def transpose(a, b=None):
    """Compute the transpose of 'a' and store it into 'b', if given,
    and return it. If 'b' is not given, allocate a new array
    and return that.

    This implements the algorithm documented in
    http://devblogs.nvidia.com/parallelforall/efficient-matrix-transpose-cuda-cc/

    :param a: an `np.ndarray` or a `DeviceNDArrayBase` subclass. If already on
        the device its stream will be used to perform the transpose (and to copy
        `b` to the device if necessary).
    """

    # prefer `a`'s stream if
    stream = getattr(a, 'stream', 0)

    if not b:
        cols, rows = a.shape
        strides = a.dtype.itemsize * cols, a.dtype.itemsize
        b = cuda.cudadrv.devicearray.DeviceNDArray(
            (rows, cols),
            strides,
            dtype=a.dtype,
            stream=stream)

    dt = nps.from_dtype(a.dtype)

    tpb = driver.get_device().MAX_THREADS_PER_BLOCK
    # we need to factor available threads into x and y axis
    tile_width = int(math.pow(2, math.log(tpb, 2) / 2))
    tile_height = int(tpb / tile_width)

    tile_shape = (tile_height, tile_width + 1)

    @cuda.jit
    def kernel(input, output):

        tile = cuda.shared.array(shape=tile_shape, dtype=dt)

        tx = cuda.threadIdx.x
        ty = cuda.threadIdx.y
        bx = cuda.blockIdx.x * cuda.blockDim.x
        by = cuda.blockIdx.y * cuda.blockDim.y
        x = by + tx
        y = bx + ty

        if by + ty < input.shape[0] and bx + tx < input.shape[1]:
            tile[ty, tx] = input[by + ty, bx + tx]
        cuda.syncthreads()
        if y < output.shape[0] and x < output.shape[1]:
            output[y, x] = tile[tx, ty]

    # one block per tile, plus one for remainders
    blocks = int(b.shape[0] / tile_height + 1), int(b.shape[1] / tile_width + 1)
    # one thread per tile element
    threads = tile_height, tile_width
    kernel[blocks, threads, stream](a, b)

    return b
Compute the transpose of 'a' and store it into 'b', if given,
    and return it. If 'b' is not given, allocate a new array
    and return that.

    This implements the algorithm documented in
    http://devblogs.nvidia.com/parallelforall/efficient-matrix-transpose-cuda-cc/

    :param a: an `np.ndarray` or a `DeviceNDArrayBase` subclass. If already on
        the device its stream will be used to perform the transpose (and to copy
        `b` to the device if necessary).
    
numba/cuda/kernels/transpose.py