interp_poly op• 데이터 종류: points × signal × points → table
• 호출: import fullseye as fs; fs.ledger.interp_scattered(points, values, query, method='linear', fill_value=nan, rescale=False, neighbors=None)(구현을 직접 호출하려면 import mathops; mathops.interp_scattered(points, values, query, method='linear', fill_value=nan, rescale=False, neighbors=None), 원장에서 가져오려면 opsmath.get("interp_scattered"))
> 이 연산자의 설명은 아직 번역이 없습니다. 원문을 그대로 싣습니다.
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 의 모든 연산자는 입력을 검증한 뒤에 계산합니다(조용히 통과시키지 않습니다):
• **complex 입력은 ValueError** —— float64 로의 강제 변환은 허수부를 조용히 버립니다(numpy 는 ComplexWarning 만 내고 「그럴듯하게 틀린」 실수를 돌려줍니다). .real/.imag/abs() 를 명시하거나 복소수를 다루는 complexops 를 쓰세요.
• **masked 요소가 있는 masked array 는 ValueError** —— 마스크를 벗겨 아래 원값을 쓰는 암묵 변환을 거부합니다. 채울지 버릴지를 명시하세요.
• **NaN/Inf 는 모든 입력에서 ValueError**(개수를 명시하고 거부 —— 결과 전체로 전파되므로).
• 형상은 엄격: 1-D 와 2-D 를 암묵적으로 승격·브로드캐스트하지 않습니다(vector 슬롯에 matrix, matrix 슬롯에 vector 는 ValueError. reshape 를 명시하세요).
• 크기 상한: 행렬을 받는 연산자와 stat_histogram 의 bins 는 mathops.MAX_ELEMENTS(2^26 ≈ 6700 만 요소)를 넘으면 ValueError.
• 샘플 데이터 카탈로그(DL URL / 라이선스) —— 2-D 는 skimage.data(BSD/public)+ 합성, 3-D 는 실데이터 소스(Stanford/PDS 등)의 DL URL.
• 연산자의 내력·참고문헌 —— 이 연산자 족의 바탕이 된 연구/기법의 출처.
• 알고리즘의 정전(저자·연도)과 용도는 위의 패밀리 사용 가이드에 적혀 있습니다.
• 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 를 입력으로 받는 것)—
interp_poly)interp_linear · interp_cubic · poly_fit · poly_eval · poly_roots
*Provenance: mathops.py — MATH 연산자 레지스트리. 이 op 노트는 tools/opdocs.py md 가 자동 생성합니다(직접 편집하지 마세요).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.