методы вычислений Поплавский / Koshi_raz_Metods

#include <iostream>
#include <cmath>
#include <vector>
#include <iomanip>

using namespace std;

float y_tochn(float x, float t) {
	return x * x * (x - t);
}

float p(float x) {
	return x * x;
}

float q(float x) {
	return x * x * x;
}

float f(float x, float t) {
	return pow(x, 6) - t * pow (x, 5) + 3 * pow (x, 4) - 2 * pow(x, 3) + 6 * x - 2 * t;
}

void print(pair <vector <vector <float>>, vector <float>> para) { // Вывод матрицы со столбцом
	vector <vector <float>> result = para.first;
	vector <float> b = para.second;

	for (int i = 0; i < result.size(); i++, cout << endl) {
		for (int j = 0; j < result[i].size(); j++) {
			cout << setw(7) << result[i][j];
		}
		cout << setw(7) << "/ " << b[i];
	}
	cout << endl;
}

void print2(vector <vector <float>> result) { // Вывод матрицы без столбца
	for (int i = 0; i < result.size(); i++, cout << endl) {
		for (int j = 0; j < result[i].size(); j++) {
			cout << setw(7) << result[i][j];
		}
	}
	cout << endl;
}

pair <vector <vector <float>>, vector <float>> iter_str (pair <vector <vector <float>>, vector <float>> para, int m, int i, int j) { // Функция замены i и j строк матрицы
	vector <vector <float>> mas = para.first;
	vector <float> b = para.second;
	vector <vector <float>> mas1 = mas;
	vector <float> b1 = b;

	for (int k = 0; k < m; k++) {

		if (k == i) {
			mas[k] = mas1[j];
			b[k] = b1[j];
		}
		else if (k == j) {
			mas[k] = mas1[i];
			b[k] = b1[i];
		}
		else {
			mas[k] = mas1[k];
			b[k] = b1[k];
		}

	}
	pair <vector <vector <float>>, vector <float>> para1(mas, b);
	return para1;
}

vector <float> inverse_vector(vector <float> mas, int m) { // Reverse
	vector <float> res;

	for (int i = m - 1; i >= 0; i--) {
		res.push_back(mas[i]);
	}

	return res;
}

vector<float> Gauss_osn(pair <vector <vector <float>>, vector <float>> para, int m, vector <float> res) {
	vector <vector <float>> mas = para.first;
	vector <float> b = para.second;
	vector <vector <float>> mas1 = mas; // Вспомогательное для замены строк

	cout << "Процесс прямого хода: " << endl;
	for (int k = 0; k < m; k++) {

		if (mas1[k][k] == 0) { // Если знаменатель равен нулю
			float max = 0;
			int max_str = k;

			for (int x = k; x < m; x++) {
				if (abs(mas1[x][k]) > 0) {
					max_str = x;
					max = abs(mas1[x][k]);
				}
			}
			if (max > 0) {
				pair <vector <vector <float>>, vector <float>> para(mas1, b);
				mas1 = iter_str(para, m, k, max_str).first;
				b = iter_str(para, m, k, max_str).second;
				cout << "Меняем местами строки с номерами " << k << " и " << max_str << endl;
				pair <vector <vector <float>>, vector <float>> para1(mas1, b);
				print(para1);
				mas = mas1;
			}
		}

		for (int j = k; j < m; j++) {
			mas[k][j] /= mas1[k][k];
		}

		b[k] /= mas1[k][k];

		for (int i = k + 1; i < m; i++) {
			for (int j = k; j < m; j++) {
				mas[i][j] -= mas1[i][k] * mas[k][j];
			}
			b[i] -= mas1[i][k] * b[k];
		}

		mas1 = mas;
		pair <vector <vector <float>>, vector <float>> para(mas, b);
		print(para);
	}

	cout << "Процесс обратного хода: " << endl;

	float raz = 0;
	for (int k = m - 1; k >= 0; k--) {
		cout << "x[" << k << "] = " << b[k];
		for (int x = 0; x < m - 1 - k; x++) {
			raz += res[x] * mas[k][m - x - 1];
			cout << " - x[" << m - x - 1 << "] * " << mas[k][m - x - 1];
		}
		res.push_back(b[k] * 1.0 - raz);
		cout << " = " << res[res.size() - 1] << endl;
		raz = 0;
	}
	return res;
}

vector <vector <float>> matrix_for_raznost_metod(int n, float h, vector <float> x) {
	vector <vector <float>> res(n);
	res[0].push_back(1);

	for (int i = 1; i < n; i++) 
		res[0].push_back(0);  // Первая строка y[0] = 0

	for (int i = 1; i < n - 1; i++) { 
		for (int j = 0; j < i - 1; j++) 
			res[i].push_back(0);

		res[i].push_back(1.0 / h / h + p(x[i]) / 2.0 / h);
		res[i].push_back(q(x[i]) - 2.0 / h / h);
		res[i].push_back(1.0 / h / h + 1.0 / 2.0 / h);

		for (int k = i - 1 + 3; k < n; k++) 
			res[i].push_back(0);
	}
	for (int i = 0; i < n - 1; i++) 
		res[n - 1].push_back(0);

	res[n - 1].push_back(1);
	return res;
}

int main() {
	setlocale(LC_ALL, "RUS");
	cout << "Введите ваш вариант: ";
	int var, m, n, i, j, val;
	cin >> var;
	vector <float> d, res1, res2;
	float a0, b0;
	cout << "Введите количество узлов: ";
	cin >> n;
	float h = var / (n - 1);
	vector <float> x, y;

	for (int i = 0; i <= n; i++) {
		x.push_back(i * h);
	}

	d.push_back(0);

	for (int i = 1; i < n - 1; i++) {
		d.push_back(f(x[i], var));
	}

	d.push_back(0);
	vector <vector <float>> res = matrix_for_raznost_metod(n, h, x);
	pair <vector <vector <float>>, vector <float>> para(res, d);
	print(para);
	y = inverse_vector (Gauss_osn(para, n, res1), n);

	cout << setw(7) << "x[i]:";
	for (int i = 0; i < n; i++) cout << x[i] << setw(7);
	cout << endl;

	cout << setw(7) << "y_m:";
	for (int i = 0; i < n; i++) cout << y[i] << setw(7);
	cout << endl;

	cout << setw(7) << "y_t:";
	for (int i = 0; i < n; i++) cout << y_tochn(x[i], var) << setw(7);
	cout << endl;

	cout << setw(7) << "e[i]:";
	for (int i = 0; i < n; i++) cout << abs (y_tochn(x[i], var) - y[i]) << setw(7);
	cout << endl;

	system("pause");
	return 0;
}