52、并行计算中的矩阵运算与线性方程组求解

并行计算中的矩阵运算与线性方程组求解

1. 矩阵乘法的 CUDA 实现

在并行计算中，矩阵乘法是一个常见且重要的操作。以下是一个使用 CUDA 实现的矩阵乘法核函数示例：

#define TILE_WIDTH 32
global
void MatMulTileKernel (Matrix A, Matrix B, Matrix C) {
    shared
    float Ads[TILE_WIDTH][TILE_WIDTH];
    shared
    float Bds[TILE_WIDTH][TILE_WIDTH];
    int bx = blockIdx.x; int by = blockIdx.y;
    int tx = threadIdx.x; int ty = threadIdx.y;
    int Row = by * TILE_WIDTH + ty;
    int Col = bx * TILE_WIDTH + tx;
    float Cval = 0.0;
    for (int m = 0; m < N/TILE_WIDTH; m++) { /* loop over tiles */
        Ads[ty][tx] = A[Row*N + (m*TILE_WIDTH + tx)];
        Bds[ty][tx] = B[(m*TILE_WIDTH + ty)*N + Col];
        syncthreads();
        for (int k = 0; k < TILE_WIDTH; k++) /* loop within tile */