programming-examples/java/Numerical_Problems/Java Program to Implement Gauss Jordan Elimination.java

/*
This is java program to find the solution to the linear equations of any number of variables using the method of Gauss-Jordan algorithm.
*/

//This is a sample program to find the solution to the linear equations using the method of Gauss-Jordan algorithm
import java.util.Scanner;

public class Gauss_Jordan_Elimination
{
    private static final double EPSILON = 1e-8;

    private final int N;      // N-by-N system
    private double[][] a;     // N-by-N+1 augmented matrix

    // Gauss-Jordan elimination with partial pivoting
    public Gauss_Jordan_Elimination(double[][] A, double[] b)
    {
        N = b.length;
        // build augmented matrix
        a = new double[N][N+N+1];
        for (int i = 0; i < N; i++)
            for (int j = 0; j < N; j++)
                a[i][j] = A[i][j];
        // only need if you want to find certificate of infeasibility (or compute inverse)
        for (int i = 0; i < N; i++)
            a[i][N+i] = 1.0;
        for (int i = 0; i < N; i++)
            a[i][N+N] = b[i];
        solve();
        assert check(A, b);
    }

    private void solve()
    {
        // Gauss-Jordan elimination
        for (int p = 0; p < N; p++)
            {
                int max = p;
                for (int i = p+1; i < N; i++)
                    {
                        if (Math.abs(a[i][p]) > Math.abs(a[max][p]))
                            {
                                max = i;
                            }
                    }
                // exchange row p with row max
                swap(p, max);
                // singular or nearly singular
                if (Math.abs(a[p][p]) <= EPSILON)
                    {
                        continue;
                        // throw new RuntimeException("Matrix is singular or nearly singular");
                    }
                // pivot
                pivot(p, p);
            }
        // show();
    }

    // swap row1 and row2
    private void swap(int row1, int row2)
    {
        double[] temp = a[row1];
        a[row1] = a[row2];
        a[row2] = temp;
    }


    // pivot on entry (p, q) using Gauss-Jordan elimination
    private void pivot(int p, int q)
    {
        // everything but row p and column q
        for (int i = 0; i < N; i++)
            {
                double alpha = a[i][q] / a[p][q];
                for (int j = 0; j <= N+N; j++)
                    {
                        if (i != p && j != q) a[i][j] -= alpha * a[p][j];
                    }
            }
        // zero out column q
        for (int i = 0; i < N; i++)
            if (i != p) a[i][q] = 0.0;
        // scale row p (ok to go from q+1 to N, but do this for consistency with simplex pivot)
        for (int j = 0; j <= N+N; j++)
            if (j != q) a[p][j] /= a[p][q];
        a[p][q] = 1.0;
    }

    // extract solution to Ax = b
    public double[] primal()
    {
        double[] x = new double[N];
        for (int i = 0; i < N; i++)
            {
                if (Math.abs(a[i][i]) > EPSILON)
                    x[i] = a[i][N+N] / a[i][i];
                else if (Math.abs(a[i][N+N]) > EPSILON)
                    return null;
            }
        return x;
    }

    // extract solution to yA = 0, yb != 0
    public double[] dual()
    {
        double[] y = new double[N];
        for (int i = 0; i < N; i++)
            {
                if ( (Math.abs(a[i][i]) <= EPSILON) && (Math.abs(a[i][N+N]) > EPSILON) )
                    {
                        for (int j = 0; j < N; j++)
                            y[j] = a[i][N+j];
                        return y;
                    }
            }
        return null;
    }

    // does the system have a solution?
    public boolean isFeasible()
    {
        return primal() != null;
    }

    // print the tableaux
    private void show()
    {
        for (int i = 0; i < N; i++)
            {
                for (int j = 0; j < N; j++)
                    {
                        System.out.print(" "+a[i][j]);
                    }
                System.out.print("| ");
                for (int j = N; j < N+N; j++)
                    {
                        System.out.print(" "+a[i][j]);
                    }
                System.out.print("| \n"+a[i][N+N]);
            }
        System.out.println();
    }


    // check that Ax = b or yA = 0, yb != 0
    private boolean check(double[][] A, double[] b)
    {
        // check that Ax = b
        if (isFeasible())
            {
                double[] x = primal();
                for (int i = 0; i < N; i++)
                    {
                        double sum = 0.0;
                        for (int j = 0; j < N; j++)
                            {
                                sum += A[i][j] * x[j];
                            }
                        if (Math.abs(sum - b[i]) > EPSILON)
                            {
                                System.out.println("not feasible");
                                System.out.println(i+" = "+b[i]+", sum = "+sum+"\n");
                                return false;
                            }
                    }
                return true;
            }
        // or that yA = 0, yb != 0
        else
            {
                double[] y = dual();
                for (int j = 0; j < N; j++)
                    {
                        double sum = 0.0;
                        for (int i = 0; i < N; i++)
                            {
                                sum += A[i][j] * y[i];
                            }
                        if (Math.abs(sum) > EPSILON)
                            {
                                System.out.println("invalid certificate of infeasibility");
                                System.out.println("sum = "+sum+"\n");
                                return false;
                            }
                    }
                double sum = 0.0;
                for (int i = 0; i < N; i++)
                    {
                        sum += y[i] * b[i];
                    }
                if (Math.abs(sum) < EPSILON)
                    {
                        System.out.println("invalid certificate of infeasibility");
                        System.out.println("yb  = "+sum+"\n");
                        return false;
                    }
                return true;
            }
    }


    public static void test(double[][] A, double[] b)
    {
        Gauss_Jordan_Elimination gaussian = new Gauss_Jordan_Elimination(A, b);
        if (gaussian.isFeasible())
            {
                System.out.println("Solution to Ax = b");
                double[] x = gaussian.primal();
                for (int i = 0; i < x.length; i++)
                    {
                        System.out.println(" "+x[i]+"\n");
                    }
            }
        else
            {
                System.out.println("Certificate of infeasibility");
                double[] y = gaussian.dual();
                for (int j = 0; j < y.length; j++)
                    {
                        System.out.println(" "+y[j]+"\n");
                    }
            }
        System.out.println();
    }

    public static void main(String[] args)
    {
        Scanner input = new Scanner(System.in);
        System.out.println("Enter the number of variables in the equations: ");
        int n = input.nextInt();
        System.out.println("Enter the coefficients of each variable for each equations");
        System.out.println("ax + by + cz + ... = d");
        double [][]mat = new double[n][n];
        double []constants = new double[n];
        //input
        for(int i=0; i<n; i++)
            {
                for(int j=0; j<n; j++)
                    {
                        mat[i][j] = input.nextDouble();
                    }
                constants[i] = input.nextDouble();
            }
        test(mat, constants);
    }
}

/*
Enter the number of variables in the equations:
2
Enter the coefficients of each variable for each equations
ax + by + cz + ... = d
1 2 3
6 5 4
Solution to Ax = b
 -1.0

  2.0

*/