向量Vector

import math


class Vector:
    """向量"""

    @classmethod
    def zero(cls, dim):
        """dim长度的0向量"""
        return cls([0] * dim)

    def __init__(self, lst):
        self._values = list(lst)

    def __repr__(self):
        print('Vector({})'.format(self._values))

    def __str__(self):
        return '({})'.format(', '.join(str(e) for e in self._values))

    def __len__(self):
        return len(self._values)

    def dot(self, other):
        """向量点乘，返回结果标量"""
        assert len(self) == len(other), 
            "Error in dot product. Length of vectors must be same."
        return sum(a * b for a, b in zip(self, other))

    def normalize(self):
        """单位向量、归一化"""
        if self.norm() < 1e-8:
            raise ZeroDivisionError("Normalize error! norm is zero.")
        return Vector(self) / self.norm()

    def norm(self):
        """模"""
        return math.sqrt(sum(a ** 2 for a in self))

    def __pos__(self):
        """返回向量取正的结果向量 positive """
        return 1 * self

    def __neg__(self):
        """返回向量取负的结果向量 negative """
        return -1 * self

    def __getitem__(self, index):
        return self._values[index]

    def __add__(self, other):
        """向量加法，返回结果向量"""
        assert len(self) == len(other), 
            "Error in adding. Length of vectors must be same."
        return Vector([a + b for a, b in zip(self, other)])

    def __sub__(self, other):
        """向量减法，返回结果向量"""
        assert len(self) == len(other), 
            "Error in subtracting. Length of vectors must be same."
        return Vector([a - b for a, b in zip(self, other)])

    def __mul__(self, k):
        """数乘"""
        return Vector([a * k for a in self])

    def __rmul__(self, k):
        return self * k

    def __truediv__(self, k):
        return self * (1 / k)

    def __iter__(self):
        return self._values.__iter__()