# -*- coding: utf-8 -*
"""
Created on March 2019
@author: yukino
@description：Create a Quaternion class
"""
class Quaternion:
def __init__(self, s, x, y, z):
"""构造函数"""
self.s = s
self.x = x
self.y = y
self.z = z
self.vector = [x, y, z]
self.all = [s, x, y, z]
def __str__(self):
"""输出操作重载"""
op = [" ", "i ", "j ", "k"]
q = self.all.copy()
result = ""
for i in range(4):
if q[i] < -1e-8 or q[i] > 1e-8:
result = result + str(round(q[i], 4)) + op[i]
if result == "":
return "0"
else:
return result
def __add__(self, quater):
"""加法运算符重载"""
q = self.all.copy()
for i in range(4):
q[i] += quater.all[i]
return Quaternion(q[0], q[1], q[2], q[3])
def __sub__(self, quater):
"""减法运算符重载"""
q = self.all.copy()
for i in range(4):
q[i] -= quater.all[i]
return Quaternion(q[0], q[1], q[2], q[3])
def __mul__(self, quater):
"""乘法运算符重载"""
q = self.all.copy()
p = quater.all.copy()
s = q[0]*p[0] - q[1]*p[1] - q[2]*p[2] - q[3]*p[3]
x = q[0]*p[1] + q[1]*p[0] + q[2]*p[3] - q[3]*p[2]
y = q[0]*p[2] - q[1]*p[3] + q[2]*p[0] + q[3]*p[1]
z = q[0]*p[3] + q[1]*p[2] - q[2]*p[1] + q[3]*p[0]
return Quaternion(s, x, y, z)
def divide(self, quaternion):
"""右除"""
result = self * quaternion.inverse()
return result
def modpow(self):
"""模的平方"""
q = self.all.copy()
result = q[0]
for i in range(1, 4):
result += q[i] ** 2
return result
def mod(self):
"""求模"""
return pow(self.modpow(), 1/2)
def conj(self):
"""转置"""
q = self.all.copy()
for i in range(1, 4):
q[i] = -q[i]
return Quaternion(q[0], q[1], q[2], q[3])
def inverse(self):
"""求逆"""
q = self.all.copy()
mod = self.modpow()
for i in range(4):
q[i] /= mod
return Quaternion(q[0], -q[1], -q[2], -q[3])测试一下：
a = Quaternion(1, 1, 2, 3)
b = Quaternion(1, 1, 2, 3)
c = a.conj()
d = b.inverse()
e = a.modpow()
f = a.divide(b)
g = f * b
print(c)
print(d)
print(e)
print(f)
print(g)
print(a, b)结果如下：
