nonlinear_eq.cpp

#include <iostream>
#include <vector>
#include<tuple>
#include <math.h>
#include "matplotlibcpp.h"

namespace plt = matplotlibcpp;
// --------------------------------------------------------------


void plotNumericalApproach(std::vector<int> ii, std::vector<double> yy)
{
    plt::figure_size(1200, 780);
    plt::title("Nonlinear solution");
    plt::plot(ii, yy);
    //plt::plot(ii, dyy);
    plt::show();
}


// --------------------------------------------------------------

double function(double x){

//return (1 / (1+ std::exp(-x))) - 0.5 ;
return 2* std::sin(x) - std::cos(x)* std::cos(x);
//return x*x - 9;

}

// --------------------------------------------------------------

std::tuple<std::vector<int>, std::vector<double>> nonlinearNewton(double (*function)(double), double start, double error, double h ){

double x0 = start;
double fx0 = function(x0);
int i{0};
std::vector <int> iteration;
std::vector<double> result;

while(std::fabs(fx0) > error){

    double diff = (function(x0 + h) - fx0)/ h ;
    x0 = x0 -fx0/diff; 
    fx0 = function(x0);

    iteration.push_back(i);
    result.push_back(x0);
    i++;
}

return std::make_tuple(iteration, result);
}


// --------------------------------------------------------------


int main(){

std::tuple<std::vector<int>, std::vector<double>> result = nonlinearNewton(function, 1.0, 0.000001, 0.001);
std::vector<int> iter = std::get<0>(result);
std::vector<double> solution = std::get<1>(result);

plotNumericalApproach (iter, solution);

for (auto &i : solution){

    std::cout<< i << std::endl;
}


}