/*
plot "D:\spline_graphic.txt" with lines title "Сплайн", "D:\original_graphic.txt" with lines title "График функции"
plot "D:\difference_graphic.txt" with lines title "Разница"
*/
#include <iostream>
#include <math.h>
#include <cmath>
#include <Windows.h>
#include <stdlib.h>
#include <fstream>
using namespace std;
const double PI = 3.141592653589793238463;

//Задание функции
typedef double(*functiontype1)(double x);
typedef double(*functiontype2)(double x, double s);
double f(double x)
{
    return exp(x) + (1 + 593.653)*x*x;
}
double K(double x, double s)
{
    return x * s;
}
functiontype1 Func1 = &f;
functiontype2 Func2 = &K;


void ValueUniformTable(double* Array, double Initial, double End, int CountSegments)
{
    double h;
    ofstream fout4("D:\setka_uni.txt");
    Array[0] = Initial;
    fout4 << Array[0] << " " << endl;
    h = abs(End - Initial) / CountSegments;

    for (int i = 1; i <= CountSegments; i++)
    {
        Array[i] = Array[i - 1] + h;
        fout4 << Array[i] << endl;
    }
    fout4.close();
}

void ValueChebyshevTable(double* Array, double Initial, double End, int CountSegments)
{
    ofstream fout5("D:\setka_cheb.txt");
    Array[0] = Initial;
    fout5 << Array[0] << " " << Array[0] << endl;
    double k1, k2, denom;
    k1 = (End + Initial) / 2;
    k2 = (End - Initial) / 2;
    denom = 2 * (CountSegments + 1);
    for (int i = 1; i < CountSegments; i++)
    {
        cout << k1 + k2 * cos(PI / (denom)) << endl;
        Array[CountSegments - i] = k1 + k2 * cos(((2 * i + 1)*PI) / (denom));
        fout5 << Array[CountSegments - i] << " " << endl;
    }

    Array[CountSegments] = End;
    fout5 << Array[CountSegments] << " " << endl;
    fout5.close();
}


void Gauss_with_vibor(double** coeffs_massiv, double* y_Massiv, int n) {

    double* tmp_mas;
    tmp_mas = new double[n];

    int p, i, j, k, q;
    double tmp, max,r;

    for (j = 0; j <= n - 2; j++) {

        max = abs(coeffs_massiv[j][j]);
        q = j;

        //Реализация перестановки перед итерацией
        for (p = j; p <= n - 1; p++) { // Идем по по столбцу, то есть меняем строки при фикс столбце j
            if (abs(coeffs_massiv[p][j]) > max) {
                max = abs(coeffs_massiv[p][j]);
                q = p;
            }
        }
        if (q != j) {
            for (p = 0; p <= n - 1; p++) {
                tmp_mas[p] = coeffs_massiv[j][p];
                coeffs_massiv[j][p] = coeffs_massiv[q][p];
                coeffs_massiv[q][p] = tmp_mas[p];

                tmp = y_Massiv[p];
                y_Massiv[p] = y_Massiv[q];
                y_Massiv[q] = tmp;
            }
        }


        for (i = j + 1; i <= n - 1; i++) {
            r = -coeffs_massiv[i][j] / coeffs_massiv[j][j];
            for (k = j; k <= n; k++) {
                coeffs_massiv[i][k] = coeffs_massiv[i][k] + r * coeffs_massiv[j][k];
            }
            y_Massiv[i] = y_Massiv[i] + r * y_Massiv[j];
        }

    }
}
/*DO FOR j = 1 TO n − 1
  DO FOR i = j + 1 TO n
    rij ←(−aij / ajj)
    DO FOR k = j TO n
      aik ← aik + rijajk
    END DO
    bi ← bi + rijbj
  END DO
END DO*/

//Запись в 3 файла: значений сплайна, интерполируемой функции и их разницы в countdots точках
void tables_in_file(functiontype1* f, double* Array, int Count_dots, int CountSegments, double Initial, double End)
{
    int i = 0;
    double step = (End - Initial) / (Count_dots - 1), y_value1, y_value2, x_value;

    ofstream fout1("D:/spline_graphic.txt");
    ofstream fout2("D:/original_graphic.txt");
    ofstream fout3("D:/difference_graphic.txt");
    x_value = Initial;
    for (i = 0; i < CountSegments; i++)
    {
        while (x_value < Array[i + 1])
        {
            fout1 << x_value << " ";
            fout2 << x_value << " ";
            fout3 << x_value << " ";
            x_value += step;
        }
    }
    fout1 << End << " ";
    fout2 << End << " ";
    fout2 << (*f)(End) << endl;
    fout1.close();
    fout2.close();
    //cout << endl << "Запись в файл осуществлена!" << endl;
}

void get_equations_massiv(functiontype2* K, functiontype1* f, int CountDots, double** coeffs_massiv, double* x_Array, double* y_Array) {
    int i, j;

    for (i = 0; i < CountDots; i++) {
        for (j = 0; j < CountDots; j++) {
            if (j == 0)
                coeffs_massiv[i][j] = 1;
            else
                coeffs_massiv[i][j] = -(x_Array[j] - x_Array[j - 1])* (*K)(x_Array[i], x_Array[j]);
        }
        y_Array[i] = (*f)(x_Array[i]);
    }

    for (i = 0; i < CountDots; i++) {
        for (j = 0; j < CountDots; j++) {
            cout << coeffs_massiv[i][j] << " ";
        }
        cout << y_Array[i] << endl;
        cout << endl;
    }

}

int main()
{
    setlocale(LC_ALL, "RUS");
    functiontype1 Func = &f;
    int CountDots = 3, i, Graphic_Dots = 250;

    /*---------------------------------Входные данные-------------------------------------*/
    double Initial = -10, End = 10;



    double** coeffs_massiv;
    coeffs_massiv = new double*[CountDots];
    for (i = 0; i < CountDots; i++)
        coeffs_massiv[i] = new double[2];
    double* y_Array = new double[CountDots];
    /*double* x_Array = new double[CountDots];
    ValueUniformTable(x_Array, Initial, End, CountDots);

    double* y_Array = new double[CountDots];
    get_equations_massiv(&Func2, &Func1, CountDots, coeffs_massiv, x_Array, y_Array);*/
    coeffs_massiv[0][0] = 1;
    coeffs_massiv[0][1] = 0;
    coeffs_massiv[0][2] = 1;
    coeffs_massiv[1][0] = 0;
    coeffs_massiv[1][1] = 1;
    coeffs_massiv[1][2] = 1;
    coeffs_massiv[2][0] = 1;
    coeffs_massiv[2][1] = 0;
    coeffs_massiv[2][2] = 0;
    y_Array[0] = 1;
    y_Array[1] = 2;
    y_Array[2] = 3;
    Gauss_with_vibor(coeffs_massiv, y_Array, CountDots);
    cout << endl;
    /*for (i = 0; i < CountDots; i++) {
        for (int j = 0; j < CountDots; j++) {
            cout << coeffs_massiv[i][j] << " ";
        }
        cout << y_Array[i] << endl;
        cout << endl;
    }*/

    cout << endl;
    system("pause");
    return 0;
}