Execution Pipeline

Why this deserves its own page

GPU SpMV is not just “launch a kernel.” The real engineering story is how the matrix is analyzed, how kernel choice is made, how execution context is reused, and how the result is interpreted with confidence.

Pipeline Breakdown

1. Input stage: load CSR / ELL data structures and prepare the input vector.
2. Analysis stage: compute avg_nnz_per_row, skewness, and row distribution characteristics.
3. Decision stage: choose Scalar CSR, Vector CSR, Merge Path, or ELL.
4. Execution stage: launch the GPU kernel and record timing / bandwidth metrics.
5. Validation stage: compare against CPU reference behavior or established baselines.

Key Decisions

Observation	Decision
avg_nnz_per_row < 4	Scalar CSR to avoid wasting warp-scale resources
Rows are uniform and low-skew	Vector CSR for stronger warp collaboration
Row lengths are highly skewed	Merge Path to prioritize load balance
Row width is nearly fixed	ELL kernel to prioritize coalesced access

Read this together with

• Kernel Selection
• Memory Layout
• Performance Methodology