用python实现向量的各种计算方法

悠悠 2022-05-29 01:49 200阅读 0赞

from math import acos,pi  
from math import sqrt  
from decimal import Decimal,getcontext  
  
getcontext().prec = 30  
  
class Vector(object):  
CANNOT\_NORMALIZE\_ZERO\_VECTOR\_MSG = 'Cannot normalize the zero vector'  
def \_\_init\_\_(self, coordinates):  
try:  
if not coordinates:  
raise ValueError  
self.coordinates = tuple(\[Decimal(x) for x in coordinates\])  
self.dimension = len(coordinates)  
except ValueError:  
raise ValueError('The coordinates must be nonempty')  
except TypeError:  
raise TypeError('The coordinates must be an iterable')  
  
  
def \_\_str\_\_(self):  
return 'Vector: \{\}'.format(self.coordinates)

\#两个向量是否相等

def \_\_eq\_\_(self, v):  
return self.coordinates == v.coordinates  
  
\# 加法  
def plus(self,v):  
return Vector(\[x + y for x,y in zip(self.coordinates,v.coordinates)\])  
  
\# 减法  
def minus(self,v):  
return Vector(\[x - y for x,y in zip(self.coordinates,v.coordinates)\])  
  
\# 向量的倍数  
def times\_scalar(self,m):  
return Vector(\[Decimal(m)\*x for x in self.coordinates\])  
  
\# 向量的大小  
def magnitude(self):  
coordinates\_squared = \[x \*\* 2 for x in self.coordinates\]  
return sqrt(sum(coordinates\_squared))  
\# 单位向量  
def normalized(self):  
try:  
magnitude = self.magnitude()  
return self.times\_scalar(1.0/magnitude)  
  
  
except ZeroDivisionError:  
raise Exception(self.CANNOT\_NORMALIZE\_ZERO\_VECTOR\_MSG)  
  
\# 两个向量的点积  
def dot(self,v):  
return sum(\[x\*y for x,y in zip(self.coordinates,v.coordinates)\])  
  
\# 两个向量之间的角度  
def angle\_with(self, v, in\_degrees=False):  
try:  
u1 = self.normalized()  
u2 = v.normalized()  
dots = u1.dot(u2)  
if abs(abs(dots) - 1) < 1e-10:  
if dots < 0:  
dots = -1  
else:  
dots = 1  
angle\_in\_radians = acos(dots)  
  
if in\_degrees:  
degrees\_per\_radian = 180. / pi  
return angle\_in\_radians \* degrees\_per\_radian  
else:  
return angle\_in\_radians  
  
  
except Exception as e:  
if str(e) == self.CANNOT\_NORMALIZE\_ZERO\_VECTOR\_MSG:  
raise Exception('Cannot compute an angle with the zero vector')  
else:  
raise e  
  
\# 判断两个向量是否正交  
def is\_orthogonal\_to(self, v, tolerance=1e-10):  
return abs(self.dot(v)) < tolerance

\# 是否是零向量

def is\_zero(self, tolerance=1e-10):  
return self.magnitude() < tolerance  
  
\# 两个向量是否平行  
def is\_parallel\_to(self,v):  
return (self.is\_zero() or  
v.is\_zero() or  
self.angle\_with(v) == 0 or  
self.angle\_with(v) == pi)  
  
\# 向量在另一个向量上的投影  
def component\_parallel\_to(self,basis):  
try:  
u = basis.normalized()  
weight = self.dot(u)  
return u.times\_scalar(weight)  
except Exception as e:  
if str(e) == self.CANNOT\_NORMALIZE\_ZERO\_VECTOR\_MSG:  
raise Exception('Cannot compute an angle with the zero vector')  
else:  
raise e  
  
\# 向量相对于投影向量的垂直向量  
def component\_orthogonal\_to(self, basis):  
try:  
projection = self.component\_parallel\_to(basis)  
return self.minus(projection)  
except Exception as e:  
if str(e) == self.CANNOT\_NORMALIZE\_ZERO\_VECTOR\_MSG:  
raise Exception('Cannot compute an angle with the zero vector')  
else:  
raise e  
  
\# 计算三维向量的向量积  
def cross(self,v):  
try:  
x\_1, y\_1, z\_1 = self.coordinates  
x\_2, y\_2, z\_2 = v.coordinates  
new\_coordinates = \[ y\_1 \* z\_2 - y\_2 \* z\_1,  
\-(x\_1 \* z\_2 - x\_2 \* z\_1),  
x\_1 \* y\_2 - x\_2 \* y\_1\]  
return Vector(new\_coordinates)  
except ValueError as e:  
msg = str(e)  
if msg == 'need more than 2 values to unpack':  
self\_embedded\_in\_R3 = Vector(self.coordinates + ('0',))  
v\_embedded\_in\_R3 = Vector(v.coordinates + ('0',))  
return self\_embedded\_in\_R3.cross(v\_embedded\_in\_R3)  
elif (msg == 'too many values to unpack' or  
msg == 'need more than 1 value to unpack' ):  
raise Exception('wrong value number')  
else:  
raise e  
  
\# 两个向量组成的平行四边形 面积  
def area\_of\_parallelogram\_with(self,v):  
cross\_product = self.cross(v)  
return cross\_product.magnitude()  
  
\# 两个向量组成的三角形 面积  
def area\_of\_triangle\_with(self,v):  
cross\_product = self.cross(v)

return cross\_product.magnitude()/2

\#例子

v = Vector(\['8.462','7.893','-8.187'\])  
w = Vector(\['6.984','-5.975','4.778'\])  
  
print v.cross(w)