty())
   {
      if(!training_direction_history[0].empty())
      {
          buffer << "% Training direction history:\n"
                 << training_direction_history << "\n"; 
      }
   }

   // Training rate history

   if(!training_rate_history.empty())
   {
       buffer << "% Training rate history:\n"
              << training_rate_history << "\n"; 
   }

   // Elapsed time history

   if(!elapsed_time_history.empty())
   {
       buffer << "% Elapsed time history:\n"
              << elapsed_time_history << "\n"; 
   }

   return(buffer.str());
}


// Matrix<std::string> write_final_results(const size_t& precision = 3) const method

Matrix<std::string> NewtonMethod::NewtonMethodResults::write_final_results(const size_t& precision) const
{
   std::ostringstream buffer;

   Vector<std::string> names;
   Vector<std::string> values;

   // Final parameters norm

   names.push_back("Final parameters norm");

   buffer.str("");
   buffer << std::setprecision(precision) << final_parameters_norm;

   values.push_back(buffer.str());

   // Final performance

   names.push_back("Final performance");

   buffer.str("");
   buffer << std::setprecision(precision) << final_performance;

   values.push_back(buffer.str());

   // Final generalization performance

   const PerformanceFunctional* performance_functional_pointer = Newton_method_pointer->get_performance_functional_pointer();

   if(performance_functional_pointer->has_generalization())
   {
       names.push_back("Final generalization performance");

       buffer.str("");
       buffer << std::setprecision(precision) << final_generalization_performance;

       values.push_back(buffer.str());
   }

   // Final gradient norm

   names.push_back("Final gradient norm");

   buffer.str("");
   buffer << std::setprecision(precision) << final_gradient_norm;

   values.push_back(buffer.str());

   // Final training rate

//   names.push_back("Final training rate");

//   buffer.str("");
//   buffer << std::setprecision(precision) << final_training_rate;

//   values.push_back(buffer.str());

   // Iterations number

   names.push_back("Iterations number");

   buffer.str("");
   buffer << iterations_number;

   values.push_back(buffer.str());

   // Elapsed time

   names.push_back("Elapsed time");

   buffer.str("");
   buffer << elapsed_time;

   values.push_back(buffer.str());

   const size_t rows_number = names.size();
   const size_t columns_number = 2;

   Matrix<std::string> final_results(rows_number, columns_number);

   final_results.set_column(0, names);
   final_results.set_column(1, values);

   return(final_results);
}


// NewtonMethodResults* perform_training(void) method


NewtonMethod::NewtonMethodResults* NewtonMethod::perform_training(void)
{
   std::ostringstream buffer;

   buffer << "OpenNN Exception: NewtonMethod class.\n"
          << "NewtonMethodResults* perform_training(void) method.\n"
          << "This method is under development.\n";

   throw std::logic_error(buffer.str());      

/*
   // Control sentence (if debug)

   #ifndef NDEBUG 

   check();

   #endif

   // Start training 

   if(display)
   {
      std::cout << "Training with Newton's method...\n";
   }

   NewtonMethodResults* Newton_method_results_pointer = new NewtonMethodResults(this);

   // Elapsed time

   time_t beginning_time, current_time;
   time(&beginning_time);
   double elapsed_time;

   // Neural network stuff

   NeuralNetwork* neural_network_pointer = performance_functional_pointer->get_neural_network_pointer();

   const size_t parameters_number = neural_network_pointer->count_parameters_number();

   const Vector<double> parameters = neural_network_pointer->arrange_parameters();
   double parameters_norm;

   Vector<double> parameters_increment(parameters_number);
   double parameters_increment_norm;

   // Performance functional stuff

   double generalization_performance = 0.0; 
   double old_generalization_performance = 0.0;
   double generalization_performance_increment = 0.0;
      
   double performance = 0.0;
   double old_performance = 0.0;
   double performance_increase = 0.0;

   Vector<double> gradient(parameters_number);
   double gradient_norm;

   Matrix<double> inverse_Hessian(parameters_number, parameters_number);

   // Training algorithm stuff 

   Vector<double> old_gradient(parameters_number);
   Vector<double> training_direction(parameters_number);
   Vector<double> gradient_descent_training_direction(parameters_number);
   Vector<double> old_training_direction(parameters_number);

   double training_slope;

   //double initial_training_rate = 0.0;
   double training_rate = 0.0;
   //double old_training_rate = 0.0;

   Vector<double> directional_point(2);
   directional_point[0] = 0.0;
   directional_point[1] = 0.0;
   
   bool stop_training = false;


   // Main loop

   for(size_t iteration = 0; iteration <= maximum_iterations_number; iteration++)
   {
      // Multilayer perceptron 

      parameters = neural_network_pointer->arrange_parameters();

      parameters_norm = parameters.calculate_norm();

      if(display && parameters_norm >= warning_parameters_norm)
      {
         std::cout << "OpenNN Warning: Parameters norm is " << parameters_norm << ".\n";          
      }

      // Performance functional stuff

      if(iteration == 0)
      {      
         performance = performance_functional_pointer->calculate_performance();
         performance_increase = 0.0; 
      }
      else
      {
         performance = directional_point[1];
         performance_increase = old_performance - performance; 
      }

      generalization_performance = performance_functional_pointer->calculate_generalization_performance();

      if(iteration == 0)
      {
         generalization_performance_increment = 0.0;
      }
      else 
      {
         generalization_performance_increment = generalization_performance - old_generalization_performance;
      }

      gradient = performance_functional_pointer->calculate_gradient();

      gradient_norm = gradient.calculate_norm();

      if(display && gradient_norm >= warning_gradient_norm)
      {
         std::cout << "OpenNN Warning: Gradient norm is " << gradient_norm << ".\n";          
      }

      inverse_Hessian = performance_functional_pointer->calculate_inverse_Hessian();

      // Training algorithm 

      training_direction = calculate_training_direction(gradient, inverse_Hessian);

      // Calculate performance training_slope

      training_slope = (gradient/gradient_norm).dot(training_direction);

      // Check for a descent direction 

      if(training_slope >= 0.0)
      {
         if(display)
         {
             std::cout << "Iteration " << iteration << ": Training slope is greater than zero. Reseting training direction.\n";
         }

         // Reset training direction

         training_direction = calculate_gradient_descent_training_direction(gradient);
      }
            
      if(iteration == 0)
      {
//         initial_training_rate = first_training_rate;
      }
      else
      {
//         initial_training_rate = old_training_rate;
      }    
      
//    directional_point = calculate_directional_point(performance, training_direction, initial_training_rate);

      training_rate = directional_point[0];

      parameters_increment = training_direction*training_rate;
      parameters_increment_norm = parameters_increment.calculate_norm();
      
      // Elapsed time

      time(&current_time);
      elapsed_time = difftime(current_time, beginning_time);

      // Training history multilayer perceptron 

      if(reserve_parameters_history)
      {
         Newton_method_results_pointer->parameters_history[iteration] = parameters;                                
      }

      if(reserve_parameters_norm_history)
      {
         Newton_method_results_pointer->parameters_norm_history[iteration] = parameters_norm; 
      }

      // Training history performance functional

      if(reserve_performance_history)
      {
         Newton_method_results_pointer->performance_history[iteration] = performance;
      }

      if(reserve_generalization_performance_history)
      {
         Newton_method_results_pointer->generalization_performance_history[iteration] = generalization_performance;
      }

      if(reserve_gradient_history)
      {
         Newton_method_results_pointer->gradient_history[iteration] = gradient;                                
      }

      if(reserve_gradient_norm_history)
      {
         Newton_method_results_pointer->gradient_norm_history[iteration] = gradient_norm;
      }

      if(reserve_inverse_Hessian_history)
      {
         Newton_method_results_pointer->inverse_Hessian_history[iteration] = inverse_Hessian;
      }

      // Training history training algorithm

      if(reserve_training_direction_history)
      {
         Newton_method_results_pointer->training_direction_history[iteration] = training_direction;                                
      }

      if(reserve_training_rate_history)
      {
         Newton_method_results_pointer->training_rate_history[iteration] = training_rate;
      }

      if(reserve_elapsed_time_history)
      {
         Newton_method_results_pointer->elapsed_time_history[iteration] = elapsed_time;
      }

      // Stopping Criteria

      if(parameters_increment_norm <= minimum_parameters_increment_norm)
      {
         if(display)
         {
            std::cout << "Iteration " << iteration << ": Minimum parameters increment norm reached.\n"
                      << "Parameters increment norm: " << parameters_increment_norm << std::endl;
         }

         stop_training = true;
      }

      else if(performance <= performance_goal)
      {
         if(display)
         {
            std::cout << "Iteration " << iteration << ": Performance goal reached.\n";
         }

         stop_training = true;
      }

      else if(iteration != 0 && performance_increase <= minimum_performance_increase)
      {
         if(display)
         {
            std::cout << "Iteration " << iteration << ": Minimum performance increase reached.\n"
                      << "Performance improvement: " << performance_increase << std::endl;
         }

         stop_training = true;
      }

      else if(iteration != 0 && generalization_performance_increment < 0.0)
      {
         if(display)
         {
            std::cout << "Iteration " << iteration << ": Generalization performance stopped improving.\n";
            std::cout << "Generalization performance increment: "<< generalization_performance_increment << std::endl;
         }

         stop_training = true;
      }

      else if(gradient_norm <= gradient_norm_goal)
      {
         if(display)
         {
            std::cout << "Iteration " << iteration << ": Gradient norm goal reached.\n";  
         }

         stop_training = true;
      }

      if(iteration == maximum_iterations_number)
      {
         if(display)
         {
            std::cout << "Iteration " << iteration << ": Maximum number of iterations reached.\n";
         }

         stop_training = true;
      }

      else if(elapsed_time >= maximum_time)
      {
         if(display)
         {
            std::cout << "Iteration " << iteration << ": Maximum training time reached.\n";
         }

         stop_training = true;
      }

      if(iteration != 0 && iteration % save_period == 0)
      {
            neural_network_pointer->save(neural_network_file_name);
      }

      if(stop_training)
      {
         Newton_method_results_pointer->final_parameters = parameters;
         Newton_method_results_pointer->final_parameters_norm = parameters_norm;

         Newton_method_results_pointer->final_performance = performance;
         Newton_method_results_pointer->final_generalization_performance = generalization_performance;

         Newton_method_results_pointer->final_gradient = gradient;
         Newton_method_results_pointer->final_gradient_norm = gradient_norm;
   
         Newton_method_results_pointer->final_training_direction = training_direction;
         Newton_method_results_pointer->final_training_rate = training_rate;
         Newton_method_results_pointer->elapsed_time = elapsed_time;

         if(display)
         {
            std::cout << "Parameters norm: " << parameters_norm << "\n"
                      << "Performance: " << performance << "\n"
                      << "Gradient norm: " << gradient_norm << "\n"
                      << performance_functional_pointer->write_information()
                      << "Training rate: " << training_rate << "\n"
                      << "Elapsed time: " << elapsed_time << std::endl; 

            if(generalization_performance != 0)
            {
               std::cout << "Generalization performance: " << generalization_performance << std::endl;
            }
         }   
 
         break;
      }
      else if(display && iteration % display_period == 0)
      {
         std::cout << "Iteration " << iteration << ";\n"
                   << "Parameters norm: " << parameters_norm << "\n"
                   << "Performance: " << performance << "\n"
                   << "Gradient norm: " << gradient_norm << "\n"
                   << performance_functional_pointer->write_information()
                   << "Training rate: " << training_rate << "\n"
                   << "Elapsed time: " << elapsed_time << std::endl; 

         if(generalization_performance != 0)
         {
            std::cout << "Generalization performance: " << generalization_performance << std::endl;
         }
      }

      // Set new parameters

      parameters += parameters_increment;

      neural_network_pointer->set_parameters(parameters);

      // Update stuff

      old_performance = performance;
      old_generalization_performance = generalization_performance;
   
      //old_training_rate = training_rate;
   } 

   return(Newton_method_results_pointer);
*/
}


// std::string write_training_algorithm_type(void) const method

std::string NewtonMethod::write_training_algorithm_type(void) const
{
   return("NEWTON_METHOD");
}


// Matrix<std::string> to_string_matrix(void) const method

// the most representative

Matrix<std::string> NewtonMethod::to_string_matrix(void) const
{
    std::ostringstream buffer;

    Vector<std::string> labels;
    Vector<std::string> values;

   // Training rate method

   labels.push_back("Training rate method");

   const std::string training_rate_method = training_rate_algorithm.write_training_rate_method();

   values.push_back(training_rate_method);

   // Training rate tolerance

   labels.push_back("Training rate tolerance");

   buffer.str("");
   buffer << training_rate_algorithm.get_training_rate_tolerance();

   values.push_back(buffer.str());

   // Minimum parameters increment norm

   labels.push_back("Minimum parameters increment norm");

   buffer.str("");
   buffer << minimum_parameters_increment_norm;

   values.push_back(buffer.str());

   // Minimum performance increase

   labels.push_back("Minimum performance increase");

   buffer.str("");
   buffer << minimum_performance_increase;

   values.push_back(buffer.str());

   // Performance goal

   labels.push_back("Performance goal");

   buffer.str("");
   buffer << performance_goal;

   values.push_back(buffer.str());

   // Gradient norm goal

   labels.push_back("Gradient norm goal");

   buffer.str("");
   buffer << gradient_norm_goal;

   values.push_back(buffer.str());

   // Maximum generalization failures

   labels.push_back("Maximum generalization failures");

   buffer.str("");
   buffer << maximum_generalization_performance_decreases;

   values.push_back(buffer.str());

   // Maximum iterations number

   labels.push_back("Maximum iterations number");

   buffer.str("");
   buffer << maximum_iterations_number;

   values.push_back(buffer.str());

   // Maximum time

   labels.push_back("Maximum time");

   buffer.str("");
   buffer << maximum_time;

   values.push_back(buffer.str());

   // Reserve parameters norm history

   labels.push_back("Reserve parameters norm history");

   buffer.str("");
   buffer << reserve_parameters_norm_history;

   values.push_back(buffer.str());

   // Reserve performance history

   labels.push_back("Reserve performance history");

   buffer.str("");
   buffer << reserve_performance_history;

   values.push_back(buffer.str());

   // Reserve gradient norm history

   labels.push_back("Reserve gradient norm history");

   buffer.str("");
   buffer << reserve_gradient_norm_history;

   values.push_back(buffer.str());

   // Reserve generalization performance history

   labels.push_back("Reserve generalization performance history");

   buffer.str("");
   buffer << reserve_generalization_performance_history;

   values.push_back(buffer.str());

   // Reserve training direction norm history

//   labels.push_back("");

//   buffer.str("");
//   buffer << reserve_training_direction_norm_history;

   // Reserve training rate history

//   labels.push_back("");

//   buffer.str("");
//   buffer << reserve_training_rate_history;

//   values.push_back(buffer.str());

   // Reserve elapsed time history

   labels.push_back("Reserve elapsed time history");

   buffer.str("");
   buffer << reserve_elapsed_time_history;

   values.push_back(buffer.str());

   const size_t rows_number = labels.size();
   const size_t columns_number = 2;

   Matrix<std::string> string_matrix(rows_number, columns_number);

   string_matrix.set_column(0, labels);
   string_matrix.set_column(1, values);

    return(string_matrix);
}


// TyXmlElement* to_XML(void) const method


tinyxml2::XMLDocument* NewtonMethod::to_XML(void) const
{ 
   std::ostringstream buffer;

   tinyxml2::XMLDocument* document = new tinyxml2::XMLDocument;

   // Training algorithm

   tinyxml2::XMLElement* root_element = document->NewElement("NewtonMethod");

   document->InsertFirstChild(root_element);

   tinyxml2::XMLElement* element = NULL;
   tinyxml2::XMLText* text = NULL;

   // Training rate algorithm
   {
      tinyxml2::XMLElement* element = document->NewElement("TrainingRateAlgorithm");
      root_element->LinkEndChild(element);

      const tinyxml2::XMLDocument* training_rate_algorithm_document = training_rate_algorithm.to_XML();

      const tinyxml2::XMLElement* training_rate_algorithm_element = training_rate_algorithm_document->FirstChildElement("TrainingRateAlgorithm");

      DeepClone(element, training_rate_algorithm_element, document, NULL);

      delete training_rate_algorithm_document;
   }

   // Warning parameters norm
   {
   element = document->NewElement("WarningParametersNorm");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << warning_parameters_norm;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Warning gradient norm 
   {
   element = document->NewElement("WarningGradientNorm");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << warning_gradient_norm;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Warning training rate 
   {
   element = document->NewElement("WarningTrainingRate");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << warning_training_rate;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Error parameters norm
   {
   element = document->NewElement("ErrorParametersNorm");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << error_parameters_norm;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Error gradient norm 
   {
   element = document->NewElement("ErrorGradientNorm");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << error_gradient_norm;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Error training rate
   {
   element = document->NewElement("ErrorTrainingRate");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << error_training_rate;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Minimum parameters increment norm
   {
   element = document->NewElement("MinimumParametersIncrementNorm");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << minimum_parameters_increment_norm;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Minimum performance increase 
   {
   element = document->NewElement("MinimumPerformanceIncrease");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << minimum_performance_increase;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Performance goal 
   {
   element = document->NewElement("PerformanceGoal");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << performance_goal;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Gradient norm goal 
   {
   element = document->NewElement("GradientNormGoal");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << gradient_norm_goal;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Maximum generalization performance decreases
   {
   element = document->NewElement("MaximumGeneralizationPerformanceDecreases");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << maximum_generalization_performance_decreases;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Maximum iterations number 
   {
   element = document->NewElement("MaximumIterationsNumber");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << maximum_iterations_number;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Maximum time 
   {
   element = document->NewElement("MaximumTime");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << maximum_time;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Reserve parameters history 
   {
   element = document->NewElement("ReserveParametersHistory");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << reserve_parameters_history;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Reserve parameters norm history 
   {
   element = document->NewElement("ReserveParametersNormHistory");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << reserve_parameters_norm_history;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Reserve performance history 
   {
   element = document->NewElement("ReservePerformanceHistory");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << reserve_performance_history;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Reserve gradient history 
   {
   element = document->NewElement("ReserveGradientHistory");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << reserve_gradient_history;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Reserve gradient norm history 
   {
   element = document->NewElement("ReserveGradientNormHistory");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << reserve_gradient_norm_history;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Reserve inverse Hessian history 
   {
   element = document->NewElement("ReserveInverseHessianHistory");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << reserve_inverse_Hessian_history;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Reserve training direction history 
   {
   element = document->NewElement("ReserveTrainingDirectionHistory");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << reserve_training_direction_history;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Reserve training rate history 
   {
   element = document->NewElement("ReserveTrainingRateHistory");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << reserve_training_rate_history;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Reserve elapsed time history 
   {
   element = document->NewElement("ReserveElapsedTimeHistory");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << reserve_elapsed_time_history;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Reserve generalization performance history 
   {
   element = document->NewElement("ReserveGeneralizationPerformanceHistory");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << reserve_generalization_performance_history;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Display period
   {
   element = document->NewElement("DisplayPeriod");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << display_period;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   // Save period
   {
       element = document->NewElement("SavePeriod");
       root_element->LinkEndChild(element);

       buffer.str("");
       buffer << save_period;

       text = document->NewText(buffer.str().c_str());
       element->LinkEndChild(text);
   }

   // Neural network file name
   {
       element = document->NewElement("NeuralNetworkFileName");
       root_element->LinkEndChild(element);

       text = document->NewText(neural_network_file_name.c_str());
       element->LinkEndChild(text);
   }

   // Display
   {
   element = document->NewElement("Display");
   root_element->LinkEndChild(element);

   buffer.str("");
   buffer << display;

   text = document->NewText(buffer.str().c_str());
   element->LinkEndChild(text);
   }

   return(document);
}


// void from_XML(const tinyxml2::XMLDocument&) method

void NewtonMethod::from_XML(const tinyxml2::XMLDocument& document)
{
   const tinyxml2::XMLElement* root_element = document.FirstChildElement("NewtonMethod");

   if(!root_element)
   {
       std::ostringstream buffer;

       buffer << "OpenNN Exception: NewtonMethod class.\n"
              << "void from_XML(const tinyxml2::XMLDocument&) method.\n"
              << "Newton method element is NULL.\n";

       throw std::logic_error(buffer.str());
   }

   // Training rate algorithm
   {
      const tinyxml2::XMLElement* training_rate_algorithm_element = root_element->FirstChildElement("TrainingRateAlgorithm");

      if(training_rate_algorithm_element)
      {
          tinyxml2::XMLDocument training_rate_algorithm_document;

          tinyxml2::XMLElement* element_clone = training_rate_algorithm_document.NewElement("TrainingRateAlgorithm");
          training_rate_algorithm_document.InsertFirstChild(element_clone);

          DeepClone(element_clone, training_rate_algorithm_element, &training_rate_algorithm_document, NULL);

          training_rate_algorithm.from_XML(training_rate_algorithm_document);
      }
   }

   // Warning parameters norm
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("WarningParametersNorm");

       if(element)
       {
          const double new_warning_parameters_norm = atof(element->GetText());

          try
          {
             set_warning_parameters_norm(new_warning_parameters_norm);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Warning gradient norm 
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("WarningGradientNorm");

       if(element)
       {
          const double new_warning_gradient_norm = atof(element->GetText());

          try
          {
             set_warning_gradient_norm(new_warning_gradient_norm);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Warning training rate 
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("WarningTrainingRate");

       if(element)
       {
          const double new_warning_training_rate = atof(element->GetText());

          try
          {
             set_warning_training_rate(new_warning_training_rate);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Error parameters norm
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("ErrorParametersNorm");

       if(element)
       {
          const double new_error_parameters_norm = atof(element->GetText());

          try
          {
              set_error_parameters_norm(new_error_parameters_norm);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Error gradient norm 
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("ErrorGradientNorm");

       if(element)
       {
          const double new_error_gradient_norm = atof(element->GetText());

          try
          {
             set_error_gradient_norm(new_error_gradient_norm);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Error training rate
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("ErrorTrainingRate");

       if(element)
       {
          const double new_error_training_rate = atof(element->GetText());

          try
          {
             set_error_training_rate(new_error_training_rate);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Minimum parameters increment norm
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("MinimumParametersIncrementNorm");

       if(element)
       {
          const double new_minimum_parameters_increment_norm = atof(element->GetText());

          try
          {
             set_minimum_parameters_increment_norm(new_minimum_parameters_increment_norm);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Minimum performance increase 
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("MinimumPerformanceIncrease");

       if(element)
       {
          const double new_minimum_performance_increase = atof(element->GetText());

          try
          {
             set_minimum_performance_increase(new_minimum_performance_increase);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Performance goal 
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("PerformanceGoal");

       if(element)
       {
          const double new_performance_goal = atof(element->GetText());

          try
          {
             set_performance_goal(new_performance_goal);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Gradient norm goal 
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("GradientNormGoal");

       if(element)
       {
          const double new_gradient_norm_goal = atof(element->GetText());

          try
          {
             set_gradient_norm_goal(new_gradient_norm_goal);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Maximum generalization performance decreases
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("MaximumGeneralizationPerformanceDecreases");

       if(element)
       {
          const size_t new_maximum_generalization_performance_decreases = atoi(element->GetText());

          try
          {
             set_maximum_generalization_performance_decreases(new_maximum_generalization_performance_decreases);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Maximum iterations number 
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("MaximumIterationsNumber");

       if(element)
       {
           const size_t new_maximum_iterations_number = atoi(element->GetText());

          try
          {
             set_maximum_iterations_number(new_maximum_iterations_number);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Maximum time 
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("MaximumTime");

       if(element)
       {
          const double new_maximum_time = atof(element->GetText());

          try
          {
             set_maximum_time(new_maximum_time);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Reserve parameters history 
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("ReserveParametersHistory");

       if(element)
       {
          const std::string new_reserve_parameters_history = element->GetText();

          try
          {
             set_reserve_parameters_history(new_reserve_parameters_history != "0");
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Reserve parameters norm history 
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("ReserveParametersNormHistory");

       if(element)
       {
          const std::string new_reserve_parameters_norm_history = element->GetText();

          try
          {
             set_reserve_parameters_norm_history(new_reserve_parameters_norm_history != "0");
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Reserve performance history 
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("ReservePerformanceHistory");

       if(element)
       {
          const std::string new_reserve_performance_history = element->GetText();

          try
          {
             set_reserve_performance_history(new_reserve_performance_history != "0");
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Reserve gradient history 
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("ReserveGradientHistory");

       if(element)
       {
          const std::string new_reserve_gradient_history = element->GetText();

          try
          {
             set_reserve_gradient_history(new_reserve_gradient_history != "0");
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Reserve gradient norm history 
   {
       const tinyxml2::XMLElement* reserve_gradient_norm_history_element = root_element->FirstChildElement("ReserveGradientNormHistory");

       if(reserve_gradient_norm_history_element)
       {
          const std::string new_reserve_gradient_norm_history = reserve_gradient_norm_history_element->GetText();

          try
          {
             set_reserve_gradient_norm_history(new_reserve_gradient_norm_history != "0");
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Reserve training direction history 
   {
       const tinyxml2::XMLElement* reserve_training_direction_history_element = root_element->FirstChildElement("ReserveTrainingDirectionHistory");

       if(reserve_training_direction_history_element)
       {
          const std::string new_reserve_training_direction_history = reserve_training_direction_history_element->GetText();

          try
          {
             set_reserve_training_direction_history(new_reserve_training_direction_history != "0");
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Reserve training rate history 
   {
       const tinyxml2::XMLElement* reserve_training_rate_history_element = root_element->FirstChildElement("ReserveTrainingRateHistory");

       if(reserve_training_rate_history_element)
       {
          const std::string new_reserve_training_rate_history = reserve_training_rate_history_element->GetText();

          try
          {
             set_reserve_training_rate_history(new_reserve_training_rate_history != "0");
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Reserve elapsed time history 
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("ReserveElapsedTimeHistory");

       if(element)
       {
          const std::string new_reserve_elapsed_time_history = element->GetText();

          try
          {
             set_reserve_elapsed_time_history(new_reserve_elapsed_time_history != "0");
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Reserve generalization performance history 
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("ReserveGeneralizationPerformanceHistory");

       if(element)
       {
          const std::string new_reserve_generalization_performance_history = element->GetText();

          try
          {
             set_reserve_generalization_performance_history(new_reserve_generalization_performance_history != "0");
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Display period
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("DisplayPeriod");

       if(element)
       {
          const size_t new_display_period = atoi(element->GetText());

          try
          {
             set_display_period(new_display_period);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Save period
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("SavePeriod");

       if(element)
       {
          const size_t new_save_period = atoi(element->GetText());

          try
          {
             set_save_period(new_save_period);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Neural network file name
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("NeuralNetworkFileName");

       if(element)
       {
          const std::string new_neural_network_file_name = element->GetText();

          try
          {
             set_neural_network_file_name(new_neural_network_file_name);
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }

   // Display
   {
       const tinyxml2::XMLElement* element = root_element->FirstChildElement("Display");

       if(element)
       {
          const std::string new_display = element->GetText();

          try
          {
             set_display(new_display != "0");
          }
          catch(const std::logic_error& e)
          {
             std::cout << e.what() << std::endl;
          }
       }
   }
}


// void set_reserve_all_training_history(bool) method

void NewtonMethod::set_reserve_all_training_history(const bool& new_reserve_all_training_history)
{
   reserve_parameters_history = new_reserve_all_training_history;
   reserve_parameters_norm_history = new_reserve_all_training_history;

   reserve_performance_history = new_reserve_all_training_history;
   reserve_gradient_history = new_reserve_all_training_history;
   reserve_gradient_norm_history = new_reserve_all_training_history;
   reserve_inverse_Hessian_history = new_reserve_all_training_history;

   reserve_training_direction_history = new_reserve_all_training_history;
   reserve_training_rate_history = new_reserve_all_training_history;
   reserve_elapsed_time_history = new_reserve_all_training_history;

   reserve_generalization_performance_history = new_reserve_all_training_history;
}

}


// OpenNN: Open Neural Networks Library.
// Copyright (c) 2005-2015 Roberto Lopez.
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or any later version.
//
// This 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
// Lesser General Public License for more details.

// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA