c语言实现strassen矩阵乘法

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：

#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！

用C语言写出Strassen矩阵乘法

好的，可以，下面是C语言实现的Strassen矩阵乘法代码：

void strassen(int **A, int **B, int **C, int n) {
    int i, j;
    if (n == 1) {
        C[0][0] = A[0][0] * B[0][0];
        return;
    }
    int **A11 = allocate(n/2), **A12 = allocate(n/2), **A21 = allocate(n/2), **A22 = allocate(n/2);
    int **B11 = allocate(n/2), **B12 = allocate(n/2), **B21 = allocate(n/2), **B22 = allocate(n/2);
    int **C11 = allocate(n/2), **C12 = allocate(n/2), **C21 = allocate(n/2), **C22 = allocate(n/2);
    int **M1 = allocate(n/2), **M2 = allocate(n/2), **M3 = allocate(n/2), **M4 = allocate(n/2), **M5 = allocate(n/2), **M6 = allocate(n/2), **M7 = allocate(n/2);
    int **temp1 = allocate(n/2), **temp2 = allocate(n/2), **temp3 = allocate(n/2), **temp4 = allocate(n/2), **temp5 = allocate(n/2), **temp6 = allocate(n/2), **temp7 = allocate(n/2);
    split_matrix(A, A11, A12, A21, A22, n);
    split_matrix(B, B11, B12, B21, B22, n);
    sub_matrix(B12, B22, temp1, n/2);
    strassen(A11, temp1, M1, n/2);
    add_matrix(A11, A12, temp2, n/2);
    strassen(temp2, B22, M2, n/2);
    add_matrix(A21, A22, temp3, n/2);
    strassen(temp3, B11, M3, n/2);
    sub_matrix(B21, B11, temp4, n/2);
    strassen(A22, temp4, M4, n/2);
    add_matrix(A11, A22, temp5, n/2);
    add_matrix(B11, B22, temp6, n/2);
    strassen(temp5, temp6, M5, n/2);
    sub_matrix(A12, A22, temp7, n/2);
    add_matrix(B21, B22, temp6, n/2);
    strassen(temp7, temp6, M6, n/2);
    sub_matrix(A11, A21, temp7, n/2);
    add_matrix(B11, B12, temp6, n/2);
    strassen(temp7, temp6, M7, n/2);
    add_matrix(M5, M4, temp1, n/2);
    sub_matrix(temp1, M2, temp2, n/2);
    add_matrix(temp2, M6, C11, n/2);
    add_matrix(M1, M2, C12, n/2);
    add_matrix(M3, M4, C21, n/2);
    add_matrix(M5, M1, temp3, n/2);
    sub_matrix(temp3, M3, temp4, n/2);
    sub_matrix(temp4, M7, C22, n/2);
    merge_matrix(C, C11, C12, C21, C22, n);
    deallocate(A11, n/2); deallocate(A12, n/2); deallocate(A21, n/2); deallocate(A22, n/2);
    deallocate(B11, n/2); deallocate(B12, n/2); deallocate(B21, n/2); deallocate(B22, n/2);
    deallocate(C11, n/2); deallocate(C12, n/2); deallocate(C21, n/2); deallocate(C22, n/2);
    deallocate(M1, n/2); deallocate(M2, n/2); deallocate(M3, n/2); deallocate(M4, n/2);
    deallocate(M5, n/2); deallocate(M6, n/2); deallocate(M7, n/2);
    deallocate(temp1, n/2); deallocate(temp2, n/2); deallocate(temp3, n/2);
    deallocate(temp4, n/2); deallocate(temp5, n/2); deallocate(temp6, n/2); deallocate(temp7, n/2);
}

希望能够帮助到你！