strassen矩阵乘法c++

以下是使用C语言实现的Strassen标准矩阵乘法算法的代码：

#include <stdio.h>

#define N 4 // 矩阵大小
#define THRESHOLD 2 // 阈值

// 矩阵加法
void add_matrix(int a[][N], int b[][N], int c[][N])
{
    int i, j;
    for (i = 0; i < N; i++) {
        for (j = 0; j < N; j++) {
            c[i][j] = a[i][j] + b[i][j];
        }
    }
}

// 矩阵减法
void sub_matrix(int a[][N], int b[][N], int c[][N])
{
    int i, j;
    for (i = 0; i < N; i++) {
        for (j = 0; j < N; j++) {
            c[i][j] = a[i][j] - b[i][j];
        }
    }
}

// Strassen矩阵乘法
void strassen_mul(int a[][N], int b[][N], int c[][N])
{
    // 达到阈值，使用标准矩阵乘法
    if (N <= THRESHOLD) {
        int i, j, k;
        for (i = 0; i < N; i++) {
            for (j = 0; j < N; j++) {
                c[i][j] = 0;
                for (k = 0; k < N; k++) {
                    c[i][j] += a[i][k] * b[k][j];
                }
            }
        }
        return;
    }

    // 处理矩阵的大小并向上取整
    int size = N / 2;
    if (N % 2 != 0) {
        size += 1;
    }

    int A[size][size], B[size][size], C[size][size], D[size][size];
    int E[size][size], F[size][size], G[size][size], H[size][size];
    int P1[size][size], P2[size][size], P3[size][size], P4[size][size], P5[size][size], P6[size][size], P7[size][size];
    int tmp1[size][size], tmp2[size][size];

    // 拆分矩阵
    int i, j;
    for (i = 0; i < size; i++) {
        for (j = 0; j < size; j++) {
            A[i][j] = a[i][j];
            B[i][j] = a[i][j + size];
            C[i][j] = a[i + size][j];
            D[i][j] = a[i + size][j + size];
            E[i][j] = b[i][j];
            F[i][j] = b[i][j + size];
            G[i][j] = b[i + size][j];
            H[i][j] = b[i + size][j + size];
        }
    }

    // 计算P1到P7
    sub_matrix(F, H, tmp1);
    strassen_mul(A, tmp1, P1);

    add_matrix(A, B, tmp1);
    strassen_mul(tmp1, H, P2);

    add_matrix(C, D, tmp1);
    strassen_mul(tmp1, E, P3);

    sub_matrix(G, E, tmp1);
    strassen_mul(D, tmp1, P4);

    add_matrix(A, D, tmp1);
    add_matrix(E, H, tmp2);
    strassen_mul(tmp1, tmp2, P5);

    sub_matrix(B, D, tmp1);
    add_matrix(G, H, tmp2);
    strassen_mul(tmp1, tmp2, P6);

    sub_matrix(A, C, tmp1);
    add_matrix(E, F, tmp2);
    strassen_mul(tmp1, tmp2, P7);

    // 计算结果矩阵
    add_matrix(P5, P4, tmp1);
    sub_matrix(tmp1, P2, tmp2);
    add_matrix(tmp2, P6, c[0]);

    add_matrix(P1, P2, c[1]);
    add_matrix(P3, P4, c[2]);

    add_matrix(P5, P1, tmp1);
    sub_matrix(tmp1, P3, tmp2);
    sub_matrix(tmp2, P7, c[3]);

}

int main()
{
    int a[N][N] = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}, {13, 14, 15, 16}};
    int b[N][N] = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}, {13, 14, 15, 16}};
    int c[N][N];
    int i, j;

    strassen_mul(a, b, c);

    printf("Result:\n");
    for (i = 0; i < N; i++) {
        for (j = 0; j < N; j++) {
            printf("%d ", c[i][j]);
        }
        printf("\n");
    }

    return 0;
}

本代码中定义了THRESHOLD变量，当矩阵大小小于等于阈值时，使用标准矩阵乘法算法计算。简单起见，本代码中矩阵大小固定为4 * 4，可以根据需要修改。