interp_poly op• Datenarten: points × signal × points → table
• Aufruf: import fullseye as fs; fs.ledger.interp_scattered(points, values, query, method='linear', fill_value=nan, rescale=False, neighbors=None) (die Implementierung direkt: import mathops; mathops.interp_scattered(points, values, query, method='linear', fill_value=nan, rescale=False, neighbors=None); aus dem Register: opsmath.get("interp_scattered"))
> Für diesen Operator gibt es noch keine Übersetzung. Es folgt der Originaltext unverändert.
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.
Jeder mathops-Operator prüft seine Eingabe vor der Berechnung (nichts rutscht stillschweigend durch):
• **Komplexe Eingaben lösen ValueError aus** — die Umwandlung nach float64 verwirft den Imaginärteil stillschweigend (numpy meldet nur eine ComplexWarning und liefert eine plausibel aussehende, falsche reelle Zahl). Schreiben Sie .real/.imag/abs() explizit oder nutzen Sie complexops.
• **Masked Arrays mit maskierten Elementen lösen ValueError aus** — die implizite Umwandlung, die die Maske abstreift und die Rohwerte darunter verwendet, wird abgelehnt. Geben Sie explizit an, ob gefüllt oder verworfen wird.
• **NaN/Inf löst bei jeder Eingabe ValueError aus** (mit Anzahl abgelehnt — es pflanzt sich durch das gesamte Ergebnis fort).
• Formen sind strikt: 1-D und 2-D werden nie implizit hochgestuft oder gebroadcastet (eine Matrix im Vektor-Slot oder ein Vektor im Matrix-Slot löst ValueError aus; reshapen Sie explizit).
• Größenobergrenze: Operatoren, die eine Matrix nehmen, sowie die stat_histogram-Bins lösen jenseits von mathops.MAX_ELEMENTS (2^26 ≈ 67 Mio. Elemente) ValueError aus.
• Leitfaden zur Familie math_metrology
• Katalog der Beispieldaten (Download-URLs / Lizenzen) — 2-D nutzt skimage.data (BSD/Public Domain) plus synthetische Bilder, 3-D nennt Download-URLs echter Datenquellen (Stanford, PDS, …).
• Herkunft und Literatur der Operatoren — die Quellen der Forschung/Verfahren, auf denen diese Operatorfamilie beruht.
• Der kanonische Algorithmus (Autor, Jahr) und seine Anwendungen stehen im Familienleitfaden oben.
• 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 als Eingabe)—
interp_poly)interp_linear · interp_cubic · poly_fit · poly_eval · poly_roots
*Provenance: mathops.py — MATH Operator-Registry. Diese Notiz wird von tools/opdocs.py md erzeugt (nicht von Hand bearbeiten).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.