numerics op• Data kinds: signal × signal → table
• Call: import fullseye as fs; fs.ledger.integrate_hamiltonian(q0, p0, dt: 'float' = 0.05, n_steps: 'int' = 1000, *, system: 'str' = 'harmonic', method: 'str' = 'verlet', **params) -> 'dict' (to call the implementation directly, import mathnumerics; mathnumerics.integrate_hamiltonian(q0, p0, dt: 'float' = 0.05, n_steps: 'int' = 1000, *, system: 'str' = 'harmonic', method: 'str' = 'verlet', **params) -> 'dict'; from the registry, opsmath.get("integrate_hamiltonian"))
> This operator's description has not been translated yet. The original text follows as it is.
名前つきのハミルトン系(質量 1)を時間積分する。返り値 `{"t","q","p","energy","energy_drift"}`。
`method`:
• `"verlet"` —— 速度 Verlet(シンプレクティック・時間反転対称)。エネルギー誤差は O(dt²) で有界のまま
振動し、長時間でも増えない。dt を負にして回すと元の状態に(丸め誤差まで)戻る。
• `"euler"` —— 陽的 Euler(比較用の失敗例)。調和振動子ではエネルギーが毎ステップ (1 + ω²dt²) 倍に増え、
位相空間で外向きの渦巻きになる。
• `"rk4"` —— 古典的 4 次 Runge–Kutta。短時間はとても正確だが、シンプレクティックではないので
エネルギーは長時間でゆっくり減り続ける(有界ではない)。
`system: "harmonic"(omega)/ "pendulum"(omega)/ "kepler"`(mu、2-D)。
門: Verlet のエネルギー誤差が有界 / 時間反転で戻る / Euler の増幅率が (1 + ω²dt²)^n。
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.
• numerics_tour — py -3.11 examples/numerics_tour.py
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
numerics)erf · erfc · bessel · gauss_quadrature · gauss_cubature · chebyshev_coeffs_nd · chebyshev_eval_nd · low_discrepancy
*Provenance: mathnumerics.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.