// Ejercicio 3 de la guia 8


#include <iostream>

#include <stdio.h>


#include "TCanvas.h"
#include "TH1F.h"
#include "TH2F.h"
#include "TRandom3.h"
#include "TF1.h"
#include "TMath.h"
#include "TGraph.h"
#include "TString.h"
#include "TText.h"
#include "TLine.h"


void g8e3()
{

    float mu    = 10.;
    float sigma = 2.;
    float N     = 1000;
    float n     = 3;
    float Nbin  = 25; // hay que sumar 1 por ser histc y no la funcion hist !!!!

    TRandom r;
    r.SetSeed(0);

    TH1F h1("h1","", Nbin, 0, 20);
    TH1F h2("h2","", Nbin, 0, 20);
    TH1F h3("h3","", Nbin, 0, 20);
    TH1F h_u("h_u","", Nbin,  -5, 5);
    TH1F h_v("h_v","", Nbin,   0, 15);
    TH1F h_w("h_w","", Nbin,   0, 12);
    TH1F h_z("h_z","", Nbin, -10, 10);

    h_u.Sumw2();
    h_v.Sumw2();
    h_w.Sumw2();
    h_z.Sumw2();

    TGraph gr1(N);
    TGraph gr2(N);
    TGraph gr3(N);
    gr1.SetMarkerColor(kRed);
    gr2.SetMarkerColor(kBlue);
    gr3.SetMarkerColor(kOrange);
    gr1.SetMarkerSize(0.5);
    gr2.SetMarkerSize(0.5);
    gr3.SetMarkerSize(0.5);
    TGraph grxp(N);
    grxp.SetMarkerColor(kBlack);
    grxp.SetMarkerSize(0.5);


    TCanvas c("c","c",500,700);
    TPad *pad1 = new TPad("pad1", "",0.0,0.8,1.0,1.0);
    TPad *pad2 = new TPad("pad2", "",0.0,0.6,1.0,0.8);
    TPad *pad3 = new TPad("pad3", "",0.0,0.0,1.0,0.6);
    pad1->Draw();
    pad2->Draw();
    pad3->Draw();

    TText text;
    text.SetTextColor(kRed);
    text.SetTextSize(0.05);

    int countu = 0;

    for (unsigned int ii = 0; ii != N; ++ii) {

        float x1 = r.Gaus(mu,sigma);
        float x2 = r.Gaus(mu,sigma);
        float x3 = r.Gaus(mu,sigma);

        gr1.SetPoint(ii, ii, x1);
        gr2.SetPoint(ii, ii, x2);
        gr3.SetPoint(ii, ii, x3);

        h1.Fill(x1);
        h2.Fill(x2);
        h3.Fill(x3);

        float xp = (x1 + x2 + x3) / n;
        float S2 = ( (x1-mu)*(x1-mu) + (x2-mu)*(x2-mu) + (x3-mu)*(x3-mu) ) / n;
        float s2 = ( (x1-xp)*(x1-xp) + (x2-xp)*(x2-xp) + (x3-xp)*(x3-xp) ) / (n - 1.);

        grxp.SetPoint(ii, ii, xp);

        float u = (xp - mu)/ ( sigma/sqrt(n) );
        float v = n *       S2 / (sigma*sigma);
        float w = (n - 1) * s2 / (sigma*sigma);
        float z = (xp - mu) / (sqrt(s2)/sqrt(n) );

        if ((xp - 2*sigma/sqrt(n) <= mu) && (mu <= xp+2*sigma/sqrt(n))) {
            ++countu;
        }

        TLine line;
        line.SetLineColor(kRed);


        h_u.Fill(u, 1.);
        h_v.Fill(v, 1./N);
        h_w.Fill(w, 1./N);
        h_z.Fill(z, 1./N);

        if (ii < 30) {
            sleep(1);
        }

        if (ii < 30 || ii%5 == 0 || ii==(N-1)) {

            TH2F frame("frame","",1,0,ii,1,0,20);
            frame.SetStats(0);

            pad1->cd();
            frame.Draw();
            gr1.Draw("P");
            gr2.Draw("P");
            gr3.Draw("P");

            pad2->cd();
            frame.Draw();
            grxp.Draw("P");

            pad3->cd();
            h_u.SetFillColor(4);
            h_u.SetBarWidth(0.7);
            h_u.SetBarOffset(0.1);
            h_u.SetStats(0);
            h_u.SetMarkerSize(0);
            h_u.Draw("Hist b e0");

            line.DrawLine(-2,0,-2,100);
            line.DrawLine(+2,0,+2,100);

            text.SetNDC();
            text.DrawText(0.2,0.85,TString::Format("%d de %d",countu, ii+1));
            text.DrawText(0.2,0.81,TString::Format("p = %2.3f",((float)countu)/(ii+1)));

            gr3.GetYaxis()->SetTitle("x");
            grxp.GetYaxis()->SetTitle("#bar{x}");
            h_u.GetXaxis()->SetTitle("#bar{x}-#mu/(#sigma/#sqrt{n})");

            TF1 f1("f1", "[0]*1./TMath::Sqrt(2.*TMath::Pi())*TMath::Exp(-x*x/2)", -5,5);
            float binWidth1 = 10./Nbin*(ii+1);
            f1.SetParameter(0,binWidth1);
            f1.Draw("SAME");

            c.Print(TString::Format("g8e3-intervalos-confianza-brownians-%d.pdf", ii));
        }

    }


}
/*
    c.cd();
    h1.Draw();
    c.Print("g8e3-intervalos-confianza-1.pdf");
    h2.Draw();
    c.Print("g8e3-intervalos-confianza-2.pdf");
    h3.Draw();
    c.Print("g8e3-intervalos-confianza-3.pdf");

    TF1 f1("f1", "[0]*1./TMath::Sqrt(2.*TMath::Pi())*TMath::Exp(-x*x/2)", -5,5);
    float binWidth1 = 10./Nbin;
    f1.SetParameter(0,binWidth1);
    TCanvas c1("c1","c1");
    h_u.SetFillColor(4);
    h_u.SetBarWidth(0.7);
    h_u.SetBarOffset(0.1);
    h_u.SetStats(0);
    h_u.Draw("b");
    f1.Draw("SAME");
    c1.Print("g8e3-intervalos-confianza-u.pdf");


    TH2F frame2("frame2","",1,0,15,1,0,0.3);
    frame2.SetStats(0);

    TF1 f2("f2", "[0]*TMath::Power(2.,-[1]/2.) / TMath::Gamma([1]/2.) * TMath::Power(x, [1]/2.-1.)*exp(-x/2.)", 0,15);
//     TF1 f22("f22", "[0]*ROOT::Math::chisquared_pdf(x,[1],0.)", 0,15);
    float binWidth2 = 15./Nbin;
    f2.SetParameter(0,binWidth2);
    f2.SetParameter(1,n);
//     f22.SetParameter(0,1.);
//     f22.SetParameter(1,3);
//     f22.SetLineColor(kRed);
    TCanvas c2("c2","c2");
    h_v.SetFillColor(4);
    h_v.SetBarWidth(0.7);
    h_v.SetBarOffset(0.1);
    h_v.SetStats(0);
    frame2.Draw();
    h_v.Draw("b SAME");
    f2.Draw("SAME");
//     f22.Draw("SAME");
    c2.Print("g8e3-intervalos-confianza-v.pdf");


    TF1 f3("f3", "[0]*1./TMath::Power(2.,[1]/2.)*1./TMath::Gamma([1]/2.)*TMath::Power(x, [1]/2.-1.)*exp(-x/2.)", 0,12);
    float binWidth3 = 12./Nbin;
    f3.SetParameter(0,binWidth3);
    f3.SetParameter(1,n-1);
    TCanvas c3("c3","c3");
    h_w.SetFillColor(4);
    h_w.SetBarWidth(0.7);
    h_w.SetBarOffset(0.1);
    h_w.SetStats(0);
    h_w.Draw("b");
    f3.Draw("SAME");
    c3.Print("g8e3-intervalos-confianza-w.pdf");


    TF1 f4("f4", "[0] * TMath::Gamma(([1]+1)/2.) / sqrt(TMath::Pi()*[1]) * TMath::Gamma([1]/2.) * TMath::Power(1+x*x/[1], -([1]+1)/2.)", -10,10);
    float binWidth4 = 20./Nbin;
    f4.SetParameter(0,binWidth4);
    f4.SetParameter(1,n-1);
    TCanvas c4("c4","c4");
    h_z.SetFillColor(4);
    h_z.SetBarWidth(0.7);
    h_z.SetBarOffset(0.1);
    h_z.SetStats(0);
    h_z.Draw("b");
    f4.Draw("SAME");
    c4.Print("g8e3-intervalos-confianza-z.pdf");

}*/