Python实现的矩阵类实例
作者:罗兵
这篇文章主要介绍了Python实现的矩阵类,结合完整实例形式分析了Python矩阵的定义、计算、转换等相关操作技巧,需要的朋友可以参考下
本文实例讲述了Python实现的矩阵类。分享给大家供大家参考,具体如下:
科学计算离不开矩阵的运算。当然,python已经有非常好的现成的库:numpy(numpy的简单安装与使用可参考https://www.jb51.net/article/66236.htm)。
我写这个矩阵类,并不是打算重新造一个轮子,只是作为一个练习,记录在此。
注:这个类的函数还没全部实现,慢慢在完善吧。
全部代码:
import copy class Matrix: '''矩阵类''' def __init__(self, row, column, fill=0.0): self.shape = (row, column) self.row = row self.column = column self._matrix = [[fill]*column for i in range(row)] # 返回元素m(i, j)的值: m[i, j] def __getitem__(self, index): if isinstance(index, int): return self._matrix[index-1] elif isinstance(index, tuple): return self._matrix[index[0]-1][index[1]-1] # 设置元素m(i,j)的值为s: m[i, j] = s def __setitem__(self, index, value): if isinstance(index, int): self._matrix[index-1] = copy.deepcopy(value) elif isinstance(index, tuple): self._matrix[index[0]-1][index[1]-1] = value def __eq__(self, N): '''相等''' # A == B assert isinstance(N, Matrix), "类型不匹配,不能比较" return N.shape == self.shape # 比较维度,可以修改为别的 def __add__(self, N): '''加法''' # A + B assert N.shape == self.shape, "维度不匹配,不能相加" M = Matrix(self.row, self.column) for r in range(self.row): for c in range(self.column): M[r, c] = self[r, c] + N[r, c] return M def __sub__(self, N): '''减法''' # A - B assert N.shape == self.shape, "维度不匹配,不能相减" M = Matrix(self.row, self.column) for r in range(self.row): for c in range(self.column): M[r, c] = self[r, c] - N[r, c] return M def __mul__(self, N): '''乘法''' # A * B (或:A * 2.0) if isinstance(N, int) or isinstance(N,float): M = Matrix(self.row, self.column) for r in range(self.row): for c in range(self.column): M[r, c] = self[r, c]*N else: assert N.row == self.column, "维度不匹配,不能相乘" M = Matrix(self.row, N.column) for r in range(self.row): for c in range(N.column): sum = 0 for k in range(self.column): sum += self[r, k] * N[k, r] M[r, c] = sum return M def __div__(self, N): '''除法''' # A / B pass def __pow__(self, k): '''乘方''' # A**k assert self.row == self.column, "不是方阵,不能乘方" M = copy.deepcopy(self) for i in range(k): M = M * self return M def rank(self): '''矩阵的秩''' pass def trace(self): '''矩阵的迹''' pass def adjoint(self): '''伴随矩阵''' pass def invert(self): '''逆矩阵''' assert self.row == self.column, "不是方阵" M = Matrix(self.row, self.column*2) I = self.identity() # 单位矩阵 I.show()############################# # 拼接 for r in range(1,M.row+1): temp = self[r] temp.extend(I[r]) M[r] = copy.deepcopy(temp) M.show()############################# # 初等行变换 for r in range(1, M.row+1): # 本行首元素(M[r, r])若为 0,则向下交换最近的当前列元素非零的行 if M[r, r] == 0: for rr in range(r+1, M.row+1): if M[rr, r] != 0: M[r],M[rr] = M[rr],M[r] # 交换两行 break assert M[r, r] != 0, '矩阵不可逆' # 本行首元素(M[r, r])化为 1 temp = M[r,r] # 缓存 for c in range(r, M.column+1): M[r, c] /= temp print("M[{0}, {1}] /= {2}".format(r,c,temp)) M.show() # 本列上、下方的所有元素化为 0 for rr in range(1, M.row+1): temp = M[rr, r] # 缓存 for c in range(r, M.column+1): if rr == r: continue M[rr, c] -= temp * M[r, c] print("M[{0}, {1}] -= {2} * M[{3}, {1}]".format(rr, c, temp,r)) M.show() # 截取逆矩阵 N = Matrix(self.row,self.column) for r in range(1,self.row+1): N[r] = M[r][self.row:] return N def jieti(self): '''行简化阶梯矩阵''' pass def transpose(self): '''转置''' M = Matrix(self.column, self.row) for r in range(self.column): for c in range(self.row): M[r, c] = self[c, r] return M def cofactor(self, row, column): '''代数余子式(用于行列式展开)''' assert self.row == self.column, "不是方阵,无法计算代数余子式" assert self.row >= 3, "至少是3*3阶方阵" assert row <= self.row and column <= self.column, "下标超出范围" M = Matrix(self.column-1, self.row-1) for r in range(self.row): if r == row: continue for c in range(self.column): if c == column: continue rr = r-1 if r > row else r cc = c-1 if c > column else c M[rr, cc] = self[r, c] return M def det(self): '''计算行列式(determinant)''' assert self.row == self.column,"非行列式,不能计算" if self.shape == (2,2): return self[1,1]*self[2,2]-self[1,2]*self[2,1] else: sum = 0.0 for c in range(self.column+1): sum += (-1)**(c+1)*self[1,c]*self.cofactor(1,c).det() return sum def zeros(self): '''全零矩阵''' M = Matrix(self.column, self.row, fill=0.0) return M def ones(self): '''全1矩阵''' M = Matrix(self.column, self.row, fill=1.0) return M def identity(self): '''单位矩阵''' assert self.row == self.column, "非n*n矩阵,无单位矩阵" M = Matrix(self.column, self.row) for r in range(self.row): for c in range(self.column): M[r, c] = 1.0 if r == c else 0.0 return M def show(self): '''打印矩阵''' for r in range(self.row): for c in range(self.column): print(self[r+1, c+1],end=' ') print() if __name__ == '__main__': m = Matrix(3,3,fill=2.0) n = Matrix(3,3,fill=3.5) m[1] = [1.,1.,2.] m[2] = [1.,2.,1.] m[3] = [2.,1.,1.] p = m * n q = m*2.1 r = m**3 #r.show() #q.show() #print(p[1,1]) #r = m.invert() #s = r*m print() m.show() print() #r.show() print() #s.show() print() print(m.det())
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