#include<TGraph.h>
#include<TCanvas.h>
#include<TMath.h>
#include<functional>
#include<vector>
#include<iostream>

std::function<double(std::vector<double>)> integrate(const std::function<double(double, std::vector<double>)>& input,double left, double right, double step = 0.001){
 auto output = [=](std::vector<double> v) -> double{ //wrapper function: integrates our function for given vector
  double result = 0;
  double left_l = left, right_l = left;
  while(right_l < right){
   result += input(right_l, v);
   right_l += step;
  }
  result *= step;
  return result; //integration result for given vector
 };
 return output; //now we may find integral for any vector given
}

int main(){
 /*std::function<double(double, std::vector<double>)> func = [](double x, std::vector<double> v) -> double{ return x*v.size(); };
 std::cout << integrate(func,0,1,0.0001)(std::vector<double>({2,4,6}));*/ //results are satisfactory, function works
 TCanvas* c = new TCanvas("canvas", "canvas");
 c->Divide(2,2);
 c->cd(1);
 
 std::function<double(double, std::vector<double>)> func_exact_cos = [](double x, std::vector<double> v) -> double{return x*TMath::Sqrt(x*x-1)*TMath::Cos(x*v[0]);};//1
 std::function<double(double, std::vector<double>)> func_exact_sin = [](double x, std::vector<double> v) -> double{return x*TMath::Sqrt(x*x-1)*TMath::Sin(x*v[0]);};//2
 std::function<double(double, std::vector<double>)> func_urel_cos = [](double x, std::vector<double> v) -> double{return x*x*TMath::Cos(x*v[0]);};//3
 std::function<double(double, std::vector<double>)> func_urel_sin = [](double x, std::vector<double> v) -> double{return x*x*TMath::Sin(x*v[0]);};//4
 
 const int numpoints = 1000; // num of points in order to build graph
 double x[numpoints], y[numpoints]; // points in order to build graph
 double lim = 2; // defines graph area as [-lim, lim]
 //double rel_coeff[4]{5,10,20,40}; // relativistic coefficient == (U-M)/m_i - upper integration limit
 for(int index = 0; index < numpoints; ++index){
  x[index] = -lim + lim*index*2.0/numpoints;
  y[index] = integrate(func_exact_cos, 1, 1+5)(std::vector<double>({x[index]}))/integrate(func_urel_sin,1,1+5)(std::vector<double>({x[index]}));
 }
 TGraph* gr1 = new TGraph(numpoints, x, y);
 gr1->SetMarkerStyle(21);
 gr1->SetMarkerSize(0.2);
 gr1->SetMarkerColor(kRed);
 gr1->Draw("APL");
 /*for(int index = 0; index < numpoints; ++index)
  y[index] = integrate(func_exact_cos, 1, 1+5)(std::vector<double>({x[index]}))/integrate(func_urel_cos,1,1+5)(std::vector<double>({x[index]}));
 TGraph* gr2 = new TGraph(numpoints, x, y);
 gr2->SetMarkerStyle(22);
 gr2->SetMarkerColor(kGreen);
 gr2->SetMarkerSize(0.2);
 //gr2->Draw("PL");*/
 //c->SaveAs("temp.pdf");
 /*double a[4]{5,10,20,40};
 for(int index = 0; index < 4; ++index){
  c->cd(index+1);
  
 }*/
}