Optimize the Memory Accesses of a GPU Matrix Transpose

Analyze and improve a GPU matrix-transpose kernel. For a row-major matrix, a naive mapping often makes either reads or writes contiguous across neighboring lanes, while the other side becomes strided.

Constraints & Assumptions

The original ROCm kernel listing is not supplied. Use this self-contained practice model: input A has R rows and C columns in row-major order, and output B has C rows and R columns with B[col,row] = A[row,col]. Explain a tiled implementation using explicitly shared scratchpad memory. Tile dimensions must fit the target device's thread and memory limits.

Clarifying Questions

Which index varies across adjacent lanes? What transaction/coalescing rules and scratchpad bank organization apply? Are dimensions multiples of the tile size? Are input and output distinct allocations?