/*
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 <vector>
#include <Windows.h>
#include <stdlib.h>
#include <fstream>
#include <string.h>
#include <time.h>
#include <iomanip>
using namespace std;
const double PI = 3.141592653589793238463;

//Для хранения сетки
typedef struct Node
{
    double x, y;
}
Node;

//Задание функции
typedef double(*functiontype)(double x);
double Myfunc(double x)
{
    return x * x*x;
    //return x;
    //return x;
}
functiontype Func = &Myfunc;

//Возведение числа в натуральную степень
double degree(double x, int n)
{
    double b = x;
    for (int i = 1; i < n; i++)
        x *= b;
    return x;
}

//Приблизительное значение 2 производной
double approximate_derivative_2(functiontype* f, double x)
{
    double delta = 1e-5;
    return (((*f)(x) - 2 * (*f)(x + delta) + (*f)(x + 2 * delta)) / (delta * delta));
}

//Приблизительное значение 1 производной
double approximate_derivative_1(functiontype* f, double x)
{
    double delta = 1e-5;
    return (((*f)(x + delta) - (*f)(x)) / delta);
}

//Возвращает значение сплайна в точке на итервале[xi,x_i+1]
double Spline(double x, int i, double* Array_steps, double* x_massiv, Node* Array)
{
    double h2, g1, g2, x1, x2, y1, y2;

    h2 = Array_steps[i + 1];
    g1 = x_massiv[i];
    g2 = x_massiv[i + 1];
    x1 = Array[i].x;
    x2 = Array[i + 1].x;
    y1 = Array[i].y;
    y2 = Array[i + 1].y;

    return (
        (y1 * (x2 - x) + y2 * (x - x1)) / h2 +
        (g1 * (degree((x2 - x), 3) - h2 * h2 * (x2 - x))) +
        (g2 * (degree((x - x1), 3) - h2 * h2 * (x - x1)) / (6 * h2))
        );
}

//Равномерная сетка
void ValueUniformTable(functiontype* f, Node* Array, double Initial, double End, int CountSegments, double* Array_steps_uni)
{
    double h;
    Array[0].x = Initial;
    Array[0].y = (*f)(Initial);
    Array_steps_uni[0] = 0;
    h = abs(End - Initial) / CountSegments;

    for (int i = 1; i <= CountSegments; i++)
    {
        Array[i].x = Array[i - 1].x + h;
        Array[i].y = (*f)(Array[i].x);
        Array_steps_uni[i] = h;
    }
}

//Чебышёвская сетка
void ValueChebyshevTable(functiontype* f, Node* Array, double Initial, double End, int CountSegments, double* Array_steps_cheb)
{
    Array_steps_cheb[0] = 0;
    Array[0].x = Initial;
    Array[0].y = (*f)(Array[0].x);

    for (int i = 1; i < CountSegments; i++)
    {
        Array[i].x = -((End + Initial) / 2) -
            ((End - Initial) / 2) * cos(((2 * i + 1) * PI) / (2 * (CountSegments + 1)));
        Array[i].y = (*f)(Array[i].x);
        Array_steps_cheb[i] = Array[i].x - Array[i - 1].x;
    }

    Array[CountSegments].x = End;
    Array[CountSegments].y = (*f)(Array[CountSegments].x);
    Array_steps_cheb[CountSegments] = Array[CountSegments].x - Array[CountSegments - 1].x;
}

//Составляем СЛАУ с учётом нач данных и закидываем это всё в один массив matrix_coeffs - массив вида[[a1,b1,c1,d1], [a2,b2,c2,d2],..., [an,bn,cn,dn]]
void get_matrix_coeffs(double Initial, double End, int CountSegments, functiontype* f, double** matrix_coeffs, Node* Array, double* Array_steps)
{
    int i;
    double h1, h2, A, B, y1, y2;
    int matrix_size = CountSegments + 1;

    A = approximate_derivative_2(&Func, Array[0].x);
    B = approximate_derivative_1(&Func, Array[CountSegments].x);

    //первое уравнение
    matrix_coeffs[0][0] = 0;
    matrix_coeffs[0][1] = 1;
    matrix_coeffs[0][2] = 0;
    matrix_coeffs[0][3] = A;

    for (i = 1; i < matrix_size - 1; i++)
    {
        h1 = Array_steps[i];
        h2 = Array_steps[i + 1];
        matrix_coeffs[i][0] = h1;
        matrix_coeffs[i][1] = 2 * (h1 + h2);
        matrix_coeffs[i][2] = h2;
        matrix_coeffs[i][3] = 6 * ((Array[i + 1].y - Array[i].y) / h2 - (Array[i].y - Array[i - 1].y) / h1);
    }

    //n+1 уравнение
    h2 = Array_steps[matrix_size - 1];
    y1 = Array[matrix_size - 2].y;
    y2 = Array[matrix_size - 1].y;
    matrix_coeffs[matrix_size - 1][0] = 0;
    matrix_coeffs[matrix_size - 1][1] = 2;
    matrix_coeffs[matrix_size - 1][2] = 1;
    matrix_coeffs[matrix_size - 1][3] = 6 * (y2 - y1 - B * h2) / (h2 * h2);


    for (i = 0; i < matrix_size; i++) {
        cout << "(" << matrix_coeffs[i][0] << ")" << "  " << "(" << matrix_coeffs[i][1] << ")" << "  " << "(" << matrix_coeffs[i][2] << ")" << "  = " << matrix_coeffs[i][3] << endl;
    }

}

/*Принимает на вход коэффициенты СЛАУ в виде массива matrix_coeffs - массив вида[[a1,b1,c1,d1], [a2,b2,c2,d2],..., [an,bn,cn,dn]].
   Заполняет Двумерный массив прогоночных коэффициентов coeffs_massiv (0 - Кси, 1 - Эта). Находит решение в виде массива x_massiv*/
void tridiagonal_matrix_algorithm(double** matrix_coeffs, double* Array_steps, Node* Array, int CountSegments, double* x_massiv)
{
    int i;
    double denominator;
    double K, E, K_prev = 0, E_prev = 0;
    int matrix_size = CountSegments + 1;

    double** coeffs_massiv;
    coeffs_massiv = new double*[matrix_size + 1];
    for (i = 0; i < matrix_size+1; i++)
        coeffs_massiv[i] = new double[2];

    //Прямой ход
    coeffs_massiv[0][0] = 0;
    coeffs_massiv[0][1] = 0;

    for (i = 0; i <= matrix_size - 1; i++)
    {
        denominator = matrix_coeffs[i][0] * K_prev + matrix_coeffs[i][1];
        K = -(matrix_coeffs[i][2]) / denominator;
        E = (matrix_coeffs[i][3] - matrix_coeffs[i][0] * E_prev) / denominator;
        K_prev = K;
        E_prev = E;
        coeffs_massiv[i + 1][0] = K;
        coeffs_massiv[i + 1][1] = E;
    }

    //Обратный ход
    x_massiv[matrix_size - 1] = coeffs_massiv[matrix_size][1];  //определяю xn = e_n+1
    for (i = matrix_size - 2; i >= 0; i--)
    {
        x_massiv[i] = coeffs_massiv[i + 1][0] * x_massiv[i + 1] + coeffs_massiv[i + 1][1];
    }

    cout << endl << "Размер матрицы = " << matrix_size << endl;
    for (i = 0; i < matrix_size; i++)
        cout << "g_ " << i << ": " << x_massiv[i] << endl;

    cout << endl;
    for (i = 0; i <= matrix_size; i++)
        cout << "e,k: " << i << ": " << coeffs_massiv[i][0] << " " << coeffs_massiv[i][1] << endl;
}

//Запись в 3 файла значений сплайна, интерполируемой функции и их разницы в соответственных точках
void tables_in_file(functiontype* f, Node* Array, int Count_dots, int Count_Segments, double Initial, double End, double* Array_steps, double* x_massiv)
{
    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 < Count_Segments; i++)
    {
        while (x_value < Array[i + 1].x)
        {
            fout1 << x_value << " ";
            fout2 << x_value << " ";
            fout3 << x_value << " ";
            y_value1 = Spline(x_value, i, Array_steps, x_massiv, Array);
            y_value2 = (*f)(x_value);
            fout1 << y_value1 << endl;
            fout2 << y_value2 << endl;
            fout3 << abs(y_value2 - y_value1) << endl;
            x_value += step;
        }
    }
    fout1 << End << " ";
    fout2 << End << " ";
    fout1 << Spline(End, Count_Segments - 1, Array_steps, x_massiv, Array) << endl;
    fout2 << (*f)(End) << endl;
    fout1.close();
    fout2.close();
    cout << endl << "Запись в файл осуществлена!" << endl;
}


int main()
{
    setlocale(LC_ALL, "RUS");
    functiontype Func = &Myfunc;
    int CountSegments, i, Countdots = 15000;

    /*---------------------------------Входные данные-------------------------------------*/
    double Initial = -5, End = 5;
    cout << "Введите N: ";
    cin >> CountSegments;

    /*---------------------------------Сетки-------------------------------------*/
    double* Array_steps_cheb = new double[CountSegments + 1];
    double* Array_steps_uni = new double[CountSegments + 1];

    //Равномерная сетка
    Node* ArrayUniformNodes = new Node[CountSegments + 1];
    ValueUniformTable(&Func, ArrayUniformNodes, Initial, End, CountSegments, Array_steps_uni);
    //Чебышёв
    Node* ArrayChebyshevNodes = new Node[CountSegments + 1];
    ValueChebyshevTable(&Func, ArrayChebyshevNodes, Initial, End, CountSegments, Array_steps_cheb);

    /*---------------------------------СЛАУ - matrix_coeffs -------------------------------------*/
    double** matrix_coeffs;
    matrix_coeffs = new double*[CountSegments+1];
    for (i = 0; i < CountSegments+1; i++)
        matrix_coeffs[i] = new double[3];

    //cout << endl << "Полученная матрица: " << endl;
    get_matrix_coeffs(Initial, End, CountSegments, &Func, matrix_coeffs, ArrayUniformNodes, Array_steps_uni);

    /*---------------------------------Прогонка - запись в x_massiv -------------------------------------*/
    //Получение ответа в x_massiv
    double* x_massiv = new double[CountSegments + 1];
    tridiagonal_matrix_algorithm(matrix_coeffs, Array_steps_uni, ArrayUniformNodes, CountSegments, x_massiv);

    /*---------------------------------Графики -------------------------------------*/
    //Запись значений сплайна и интерполируемой функции в файлы соответсвенно
    //tables_in_file(&Func, ArrayUniformNodes, Countdots, CountSegments, Initial, End, Array_steps_uni, x_massiv);

    /*---------------------------------Вывод в консоль значений -------------------------------------*/

    //Шаги
    cout << endl;
    for (i = 1; i <= CountSegments; i++) {
        cout << "h_" << i << ": " << Array_steps_uni[i] << endl;
    }

    cout << endl << "Cетка:  " << endl;
        for (int i = 0; i < CountSegments + 1; i++)
    cout << "(" << ArrayUniformNodes[i].x << ":" << ArrayUniformNodes[i].y << ")" << endl;


    cout << endl;
    for (i = 0; i < CountSegments; i++)
        cout << "Spline in x_" << i << " " << Spline(ArrayUniformNodes[i].x, i, Array_steps_uni, x_massiv, ArrayUniformNodes) << endl;
    cout << "Spline in x_" << CountSegments << " " << Spline(ArrayUniformNodes[CountSegments].x, CountSegments - 1, Array_steps_uni, x_massiv, ArrayUniformNodes) << endl;


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