矩阵乘法

 1 #矩阵乘法 O(n*3)
 2 def square_matrix_multiply(A,B):
 3     C = []
 4     n = len(A)#A的阶
 5     C = [[0 for col in range(n)] for row in range(n)]#生成n*n的全0矩阵
 6     for i in range(0,n):
 7         for j in range(0,n):
 8             for k in range(0,n):
 9                 C[i][j]=C[i][j]+A[i][k]*B[k][j]#矩阵乘法规则
10     return C
11 A=[[1,3],[7,5]]
12 B=[[6,8],[4,2]]
13 print(square_matrix_multiply(A, B))
14 --------------------------------------------
15 [[18, 14], [62, 66]]

 1 #递归分治法-矩阵乘法
 2 def square_matrix_multiply_recursive(A, B):
 3     n = len(A)
 4     C = [[0 for col in range(n)] for row in range(n)]
 5     if n == 1:
 6         C[0][0] = A[0][0] * B[0][0]
 7     else:
 8         (A11, A12, A21, A22) = partition_matrix(A)
 9         (B11, B12, B21, B22) = partition_matrix(B)
10         (C11, C12, C21, C22) = partition_matrix(C)
11         C11 = add_matrix(square_matrix_multiply_recursive(A11, B11), square_matrix_multiply_recursive(A12, B21))
12         C12 = add_matrix(square_matrix_multiply_recursive(A11, B12), square_matrix_multiply_recursive(A12, B22))
13         C21 = add_matrix(square_matrix_multiply_recursive(A21, B11), square_matrix_multiply_recursive(A22, B21))
14         C22 = add_matrix(square_matrix_multiply_recursive(A21, B12), square_matrix_multiply_recursive(A22, B22))
15         C = merge_matrix(C11, C12, C21, C22)
16     return C
17 
18 #分解矩阵，把矩阵分成4分
19 def partition_matrix(A):
20     n = len(A)
21     n2 = int(n / 2)
22     #生成四个初始零矩阵
23     A11 = [[0 for col in range(n2)] for row in range(n2)]
24     A12 = [[0 for col in range(n2)] for row in range(n2)]
25     A21 = [[0 for col in range(n2)] for row in range(n2)]
26     A22 = [[0 for col in range(n2)] for row in range(n2)]
27     #给这四个矩阵赋值
28     for i in range(0, n2):
29         for j in range(0, n2):
30             A11[i][j] = A[i][j]
31             A12[i][j] = A[i][j + n2]
32             A21[i][j] = A[i + n2][j]
33             A22[i][j] = A[i + n2][j + n2]
34     return (A11, A12, A21, A22)
35 
36 #合并矩阵，把四个矩阵合并为一个
37 def merge_matrix(A11, A12, A21, A22):
38     n2 = len(A11)
39     n = 2 * n2
40     A = [[0 for col in range(n)] for row in range(n)]
41     for i in range(0, n):
42         for j in range(0, n):
43             if i <= (n2 - 1) and j <= (n2 - 1):
44                 A[i][j] = A11[i][j]
45             elif i <= (n2 - 1) and j > (n2 - 1):
46                 A[i][j] = A12[i][j - n2]
47             elif i > (n2 - 1) and j <= (n2 - 1):
48                 A[i][j] = A21[i - n2][j]
49             else:
50                 A[i][j] = A22[i - n2][j - n2]
51     return A
52 
53 #添加矩阵，把A 和 B对应添加进一个矩阵C
54 def add_matrix(A, B):
55     n = len(A)
56     C = [[0 for col in range(n)] for row in range(n)]
57     for i in range(0, n):
58         for j in range(0, n):
59             C[i][j] = A[i][j] + B[i][j]
60     return C
61 
62 A=[[1,3],[7,5]]
63 B=[[6,8],[4,2]]
64 C=square_matrix_multiply_recursive(A,B)
65 print(C)
66 ----------------------------------------------------------
67 [[18, 14], [62, 66]]