使用 CUDA 在 GPU 上的并行 Kronecker 张量积

Question

我正在使用 [PTX 文件和 matlab parallel.gpu.CUDAkernel][2] 在 GPU 上并行化 [此文件][1]。我对 [kron 张量积][3] 的问题如下。我的代码应该通过将第一个向量a=<32x1> 的每个元素乘以另一个向量b=<1x32> 的所有元素来将两个向量kron(a,b) 相乘，并且输出向量大小将为k<32x32>=a.*b。我尝试用 C++ 编写它并且它有效，因为我只关心对 2d 数组的所有元素求和。我想我可以让它像一维数组一样简单，因为m=sum(sum(kron(a,b))) 是我正在处理的代码

for(i=0;i<32;i++)
 for(j=0;j<32;j++)
   k[i*32+j]=a[i]*b[j]

它的意思是让a[i]th 元素乘以b 中的每个元素，我想使用32 块，每个块都有一个32 线程，代码应该是

__global__ void myKrom(int* c,int* a, int*b) {
  int i=blockDim.x*blockIdx.x+threadIdx.x;
  while(i<32) {
    c[i]=a[blockIdx.x]+b[blockDim.x*blockIdx.x+threadIdx.x];
  }

这应该可以解决问题，因为 blockIdx.x 是外循环，但它没有。任何人都可以告诉我在哪里，我可以要求并行方式来进行并行求和。

Answer 1

如果第一个操作数是单位矩阵，则可以使用 cuSPARSE 的 bsr 格式简单地表示 Kronecker 乘积的结果。

下面，一个实现以下Matlab指令的简单示例

 m = 5;
 I = speye(m);
 e = ones(m, 1);
 T = spdiags([e -4 * e e],[-1 0 1], m, m);
 kron(I, T)

克朗(I, T)

#include <stdio.h>
#include <assert.h>

#include <cusparse.h>

#define blockMatrixSize         3           // --- Each block of the sparse block matrix is blockMatrixSize x blockMatrixSize

/*******************/
/* iDivUp FUNCTION */
/*******************/
int iDivUp(int a, int b){ return ((a % b) != 0) ? (a / b + 1) : (a / b); }

/********************/
/* CUDA ERROR CHECK */
/********************/
// --- Credit to http://stackoverflow.com/questions/14038589/what-is-the-canonical-way-to-check-for-errors-using-the-cuda-runtime-api
void gpuAssert(cudaError_t code, const char *file, int line, bool abort = true)
{
    if (code != cudaSuccess)
    {
        fprintf(stderr, "GPUassert: %s %s %d\n", cudaGetErrorString(code), file, line);
        if (abort) { exit(code); }
    }
}

void gpuErrchk(cudaError_t ans) { gpuAssert((ans), __FILE__, __LINE__); }

/***************************/
/* CUSPARSE ERROR CHECKING */
/***************************/
static const char *_cusparseGetErrorEnum(cusparseStatus_t error)
{
    switch (error)
    {

    case CUSPARSE_STATUS_SUCCESS:
        return "CUSPARSE_STATUS_SUCCESS";

    case CUSPARSE_STATUS_NOT_INITIALIZED:
        return "CUSPARSE_STATUS_NOT_INITIALIZED";

    case CUSPARSE_STATUS_ALLOC_FAILED:
        return "CUSPARSE_STATUS_ALLOC_FAILED";

    case CUSPARSE_STATUS_INVALID_VALUE:
        return "CUSPARSE_STATUS_INVALID_VALUE";

    case CUSPARSE_STATUS_ARCH_MISMATCH:
        return "CUSPARSE_STATUS_ARCH_MISMATCH";

    case CUSPARSE_STATUS_MAPPING_ERROR:
        return "CUSPARSE_STATUS_MAPPING_ERROR";

    case CUSPARSE_STATUS_EXECUTION_FAILED:
        return "CUSPARSE_STATUS_EXECUTION_FAILED";

    case CUSPARSE_STATUS_INTERNAL_ERROR:
        return "CUSPARSE_STATUS_INTERNAL_ERROR";

    case CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED:
        return "CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED";

    case CUSPARSE_STATUS_ZERO_PIVOT:
        return "CUSPARSE_STATUS_ZERO_PIVOT";
    }

    return "<unknown>";
}

inline void __cusparseSafeCall(cusparseStatus_t err, const char *file, const int line)
{
    if (CUSPARSE_STATUS_SUCCESS != err) {
        fprintf(stderr, "CUSPARSE error in file '%s', line %d, error %s\nterminating!\n", __FILE__, __LINE__, \
            _cusparseGetErrorEnum(err)); \
            assert(0); \
    }
}

extern "C" void cusparseSafeCall(cusparseStatus_t err) { __cusparseSafeCall(err, __FILE__, __LINE__); }

/********/
/* MAIN */
/********/
int main() {

    // --- Initialize cuSPARSE
    cusparseHandle_t handle;    cusparseSafeCall(cusparseCreate(&handle));

    // --- Initialize matrix descriptors
    cusparseMatDescr_t descrA, descrC;
    cusparseSafeCall(cusparseCreateMatDescr(&descrA));
    cusparseSafeCall(cusparseCreateMatDescr(&descrC));

    const int Mb = 5;                                       // --- Number of blocks along rows
    const int Nb = 5;                                       // --- Number of blocks along columns

    const int M = Mb * blockMatrixSize;                     // --- Number of rows
    const int N = Nb * blockMatrixSize;                     // --- Number of columns

    const int nnzb = Mb;                                    // --- Number of non-zero blocks

    float h_block[blockMatrixSize * blockMatrixSize] = { 4.f, -1.f, 0.f, -1.f, 4.f, -1.f, 0.f, -1.f, 4.f };

    // --- Host vectors defining the block-sparse matrix
    float *h_bsrValA = (float *)malloc(blockMatrixSize * blockMatrixSize * nnzb * sizeof(float));
    int *h_bsrRowPtrA = (int *)malloc((Mb + 1) * sizeof(int));
    int *h_bsrColIndA = (int *)malloc(nnzb * sizeof(int));

    for (int k = 0; k < nnzb; k++) memcpy(h_bsrValA + k * blockMatrixSize * blockMatrixSize, h_block, blockMatrixSize * blockMatrixSize * sizeof(float));

    h_bsrRowPtrA[0] = 0;
    h_bsrRowPtrA[1] = 1;
    h_bsrRowPtrA[2] = 2;
    h_bsrRowPtrA[3] = 3;
    h_bsrRowPtrA[4] = 4;
    h_bsrRowPtrA[5] = 5;

    h_bsrColIndA[0] = 0;
    h_bsrColIndA[1] = 1;
    h_bsrColIndA[2] = 2;
    h_bsrColIndA[3] = 3;
    h_bsrColIndA[4] = 4;

    // --- Device vectors defining the block-sparse matrix
    float *d_bsrValA;       gpuErrchk(cudaMalloc(&d_bsrValA, blockMatrixSize * blockMatrixSize * nnzb * sizeof(float)));
    int *d_bsrRowPtrA;      gpuErrchk(cudaMalloc(&d_bsrRowPtrA, (Mb + 1) * sizeof(int)));
    int *d_bsrColIndA;      gpuErrchk(cudaMalloc(&d_bsrColIndA, nnzb * sizeof(int)));

    gpuErrchk(cudaMemcpy(d_bsrValA, h_bsrValA, blockMatrixSize * blockMatrixSize * nnzb * sizeof(float), cudaMemcpyHostToDevice));
    gpuErrchk(cudaMemcpy(d_bsrRowPtrA, h_bsrRowPtrA, (Mb + 1) * sizeof(int), cudaMemcpyHostToDevice));
    gpuErrchk(cudaMemcpy(d_bsrColIndA, h_bsrColIndA, nnzb * sizeof(int), cudaMemcpyHostToDevice));

    // --- Transforming bsr to csr format
    cusparseDirection_t dir = CUSPARSE_DIRECTION_COLUMN;
    const int nnz = nnzb * blockMatrixSize * blockMatrixSize; // --- Number of non-zero elements
    int *d_csrRowPtrC;      gpuErrchk(cudaMalloc(&d_csrRowPtrC, (M + 1) * sizeof(int)));
    int *d_csrColIndC;      gpuErrchk(cudaMalloc(&d_csrColIndC, nnz     * sizeof(int)));
    float *d_csrValC;       gpuErrchk(cudaMalloc(&d_csrValC, nnz        * sizeof(float)));
    cusparseSafeCall(cusparseSbsr2csr(handle, dir, Mb, Nb, descrA, d_bsrValA, d_bsrRowPtrA, d_bsrColIndA, blockMatrixSize, descrC, d_csrValC, d_csrRowPtrC, d_csrColIndC));

    // --- Transforming csr to dense format
    float *d_A;             gpuErrchk(cudaMalloc(&d_A, M * N * sizeof(float)));
    cusparseSafeCall(cusparseScsr2dense(handle, M, N, descrC, d_csrValC, d_csrRowPtrC, d_csrColIndC, d_A, M));

    float *h_A = (float *)malloc(M * N * sizeof(float));
    gpuErrchk(cudaMemcpy(h_A, d_A, M * N * sizeof(float), cudaMemcpyDeviceToHost));

    // --- m is row index, n column index
    for (int m = 0; m < M; m++) {
        for (int n = 0; n < N; n++) {
            printf("%f ", h_A[m + n * M]);
        }
        printf("\n");
    }

    return 0;
}

同样在第二个操作数是单位矩阵的简单情况下，克罗内克积的结果可以使用 cuSPARSE 的 bsr 格式表示。

下面，一个简单的例子

m = 5;
I = speye(3);
e = ones(m, 1);
S = spdiags([e e], [-1 1], m, m);
kron(S, I)

克朗(S, I)

#include <stdio.h>
#include <assert.h>

#include <cusparse.h>

#define blockMatrixSize         3           // --- Each block of the sparse block matrix is blockMatrixSize x blockMatrixSize

/*******************/
/* iDivUp FUNCTION */
/*******************/
int iDivUp(int a, int b){ return ((a % b) != 0) ? (a / b + 1) : (a / b); }

/********************/
/* CUDA ERROR CHECK */
/********************/
// --- Credit to http://stackoverflow.com/questions/14038589/what-is-the-canonical-way-to-check-for-errors-using-the-cuda-runtime-api
void gpuAssert(cudaError_t code, const char *file, int line, bool abort = true)
{
    if (code != cudaSuccess)
    {
        fprintf(stderr, "GPUassert: %s %s %d\n", cudaGetErrorString(code), file, line);
        if (abort) { exit(code); }
    }
}

void gpuErrchk(cudaError_t ans) { gpuAssert((ans), __FILE__, __LINE__); }

/***************************/
/* CUSPARSE ERROR CHECKING */
/***************************/
static const char *_cusparseGetErrorEnum(cusparseStatus_t error)
{
    switch (error)
    {

    case CUSPARSE_STATUS_SUCCESS:
        return "CUSPARSE_STATUS_SUCCESS";

    case CUSPARSE_STATUS_NOT_INITIALIZED:
        return "CUSPARSE_STATUS_NOT_INITIALIZED";

    case CUSPARSE_STATUS_ALLOC_FAILED:
        return "CUSPARSE_STATUS_ALLOC_FAILED";

    case CUSPARSE_STATUS_INVALID_VALUE:
        return "CUSPARSE_STATUS_INVALID_VALUE";

    case CUSPARSE_STATUS_ARCH_MISMATCH:
        return "CUSPARSE_STATUS_ARCH_MISMATCH";

    case CUSPARSE_STATUS_MAPPING_ERROR:
        return "CUSPARSE_STATUS_MAPPING_ERROR";

    case CUSPARSE_STATUS_EXECUTION_FAILED:
        return "CUSPARSE_STATUS_EXECUTION_FAILED";

    case CUSPARSE_STATUS_INTERNAL_ERROR:
        return "CUSPARSE_STATUS_INTERNAL_ERROR";

    case CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED:
        return "CUSPARSE_STATUS_MATRIX_TYPE_NOT_SUPPORTED";

    case CUSPARSE_STATUS_ZERO_PIVOT:
        return "CUSPARSE_STATUS_ZERO_PIVOT";
    }

    return "<unknown>";
}

inline void __cusparseSafeCall(cusparseStatus_t err, const char *file, const int line)
{
    if (CUSPARSE_STATUS_SUCCESS != err) {
        fprintf(stderr, "CUSPARSE error in file '%s', line %d, error %s\nterminating!\n", __FILE__, __LINE__, \
            _cusparseGetErrorEnum(err)); \
            assert(0); \
    }
}

extern "C" void cusparseSafeCall(cusparseStatus_t err) { __cusparseSafeCall(err, __FILE__, __LINE__); }

/********/
/* MAIN */
/********/
int main() {

    // --- Initialize cuSPARSE
    cusparseHandle_t handle;    cusparseSafeCall(cusparseCreate(&handle));

    // --- Initialize matrix descriptors
    cusparseMatDescr_t descrA, descrC;
    cusparseSafeCall(cusparseCreateMatDescr(&descrA));
    cusparseSafeCall(cusparseCreateMatDescr(&descrC));

    const int Mb = 5;                                       // --- Number of blocks along rows
    const int Nb = 5;                                       // --- Number of blocks along columns

    const int M = Mb * blockMatrixSize;                     // --- Number of rows
    const int N = Nb * blockMatrixSize;                     // --- Number of columns

    const int nnzb = 2 * (Mb - 1);                          // --- Number of non-zero blocks

    float h_block[blockMatrixSize * blockMatrixSize] = { 1.f, 0.f, 0.f, 0.f, 1.f, 0.f, 0.f, 0.f, 1.f };

    // --- Host vectors defining the block-sparse matrix
    float *h_bsrValA = (float *)malloc(blockMatrixSize * blockMatrixSize * nnzb * sizeof(float));
    int *h_bsrRowPtrA = (int *)malloc((Mb + 1) * sizeof(int));
    int *h_bsrColIndA = (int *)malloc(nnzb * sizeof(int));

    for (int k = 0; k < nnzb; k++) memcpy(h_bsrValA + k * blockMatrixSize * blockMatrixSize, h_block, blockMatrixSize * blockMatrixSize * sizeof(float));

    h_bsrRowPtrA[0] = 0;
    h_bsrRowPtrA[1] = 1;
    h_bsrRowPtrA[2] = 3;
    h_bsrRowPtrA[3] = 5;
    h_bsrRowPtrA[4] = 7;
    h_bsrRowPtrA[5] = 2 * (Mb - 1);

    h_bsrColIndA[0] = 1;
    h_bsrColIndA[1] = 0;
    h_bsrColIndA[2] = 2;
    h_bsrColIndA[3] = 1;
    h_bsrColIndA[4] = 3;
    h_bsrColIndA[5] = 2;
    h_bsrColIndA[6] = 4;
    h_bsrColIndA[7] = 3;

    // --- Device vectors defining the block-sparse matrix
    float *d_bsrValA;       gpuErrchk(cudaMalloc(&d_bsrValA, blockMatrixSize * blockMatrixSize * nnzb * sizeof(float)));
    int *d_bsrRowPtrA;      gpuErrchk(cudaMalloc(&d_bsrRowPtrA, (Mb + 1) * sizeof(int)));
    int *d_bsrColIndA;      gpuErrchk(cudaMalloc(&d_bsrColIndA, nnzb * sizeof(int)));

    gpuErrchk(cudaMemcpy(d_bsrValA, h_bsrValA, blockMatrixSize * blockMatrixSize * nnzb * sizeof(float), cudaMemcpyHostToDevice));
    gpuErrchk(cudaMemcpy(d_bsrRowPtrA, h_bsrRowPtrA, (Mb + 1) * sizeof(int), cudaMemcpyHostToDevice));
    gpuErrchk(cudaMemcpy(d_bsrColIndA, h_bsrColIndA, nnzb * sizeof(int), cudaMemcpyHostToDevice));

    // --- Transforming bsr to csr format
    cusparseDirection_t dir = CUSPARSE_DIRECTION_COLUMN;
    const int nnz = nnzb * blockMatrixSize * blockMatrixSize; // --- Number of non-zero elements
    int *d_csrRowPtrC;      gpuErrchk(cudaMalloc(&d_csrRowPtrC, (M + 1) * sizeof(int)));
    int *d_csrColIndC;      gpuErrchk(cudaMalloc(&d_csrColIndC, nnz     * sizeof(int)));
    float *d_csrValC;       gpuErrchk(cudaMalloc(&d_csrValC, nnz        * sizeof(float)));
    cusparseSafeCall(cusparseSbsr2csr(handle, dir, Mb, Nb, descrA, d_bsrValA, d_bsrRowPtrA, d_bsrColIndA, blockMatrixSize, descrC, d_csrValC, d_csrRowPtrC, d_csrColIndC));

    // --- Transforming csr to dense format
    float *d_A;             gpuErrchk(cudaMalloc(&d_A, M * N * sizeof(float)));
    cusparseSafeCall(cusparseScsr2dense(handle, M, N, descrC, d_csrValC, d_csrRowPtrC, d_csrColIndC, d_A, M));

    float *h_A = (float *)malloc(M * N * sizeof(float));
    gpuErrchk(cudaMemcpy(h_A, d_A, M * N * sizeof(float), cudaMemcpyDeviceToHost));

    // --- m is row index, n column index
    for (int m = 0; m < M; m++) {
        for (int n = 0; n < N; n++) {
            printf("%f ", h_A[m + n * M]);
        }
        printf("\n");
    }

    return 0;
}

Answer 2

你的意思可能是这样的：

__global__ void myKrom(int* c,int* a, int*b)
{
  int i=blockDim.x*blockIdx.x+threadIdx.x;
  if(i<32*32){
    c[i]=a[blockIdx.x]+b[threadIdx.x];
  }

}

当你通过myKrom<<<32, 32>>> (c, a, b);调用内核时