def divide_and_conquer_multiply_matrix(M1, M2): # 分治法求解矩阵相乘问题 def divide_conquer(M1, M2): n = len(M1) if n == 1: return [[M1[0][0] * M2[0][0]]] else: # Divide A11 = [M1[i][:n//2] for i in range(n//2)] A12 = [M1[i][n//2:] for i in range(n//2)] A21 = [M1[i][:n//2] for i in range(n//2, n)] A22 = [M1[i][n//2:] for i in range(n//2, n)] B11 = [M2[i][:n//2] for i in range(n//2)] B12 = [M2[i][n//2:] for i in range(n//2)] B21 = [M2[i][:n//2] for i in range(n//2, n)] B22 = [M2[i][n//2:] for i in range(n//2, n)] # Conquer C11 = matrix_add(divide_conquer(A11, B11), divide_conquer(A12, B21)) C12 = matrix_add(divide_conquer(A11, B12), divide_conquer(A12, B22)) C21 = matrix_add(divide_conquer(A21, B11), divide_conquer(A22, B21)) C22 = matrix_add(divide_conquer(A21, B12), divide_conquer(A22, B22)) # Combine C = [[0 for _ in range(n)] for _ in range(n)] for i in range(n//2): for j in range(n//2): C[i][j] = C11[i][j] C[i][j+n//2] = C12[i][j] C[i+n//2][j] = C21[i][j] C[i+n//2][j+n//2] = C22[i][j] return C解释这段代码
时间: 2024-02-07 21:03:41 浏览: 22
这段代码是实现了分治法求解矩阵相乘问题。具体来说,这个函数接受两个矩阵 M1 和 M2,它们的乘积将被计算。函数的实现基于分治法,它将输入的矩阵逐层分割成四个矩阵,然后递归地计算这些矩阵的乘积,最终将它们合并成一个结果矩阵。
具体来说,函数中的 divide_conquer 函数用于递归地计算矩阵乘积。当输入的矩阵大小为 1 时,它将直接返回这两个元素的乘积。否则,它将输入矩阵分割成四个子矩阵,然后递归地计算这些子矩阵的乘积。接下来,它将这些子矩阵的乘积合并成一个结果矩阵。
最后,函数中的 matrix_add 函数用于实现矩阵的加法,它接受两个矩阵作为输入,计算它们的和并返回结果。函数中的 C 矩阵用于保存最终的结果。
相关问题
分治法 java_Java实现用传统分治法解决矩阵相乘问题
好的,下面是用传统分治法解决矩阵相乘问题的Java实现:
```java
public class MatrixMultiplication {
public static int[][] multiply(int[][] A, int[][] B) {
int n = A.length;
int[][] C = new int[n][n];
if (n == 1) {
C[0][0] = A[0][0] * B[0][0];
} else {
int[][] A11 = new int[n/2][n/2];
int[][] A12 = new int[n/2][n/2];
int[][] A21 = new int[n/2][n/2];
int[][] A22 = new int[n/2][n/2];
int[][] B11 = new int[n/2][n/2];
int[][] B12 = new int[n/2][n/2];
int[][] B21 = new int[n/2][n/2];
int[][] B22 = new int[n/2][n/2];
// Divide A matrix into 4 sub-matrices
divideMatrix(A, A11, 0 , 0);
divideMatrix(A, A12, 0 , n/2);
divideMatrix(A, A21, n/2, 0);
divideMatrix(A, A22, n/2, n/2);
// Divide B matrix into 4 sub-matrices
divideMatrix(B, B11, 0 , 0);
divideMatrix(B, B12, 0 , n/2);
divideMatrix(B, B21, n/2, 0);
divideMatrix(B, B22, n/2, n/2);
// Recursively multiply sub-matrices
int[][] C11 = addMatrix(multiply(A11,B11), multiply(A12,B21));
int[][] C12 = addMatrix(multiply(A11,B12), multiply(A12,B22));
int[][] C21 = addMatrix(multiply(A21,B11), multiply(A22,B21));
int[][] C22 = addMatrix(multiply(A21,B12), multiply(A22,B22));
// Combine sub-matrices into the result matrix
combineMatrix(C11, C, 0 , 0);
combineMatrix(C12, C, 0 , n/2);
combineMatrix(C21, C, n/2, 0);
combineMatrix(C22, C, n/2, n/2);
}
return C;
}
// Divide matrix into sub-matrices
public static void divideMatrix(int[][] P, int[][] C, int iB, int jB) {
for(int i1 = 0, i2 = iB; i1 < C.length; i1++, i2++) {
for(int j1 = 0, j2 = jB; j1 < C.length; j1++, j2++) {
C[i1][j1] = P[i2][j2];
}
}
}
// Combine sub-matrices into the result matrix
public static void combineMatrix(int[][] C, int[][] P, int iB, int jB) {
for(int i1 = 0, i2 = iB; i1 < C.length; i1++, i2++) {
for(int j1 = 0, j2 = jB; j1 < C.length; j1++, j2++) {
P[i2][j2] = C[i1][j1];
}
}
}
// Add two matrices
public static int[][] addMatrix(int[][] A, int[][] B) {
int n = A.length;
int[][] C = new int[n][n];
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
C[i][j] = A[i][j] + B[i][j];
}
}
return C;
}
public static void main(String[] args) {
int[][] A = {{1, 2}, {3, 4}};
int[][] B = {{5, 6}, {7, 8}};
int[][] C = multiply(A, B);
for (int i = 0; i < C.length; i++) {
for (int j = 0; j < C.length; j++) {
System.out.print(C[i][j] + " ");
}
System.out.println();
}
}
}
```
这个程序将两个n×n的矩阵相乘,其中n是2的幂。如果n等于1,则直接计算乘积。否则,将每个矩阵分成四个n/2×n/2的子矩阵,并递归地计算子矩阵的乘积。最后,将四个子矩阵的乘积组合成结果矩阵。
def generate_scaled(self): return self.distribution(*self.dist_params) / self.divide_scale
这是一个Python中的函数,它的名称是generate_scaled,看起来是定义在某个类中的一个方法。这个函数通过调用self.distribution(*self.dist_params)来生成一个随机数,并将其除以self.divide_scale,然后返回结果。这里的self是指类的实例本身,而self.distribution和self.dist_params应该是类的成员变量,用于指定随机数生成的分布类型和参数。其中,*self.dist_params表示将self.dist_params这个元组中的所有元素作为参数传入self.distribution函数中。这个函数的作用是将生成的随机数按比例缩放,以适应一些特定的需求。