Numeryczne rozwiązywanie układu równań liniowych metodą Jacobiego.

Jacobian.cpp

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

using namespace std;



void metoda_Jacobiego();
bool gauss(int, double**, double*);
void metoda_eliminacji_gaussa();

int main()
{
//	metoda_eliminacji_gaussa();
	metoda_Jacobiego();

	cout << "\n\n";
	system("pause");
	return 0;
}



bool gauss(int n, double ** AB, double * X)
{
	const double eps = 1e-12; // stala przyblizenia zera
	int i, j, k;
	double m, s;

	for (i = 0; i < n - 1; i++)
	{
		for (j = i + 1; j < n; j++)
		{
			if (fabs(AB[i][i]) < eps) return false;
			m = -AB[j][i] / AB[i][i];
			for (k = i + 1; k <= n; k++)
				AB[j][k] += m * AB[i][k];
		}
	}

	for (i = n - 1; i >= 0; i--)
	{
		s = AB[i][n];
		for (j = n - 1; j >= i + 1; j--)
			s -= AB[i][j] * X[j];
		if (fabs(AB[i][i]) < eps) return false;
		X[i] = s / AB[i][i];
	}
	return true;
}

void metoda_eliminacji_gaussa()
{
	double **AB, *X;
	int n, i, j;
	cout << setprecision(4) << fixed;

	cout << "podajliczbe niewiadomych" << endl;
	cin >> n;

	AB = new double *[n];
	X = new double[n];

	for (i = 0; i < n; i++)
		AB[i] = new double[n + 1];

	cout << "podaj dane dla macierzy" << endl;
	for (i = 0; i < n; i++)
		for (j = 0; j <= n; j++) cin >> AB[i][j];

	if (gauss(n, AB, X))
	{
		for (i = 0; i < n; i++)
			cout << "x" << i + 1 << " = " << setw(9) << X[i]
			<< endl;
	}
	else
		cout << "DZIELNIK ZERO\n";

	for (i = 0; i < n; i++) delete[] AB[i];
	delete[] AB;
	delete[] X;
}

void metoda_Jacobiego()
{
	float A[100][100];
	float M[100][100];
	float N[100][100];
	float b[100];
	float x1[100];
	float x2[100];

	int num, iter;

	/*
	cout << "Metoda Jacobiego\n" << endl;
	cout << "Rozwiazywanie ukladu n-rownan z n-niewiadomymi Ax=b\n" << endl;
	cout << "Podaj n\n" << endl;
	cin >> num;
	
	if ((num < 1) && (num > 100))
	{
		cout << "Nieprawidlowa warosc parametru n\n" << endl;
		return;
	}
	*/
	num = 3;
	/*
	for (int i = 0; i<num; i++)
	for (int j = 0; j<num; j++)
	{
	cout << "A[" << (i + 1) << "][" << (j + 1) << "] = ";
	cin >> A[i][j];
	if ((i == j) && (A[i][j] == 0))
	{
	cout << "Wartosci na przekatnej musza byc rozne od 0\n";
	return;
	}
	}

	cout << endl;
	for (int i = 0; i<num; i++)
	{
	cout << "b" << (i + 1) << ": ";
	cin >> b[i];
	}
	*/
	A[0][0] = 5;
	A[0][1] = -2;
	A[0][2] = 3;

	A[1][0] = -3;
	A[1][1] = 9;
	A[1][2] = 1;

	A[2][0] = 2;
	A[2][1] = -1;
	A[2][2] = -7;
	b[0] = -1;
	b[1] = 2;
	b[2] = 3;
	
	for (int i = 0; i < num; i++){
		for (int j = 0; j < num; j++){
			if(i ==j)N[i][j] = 1 / A[i][i];
			else N[i][j] = 0;
		}
	}
	for (int i = 0; i<num; i++)
		for (int j = 0; j<num; j++)
			if (i == j)
				M[i][j] = 0;
			else
				M[i][j] = -(A[i][j] * N[i][i]);

	for (int i = 0; i<num; i++)
		x1[i] = 0;

	iter = 5;

	for (int k = 0; k<iter; k++)
	{
		for (int i = 0; i<num; i++)
		{
			x2[i] = N[i][i] * b[i];
			for (int j = 0; j<num; j++)
				x2[i] += M[i][j] * x1[j];
		}
		for (int i = 0; i<num; i++)
			x1[i] = x2[i];
		
		for (int i = 0; i<num; i++)
			cout << "x" << (i + 1) << " = " << setprecision(4) << x1[i] << endl;
	}

	cout << endl;
	cout << "N matrix:" << endl;
	for (int i = 0; i < num; i++){
		for (int j = 0; j < num; j++){
			cout << N[i][j] << " ";
		}
		cout << endl;
	}


	cout << endl;
	cout << endl;
	cout << "A matrix:" << endl;
	for (int i = 0; i < num; i++){
		for (int j = 0; j < num; j++){
			cout << A[i][j] << " ";
		}
		cout << endl;
	}


	cout << endl;
	cout << "M matrix:" << endl;
	for (int i = 0; i < num; i++){
		for (int j = 0; j < num; j++){
			cout << M[i][j] << " ";
		}
		cout << endl;
	}

	cout << endl;

	for (int i = 0; i<num; i++)
		cout << "x" << (i + 1) << " = " << setprecision(4) << x1[i] << endl;
}