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：
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())
