c语言实现strassen矩阵乘法
时间: 2023-06-07 10:03:00 浏览: 235
Strassen矩阵乘法是一种快速的矩阵乘法算法,它利用分治思想将原矩阵分解成多个小矩阵进行计算,从而减少乘法次数。
C语言实现Strassen矩阵乘法需要以下步骤:
1. 定义一个矩阵结构体,包括矩阵大小和元素数组。
2. 实现矩阵的初始化和释放函数。
3. 实现Strassen矩阵乘法函数,包括以下几个步骤:
a. 判断矩阵大小是否为2的幂,如果不是则补充0使其变为2的幂大小。
b. 将两个矩阵分解成四个小矩阵,并计算每个小矩阵的乘积。
c. 利用递归,对四个小矩阵进行Strassen矩阵乘法。
d. 根据Strassen矩阵乘法公式,合并四个小矩阵得到结果矩阵。
4. 对于矩阵大小小于某个阈值(如32)的情况,采用朴素的矩阵乘法算法。
5. 编写测试函数,对Strassen矩阵乘法进行测试。
需要注意的是,C语言实现Strassen矩阵乘法的时间复杂度为O(n^log2(7)),比朴素矩阵乘法的O(n^3)要快,但由于Strassen矩阵乘法的常数较大,实际运行效率可能会受到影响。此外,Strassen矩阵乘法还会占用更多的内存空间。因此,在应用时需要根据具体情况进行权衡和选择。
相关问题
用C语言写strassen矩阵乘法代码
我可以回答您的问题。以下是用C语言编写的Strassen矩阵乘法代码:
```c
#include <stdio.h>
void strassen(int n, int A[][n], int B[][n], int C[][n]) {
if (n == 1) {
C[0][0] = A[0][0] * B[0][0];
return;
}
int m = n / 2;
int A11[m][m], A12[m][m], A21[m][m], A22[m][m];
int B11[m][m], B12[m][m], B21[m][m], B22[m][m];
int C11[m][m], C12[m][m], C21[m][m], C22[m][m];
int P1[m][m], P2[m][m], P3[m][m], P4[m][m], P5[m][m], P6[m][m], P7[m][m];
int temp1[m][m], temp2[m][m];
// Divide A and B into 4 submatrices
for (int i = 0; i < m; i++) {
for (int j = 0; j < m; j++) {
A11[i][j] = A[i][j];
A12[i][j] = A[i][j + m];
A21[i][j] = A[i + m][j];
A22[i][j] = A[i + m][j + m];
B11[i][j] = B[i][j];
B12[i][j] = B[i][j + m];
B21[i][j] = B[i + m][j];
B22[i][j] = B[i + m][j + m];
}
}
// Compute P1, P2, P3, P4, P5, P6, P7
strassen(m, A11, subtract(m, B12, B22, temp1), P1);
strassen(m, add(m, A11, A12, temp1), B22, P2);
strassen(m, add(m, A21, A22, temp1), B11, P3);
strassen(m, A22, subtract(m, B21, B11, temp1), P4);
strassen(m, add(m, A11, A22, temp1), add(m, B11, B22, temp2), P5);
strassen(m, subtract(m, A12, A22, temp1), add(m, B21, B22, temp2), P6);
strassen(m, subtract(m, A11, A21, temp1), add(m, B11, B12, temp2), P7);
// Compute C11, C12, C21, C22
add(m, subtract(m, add(m, P5, P4, temp1), P2, temp2), P6, C11);
add(m, P1, P2, C12);
add(m, P3, P4, C21);
subtract(m, subtract(m, add(m, P5, P1, temp1), P3, temp2), P7, C22);
// Combine C11, C12, C21, C22 into C
for (int i = 0; i < m; i++) {
for (int j = 0; j < m; j++) {
C[i][j] = C11[i][j];
C[i][j + m] = C12[i][j];
C[i + m][j] = C21[i][j];
C[i + m][j + m] = C22[i][j];
}
}
}
void add(int n, int A[][n], int B[][n], int C[][n]) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
C[i][j] = A[i][j] + B[i][j];
}
}
}
void subtract(int n, int A[][n], int B[][n], int C[][n]) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
C[i][j] = A[i][j] - B[i][j];
}
}
}
int main() {
int n = 4;
int A[n][n] = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}, {13, 14, 15, 16}};
int B[n][n] = {{17, 18, 19, 20}, {21, 22, 23, 24}, {25, 26, 27, 28}, {29, 30, 31, 32}};
int C[n][n];
strassen(n, A, B, C);
printf("Result:\n");
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
printf("%d ", C[i][j]);
}
printf("\n");
}
return 0;
}
```
希望这个代码能够帮到您!
strassen矩阵乘法算法c语言
### 回答1:
Strassen矩阵乘法算法是一种用于计算两个矩阵乘积的高效方法,其基本思想是将原始矩阵划分为较小的子矩阵,并通过递归调用来计算乘积。下面是使用C语言实现Strassen矩阵乘法算法的一个示例:
```c
#include<stdio.h>
void strassen(int n, int A[][n], int B[][n], int C[][n]) {
if (n == 1) {
C[0][0] = A[0][0] * B[0][0];
return;
}
// 计算矩阵的中间大小
int half = n / 2;
// 划分原始矩阵为四个子矩阵
int A11[half][half], A12[half][half], A21[half][half], A22[half][half];
int B11[half][half], B12[half][half], B21[half][half], B22[half][half];
int C11[half][half], C12[half][half], C21[half][half], C22[half][half];
int P[half][half], Q[half][half], R[half][half], S[half][half], T[half][half], U[half][half], V[half][half];
// 初始化子矩阵
for (int i = 0; i < half; i++) {
for (int j = 0; j < half; j++) {
A11[i][j] = A[i][j];
A12[i][j] = A[i][j + half];
A21[i][j] = A[i + half][j];
A22[i][j] = A[i + half][j + half];
B11[i][j] = B[i][j];
B12[i][j] = B[i][j + half];
B21[i][j] = B[i + half][j];
B22[i][j] = B[i + half][j + half];
}
}
// 递归调用计算子矩阵
strassen(half, A11, B11, P);
strassen(half, A12, B21, Q);
strassen(half, A11, B12, R);
strassen(half, A12, B22, S);
strassen(half, A21, B11, T);
strassen(half, A22, B21, U);
strassen(half, A21, B12, V);
// 计算结果矩阵的子矩阵
for (int i = 0; i < half; i++) {
for (int j = 0; j < half; j++) {
C11[i][j] = P[i][j] + Q[i][j];
C12[i][j] = R[i][j] + S[i][j];
C21[i][j] = T[i][j] + U[i][j];
C22[i][j] = R[i][j] + T[i][j] + U[i][j] + V[i][j];
}
}
// 将子矩阵组合为结果矩阵
for (int i = 0; i < half; i++) {
for (int j = 0; j < half; j++) {
C[i][j] = C11[i][j];
C[i][j + half] = C12[i][j];
C[i + half][j] = C21[i][j];
C[i + half][j + half] = C22[i][j];
}
}
}
int main() {
int n;
printf("请输入矩阵维度n:");
scanf("%d", &n);
int A[n][n], B[n][n], C[n][n];
printf("请输入矩阵A:\n");
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
scanf("%d", &A[i][j]);
}
}
printf("请输入矩阵B:\n");
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
scanf("%d", &B[i][j]);
}
}
strassen(n, A, B, C);
printf("结果矩阵C:\n");
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
printf("%d ", C[i][j]);
}
printf("\n");
}
return 0;
}
```
这个示例代码实现了一个递归的Strassen矩阵乘法算法。用户需要在运行代码时输入矩阵的维度n,以及矩阵A和B的元素。程序将计算A和B的乘积,并打印结果矩阵C。
### 回答2:
Strassen矩阵乘法算法是一种用于快速计算矩阵乘法的算法,采用分治策略,并且在一些情况下具有比传统算法更高的效率。下面是一个使用C语言实现Strassen矩阵乘法算法的例子:
```c
#include <stdio.h>
#include <stdlib.h>
void strassen(int n, int A[][n], int B[][n], int C[][n]) {
if (n == 2) { // 基本情况,直接使用传统算法计算
int P = (A[0][0] + A[1][1]) * (B[0][0] + B[1][1]);
int Q = (A[1][0] + A[1][1]) * B[0][0];
int R = A[0][0] * (B[0][1] - B[1][1]);
int S = A[1][1] * (B[1][0] - B[0][0]);
int T = (A[0][0] + A[0][1]) * B[1][1];
int U = (A[1][0] - A[0][0]) * (B[0][0] + B[0][1]);
int V = (A[0][1] - A[1][1]) * (B[1][0] + B[1][1]);
C[0][0] = P + S - T + V;
C[0][1] = R + T;
C[1][0] = Q + S;
C[1][1] = P + R - Q + U;
} else {
int newSize = n/2;
int A11[newSize][newSize], A12[newSize][newSize], A21[newSize][newSize], A22[newSize][newSize];
int B11[newSize][newSize], B12[newSize][newSize], B21[newSize][newSize], B22[newSize][newSize];
int C11[newSize][newSize], C12[newSize][newSize], C21[newSize][newSize], C22[newSize][newSize];
int P1[newSize][newSize], P2[newSize][newSize], P3[newSize][newSize], P4[newSize][newSize], P5[newSize][newSize], P6[newSize][newSize], P7[newSize][newSize];
int i, j;
for (i = 0; i < newSize; i++) {
for (j = 0; j < newSize; j++) {
A11[i][j] = A[i][j];
A12[i][j] = A[i][j + newSize];
A21[i][j] = A[i + newSize][j];
A22[i][j] = A[i + newSize][j + newSize];
B11[i][j] = B[i][j];
B12[i][j] = B[i][j + newSize];
B21[i][j] = B[i + newSize][j];
B22[i][j] = B[i + newSize][j + newSize];
}
}
strassen(newSize, A11, B11, P1);
strassen(newSize, A12, B21, P2);
strassen(newSize, A11, B12, P3);
strassen(newSize, A12, B22, P4);
strassen(newSize, A21, B11, P5);
strassen(newSize, A22, B21, P6);
strassen(newSize, A21, B12, P7);
for (i = 0; i < newSize; i++) {
for (j = 0; j < newSize; j++) {
C11[i][j] = P1[i][j] + P4[i][j] - P5[i][j] + P7[i][j];
C12[i][j] = P3[i][j] + P5[i][j];
C21[i][j] = P2[i][j] + P4[i][j];
C22[i][j] = P1[i][j] + P3[i][j] - P2[i][j] + P6[i][j];
C[i][j] = C11[i][j];
C[i][j + newSize] = C12[i][j];
C[i + newSize][j] = C21[i][j];
C[i + newSize][j + newSize] = C22[i][j];
}
}
}
}
int main() {
int n = 4; // 矩阵维数
int A[][4] = {{1, 2, 3, 4},
{5, 6, 7, 8},
{9, 10, 11, 12},
{13, 14, 15, 16}};
int B[][4] = {{17, 18, 19, 20},
{21, 22, 23, 24},
{25, 26, 27, 28},
{29, 30, 31, 32}};
int C[4][4];
strassen(n, A, B, C);
int i, j;
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
printf("%d ", C[i][j]);
}
printf("\n");
}
return 0;
}
```
以上是一个简单的C语言实现的Strassen矩阵乘法算法。在此例子中,我们使用了一个4x4的矩阵作为输入,并打印出计算结果。
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