Code:
/**
** Java Program to Implement Gaussian Elimination Algorithm
**/
import java.util.Scanner;
/** Class GaussianElimination **/
public class GaussianElimination
{
public void solve(double[][] A, double[] B)
{
int N = B.length;
for (int k = 0; k < N; k++)
{
/** find pivot row **/
int max = k;
for (int i = k + 1; i < N; i++)
if (Math.abs(A[i][k]) > Math.abs(A[max][k]))
max = i;
/** swap row in A matrix **/
double[] temp = A[k];
A[k] = A[max];
A[max] = temp;
/** swap corresponding values in constants matrix **/
double t = B[k];
B[k] = B[max];
B[max] = t;
/** pivot within A and B **/
for (int i = k + 1; i < N; i++)
{
double factor = A[i][k] / A[k][k];
B[i] -= factor * B[k];
for (int j = k; j < N; j++)
A[i][j] -= factor * A[k][j];
}
}
/** Print row echelon form **/
printRowEchelonForm(A, B);
/** back substitution **/
double[] solution = new double[N];
for (int i = N - 1; i >= 0; i--)
{
double sum = 0.0;
for (int j = i + 1; j < N; j++)
sum += A[i][j] * solution[j];
solution[i] = (B[i] - sum) / A[i][i];
}
/** Print solution **/
printSolution(solution);
}
/** function to print in row echleon form **/
public void printRowEchelonForm(double[][] A, double[] B)
{
int N = B.length;
System.out.println("\nRow Echelon form : ");
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
System.out.printf("%.3f ", A[i][j]);
System.out.printf("| %.3f\n", B[i]);
}
System.out.println();
}
/** function to print solution **/
public void printSolution(double[] sol)
{
int N = sol.length;
System.out.println("\nSolution : ");
for (int i = 0; i < N; i++)
System.out.printf("%.3f ", sol[i]);
System.out.println();
}
/** Main function **/
public static void main (String[] args)
{
Scanner scan = new Scanner(System.in);
System.out.println("Gaussian Elimination Algorithm Test\n");
/** Make an object of GaussianElimination class **/
GaussianElimination ge = new GaussianElimination();
System.out.println("\nEnter number of variables");
int N = scan.nextInt();
double[] B = new double[N];
double[][] A = new double[N][N];
System.out.println("\nEnter "+ N +" equations coefficients ");
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++)
A[i][j] = scan.nextDouble();
System.out.println("\nEnter "+ N +" solutions");
for (int i = 0; i < N; i++)
B[i] = scan.nextDouble();
ge.solve(A,B);
}
}
Output:
Gaussian Elimination Algorithm Test
Enter number of variables
3
Enter 3 equations coefficients
2 1 -1
-3 -1 2
-2 1 2
Enter 3 solutions
8
-11
-3
Row Echelon form :
-3.000 -1.000 2.000 | -11.000
0.000 1.667 0.667 | 4.333
0.000 0.000 0.200 | -0.200
Solution :
2.000 3.000 -1.000
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