interp_poly op• Data kinds: signal × signal → table
• Call: import fullseye as fs; fs.ledger.poly_fit(x, y, degree) (to call the implementation directly, import mathops; mathops.poly_fit(x, y, degree); from the registry, opsmath.get("poly_fit"))
Least-squares polynomial fit with its conditioning on the record.
Fits y ≈ c[0] x^d + ... + c[d] (coefficients highest-power-first, the poly_eval / np.polyval convention) by SVD least squares on the Vandermonde matrix. *degree* must be an integer >= 0 with at least degree + 1 samples (fail-closed: an exactly-determined fit is allowed, an under-determined one is not).
Returns a dict — the fit and its health, inseparable:
coeffs (degree + 1,) float64 · degree · cond the Vandermonde condition number (mat_cond of the design matrix) · rms_residual root-mean-square of y - p(x).
The conditioning mechanism: when cond > POLY_COND_WARN (1e10) a RuntimeWarning is emitted *and* the number is in the result — an equispaced degree-10 fit on raw pixel coordinates is already past it. High degree on a raw coordinate range is the classic double trap: the Vandermonde columns become near-collinear (digits lost, coefficients unstable) and the fit oscillates between nodes (Runge phenomenon, Runge 1901). Centre and scale x to [-1, 1] first, or keep degree ≤ ~6.
HALCON: no public polynomial-fitting tuple operator (fitting of this kind lives inside HALCON's calibration internals).
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
• poc_strain_history — py -3.11 examples/poc_strain_history.py
• poc_thermal_radiometry — py -3.11 examples/poc_thermal_radiometry.py
• signal_filter — py -3.11 examples/signal_filter.py
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
interp_poly)interp_linear · interp_cubic · interp_scattered · 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.