interp_poly op• データ種: points × signal × points → table
• 呼び出し: import fullseye as fs; fs.ledger.interp_scattered(points, values, query, method='linear', fill_value=nan, rescale=False, neighbors=None) (実装を直接呼ぶなら import mathops; mathops.interp_scattered(points, values, query, method='linear', fill_value=nan, rescale=False, neighbors=None)、台帳から引くなら opsmath.get("interp_scattered"))
Values at *query* from scattered samples — sensor nets, boreholes, weather.
:func:interp_linear and :func:interp_cubic need samples on a sorted 1-D
axis. A great deal of measurement does not arrive that way: temperature
sensors bolted wherever a rack allowed, boreholes drilled where access
permitted, weather stations placed by history. This is the N-D scattered
entry point (`scipy.interpolate`), and it returns **how much of the answer
was not interpolation at all**.
*method*:
`"nearest"`
the value of the closest sample. Defined everywhere, and never
overshoots, but it is a staircase: on a smooth field the step itself
becomes a false feature. Measured on a smooth 3-D field sampled at 0.60,
the nearest-neighbour reconstruction leaves a residual of 0.975 units
where the sensor noise is only 0.15 — 6.5 times the noise, and none of
it is noise.
`"linear"`
barycentric interpolation on a Delaunay triangulation. Never exceeds the
surrounding samples, and is undefined outside their convex hull.
`"rbf"`
a thin-plate radial basis function through every sample. Smooth and
defined everywhere, but it overshoots its own nodes: measured on the
same field it returns peaks 1.372 times the sampled height, which is a
37 % over-statement of a hot spot that no interpolation of the data can
justify.
**The point of the `outside` return value.** Sensors sit inside a room, a
site, a country; the corners are always outside their hull. Ask a linear
interpolator there and it returns `fill_value`, or, if a caller quietly
falls back to nearest, it returns a different method's answer under the
first method's name. Measured on a 12 x 8.4 x 3.0 m room sampled at 1.20 m
spacing, 71.2 % of the evaluation grid lay outside the hull. A number
that large has to be visible, so it is returned rather than logged.
Parameters
----------
points : (n, d) array_like
Sample coordinates. 1-D input is accepted and treated as `(n, 1)`.
values : (n,) array_like
query : (m, d) or (..., d) array_like
Where to evaluate. The leading shape is preserved in the result.
method : {"linear", "nearest", "rbf"}
fill_value : float
Returned outside the convex hull for `"linear". "nearest"` and
`"rbf"` are defined everywhere and ignore it.
rescale : bool
Normalise each axis before triangulating. Needed when the axes have very
different units (metres against millimetres); ignored by `"rbf"`.
neighbors : int or None
`"rbf"` only: solve against the *k* nearest samples instead of all of
them. The global solve is O(n^3); measured on 5000 query points in 3-D,
it costs 0.55 / 1.76 / 7.53 s at 1400 / 4000 / 8000 samples, while
`neighbors=48` costs 0.38 / 0.55 / 0.81 s. Below a few thousand
samples the global solve is fine and exact — the knob earns its place
above that. `None` keeps the exact global solution.
Returns
-------
dict
`value (query shape), outside` (bool mask, query shape, of query
points beyond the convex hull of the samples), `outside_fraction`,
`method, n_points`.
Fail-closed: fewer samples than `d + 1` cannot define a simplex, and
raises `ValueError rather than returning a field made of fill_value`.
See also
--------
interp_linear : the sorted 1-D case, which is cheaper and needs no hull.
mathops の全 op は入力を検証してから計算する(黙って通さない):
• **complex 入力は ValueError** — float64 への強制変換は虚部を黙って捨てる(numpy は ComplexWarning だけ出して「もっともらしく間違った」実数を返す)。.real/.imag/abs() を明示するか、複素対応の complexops を使う。
• **masked array(masked 要素あり)は ValueError** — マスクを剥がして下の生値を使う暗黙変換を拒否。埋める/落とすを明示する。
• **NaN/Inf は全入力で ValueError**(件数を明示して拒否 — 結果全体に伝播するため)。
• 形状は厳格: 1-D と 2-D を暗黙昇格・ブロードキャストしない(vector 枠に matrix、matrix 枠に vector は ValueError。reshape を明示する)。
• サイズ上限: 行列を取る op と stat_histogram の bins は mathops.MAX_ELEMENTS(2^26 ≈ 6700 万要素)超で ValueError。
• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。
• poc_datacenter_thermal_field — py -3.11 examples/poc_datacenter_thermal_field.py
• poc_multibeam_bathymetry — py -3.11 examples/poc_multibeam_bathymetry.py
• poc_stockpile_volume — py -3.11 examples/poc_stockpile_volume.py
table を入力に取れる)—
interp_poly)interp_linear · interp_cubic · poly_fit · poly_eval · poly_roots
*Provenance: mathops.py — MATH operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.