interp_poly op• Data kinds: signal × signal × signal → signal
• Call: import mathops; mathops.interp_cubic(x, y, xq, out_of_range='raise', bc_type='not-a-knot') (or opsmath.get("interp_cubic"))
Cubic-spline interpolation (`scipy.interpolate.CubicSpline`).
C²-smooth through all nodes — the step up from :func:interp_linear when
the underlying curve is smooth (a lens-distortion or gamma curve). Needs at
least 4 points. *bc_type* is the boundary condition: `'not-a-knot'`
(default — reproduces a global cubic polynomial *exactly*, the property the
tests pin), `'natural'` (zero second derivative at the ends; slightly
smoother-looking, but it will NOT reproduce a cubic), or `'clamped'`.
Same strict grid and the same explicit *out_of_range* policy as
:func:interp_linear ('raise' by default, 'clamp' to hold end values) —
spline extrapolation diverges cubically and is refused outright.
Honest note: between nodes a spline can overshoot (it is a minimum-
curvature interpolant, not shape-preserving); for monotone data whose
interpolant must stay monotone, use a PCHIP-type method instead — not
provided here, stated so nobody assumes otherwise.
HALCON: no cubic tuple interpolation operator (`create_funct_1d_pairs`
feeds linear interpolation only).
Every mathops op validates its input before computing (nothing slips through silently):
• **complex input raises ValueError** — coercing to float64 silently discards the imaginary part (numpy only emits a ComplexWarning and returns a plausible-looking wrong real number). State .real/.imag/abs() explicitly, or use complexops, which handles complex data.
• **masked arrays with masked elements raise ValueError** — the implicit conversion that peels off the mask and uses the raw values underneath is refused. Say explicitly whether to fill or to drop.
• **NaN/Inf raises ValueError on every input** (refused with the count stated — it propagates through the whole result).
• Shapes are strict: 1-D and 2-D are never implicitly promoted or broadcast (a matrix in a vector slot, or a vector in a matrix slot, raises ValueError; reshape explicitly).
• Size cap: ops that take a matrix, and the stat_histogram bins, raise ValueError beyond mathops.MAX_ELEMENTS (2^26 ≈ 67 million elements).
• 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.
• math_metrology — py -3.11 examples/math_metrology.py
signal as input)mat_solve · mat_lstsq · stat_describe · stat_histogram · stat_zscore · interp_linear · poly_fit · poly_eval
interp_poly)interp_linear · poly_fit · poly_eval · poly_roots
*Provenance: mathops.py — MATH 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.