How to transpose a matrix in CUDA/cublas?

Question

Say I have a matrix with a dimension of A*B on GPU, where B (number of columns) is the leading dimension assuming a C style. Is there any method in CUDA (or cublas) to transpose this matrix to FORTRAN style, where A (number of rows) becomes the leading dimension?

It is even better if it could be transposed during host->device transfer while keep the original data unchanged.

Solution 1

The CUDA SDK includes a matrix transpose, you can see here examples of code on how to implement one, ranging from a naive implementation to optimized versions.

For example:

Naïve transpose

__global__ void transposeNaive(float *odata, float* idata,
int width, int height, int nreps)
{
    int xIndex = blockIdx.x*TILE_DIM + threadIdx.x;
    int yIndex = blockIdx.y*TILE_DIM + threadIdx.y;
    int index_in = xIndex + width * yIndex;
    int index_out = yIndex + height * xIndex;

    for (int r=0; r < nreps; r++)
    {
        for (int i=0; i<TILE_DIM; i+=BLOCK_ROWS)
        {
          odata[index_out+i] = idata[index_in+i*width];
        }
    }
}

Like talonmies had point out you can specify if you want operate the matrix as transposed or not, in cublas matrix operations eg.: for cublasDgemm() where C = a * op(A) * op(B) + b * C, assuming you want to operate A as transposed (A^T), on the parameters you can specify if it is ('N' normal or 'T' transposed)

Solution 2

as asked within the title, to transpose a device row-major matrix A[m][n], one can do it this way:

    float* clone = ...;//copy content of A to clone
    float const alpha(1.0);
    float const beta(0.0);
    cublasHandle_t handle;
    cublasCreate(&handle);
    cublasSgeam( handle, CUBLAS_OP_T, CUBLAS_OP_N, m, n, &alpha, clone, n, &beta, clone, m, A, m );
    cublasDestroy(handle);

And, to multiply two row-major matrices A[m][k] B[k][n], C=A*B

    cublasSgemm( handle, CUBLAS_OP_N, CUBLAS_OP_N, n, m, k, &alpha, B, n, A, k, &beta, C, n );

where C is also a row-major matrix.

Solution 3

The version of CUBLAS bundled with the CUDA 5 toolkit contains a BLAS-like method (cublasgeam) that could be used to transpose a matrix. It's documented here.