#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() {
    int I = 10; //le nombre de strates
    vector<double> q = quantile_norm(10, 1);
    vector<double> p(I, 1/(double)I);
    vector<gaussian_truncated> rvar;
    rvar.push_back(gaussian_truncated(GSL_NEGINF, q[0]));
    for (int i=1; i<I; 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 (size_t i=0; i<N.size(); 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(size_t i =0; i<N.size(); 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;
}


vector <vector<double> > exemple2_stratified (int d, bool call = true){
    vector<double> K = {45, 50, 55};
    vector<int> N = {100000, 400000, 500000};
    int I = 100; //le nombre de strates
    vector< vector<double> > data(3);
    vector<double> q = quantile_norm(I, 1);
    vector<double> p(I, 1/(double)I);
    double r = 0.05;
    double T = 1.0;
    double S0 = 50;
    double V = 0.1;
    typedef compose_t<exponential_tilt<asian_option>, multi_gaussian_truncated> tilted_option;
    for (size_t i=0; i < K.size(); i++){
        vector<double> mu = argmax(r, T, S0, V, K[i], d, call);
        std::vector<double> u = normalize(mu);
        asian_option A(r, T, S0, V, K[i], call);
        exponential_tilt<asian_option> G(mu, A);
        std::vector<tilted_option> X;
        X.push_back(compose(G, multi_gaussian_truncated(GSL_NEGINF, q[0], u)));
        for(int j=1; j < I; j++) {
            X.push_back(compose(G, multi_gaussian_truncated(q[j-1], q[j], u)));
        }
        stratified_sampling<tilted_option> S(p, X);
        vector<double> r(3, 0);
        for (size_t j=0; j < N.size(); j++){
            S.draw(N[j]);
        }
        r[0] = K[i];
        r[1] = S.estimator().first;
        r[2] = S.estimator().second;
        data[i] = r;
    }
    return data;
}

vector< vector<double> > exemple2_rqmc(int d, bool call = true) {
    int N= 10000;
    double r = 0.05;
    double T = 1.0;
    double S0 = 50;
    double V = 0.1;
    vector< vector<double> > data(3);
    vector<double> K = {45, 50, 55};
    int I=100;//la taille du vrai Monte-Carlo
    for(int i =0; i<3; i++) {
        asian_option A(r, T, S0, V, K[i], call);
        data[i] = monte_carlo(I, quasi_mean<asian_option, sobol> (N, d, A));
    }
    return data;
};

int make_table1(vector< vector<double> > const &data1, vector< vector<double> > const &data2) {
    std::fstream fs("doc/table1.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 make_table2(vector< vector<double> > data1, vector< vector<double> > data2, vector< vector<double> > data3, vector< vector<double> > data4, string table_name) {
    std::fstream fs("doc/" + table_name, std::fstream::out);
    fs<<R"(\begin{tabular}{|r|r|rr|rr|c|})"<<std::endl;
    fs<<R"(\hline)"<<endl;
    fs<<"d"<<" & "<<"K"<<" & "<<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(3);
    int N = 1000000;
    for (int i=0; i< 3; i++) {
        double ic_strat = 1.95996*sqrt(data1[i][2]/(double) N);
        fs<<"16"<<" & "<< (int) (data1[i][0]) <<"&"<< fixed <<data1[i][1] <<" & "<<data2[i][0]<<" & "<< scientific <<ic_strat<<" & "<<data2[i][2]/2<<" & "<<fixed<<ic_strat/(data2[i][2]/2)<<R"(\\)"<<std::endl;
    }
    fs<<R"(\hline\hline)"<<endl;
    for (int i=0; i< 3; i++) {
        double ic_strat = 1.95996*sqrt(data3[i][2]/(double) N);
        fs<<"64"<<" & "<< (int) (data3[i][0]) <<"&"<< fixed << data3[i][1] <<" & "<<data4[i][0]<<" & "<< scientific <<ic_strat<<" & "<<data4[i][2]/2<<" & "<<fixed<<ic_strat/(data4[i][2]/2)<<R"(\\)"<<std::endl;
    }
    fs<<R"(\hline)"<<endl;
    fs<<R"(\end{tabular})"<<std::endl;
    fs.close();
    return 0;
}

int main()
{

    init_alea(0);
    cout<<"comparaison stratified sampling/RQMC sur l'example 1\n"<<endl;
    make_table1(exemple1_stratified(), exemple1_rqmc());

    vector< vector<double> > data1 = exemple2_stratified(16);
    vector< vector<double> > data2 = exemple2_rqmc(16);
    vector< vector<double> > data3 = exemple2_stratified(64);
    vector< vector<double> > data4 = exemple2_rqmc(64);
    make_table2(data1, data2, data3, data4, "table2.tex");
    vector< vector<double> > data5 = exemple2_stratified(16, false);
    vector< vector<double> > data6 = exemple2_rqmc(16, false);
    vector< vector<double> > data7 = exemple2_stratified(64, false);
    vector< vector<double> > data8 = exemple2_rqmc(64,false);
    make_table2(data5, data6, data7, data8, "table3.tex");
    return 0;

}