LinearEquations.java

/*
 * @(#)LinearEquations.java  
 * 
 * Copyright (c) 2012 Werner Randelshofer, Goldau, Switzerland.
 * All rights reserved.
 * 
 * You may not use, copy or modify this file, except in compliance with the
 * license agreement you entered into with Werner Randelshofer.
 * For details see accompanying license terms.
 */
package org.monte.media.math;

/**
 * {@code LinearEquations}.
 * <p>
 * Reference:
 * http://en.wikipedia.org/wiki/Cramer's_rule
 * http://en.wikipedia.org/wiki/Determinant
 *
 * @author Werner Randelshofer
 * @version $Id: LinearEquations.java 299 2013-01-03 07:40:18Z werner $
 */
public class LinearEquations {

    private LinearEquations() {
    }

    ;
    
    /** Solves a linear system for x,y with cramer's rule.
     * 
     * <pre>
     * a*x + b*y = e
     * c*x + d*y = f
     * </pre>
     * 
     * @param a
     * @param b
     * @param c
     * @param d
     * @param e
     * @param f 
     */
    public static double[] solve(double a, double b, double c, double d, double e, double f) {
        System.out.println("["+a+" "+b+";"+c+" "+d+"]\\["+e+";"+f+"]");
        double x = (e * d - b * f) / (a * d - b * c);
        double y = (a * f - e * c) / (a * d - b * c);
        return new double[]{x, y};
    }

    /** Solves a linear system for x,y,z with cramer's rule.
     * 
     * <pre>
     * a*x + b*y + c*z = j
     * d*x + e*y + f*z = k
     * g*x + h*y + i*z = l
     * </pre>
     * 
     * @param a
     * @param b
     * @param c
     * @param d
     * @param e
     * @param f 
     */
    public static double[] solve(double a, double b, double c, double d, double e, double f, double g, double h, double i, double j, double k, double l) {
        double det_abcdefghi=det(a,b,c,d,e,f,g,h,i);
        double x = det(j,b,c,k,e,f,l,h,i)/det_abcdefghi;
        double y = det(a,j,c,d,k,f,g,l,i)/det_abcdefghi;
        double z = det(a,b,j,d,e,k,g,h,l)/det_abcdefghi;
        return new double[]{x, y,z};
    }

    /** Computes the determinant of a 2x2 matrix using Sarrus' rule.
     * <pre>
     * | a, b, c |     |e, f|   |d, f|   |d, e|
     * | d, e, f | = a*|h, i|-b*|g, i|+c*|g, h|=aei+bfg+cdh-ceg-bdi-afh
     * | g, h, i |
     * </pre>
     * 
     * @param a
     * @param b
     * @param c
     * @param d
     * @param e
     * @param f
     * @param g
     * @param h
     * @param i
     * @return the determinant
     */
    public static double det(double a, double b, double c, double d, double e, double f, double g, double h, double i) {
        return a * e * i//
                + b * f * g //
                + c * d * h //
                - c * e * g //
                - b * d * i //
                - a * f * h;
    }

    /** Computes the determinant of a 3x3 matrix using Sarrus' rule.
     * <pre>
     * | a, b |
     * | c, d | = a*d - b*c
     * </pre>
     * 
     * @param a
     * @param b
     * @param c
     * @param d
     * @return the determinant
     */
    public static double det(double a, double b, double c, double d) {
        return a * d - b * c;
    }
}