用python实现向量的各种计算方法

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)