Unless noted otherwise, every result above uses unit stride (incx = incy = 1) — the normal case, and the coalesced, best-case GPU access pattern. Real usage sometimes passes a non-unit stride (e.g. operating on a row or column of a larger matrix, where incx = lda), which breaks memory coalescing and costs measurably more. This section sweeps a few representative strides to characterize that cost separately, collapsed below by default — expand a stride to see its table and chart.
stride.dtrmv.c — CUDA / cuBLAS stride-sweep reference script
Transpose sweep
Unless noted otherwise, every result above uses trans = "no-transpose". trans = "transpose" reads A with a cross-thread lda-strided mirror pattern instead of a coalesced one, and the gap grows with n — collapsed below by default, expand a trans value to see its table and chart.
trans.dtrmv.c — CUDA / cuBLAS trans-sweep reference script
Uplo sweep
Unless noted otherwise, every result above uses uplo = "lower". Real workgroups dispatch in increasing index order, so uplo = "upper" front-loads the heaviest rows first (worse — long-running heavy workgroups have nothing to overlap with) while lower back-loads them (better — light rows clear fast, the heavy tail gets full GPU to itself) — collapsed below by default, expand a uplo value to see its table and chart.
uplo.dtrmv.c — CUDA / cuBLAS uplo-sweep reference script
Lda sweep
Unless noted otherwise, every result above uses a tight lda (no padding). Padding the row stride only matters for trans = "transpose" here (swept at both trans values below so that's visible in the data, not just claimed). Collapsed below by default — expand a trans value, then a pad, to see its table and chart.
lda.dtrmv.c — CUDA / cuBLAS lda-sweep reference script
diag sweep
A unit diagonal lets the kernel skip the diagonal load — and for the triangular solve, the reciprocal as well — so any difference here is exactly that skipped work.
diag.dtrmv.c — CUDA / cuBLAS diag-sweep reference script
layout sweep
Column-major swaps the effective m/n and flips the transpose flag internally, changing which axis is contiguous and therefore how the matrix reads coalesce. wgblas-only: cuBLAS is column-major and has no layout argument, so there is no reference curve to compare against.
Benchmark results for dtrmv on Nvidia Geforce Gtx 1650.
Nvidia Geforce Gtx 1650 — wgblas vs cuBLAS
See also
Stride sweep
Unless noted otherwise, every result above uses unit stride (
incx = incy = 1) — the normal case, and the coalesced, best-case GPU access pattern. Real usage sometimes passes a non-unit stride (e.g. operating on a row or column of a larger matrix, whereincx = lda), which breaks memory coalescing and costs measurably more. This section sweeps a few representative strides to characterize that cost separately, collapsed below by default — expand a stride to see its table and chart.Nvidia Geforce Gtx 1650 — stride = 4
Nvidia Geforce Gtx 1650 — stride = 5
Nvidia Geforce Gtx 1650 — stride = 32
Nvidia Geforce Gtx 1650 — stride = 33
Nvidia Geforce Gtx 1650 — stride = 255
Nvidia Geforce Gtx 1650 — stride = 256
See also:
Transpose sweep
Unless noted otherwise, every result above uses
trans = "no-transpose".trans = "transpose"reads A with a cross-threadlda-strided mirror pattern instead of a coalesced one, and the gap grows withn— collapsed below by default, expand atransvalue to see its table and chart.Nvidia Geforce Gtx 1650 — trans = no-transpose
Nvidia Geforce Gtx 1650 — trans = transpose
See also:
Uplo sweep
Unless noted otherwise, every result above uses
uplo = "lower". Real workgroups dispatch in increasing index order, souplo = "upper"front-loads the heaviest rows first (worse — long-running heavy workgroups have nothing to overlap with) whilelowerback-loads them (better — light rows clear fast, the heavy tail gets full GPU to itself) — collapsed below by default, expand auplovalue to see its table and chart.Nvidia Geforce Gtx 1650 — uplo = lower
Nvidia Geforce Gtx 1650 — uplo = upper
See also:
Lda sweep
Unless noted otherwise, every result above uses a tight
lda(no padding). Padding the row stride only matters fortrans = "transpose"here (swept at bothtransvalues below so that's visible in the data, not just claimed). Collapsed below by default — expand atransvalue, then apad, to see its table and chart.Nvidia Geforce Gtx 1650 — trans = no-transpose (8 pads)
pad = 0
pad = 1
pad = 8
pad = 16
pad = 32
pad = 48
pad = 64
pad = 128
Nvidia Geforce Gtx 1650 — trans = transpose (8 pads)
pad = 0
pad = 1
pad = 8
pad = 16
pad = 32
pad = 48
pad = 64
pad = 128
See also:
diag sweep
A unit diagonal lets the kernel skip the diagonal load — and for the triangular solve, the reciprocal as well — so any difference here is exactly that skipped work.
Nvidia Geforce Gtx 1650 — diag = non-unit
Nvidia Geforce Gtx 1650 — diag = unit
See also:
layout sweep
Column-major swaps the effective
m/nand flips the transpose flag internally, changing which axis is contiguous and therefore how the matrix reads coalesce. wgblas-only: cuBLAS is column-major and has no layout argument, so there is no reference curve to compare against.Nvidia Geforce Gtx 1650 — layout = column-major
Nvidia Geforce Gtx 1650 — layout = row-major
See also: