Python如何实现矩阵类的代码示例详解

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

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 __p__(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())