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Sigma knowledge engineering system is an system for developing, viewing and debugging theories in first order logic. It works with Knowledge Interchange Format (KIF) and is optimized for the Suggested Upper Merged Ontology (SUMO) www.ontologyportal.org.

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package com.articulate.sigma.nlp;

import java.util.Arrays;

/**
 * Created by apease on 4/24/15.
 */
public class GaussElim {

    /****************************************************************
     */
    private static void printRow(float[] row) {

        for (int j = 0; j < row.length; j++) {
            if (j > 0)
                System.out.print(", ");
            System.out.print(row[j]);
        }
        System.out.println();
    }

    /****************************************************************
     */
    private static void printMatrix(float[][] matrix) {

        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[0].length; j++) {
                if (j > 0)
                    System.out.print(", ");
                System.out.print(matrix[i][j]);
            }
            System.out.println();
        }
        System.out.println();
    }

    /****************************************************************
     * Perform Gaussian elimination on a set of simultaneous equations
     */
    private static float[] gaussianElim(float[][] matrix) {

        int n = matrix.length; // number of rows
        int m = matrix[0].length; // number of columns
        float[] x = new float[n];
        //System.out.println("# rows: " + n + " # columns: " + m);
        if (n + 1 != m)
            //System.out.println("Error in SVM.gaussianElim(): m != n+1");
        for (int row1 = 0; row1 < n-1; row1++) { // looking by row
            //printRow(matrix[k]);
            for (int row2 = row1 + 1; row2 < n; row2++) { // looking by row
                if (matrix[row1][row1] == 0) {
                    //System.out.println("Error in GaussElim.gaussianElim(): Singular matrix!");
                    return null;
                }

                float divisor = matrix[row2][row1] / matrix[row1][row1];
                //System.out.println("divisor: " + divisor);
                //Do for all remaining elements in current row:
                for (int j = row1; j < m; j++) { // looking by column
                    //System.out.println("looking at element row: " + row2 + " column: " + j + " with value: " + matrix[row2][j]);
                    matrix[row2][j] = matrix[row2][j] - (matrix[row1][j] * divisor);
                }
            }
            //printMatrix(matrix);
        }
        //System.out.println();
        //System.out.println("Backward substitution");
        for (int row1 = n - 1; row1 > -1; row1--) {
            //System.out.println("Pivot row: " + row1);
            for (int row2 = row1-1; row2 > -1; row2--) {
                //System.out.println("Modifying row: " + row2);
                float divisor = matrix[row2][row1] / matrix[row1][row1];
                //System.out.println("divisor: " + divisor);
                for (int j = row1; j < m; j++) {
                    //System.out.println("looking at element row: " + row2 + " column: " + j + " with value: " + matrix[row2][j]);
                    matrix[row2][j] = matrix[row2][j] - matrix[row1][j] * divisor;
                }
            }
            //printMatrix(matrix);
            x[row1] = matrix[row1][m-1] / matrix[row1][row1];
        }
        //printMatrix(matrix);
        //printRow(x);
        return x;
    }

    /** **************************************************************
     * test method
     */
    public static void main(String[] args) {

        float[][] matrix = {{2, 4,  4, -1},
                          {4, 11, 9, 1},
                          {4, 9, 11, 1}};
       // float[][] matrix = {{2, 1, -1, 8},
       //         {-3, -1, 2, -11},
       //         {-2, 1, 2, -3}};
        // answer is 2,3,-1
        printMatrix(matrix);
        gaussianElim(matrix);
    }
}