cross_covariance_reproducible — DRIVE ozaki op

• Data kinds: points × points → matrix

• Call: import fullseye as fs; fs.ledger.cross_covariance_reproducible(P, Q, tol: 'float' = 1.1102230246251565e-16) (to call the implementation directly, import ozakimm; ozakimm.cross_covariance_reproducible(P, Q, tol: 'float' = 1.1102230246251565e-16); from the registry, opsdrive.get("cross_covariance_reproducible"))

Usage

Returns the Kabsch / ICP cross-covariance H = (P − P̄)ᵀ (Q − Q̄) (3×3) with bits independent of the point order.

The mean uses math.fsum (correctly rounded sum), centring is element-wise, and the contraction is matmul_reproducible. P and Q are (N, 3) (N ≥ 3) corresponding row by row. Accuracy is on the same level as FP64 products (per element tol · (|P−P̄|ᵀ|Q−Q̄|)_ij + a few ulp).

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

Runnable examples (verified samples that actually call this op)

• poc_reproducible_icp — py -3.11 examples/poc_reproducible_icp.py

Ops the type connects to (they accept matrix as input)

world_camera · lidar_scan · relative_motion · foe_from_motion · flow_from_depth_motion · ttc_truth · world_materials · mesh_signed_volume

Same category (ozaki)

matmul_ozaki · matmul_reproducible · ozaki_error_bound · kabsch_reproducible · fp64_emulation_probe

*Provenance: ozakimm.py — DRIVE operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.