How performing multiple matrix multiplications in CUDA?

I think it’s likely that the fastest performance will be achieved by using the CUBLAS batch gemm function which was specifically designed for this purpose (performing a large number of “relatively small” matrix-matrix multiply operations).

Even though you want to multiply your array of matrices (M[]) by a single matrix (N), the batch gemm function will require you to pass also an array of matrices for N (i.e. N[]), which will all be the same in your case.

EDIT: Now that I have worked thru an example, it seems clear to me that with a modification to the example below, we can pass a single N matrix and have the GPU_Multi function simply send the single N matrix to the device, while passing an array of pointers for N, i.e. d_Narray in the example below, with all of the pointers pointing to the same N matrix on the device.

Here is a fully worked batch GEMM example:

#include <stdio.h>
#include <cuda_runtime.h>
#include <cublas_v2.h>
#include <assert.h>

#define ROWM 4
#define COLM 3
#define COLN 5

#define cudaCheckErrors(msg) \
    do { \
        cudaError_t __err = cudaGetLastError(); \
        if (__err != cudaSuccess) { \
            fprintf(stderr, "Fatal error: %s (%s at %s:%d)\n", \
                msg, cudaGetErrorString(__err), \
                __FILE__, __LINE__); \
            fprintf(stderr, "*** FAILED - ABORTING\n"); \
            exit(1); \
        } \
    } while (0)


typedef float mytype;
// Pi = Mi x Ni
// pr = P rows = M rows
// pc = P cols = N cols
// mc = M cols = N rows
void GPU_Multi(mytype **M, mytype **N, mytype **P
  , size_t pr, size_t pc, size_t mc
  , size_t num_mat, mytype alpha, mytype beta)
{

    mytype *devM[num_mat];
    mytype *devN[num_mat];
    mytype *devP[num_mat];
    size_t p_size =sizeof(mytype) *pr*pc;
    size_t m_size =sizeof(mytype) *pr*mc;
    size_t n_size =sizeof(mytype) *mc*pc;
    const mytype **d_Marray, **d_Narray;
    mytype **d_Parray;
    cublasHandle_t myhandle;
    cublasStatus_t cublas_result;

    for(int i = 0 ; i < num_mat; i ++ )
    {
        cudaMalloc((void**)&devM[ i ], m_size );
        cudaMalloc((void**)&devN[ i ], n_size );
        cudaMalloc((void**)&devP[ i ], p_size );
    }
    cudaMalloc((void**)&d_Marray, num_mat*sizeof(mytype *));
    cudaMalloc((void**)&d_Narray, num_mat*sizeof(mytype *));
    cudaMalloc((void**)&d_Parray, num_mat*sizeof(mytype *));
    cudaCheckErrors("cudaMalloc fail");
    for(int i = 0 ; i < num_mat; i ++ ) {

        cudaMemcpy(devM[i], M[i], m_size , cudaMemcpyHostToDevice);
        cudaMemcpy(devN[i], N[i], n_size , cudaMemcpyHostToDevice);
        cudaMemcpy(devP[i], P[i], p_size , cudaMemcpyHostToDevice);
    }
    cudaMemcpy(d_Marray, devM, num_mat*sizeof(mytype *), cudaMemcpyHostToDevice);
    cudaMemcpy(d_Narray, devN, num_mat*sizeof(mytype *), cudaMemcpyHostToDevice);
    cudaMemcpy(d_Parray, devP, num_mat*sizeof(mytype *), cudaMemcpyHostToDevice);
    cudaCheckErrors("cudaMemcpy H2D fail");
    cublas_result = cublasCreate(&myhandle);
    assert(cublas_result == CUBLAS_STATUS_SUCCESS);
    // change to    cublasDgemmBatched for double
    cublas_result = cublasSgemmBatched(myhandle, CUBLAS_OP_N, CUBLAS_OP_N
      , pr, pc, mc
      , &alpha, d_Marray, pr, d_Narray, mc
      , &beta, d_Parray, pr
      , num_mat);
    assert(cublas_result == CUBLAS_STATUS_SUCCESS);

    for(int i = 0 ; i < num_mat ; i ++ )
    {
        cudaMemcpy(P[i], devP[i], p_size, cudaMemcpyDeviceToHost);
        cudaFree(devM[i]);
        cudaFree(devN[i]);
        cudaFree(devP[i]);
    }
    cudaFree(d_Marray);
    cudaFree(d_Narray);
    cudaFree(d_Parray);
    cudaCheckErrors("cudaMemcpy D2H fail");

}

int main(){

  mytype h_M1[ROWM][COLM], h_M2[ROWM][COLM];
  mytype h_N1[COLM][COLN], h_N2[COLM][COLN];
  mytype h_P1[ROWM][COLN], h_P2[ROWM][COLN];
  mytype *h_Marray[2], *h_Narray[2], *h_Parray[2];
  for (int i = 0; i < ROWM; i++)
    for (int j = 0; j < COLM; j++){
      h_M1[i][j] = 1.0f; h_M2[i][j] = 2.0f;}
  for (int i = 0; i < COLM; i++)
    for (int j = 0; j < COLN; j++){
      h_N1[i][j] = 1.0f; h_N2[i][j] = 1.0f;}
  for (int i = 0; i < ROWM; i++)
    for (int j = 0; j < COLN; j++){
      h_P1[i][j] = 0.0f; h_P2[i][j] = 0.0f;}

  h_Marray[0] = &(h_M1[0][0]);
  h_Marray[1] = &(h_M2[0][0]);
  h_Narray[0] = &(h_N1[0][0]);
  h_Narray[1] = &(h_N2[0][0]);
  h_Parray[0] = &(h_P1[0][0]);
  h_Parray[1] = &(h_P2[0][0]);

  GPU_Multi(h_Marray, h_Narray, h_Parray, ROWM, COLN, COLM, 2, 1.0f, 0.0f);
  for (int i = 0; i < ROWM; i++)
    for (int j = 0; j < COLN; j++){
      if (h_P1[i][j] != COLM*1.0f)
      {
        printf("h_P1 mismatch at %d,%d was: %f should be: %f\n"
          , i, j, h_P1[i][j], COLM*1.0f); return 1;
      }
      if (h_P2[i][j] != COLM*2.0f)
      {
        printf("h_P2 mismatch at %d,%d was: %f should be: %f\n"
          , i, j, h_P2[i][j], COLM*2.0f); return 1;
      }
    }
  printf("Success!\n");
  return 0;
}