cublasDgemm
concept
cublasDgemm is a convenient function in cublas to compute the product of two matrix, while letter ‘D’ in cublasDgemm means double.
Before reading this post, basic cuda functions like cudaMalloc are what you are supposed to know.
basic use
Definition of this function
cublasStatus_t cublasDgemm(cublasHandle_t handle,
cublasOperation_t transa, cublasOperation_t transb,
int m, int n, int k,
const double *alpha,
const double *A, int lda,
const double *B, int ldb,
const double *beta,
double *C, int ldc)Basic information of parameters is show in this page. Simply put, $C = \alpha A \times B + \beta C $ .But it may remains confused for fresher. Below is an simple example.
/* A is matrix in gpu memory looks like
* 1 2 3
* 4 5 6
* 7 8 9
* and ptr_A is a pointer to A
*
* B is matrix in gpu memory looks like
* 1 2
* 3 4
* 5 6
* and ptr_A is a pointer to A
*
* While memory is one-dimensional while matrix is two-dimensional, I
* suggeset that all matrix in gpu memory are stored in column major for
* convevient use of cublas. In this case, A in memory is like
* [1, 4, 7, 2, 5, 8, 3, 6, 9].
* C is a matrix to store the product of A * B
*/
//get handle and stat of this function
cublasHandle_t handle;
cublasStatus_t stat = cublasCreate(&handle);
if (stat != CUBLAS_STATUS_SUCCESS)
{
printf("CUBLAS initialization failed\n");
return EXIT_FAILURE;
}
//setting alpha and cuda
double alpha = 1.0, beta = 0.0;
stat = cublasDgemm( handle,
CUBLAS_OP_N, // we use matrix A instead of A^T
CUBLAS_OP_N, // we use matrix B instead of B^T
3, // the row of A
2, // the col of B
3, // the row of B(ro col of A)
&alpha,
devPtrA,
3, // the leading dimension of A
devPtrB,
3, // the leading dimension of B
&beta,
devPtrC,
3); // the leading dimension of C
/*
* if we want to compute C = A^T * B
*/
stat = cublasDgemm( handle,
CUBLAS_OP_T, // we use matrix A^T instead of A
CUBLAS_OP_N, // we use matrix A instead of B^T
3, // the row of A^T
2, // the col of B
3, // the row of B(or col of A^T)
&alpha,
devPtrA,
3, // the leading dimension of A^T.
// So whether or not A or A^T, the leading dimension
// of A or A^T is the row of A, decided when A is
// initialized in memory
devPtrB,
3, // the leading dimension of B
&beta,
devPtrC,
3); // the leading dimension of C
if (stat != CUBLAS_STATUS_SUCCESS)
{
printf("cublasSgemm failed\n");
return EXIT_FAILURE;
}An obvious question is what is leading dimension for we have know the column and row of A and B, no more information is need to finish this computation.
My understanding of leading dimension is the offest to get the element in next column at the same row. An implement to compute the product of submatrix. below is an example. A and B are the same matrix in the previous example.
And what we want to compute is $A[0:1][0:1] \times B[1:2][0:1]$.
stat = cublasDgemm( handle,
CUBLAS_OP_N, // we use matrix A[0:1][0:1] instead of A[0:1][0:1]^T
CUBLAS_OP_N, // we use matrix B[1:2][0:1] instead of B[1:2][0:1]^T
2, // the row of A[0:1][0:1]
2, // the col of B[1:2][0:1]
2, // the row of A[0:1][0:1](or col of B[1:2][0:1])
&alpha,
devPtrA, // pointer to A[0][0]
3, // the offset of A[0][0] to A[0][1] is 3 of double size
devPtrB + 1, // pointer to B[1][0]
3, // the offset of B[1][0] to B[1][1] is 3 of double size
&beta,
devPtrC,
2); // the leading dimension of C
So it’s the use of leading dimension which makes matrix production more flexible