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http://www.zzvips.com/article/80457.html)。
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：
|
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
|
import copyclass 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()) |
希望本文所述对大家Python程序设计有所帮助。
原文链接：http://www.cnblogs.com/hhh5460/p/4314231.html
