/********************************************************************************************************************
 *                                                                                                                  *
 *      This program is to adjust marks of students, which are divided into many sections, using Z-score method.    *
 *      The program needs to read input data from file "Data.txt".                                                  *
 *      It will adjust the original marks and write the adjusted marks to a new file named "AdjustedData.txt".      *
 *                                                                                                                  *
 ********************************************************************************************************************
 *                                                                                                                  *
 *      Author:         Kachanon Nirunpong                                                                          *
 *      Created:        28 May 2015                                                                                 *
 *      Last update:    18 September 2015                                                                           *
 *                                                                                                                  *
 ********************************************************************************************************************
 *                                                                                                                  *
 *      Version Note:                                                                                               *
 *      This alphaRoot version is a Root Macro of the alpha version.                                                *
 *      It can make and plot histograms of the original and the adjusted marks                                      *
 *                                                                                                                  *
 ********************************************************************************************************************/

#include <iostream>
#include <fstream>
#include <string>
#include <math.h>
#include "StudentMark.h"

using std::cout;
using std::cin;
using std::endl;
using std::string;
using std::ifstream;
using std::ofstream;

double **Xbar(std::vector<StudentMark>, int n_item, int n_section);
double **SD(std::vector<StudentMark> student, int n_section, int n_item);

int Z_Adjustment_alphaRoot()
{
    const int N_SECTION(5);
    const int N_ITEM(4);
    std::vector<StudentMark> student;
    
    /********** Read data from file **********/
    string line;
    ifstream dataFile;
    dataFile.open("Data.txt");
    
    if(dataFile.is_open())
    {
        StudentMark tempStudent;
        int iLine(0);
        while(!dataFile.eof())
        {
            std::vector<double> tempMark;
            for(int j=0; j<=N_ITEM+1; j++)
            {
                double a;
                dataFile >> a;
                if(j==0)
                {
                    tempStudent.SetSection(a);
                }
                else if(j==1)
                {
                    tempStudent.SetNumber(a);
                }
                else
                {
                    tempMark.push_back(a);
                }
            }
            tempStudent.SetMark(tempMark);
            student.push_back(tempStudent);
        }
        dataFile.close();
        student.erase(student.end());
    }
    else cout << "Unable to open file.";
    /*****************************************/
    
    /************ Get mean and SD ************/
    
    // Get number of students in each section.
    int n_studentsInSec[N_SECTION+1];
    for(int i=0; i<=N_SECTION; i++)
    {
        n_studentsInSec[i] = 0;
    }
    for(int i=0; i<student.size(); i++)
    {
        n_studentsInSec[student.at(i).Section()] = n_studentsInSec[student.at(i).Section()]+1;
    }
    
    // Declare and initialise mu[] and sigma[].
    double mu[N_ITEM];
    double sigma[N_ITEM];
    for(int i=0; i<N_ITEM; i++)
    {
        mu[i] = 0.0;
        sigma[i] = 0.0;
    }
    
    // Get xbar and sd of each section for each item.
    double **xbar = Xbar(student, N_ITEM, N_SECTION);
    double **sd = SD(student, N_ITEM, N_SECTION);
    
    // Calculate mu of each item;
    for(int i=0; i<N_ITEM; i++)
    {
        for(int j=1; j<=N_SECTION; j++)
        {
            mu[i] = mu[i]+xbar[i][j]*n_studentsInSec[j]/student.size();
        }
    }
    
    // Calculate sigma of each item;
    for(int i=0; i<N_ITEM; i++)
    {
        double t1(0.0), t2(0.0), t3(0.0);
        for(int j=1; j<=N_SECTION; j++)
        {
            t1 = t1+pow(sd[i][j],2)*n_studentsInSec[j];
            t2 = t2+pow(xbar[i][j],2)*n_studentsInSec[j];
            t3 = -mu[i]*mu[i]*student.size();
        }
        sigma[i] = sqrt((t1+t2+t3)/double(student.size()));
    }
    
    /*****************************************/
    
    /************* Adjust marks **************/
    
    // Make a copy of of the original marks to adjust.
    std::vector<StudentMark> student_adjusted;
    student_adjusted = student;
    
    for(int i=0; i<student_adjusted.size(); i++)
    {
        std::vector<double> tempMark;
        int sec(student_adjusted.at(i).Section());
        for(int j=0; j<N_ITEM; j++)
        {
            tempMark.push_back((student.at(i).Mark().at(j)-xbar[j][sec])/sd[j][sec]*sigma[j] + mu[j]);
        }
        student_adjusted.at(i).SetMark(tempMark);
    }
    
    /*****************************************/
    
    /***** Test the adjusted mean and SD *****/
    
    // Declare and initialise mu[] and sigma[].
    double mu_adjusted[N_ITEM];
    double sigma_adjusted[N_ITEM];
    for(int i=0; i<N_ITEM; i++)
    {
        mu_adjusted[i] = 0.0;
        sigma_adjusted[i] = 0.0;
    }
    
    // Get xbar and sd of each section for each item.
    double **xbar_adjusted = Xbar(student_adjusted, N_ITEM, N_SECTION);
    double **sd_adjusted = SD(student_adjusted, N_ITEM, N_SECTION);
    
    // Calculate mu of each item;
    for(int i=0; i<N_ITEM; i++)
    {
        for(int j=1; j<=N_SECTION; j++)
        {
            mu_adjusted[i] = mu_adjusted[i]+xbar_adjusted[i][j]*n_studentsInSec[j]/student_adjusted.size();
        }
    }
    
    // Calculate sigma of each item;
    for(int i=0; i<N_ITEM; i++)
    {
        double t1(0.0), t2(0.0), t3(0.0);
        for(int j=1; j<=N_SECTION; j++)
        {
            t1 = t1+pow(sd_adjusted[i][j],2)*n_studentsInSec[j];
            t2 = t2+pow(xbar_adjusted[i][j],2)*n_studentsInSec[j];
            t3 = -mu[i]*mu[i]*student_adjusted.size();
        }
        sigma_adjusted[i] = sqrt((t1+t2+t3)/double(student_adjusted.size()));
    }
    
    /*****************************************/
    
    /************** Print value **************/
    
    // Original Mark
    for(std::vector<StudentMark>::iterator it=student.begin(); it != student.end(); ++it)
    {
        cout << (*it).Section() << "-" << (*it).Number() << "  ";
        for(int i=0; i<(*it).Mark().size(); ++i)
        {
            cout << (*it).Mark().at(i) << " ";
        }
        cout << endl;
    }
    cout << endl;
    
    // Original xbar
    for(int i=0; i<N_ITEM; i++)
    {
        cout << "Xbar of Item " << i+1 << ": ";
        for(int j=1; j<=N_SECTION; j++)
        {
            cout << xbar[i][j] << "    ";
        }
        cout << endl;
    }
    cout << endl;
    
    // Original sd
    for(int i=0; i<N_ITEM; i++)
    {
        cout << "SD of Item " << i+1 << ": ";
        for(int j=1; j<=N_SECTION; j++)
        {
            cout << sd[i][j] << "    ";
        }
        cout << endl;
    }
    cout << endl;
    
    // Original mu
    for(int i=0; i<N_ITEM; i++)
    {
        cout << "Mu of Item " << i+1 << "= " << mu[i] <<endl;
        
    }
    cout << endl;
    
    // Original sigma
    for(int i=0; i<N_ITEM; i++)
    {
        cout << "Sigma of Item " << i+1 << "= " << sigma[i] <<endl;
        
    }
    cout << endl;
    
    // Adjusted mark
    
    ofstream outputFile;
    outputFile.open("AdjustedData.txt");
    
    for(std::vector<StudentMark>::iterator it=student_adjusted.begin(); it != student_adjusted.end(); ++it)
    {
        cout << (*it).Section() << "-" << (*it).Number() << "  ";
        outputFile << (*it).Section() << "-" << (*it).Number() << "  ";
        for(int i=0; i<(*it).Mark().size(); ++i)
        {
            cout << (*it).Mark().at(i) << " ";
            outputFile << (*it).Mark().at(i) << " ";
        }
        cout << endl;
        outputFile << endl;
    }
    cout << endl;
    outputFile << endl;
    
    // Adjusted xbar
    for(int i=0; i<N_ITEM; i++)
    {
        cout << "Xbar of Item " << i+1 << ": ";
        outputFile << "Xbar of Item " << i+1 << ": ";
        for(int j=1; j<=N_SECTION; j++)
        {
            cout << xbar_adjusted[i][j] << "    ";
            outputFile << xbar_adjusted[i][j] << "    ";
        }
        cout << endl;
        outputFile << endl;
    }
    cout << endl;
    outputFile << endl;
    
    // Adjusted sd
    for(int i=0; i<N_ITEM; i++)
    {
        cout << "SD of Item " << i+1 << ": ";
        outputFile << "SD of Item " << i+1 << ": ";
        for(int j=1; j<=N_SECTION; j++)
        {
            cout << sd_adjusted[i][j] << "    ";
            outputFile << sd_adjusted[i][j] << "    ";
        }
        cout << endl;
        outputFile << endl;
    }
    cout << endl;
    outputFile << endl;
    
    // Adjusted mu
    for(int i=0; i<N_ITEM; i++)
    {
        cout << "Mu of Item " << i+1 << "= " << mu_adjusted[i] <<endl;
        outputFile << "Mu of Item " << i+1 << "= " << mu_adjusted[i] <<endl;
        
    }
    cout << endl;
    outputFile << endl;
    
    // Adjusted sigma
    for(int i=0; i<N_ITEM; i++)
    {
        cout << "Sigma of Item " << i+1 << "= " << sigma_adjusted[i] <<endl;
        outputFile << "Sigma of Item " << i+1 << "= " << sigma_adjusted[i] <<endl;
        
    }
    cout << endl;
    outputFile << endl;
    
    outputFile.close();
    /*****************************************/
    
    return 0;
}

/***************************************** Sub-routine definition *****************************************/

double **Xbar(std::vector<StudentMark> student, int n_item, int n_section)
{
    const int N_SECTION(n_section);
    const int N_ITEM(n_item);
    
    // Create new 2D array and initialise it.
    double **xbar = new double*[N_ITEM];
    for(int i=0; i<N_ITEM; i++)
    {
        xbar[i] = new double[N_SECTION+1];
        for(int j=0; j<=N_SECTION; j++)
        {
            xbar[i][j] = 0.0;
        }
    }
    
    // Get number of student in each section.
    int n_studentsInSec[N_SECTION+1];
    for(int i=0; i<=N_SECTION; i++)
    {
        n_studentsInSec[i] = 0;
    }
    for(int i=0; i<student.size(); i++)
    {
        n_studentsInSec[student.at(i).Section()] = n_studentsInSec[student.at(i).Section()]+1;
    }
    
    // Calculate xbar of each section for each item.
    for(int i=0; i<N_ITEM; i++)
    {
        for(int j=0; j<student.size(); j++)
        {
            int sec(student.at(j).Section());   // Get section number of student j.
            xbar[i][sec] = xbar[i][sec] + (student.at(j).Mark().at(i))/n_studentsInSec[sec];
        }
    }
    
    return xbar;
}

double **SD(std::vector<StudentMark> student, int n_item, int n_section)
{
    const int N_SECTION(n_section);
    const int N_ITEM(n_item);
    
    // Create new 2D array and initialise it.
    double **xbar = new double*[N_ITEM];
    double **sd = new double*[N_ITEM];
    for(int i=0; i<N_ITEM; i++)
    {
        xbar[i] = new double[N_SECTION+1];
        sd[i] = new double[N_SECTION+1];
        for(int j=0; j<=N_SECTION; j++)
        {
            xbar[i][j] =0.0;
            sd[i][j] = 0.0;
        }
    }
    
    // Get number of student in each section.
    int n_studentsInSec[N_SECTION+1];
    for(int i=0; i<=N_SECTION; i++)
    {
        n_studentsInSec[i] = 0;
    }
    for(int i=0; i<student.size(); i++)
    {
        n_studentsInSec[student.at(i).Section()] = n_studentsInSec[student.at(i).Section()]+1;
    }
    
    // Calculate xbar of each section for each item.
    for(int i=0; i<N_ITEM; i++)
    {
        for(int j=0; j<student.size(); j++)
        {
            int sec(student.at(j).Section());   // Get section number of student j.
            xbar[i][sec] = xbar[i][sec] + (student.at(j).Mark().at(i))/n_studentsInSec[sec];
        }
    }
    
    // Calculate sd of each section for each item.
    for(int i=0; i<N_ITEM; i++)
    {
        for(int j=0; j<student.size(); j++)
        {
            int sec(student.at(j).Section());   // Get section number of student j.
            sd[i][sec] = sd[i][sec] + pow(student.at(j).Mark().at(i)-xbar[i][sec],2);
        }
        for(int j=0; j<=N_SECTION; j++)
        {
            sd[i][j] = sqrt(sd[i][j]/n_studentsInSec[j]);
        }
    }
    
    return sd;
}