guasselim.java

import java.util.*;

public class guasselim {

    public static void main(String[] args) {
        // Test input; should give <1, 2, 3>
        double[][] mat = { { 1, 1, 2, 9 }, { 2, 4, -3, 1 }, { 3, 6, -5, 0 } };
        double[] ans = GaussianElimination(mat);
        System.out.println(Arrays.toString(ans));
    }

    // Aug is an n x n + 1 augmented matrix
    static double[] GaussianElimination(double[][] aug) {
        int n = aug.length;
        double[] X = new double[n]; // represents a column vector

        // Convert matrix to row-echelon form
        for (int j = 0; j < n - 1; j++) {
            int l = j;
            for (int i = j + 1; i < n; i++)
                // Find the row with the largest column value
                if (Math.abs(aug[i][j]) > Math.abs(aug[l][j]))
                    l = i;

            // Swap rows
            for (int k = j; k <= n; k++) {
                double tmp = aug[j][k];
                aug[j][k] = aug[l][k];
                aug[l][k] = tmp;
            }
            // Forward elimination
            for (int i = j + 1; i < n; i++)
                for (int k = n; k >= j; k--)
                    aug[i][k] -= aug[j][k] * aug[i][j] / aug[j][j];
        }

        // Back-substitute
        for (int j = n - 1; j >= 0; j--) {
            double t = 0.0;
            for (int k = j + 1; k < n; k++)
                t += aug[j][k] * X[k];

            X[j] = (aug[j][n] - t) / aug[j][j];
        }

        return X;
    }

}