Code:
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
{
for(int j=0; j
{
mat[i][j] = input.nextDouble();
}
constants[i] = input.nextDouble();
}
test(mat, constants);
}
}
Output:
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
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