JAVA-四元數類

public class Quaternion { private final double x0, x1, x2, x3; // 四元數構造函數 public Quaternion(double x0, double x1, double x2, double x3) { this.x0 = x0; this.x1 = x1; this.x2 = x2; this.x3 = x3; } // 轉化 public String toString() { return x0 + " + " + x1 + "i + " + x2 + "j + " + x3 + "k"; } // 模 public double norm() { return Math.sqrt(x0*x0 + x1*x1 +x2*x2 + x3*x3); } // 共軛 public Quaternion conjugate() { return new Quaternion(x0, -x1, -x2, -x3); } // 加法 public Quaternion plus(Quaternion b) { Quaternion a = this; return new Quaternion(a.x0+b.x0, a.x1+b.x1, a.x2+b.x2, a.x3+b.x3); } // 乘法 public Quaternion times(Quaternion b) { Quaternion a = this; double y0 = a.x0*b.x0 - a.x1*b.x1 - a.x2*b.x2 - a.x3*b.x3; double y1 = a.x0*b.x1 + a.x1*b.x0 + a.x2*b.x3 - a.x3*b.x2; double y2 = a.x0*b.x2 - a.x1*b.x3 + a.x2*b.x0 + a.x3*b.x1; double y3 = a.x0*b.x3 + a.x1*b.x2 - a.x2*b.x1 + a.x3*b.x0; return new Quaternion(y0, y1, y2, y3); } // 逆 public Quaternion inverse() { double d = x0*x0 + x1*x1 + x2*x2 + x3*x3; return new Quaternion(x0/d, -x1/d, -x2/d, -x3/d); } // 除法 // 轉化爲乘法問題 a * b^-1 (b^-1 a) public Quaternion divides(Quaternion b) { Quaternion a = this; return a.times(b.inverse()); } // test public static void main(String[] args) { Quaternion a = new Quaternion(3.0, 1.0, 0.0, 0.0); StdOut.println("a = " + a); Quaternion b = new Quaternion(0.0, 5.0, 1.0, -2.0); StdOut.println("b = " + b); StdOut.println("norm(a) = " + a.norm()); StdOut.println("conj(a) = " + a.conjugate()); StdOut.println("a + b = " + a.plus(b)); StdOut.println("a * b = " + a.times(b)); StdOut.println("b * a = " + b.times(a)); StdOut.println("a / b = " + a.divides(b)); StdOut.println("a^-1 = " + a.inverse()); StdOut.println("a^-1 * a = " + a.inverse().times(a)); StdOut.println("a * a^-1 = " + a.times(a.inverse())); } }