标准化向量时的数学域错误

Question

我正在学习一个关于向量的类，并尝试在Python中实现向量操作，我在这个过程中正在学习。在规范化向量时，我得到了一个数学域错误。知道为什么吗？

我得到的错误是：

线67，与成角度升高（e）ValueError：数学域错误

import math
from decimal import Decimal, getcontext
getcontext().prec = 30
class Vector(object):
    def __init__(self, coordinates):
        try:
            if not coordinates:
                raise ValueError
            self.coordinates = tuple([Decimal(x) for x in coordinates])
            self.dim ension = 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)
def plus(self, v):
    new_coordinates = [x+y for x,y in zip(self.coordinates, v.coordinates)]
    return Vector(new_coordinates)
def minus(self, v):
    new_coordinates = [x-y for x,y in zip(self.coordinates, v.coordinates)]
    return Vector(new_coordinates)
def times_scalar(self, c):
    new_coordinates = [Decimal(c)*x for x in self.coordinates]
    return Vector(new_coordinates)
def magnitude(self):
    coordinates_squared = [x**2 for x in self.coordinates]
    return Decimal(math.sqrt(sum(coordinates_squared)))
def normalized(self):
    try:
        magnitude = self.magnitude()
        return self.times_scalar(Decimal('1.0')/magnitude)
    except ZeroDivisionError:
        raise Exception('Cannot normalize the zero vector')
def dot_product(self, v):
    return sum([x*y for x,y in zip(self.coordinates, v.coordinates)])
def angle_with(self, v, in_degrees=False):
    try:
        u1 = self.normalized()
        u2 = v.normalized()
        angle_in_radians = math.acos(u1.dot_product(u2))
        if in_degrees:
            degrees_per_radian = 180 / math.pi
            return angle_in_radians * degrees_per_radian
        else:
            return angle_in_radians
    except Exception as e:
        if str(e) == 'Cannot normalize the zero vector':
            raise Exception('Cannot compute an angle with the zero vector')
        else:
            raise(e)
a = Vector(['-7.579', '-7.88'])
b = Vector(['22.737', '23.64'])
print a.is_parallel_to(b)
print a.is_orthogonal(b)

Answer 1

Łukasz Rogalski指出，如果u1和u2的点积在[-1，1]之外，acos将导致此错误。如果你对向量a和b进行归一化，并像现在这样以30的精度检查点积，你就会发现问题。

将您的精度更改为10左右以解决此错误。