complex opcpoints × cpoints → cscalarimport fullseye as fs; fs.ledger.cplx_contour_integral(z, fz) (実装を直接呼ぶなら import mathops; mathops.cplx_contour_integral(z, fz)、台帳から引くなら opsmath.get("cplx_contour_integral"))Closed contour integral ∮ f(z) dz by the chordal trapezoidal rule.
z are the contour vertices (closing segment implicit, see
:func:cplx_contour_circle) and fz the function sampled at exactly those
points — the op never calls back into Python, so any f is allowed as
long as you can sample it. The quadrature is
sum_k (f_k + f_{k+1})/2 * (z_{k+1} - z_k), i.e. the trapezoidal rule
along the chords; it is exact for a piecewise-linear integrand and second
order otherwise.
Ground truth it reproduces: f = 1/(z - a) around a circle enclosing
a integrates to 2*pi*i (Cauchy); measured on the unit circle with
a = 0, the relative error is 1.0e-4 at n = 256 and
6.3e-6 at n = 1024 — a factor 16.0 for 4x
refinement, i.e. the O(n^-2) rate, not the spectral accuracy the
trapezoid rule enjoys when applied in the angle parameter. That difference
is the honest price of accepting an arbitrary point list instead of a
parametrisation.
Orientation follows the sample order: a clockwise contour returns the negative of the counter-clockwise one.
Raises ValueError: fewer than 3 points, len(z) != len(fz), a
degenerate contour (all points coincide), non-finite/masked input, or a sum
that overflowed (|f| near a pole on the path).
HALCON: no operator (contour integration is not part of its tuple/XLD API).
mathops の全 op は入力を検証してから計算する(黙って通さない):
ValueError — float64 への強制変換は虚部を黙って捨てる(numpy は ComplexWarning だけ出して「もっともらしく間違った」実数を返す)。.real/.imag/abs() を明示するか、複素対応の complexops を使う。ValueError — マスクを剥がして下の生値を使う暗黙変換を拒否。埋める/落とすを明示する。ValueError(件数を明示して拒否 — 結果全体に伝播するため)。ValueError。reshape を明示する)。stat_histogram の bins は mathops.MAX_ELEMENTS(2^26 ≈ 6700 万要素)超で ValueError。py -3.11 examples/math_complex.pypy -3.11 examples/representation_conversion.pycscalar を入力に取れる)—
complex)cplx_contour_circle · cplx_poly_eval · cplx_winding_number · cplx_cauchy_value · cplx_argument_principle · cplx_laurent_coeffs · cplx_joukowski · cplx_mobius
Provenance: mathops.py — MATH operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.