Java Program to Find Inverse of a Matrix

This is the java program to find the inverse of square invertible matrix. The matrix is invertible if its determinant is non zero.

Here is the source code of the Java Program to Find Inverse of a Matrix. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

//This is sample program to find the inverse of a matrix
 
import java.util.Scanner;
 
public class Inverse 
{
    public static void main(String argv[]) 
    {
        Scanner input = new Scanner(System.in);
        System.out.println("Enter the dimension of square matrix: ");
        int n = input.nextInt();
        double a[][]= new double[n][n];
        System.out.println("Enter the elements of matrix: ");
        for(int i=0; i<n; i++)
            for(int j=0; j<n; j++)
                a[i][j] = input.nextDouble();
 
        double d[][] = invert(a);
 
        System.out.println("The inverse is: ");
        for (int i=0; i<n; ++i) 
        {
            for (int j=0; j<n; ++j)
            {
                System.out.print(d[i][j]+"  ");
            }
            System.out.println();
        }
        input.close();
    }	
 
    public static double[][] invert(double a[][]) 
    {
        int n = a.length;
        double x[][] = new double[n][n];
        double b[][] = new double[n][n];
        int index[] = new int[n];
        for (int i=0; i<n; ++i) 
            b[i][i] = 1;
 
 // Transform the matrix into an upper triangle
        gaussian(a, index);
 
 // Update the matrix b[i][j] with the ratios stored
        for (int i=0; i<n-1; ++i)
            for (int j=i+1; j<n; ++j)
                for (int k=0; k<n; ++k)
                    b[index[j]][k]
                    	    -= a[index[j]][i]*b[index[i]][k];
 
 // Perform backward substitutions
        for (int i=0; i<n; ++i) 
        {
            x[n-1][i] = b[index[n-1]][i]/a[index[n-1]][n-1];
            for (int j=n-2; j>=0; --j) 
            {
                x[j][i] = b[index[j]][i];
                for (int k=j+1; k<n; ++k) 
                {
                    x[j][i] -= a[index[j]][k]*x[k][i];
                }
                x[j][i] /= a[index[j]][j];
            }
        }
        return x;
    }
 
// Method to carry out the partial-pivoting Gaussian
// elimination.  Here index[] stores pivoting order.
 
    public static void gaussian(double a[][], int index[]) 
    {
        int n = index.length;
        double c[] = new double[n];
 
 // Initialize the index
        for (int i=0; i<n; ++i) 
            index[i] = i;
 
 // Find the rescaling factors, one from each row
        for (int i=0; i<n; ++i) 
        {
            double c1 = 0;
            for (int j=0; j<n; ++j) 
            {
                double c0 = Math.abs(a[i][j]);
                if (c0 > c1) c1 = c0;
            }
            c[i] = c1;
        }
 
 // Search the pivoting element from each column
        int k = 0;
        for (int j=0; j<n-1; ++j) 
        {
            double pi1 = 0;
            for (int i=j; i<n; ++i) 
            {
                double pi0 = Math.abs(a[index[i]][j]);
                pi0 /= c[index[i]];
                if (pi0 > pi1) 
                {
                    pi1 = pi0;
                    k = i;
                }
            }
 
   // Interchange rows according to the pivoting order
            int itmp = index[j];
            index[j] = index[k];
            index[k] = itmp;
            for (int i=j+1; i<n; ++i) 	
            {
                double pj = a[index[i]][j]/a[index[j]][j];
 
 // Record pivoting ratios below the diagonal
                a[index[i]][j] = pj;
 
 // Modify other elements accordingly
                for (int l=j+1; l<n; ++l)
                    a[index[i]][l] -= pj*a[index[j]][l];
            }
        }
    }
}

Output:

$ javac Inverse.java
$ java Inverse
Enter the dimension of square matrix: 
2
Enter the elements of matrix: 
1 2 
3 4 
The Inverse is: 
-1.9999999999999998  1.0  
1.4999999999999998  -0.49999999999999994