programming-examples/java/Numerical_Problems/Java Program to Implement Gaussian Elimination Algorithm.java

/*
This is a Java Program to Implement Gaussian Elimination Algorithm. Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.
*/

/**
 ** 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);
    }
}

/*
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