The matrix is built directly on the host in Sliced ELLPACK (SELL) format — the format the Tile kernel actually reads. SELL is the same idea as ELLPACK applied per-slice: rows are grouped into slices of ROWS consecutive rows (sorted by length to minimize padding within a slice) and stored column-major so that the k-th nonzero of every row in the slice occupies a contiguous span of ROWS elements in memory.

Each CTA processes one slice using a 2D tile of shape<ROWS, COLS>:

Dimension 0 (ROWS): the rows of the slice (one tile row per matrix row in the slice)
Dimension 1 (COLS): the next COLS nonzeros of every row in the slice, processed simultaneously

The kernel computes partial products against the x-vector (an irreducible gather), accumulates into a 2D tile, reduces along the column dimension with cuda::tiles::sum(acc, 1_ic) to produce one sum per row, and scatters the per-row sums to y using the slice permutation array.

The sample generates a single random sparse matrix and verifies the Tile kernel's output against a CPU reference SpMV.

Expected Output

Random sparse matrix: rows=100000, cols=100000, nnz=..., avg nnz/row=...
Tile configuration: ROWS=64, COLS=16 (... slices)
Success! Tile SpMV matches the CPU reference.

Prerequisites

CUDA Toolkit version 13.3 or later.
CUDA Driver version 580 or later.
Host compiler with C++20 support.