cplx_poly_eval — MATH complex op

Data kinds: signal × cpointscpoints

Call: import mathops; mathops.cplx_poly_eval(coeffs, z) (or opsmath.get("cplx_poly_eval"))

Usage

Evaluate a polynomial on the complex plane (Horner, complex-capable).

The complex twin of :func:poly_eval: *coeffs* is highest-power-first

(`[c_d, ..., c_1, c_0]`, possibly complex) and *z* is a complex scalar or

1-D array. A scalar query returns a Python `complex`, an array returns

`complex128 — mirroring :func:poly_eval`'s scalar/array behaviour.

This is what makes the rest of the family usable: sample a polynomial on a

contour from :func:cplx_contour_circle, then count its zeros with

:func:cplx_argument_principle or reconstruct interior values with

:func:cplx_cauchy_value. (:func:poly_eval refuses complex input by

design — silent imaginary-part truncation — so it cannot serve here.)

Raises `ValueError`: empty/multi-dimensional *coeffs*, non-finite or

masked input, over-cap size, and — the honest one — a result that

overflowed to Inf/NaN (a degree-200 polynomial on `|z| = 10` genuinely

exceeds float64 range; that is refused rather than returned as `inf`).

HALCON: no complex polynomial operator.

Family-wide input contract (fail-closed)

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).

Detailed usage guide

math_metrology family guide

References (sample data, literature)

• 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.

Runnable examples (verified samples that actually call this op)

math_complexpy -3.11 examples/math_complex.py

Ops the type connects to (they accept cpoints as input)

cplx_contour_integral · cplx_winding_number · cplx_cauchy_value · cplx_argument_principle · cplx_laurent_coeffs · cplx_joukowski · cplx_mobius

Same category (complex)

cplx_contour_circle · cplx_contour_integral · cplx_winding_number · cplx_cauchy_value · cplx_argument_principle · cplx_laurent_coeffs · cplx_joukowski · cplx_mobius


*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.