#include <iostream>
#include <fstream>
#include <vector>
#include <gsl/gsl_cdf.h>
#include <gsl/gsl_math.h>
#include "stratified_sampling.hpp"
#include <cmath>
#include <algorithm>
#include "opti.hpp"
#include "option.hpp"
#include "rqmc.hpp"

using namespace std;

struct first:public std::unary_function<std::vector<double>, double>
{ 
    double operator()(std::vector<double> X){
        return X[0];
        }
};

vector< vector<double> > exemple1_stratified() {
    vector<double> q = quantile_norm(10, 1);
    vector<double> p(10, 0.1);
    vector<gaussian_truncated> rvar;
    rvar.push_back(gaussian_truncated(GSL_NEGINF, q[0]));
    for (int i=1; i<10; i++){
        rvar.push_back(gaussian_truncated(q[i-1], q[i]));
    };
    vector<int> N = {300, 1000, 10000, 20000}; //notre tableau du nombre successif de tirages, qui correspondent aux 300, 1300, 11300 et 31300
                                               //de l'article de Etoré et Jourdain
    vector< vector<double> > data (4);
    stratified_sampling<gaussian_truncated> S(p,rvar);
    cout<<"N"<<"\t"<<"moyenne"<<"\t\t"<<"sigma"<<"\t"<<"théorique"<<endl;
    vector<double> r(4,0);
    for (int i=0; i<4; i++){
        S.draw(N[i]);
        r[0]= r[0] + N[i];
        r[1] = S.estimator().first;
        r[2] = S.estimator().second;
        r[3] = 0.1559335;
        cout<<r[0]<<"\t"<<r[1]<<"\t"<<r[2]<<"\t"<<r[3]<<endl;
        data[i] = r;
    };
    return data;
};

vector< vector<double> > exemple1_rqmc(){
    int I = 100;
    vector<int> N = {3, 13, 113, 313}; //les N choisis pour que les NI soient égaux aux N de l'exemple 1 stratified_sampling
    first f; //comme quasi_gaussian retourne un vecteur, on doit composer avec f pour avoir le double QG()[0]
    vector< vector<double> > data (4);
    for(int i =0; i<4; i++){
        data[i] = monte_carlo (I,quasi_mean<struct first, sobol> (N[i], 1, f));
    }
    cout<<"moyenne"<<"\t\t"<<"sigma"<<"\t\t"<<"taille IC"<<endl;
    for(int i =0; i<3; i++){
        cout<<data[i][0]<<"\t"<<data[i][1]<<"\t"<<data[i][2]<<endl;
    }
    return data;
};


std::vector<double> normalize (std::vector<double> mu) { 
    int d = mu.size();
    double norm_mu = 0; 
    std::vector<double> u(d); 
    for(int i=0; i<d; i++) { 
        norm_mu += mu[i]*mu[i]; 
        } 
    for(int i=0; i<d; i++) {
        u[i] = mu[i]/sqrt(norm_mu);
        }
    return u;
}
      
    
 void exemple2_stratified (int d){
     std::vector<double> mu(d);
     mu = argmax(0.05, 1.0, 50, 0.1, 45, d); 
     std::vector<double> u(d);
     u = normalize(mu);
     vector<double> q = quantile_norm(100, 1);
     vector<double> p(100, 0.01);
     asian_option A(0.05, 1.0, 50, 0.1, d, 45);
     exponential_tilt<asian_option> G(mu, A);
     typedef compose_t<exponential_tilt<asian_option>, multi_gaussian_truncated> tilted_option;
     std::vector<tilted_option> X;
     X.push_back(compose(G, multi_gaussian_truncated(GSL_NEGINF,q[0], u)));
     for(int i=1; i<100; i++) {
         X.push_back(compose(G, multi_gaussian_truncated(q[i-1],q[i], u)));
     }
     for(int i=0; i<100; i=i+10){
         std::cout<<X[i]()<<endl;
     }
     stratified_sampling<tilted_option> S(p, X);
     S.draw(1000);
     cout<<"l'estimateur de la moyenne est :"<<S.estimator().first<<endl;
}

void exemple2_rqmc(int d) {
    asian_option A(0.05, 1.0, 50.0, 0.1, 16, 45);
    int N= 10000;

    
    std::vector<double> result(3);
    result = monte_carlo(100, quasi_mean<asian_option, sobol> (N, d, A));
    for(int i =0; i<3; i++){
        std::cout<<result[i]<<std::endl;
    }
    
    std::vector<double> result2(3);
    result2 = monte_carlo(100, quasi_mean<asian_option, halton> (N, d, A));
    for(int i =0; i<3; i++){
        std::cout<<result2[i]<<std::endl;
    }
};

int make_table(vector< vector<double> > data1, vector< vector<double> > data2) {
    std::fstream fs("doc/table.tex", std::fstream::out);;
    fs<<R"(\begin{tabular}{|r|rr|rr|c|})"<<std::endl;
    fs<<R"(\hline)"<<endl;
    fs<<"N"<<" & "<<R"($\mu_{strat}$)"<<" & "<<R"($\mu_{rqmc}$)"<<" & "<<R"($\textrm{IC}_{strat}$)"<<" & "<<R"($\textrm{IC}_{rqmc}$)"<<" & "<< R"($\textrm{IC}_{strat}/\textrm{IC}_{rqmc}$)"<<R"(\\ \hline)"<<std::endl;
    fs.precision(2);
    for (int i=0; i< 4; i++) {
        double ic_strat = 1.95996*sqrt(data1[i][2]/(double) data1[i][0]);
        fs<<(int)data1[i][0]<<"&"<<scientific<<data1[i][1]<<"&"<<data2[i][0]<<"&"<<ic_strat<<"&"<<data2[i][2]/2<<"&"<<fixed<<ic_strat/(data2[i][2]/2)<<R"(\\ \hline)"<<std::endl;
    }
    fs<<R"(\end{tabular})"<<std::endl;
    fs.close();
    return 0;
}

int main()
{   
    init_alea(1);
    cout<<gsl_cdf_gaussian_Pinv(0.975,1)<<endl;
    cout<<"Stratified_sampling sur l'exemple 1 de la normale"<<endl;
    vector< vector<double> > data1 = exemple1_stratified(); 
    cout<<"Randomised quasi Monte-Carlo sur l'exemple 1 de la normale"<<endl;
    vector< vector<double> > data2 = exemple1_rqmc();
    make_table(data1, data2);
    
    exemple2_stratified(16);
    return 0;
    
}