矩阵类的python实现

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我是靠谱客的博主甜蜜音响，这篇文章主要介绍矩阵类的python实现，现在分享给大家，希望可以做个参考。
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。
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：
复制代码1 import copy

2

3 class Matrix:

4
'''矩阵类'''

5
def __init__(self, row, column, fill=0.0):

6
self.shape = (row, column)

7
self.row = row

8
self.column = column

9
self._matrix = [[fill]*column for i in range(row)]
 10
 11
# 返回元素m(i, j)的值:
m[i, j]
 12
def __getitem__(self, index):
 13
if isinstance(index, int):
 14
return self._matrix[index-1]
 15
elif isinstance(index, tuple):
 16
return self._matrix[index[0]-1][index[1]-1]
 17
 18
# 设置元素m(i,j)的值为s:
m[i, j] = s
 19
def __setitem__(self, index, value):
 20
if isinstance(index, int):
 21
self._matrix[index-1] = copy.deepcopy(value)
 22
elif isinstance(index, tuple):
 23
self._matrix[index[0]-1][index[1]-1] = value
 24
 25
def __eq__(self, N):
 26
'''相等'''
 27
# A == B
 28
assert isinstance(N, Matrix), "类型不匹配，不能比较"
 29
return N.shape == self.shape
# 比较维度，可以修改为别的
 30
 31
def __add__(self, N):
 32
'''加法'''
 33
# A + B
 34
assert N.shape == self.shape, "维度不匹配，不能相加"
 35
M = Matrix(self.row, self.column)
 36
for r in range(self.row):
 37
for c in range(self.column):
 38
M[r, c] = self[r, c] + N[r, c]
 39
return M
 40
 41
def __sub__(self, N):
 42
'''减法'''
 43
# A - B
 44
assert N.shape == self.shape, "维度不匹配，不能相减"
 45
M = Matrix(self.row, self.column)
 46
for r in range(self.row):
 47
for c in range(self.column):
 48
M[r, c] = self[r, c] - N[r, c]
 49
return M
 50
 51
def __mul__(self, N):
 52
'''乘法'''
 53
# A * B (或：A * 2.0)
 54
if isinstance(N, int) or isinstance(N,float):
 55
M = Matrix(self.row, self.column)
 56
for r in range(self.row):
 57
for c in range(self.column):
 58
M[r, c] = self[r, c]*N
 59
else:
 60
assert N.row == self.column, "维度不匹配，不能相乘"
 61
M = Matrix(self.row, N.column)
 62
for r in range(self.row):
 63
for c in range(N.column):
 64
sum = 0
 65
for k in range(self.column):
 66
sum += self[r, k] * N[k, r]
 67
M[r, c] = sum
 68
return M
 69
 70
def __div__(self, N):
 71
'''除法'''
 72
# A / B
 73
pass
 74
def __pow__(self, k):
 75
'''乘方'''
 76
# A**k
 77
assert self.row == self.column, "不是方阵，不能乘方"
 78
M = copy.deepcopy(self)
 79
for i in range(k):
 80
M = M * self
 81
return M
 82
 83
def rank(self):
 84
'''矩阵的秩'''
 85
pass
 86
 87
def trace(self):
 88
'''矩阵的迹'''
 89
pass
 90
 91
def adjoint(self):
 92
'''伴随矩阵'''
 93
pass
 94
 95
def invert(self):
 96
'''逆矩阵'''
 97
assert self.row == self.column, "不是方阵"
 98
M = Matrix(self.row, self.column*2)
 99
I = self.identity() # 单位矩阵
100
I.show()#############################
101
102
# 拼接
103
for r in range(1,M.row+1):
104
temp = self[r]
105 
temp.extend(I[r])
106
M[r] = copy.deepcopy(temp)
107
M.show()#############################
108
109
# 初等行变换
110
for r in range(1, M.row+1):
111
# 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
112
if M[r, r] == 0:
113
for rr in range(r+1, M.row+1):
114
if M[rr, r] != 0:
115
M[r],M[rr] = M[rr],M[r] # 交换两行
116
break
117
118
assert M[r, r] != 0, '矩阵不可逆'
119
120
# 本行首元素(M[r, r])化为 1
121
temp = M[r,r] # 缓存
122
for c in range(r, M.column+1):
123
M[r, c] /= temp
124
print("M[{0}, {1}] /=
{2}".format(r,c,temp))
125 
M.show()
126
127
# 本列上、下方的所有元素化为 0
128
for rr in range(1, M.row+1):
129
temp = M[rr, r] # 缓存
130
for c in range(r, M.column+1):
131
if rr == r:
132
continue
133
M[rr, c] -= temp * M[r, c]
134
print("M[{0}, {1}] -= {2} * M[{3}, {1}]".format(rr, c, temp,r))
135 
M.show()
136
137
# 截取逆矩阵
138
N = Matrix(self.row,self.column)
139
for r in range(1,self.row+1):
140
N[r] = M[r][self.row:]
141
return N
142
143
144
def jieti(self):
145
'''行简化阶梯矩阵'''
146
pass
147
148
149
def transpose(self):
150
'''转置'''
151
M = Matrix(self.column, self.row)
152
for r in range(self.column):
153
for c in range(self.row):
154
M[r, c] = self[c, r]
155
return M
156
157
def cofactor(self, row, column):
158
'''代数余子式（用于行列式展开）'''
159
assert self.row == self.column, "不是方阵，无法计算代数余子式"
160
assert self.row >= 3, "至少是3*3阶方阵"
161
assert row <= self.row and column <= self.column, "下标超出范围"
162
M = Matrix(self.column-1, self.row-1)
163
for r in range(self.row):
164
if r == row:
165
continue
166
for c in range(self.column):
167
if c == column:
168
continue
169
rr = r-1 if r > row else r
170
cc = c-1 if c > column else c
171
M[rr, cc] = self[r, c]
172
return M
173
174
def det(self):
175
'''计算行列式(determinant)'''
176
assert self.row == self.column,"非行列式，不能计算"
177
if self.shape == (2,2):
178
return self[1,1]*self[2,2]-self[1,2]*self[2,1]
179
else:
180
sum = 0.0
181
for c in range(self.column+1):
182
sum += (-1)**(c+1)*self[1,c]*self.cofactor(1,c).det()
183
return sum
184
185
def zeros(self):
186
'''全零矩阵'''
187
M = Matrix(self.column, self.row, fill=0.0)
188
return M
189
190
def ones(self):
191
'''全1矩阵'''
192
M = Matrix(self.column, self.row, fill=1.0)
193
return M
194
195
def identity(self):
196
'''单位矩阵'''
197
assert self.row == self.column, "非n*n矩阵，无单位矩阵"
198
M = Matrix(self.column, self.row)
199
for r in range(self.row):
200
for c in range(self.column):
201
M[r, c] = 1.0 if r == c else 0.0
202
return M
203
204
def show(self):
205
'''打印矩阵'''
206
for r in range(self.row):
207
for c in range(self.column):
208
print(self[r+1, c+1],end='
')
209
print()
210
211
212 if __name__ == '__main__':
213
m = Matrix(3,3,fill=2.0)
214
n = Matrix(3,3,fill=3.5)
215
216
m[1] = [1.,1.,2.]
217
m[2] = [1.,2.,1.]
218
m[3] = [2.,1.,1.]
219
220
p = m * n
221
q = m*2.1
222
r = m**3
223
#r.show()
224
#q.show()
225
#print(p[1,1])
226
227
#r = m.invert()
228
#s = r*m
229
230
print()
231 
m.show()
232
print()
233
#r.show()
234
print()
235
#s.show()
236
print()
237
print(m.det())
1 import copy

2

3 class Matrix:

4
'''矩阵类'''

5
def __init__(self, row, column, fill=0.0):

6
self.shape = (row, column)

7
self.row = row

8
self.column = column

9
self._matrix = [[fill]*column for i in range(row)]
 10
 11
# 返回元素m(i, j)的值:
m[i, j]
 12
def __getitem__(self, index):
 13
if isinstance(index, int):
 14
return self._matrix[index-1]
 15
elif isinstance(index, tuple):
 16
return self._matrix[index[0]-1][index[1]-1]
 17
 18
# 设置元素m(i,j)的值为s:
m[i, j] = s
 19
def __setitem__(self, index, value):
 20
if isinstance(index, int):
 21
self._matrix[index-1] = copy.deepcopy(value)
 22
elif isinstance(index, tuple):
 23
self._matrix[index[0]-1][index[1]-1] = value
 24
 25
def __eq__(self, N):
 26
'''相等'''
 27
# A == B
 28
assert isinstance(N, Matrix), "类型不匹配，不能比较"
 29
return N.shape == self.shape
# 比较维度，可以修改为别的
 30
 31
def __add__(self, N):
 32
'''加法'''
 33
# A + B
 34
assert N.shape == self.shape, "维度不匹配，不能相加"
 35
M = Matrix(self.row, self.column)
 36
for r in range(self.row):
 37
for c in range(self.column):
 38
M[r, c] = self[r, c] + N[r, c]
 39
return M
 40
 41
def __sub__(self, N):
 42
'''减法'''
 43
# A - B
 44
assert N.shape == self.shape, "维度不匹配，不能相减"
 45
M = Matrix(self.row, self.column)
 46
for r in range(self.row):
 47
for c in range(self.column):
 48
M[r, c] = self[r, c] - N[r, c]
 49
return M
 50
 51
def __mul__(self, N):
 52
'''乘法'''
 53
# A * B (或：A * 2.0)
 54
if isinstance(N, int) or isinstance(N,float):
 55
M = Matrix(self.row, self.column)
 56
for r in range(self.row):
 57
for c in range(self.column):
 58
M[r, c] = self[r, c]*N
 59
else:
 60
assert N.row == self.column, "维度不匹配，不能相乘"
 61
M = Matrix(self.row, N.column)
 62
for r in range(self.row):
 63
for c in range(N.column):
 64
sum = 0
 65
for k in range(self.column):
 66
sum += self[r, k] * N[k, r]
 67
M[r, c] = sum
 68
return M
 69
 70
def __div__(self, N):
 71
'''除法'''
 72
# A / B
 73
pass
 74
def __pow__(self, k):
 75
'''乘方'''
 76
# A**k
 77
assert self.row == self.column, "不是方阵，不能乘方"
 78
M = copy.deepcopy(self)
 79
for i in range(k):
 80
M = M * self
 81
return M
 82
 83
def rank(self):
 84
'''矩阵的秩'''
 85
pass
 86
 87
def trace(self):
 88
'''矩阵的迹'''
 89
pass
 90
 91
def adjoint(self):
 92
'''伴随矩阵'''
 93
pass
 94
 95
def invert(self):
 96
'''逆矩阵'''
 97
assert self.row == self.column, "不是方阵"
 98
M = Matrix(self.row, self.column*2)
 99
I = self.identity() # 单位矩阵
100
I.show()#############################
101
102
# 拼接
103
for r in range(1,M.row+1):
104
temp = self[r]
105 
temp.extend(I[r])
106
M[r] = copy.deepcopy(temp)
107
M.show()#############################
108
109
# 初等行变换
110
for r in range(1, M.row+1):
111
# 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
112
if M[r, r] == 0:
113
for rr in range(r+1, M.row+1):
114
if M[rr, r] != 0:
115
M[r],M[rr] = M[rr],M[r] # 交换两行
116
break
117
118
assert M[r, r] != 0, '矩阵不可逆'
119
120
# 本行首元素(M[r, r])化为 1
121
temp = M[r,r] # 缓存
122
for c in range(r, M.column+1):
123
M[r, c] /= temp
124
print("M[{0}, {1}] /=
{2}".format(r,c,temp))
125 
M.show()
126
127
# 本列上、下方的所有元素化为 0
128
for rr in range(1, M.row+1):
129
temp = M[rr, r] # 缓存
130
for c in range(r, M.column+1):
131
if rr == r:
132
continue
133
M[rr, c] -= temp * M[r, c]
134
print("M[{0}, {1}] -= {2} * M[{3}, {1}]".format(rr, c, temp,r))
135 
M.show()
136
137
# 截取逆矩阵
138
N = Matrix(self.row,self.column)
139
for r in range(1,self.row+1):
140
N[r] = M[r][self.row:]
141
return N
142
143
144
def jieti(self):
145
'''行简化阶梯矩阵'''
146
pass
147
148
149
def transpose(self):
150
'''转置'''
151
M = Matrix(self.column, self.row)
152
for r in range(self.column):
153
for c in range(self.row):
154
M[r, c] = self[c, r]
155
return M
156
157
def cofactor(self, row, column):
158
'''代数余子式（用于行列式展开）'''
159
assert self.row == self.column, "不是方阵，无法计算代数余子式"
160
assert self.row >= 3, "至少是3*3阶方阵"
161
assert row <= self.row and column <= self.column, "下标超出范围"
162
M = Matrix(self.column-1, self.row-1)
163
for r in range(self.row):
164
if r == row:
165
continue
166
for c in range(self.column):
167
if c == column:
168
continue
169
rr = r-1 if r > row else r
170
cc = c-1 if c > column else c
171
M[rr, cc] = self[r, c]
172
return M
173
174
def det(self):
175
'''计算行列式(determinant)'''
176
assert self.row == self.column,"非行列式，不能计算"
177
if self.shape == (2,2):
178
return self[1,1]*self[2,2]-self[1,2]*self[2,1]
179
else:
180
sum = 0.0
181
for c in range(self.column+1):
182
sum += (-1)**(c+1)*self[1,c]*self.cofactor(1,c).det()
183
return sum
184
185
def zeros(self):
186
'''全零矩阵'''
187
M = Matrix(self.column, self.row, fill=0.0)
188
return M
189
190
def ones(self):
191
'''全1矩阵'''
192
M = Matrix(self.column, self.row, fill=1.0)
193
return M
194
195
def identity(self):
196
'''单位矩阵'''
197
assert self.row == self.column, "非n*n矩阵，无单位矩阵"
198
M = Matrix(self.column, self.row)
199
for r in range(self.row):
200
for c in range(self.column):
201
M[r, c] = 1.0 if r == c else 0.0
202
return M
203
204
def show(self):
205
'''打印矩阵'''
206
for r in range(self.row):
207
for c in range(self.column):
208
print(self[r+1, c+1],end='
')
209
print()
210
211
212 if __name__ == '__main__':
213
m = Matrix(3,3,fill=2.0)
214
n = Matrix(3,3,fill=3.5)
215
216
m[1] = [1.,1.,2.]
217
m[2] = [1.,2.,1.]
218
m[3] = [2.,1.,1.]
219
220
p = m * n
221
q = m*2.1
222
r = m**3
223
#r.show()
224
#q.show()
225
#print(p[1,1])
226
227
#r = m.invert()
228
#s = r*m
229
230
print()
231 
m.show()
232
print()
233
#r.show()
234
print()
235
#s.show()
236
print()
237
print(m.det())