Single-pass LSMR iterations and sorted observation layout - #86
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- Keep the Golub-Kahan u unnormalized, folding 1/beta into the scalar recurrences, so the gather A'u can be accumulated in the same loop that builds u (linearity: A'(u/beta) = (A'u)/beta) - bidiag_forward!: scatter of every block, the norm, and (when all blocks have per-thread buffers) the gathers in one pass over u; generic mul!-based fallback keeps the GPU extensions working - lsmr! now requires x = 0 on entry (both solvers already pass it)
- Sort observations by the block with the largest coefficient tile when it outgrows the cache: its coefficient accesses stream instead of scatter, and its gather runs race-free without per-thread buffers at any cardinality (SortedGather), inside the fused single-pass iteration - Metal: launch kernels asynchronously with one host wait per LSMR iteration, and pick threadgroup widths from each compiled pipeline - CUDA/Metal: fused bidiagonalization kernel (all scatters plus the norm in one launch), with the cross-block norm reduced without Float32 drift - Store the A'u workspace on the solvers instead of allocating per solve
benchmark.jl defines each problem once (simple, hard worker-firm, interacted, three-way, large-cardinality sorted) and runs 6 columns through one solver on cpu, Metal, and CUDA, with measured timings as comments; replaces the previous per-topic benchmark scripts.
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lsmr!so each iteration runs one fused pass over the observations (bidiag_forward!).