import math
from ._globals import EPSILONclass Vector:def __init__(self, lst):self._values = list(lst)@classmethoddef zero(cls, dim):"""返回一个dim维的零向量"""return cls([0] * dim)def __add__(self, another):"""向量加法，返回结果向量"""assert len(self) == len(another), "Error in adding. Length of vectors must be same."return Vector([a + b for a, b in zip(self, another)])def __sub__(self, another):"""向量减法，返回结果向量"""assert len(self) == len(another), "Error in subtracting. Length of vectors must be same."return Vector([a - b for a, b in zip(self, another)])def norm(self):"""返回向量的模"""return math.sqrt(sum(e**2 for e in self))def normalize(self):"""返回向量的单位向量"""if self.norm() < EPSILON:raise ZeroDivisionError("Normalize error! norm is zero.")return Vector(self._values) / self.norm()def dot(self, another):"""向量点乘，返回结果标量"""assert len(self) == len(another), "Error in dot product. Length of vectors must be same."return sum(a * b for a, b in zip(self, another))def __mul__(self, k):"""返回数量乘法的结果向量：self * k"""return Vector([k * e for e in self])def __rmul__(self, k):"""返回数量乘法的结果向量：k * self"""return self * kdef __truediv__(self, k):"""返回数量除法的结果向量：self / k"""return (1 / k) * selfdef __pos__(self):"""返回向量取正的结果向量"""return 1 * selfdef __neg__(self):"""返回向量取负的结果向量"""return -1 * selfdef __iter__(self):"""返回向量的迭代器"""return self._values.__iter__()def __getitem__(self, index):"""取向量的第index个元素"""return self._values[index]def __len__(self):"""返回向量长度（有多少个元素）"""return len(self._values)def __repr__(self):return "Vector({})".format(self._values)def __str__(self):return "({})".format(", ".join(str(e) for e in self._values))

EPSILON = 1e-8

from .Vector import Vectorclass Matrix:def __init__(self, list2d):self._values = [row[:] for row in list2d]@classmethoddef zero(cls, r, c):"""返回一个r行c列的零矩阵"""return cls([[0] * c for _ in range(r)])def __add__(self, another):"""返回两个矩阵的加法结果"""assert self.shape() == another.shape(), "Error in adding. Shape of matrix must be same."return Matrix([[a + b for a, b in zip(self.row_vector(i), another.row_vector(i))]for i in range(self.row_num())])def __sub__(self, another):"""返回两个矩阵的减法结果"""assert self.shape() == another.shape(), "Error in subtracting. Shape of matrix must be same."return Matrix([[a - b for a, b in zip(self.row_vector(i), another.row_vector(i))]for i in range(self.row_num())])def __mul__(self, k):"""返回矩阵的数量乘结果: self * k"""return Matrix([[e * k for e in self.row_vector(i)]for i in range(self.row_num())])def __rmul__(self, k):"""返回矩阵的数量乘结果: k * self"""return self * kdef __truediv__(self, k):"""返回数量除法的结果矩阵：self / k"""return (1 / k) * selfdef __pos__(self):"""返回矩阵取正的结果"""return 1 * selfdef __neg__(self):"""返回矩阵取负的结果"""return -1 * selfdef row_vector(self, index):"""返回矩阵的第index个行向量"""return Vector(self._values[index])def col_vector(self, index):"""返回矩阵的第index个列向量"""return Vector([row[index] for row in self._values])def __getitem__(self, pos):"""返回矩阵pos位置的元素"""r, c = posreturn self._values[r][c]def size(self):"""返回矩阵的元素个数"""r, c = self.shape()return r * cdef row_num(self):"""返回矩阵的行数"""return self.shape()[0]__len__ = row_numdef col_num(self):"""返回矩阵的列数"""return self.shape()[1]def shape(self):"""返回矩阵的形状: (行数， 列数)"""return len(self._values), len(self._values[0])def __repr__(self):return "Matrix({})".format(self._values)__str__ = __repr__

from playLA.Matrix import Matrixif __name__ == "__main__":matrix = Matrix([[1, 2], [3, 4]])print(matrix)print("matrix.shape = {}".format(matrix.shape()))print("matrix.size = {}".format(matrix.size()))print("len(matrix) = {}".format(len(matrix)))print("matrix[0][0] = {}".format(matrix[0, 0]))matrix2 = Matrix([[5, 6], [7, 8]])print(matrix2)print("add: {}".format(matrix + matrix2))print("subtract: {}".format(matrix - matrix2))print("scalar-mul: {}".format(2 * matrix))print("scalar-mul: {}".format(matrix * 2))print("zero_2_3: {}".format(Matrix.zero(2, 3)))