wasserstein_1d — COLORTRANSPORT `transport` op

• Data kinds: signal × signal → scalar

• Call: import fullseye as fs; fs.ledger.wasserstein_1d(u_values, v_values, p=1, u_weights=None, v_weights=None) (to call the implementation directly, import colortransport; colortransport.wasserstein_1d(u_values, v_values, p=1, u_weights=None, v_weights=None); from the registry, opscolortransport.get("wasserstein_1d"))

Usage

The 1-D p-Wasserstein distance. Exact.

In 1 dimension optimal transport has a closed form: the L^p distance between the inverse cumulative distribution functions -- no iteration or approximation needed. That it agrees exactly with the brute-force assignment problem (scipy.optimize.linear_sum_assignment) is pinned by a test.

Parameters

u_values, v_values : array_like

Samples (flattened to 1 dimension). The lengths may differ.

p : float

The order. p=1 is the Earth Mover distance, p=2 the 2-Wasserstein.

u_weights, v_weights : array_like, optional

Per-sample weights (normalised internally to sum to 1).

Returns

float

Background guides (the physics and conventions behind this op)

• colorimetry — Colorimetry and spectra — colour is fixed only by spectrum × illuminant × observer

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)

• color_transport — py -3.11 examples/color_transport.py

• poc_physarum_transport — py -3.11 examples/poc_physarum_transport.py

Ops the type connects to (they accept `scalar` as input)

—

Same category (`transport`)

transport_plan_1d · sinkhorn · sinkhorn_distance · sinkhorn_divergence

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

wasserstein_1d — COLORTRANSPORT transport op