interp_poly op• 数据种类:signal × signal → table
• 调用: import fullseye as fs; fs.ledger.poly_fit(x, y, degree)(要直接调用实现,import mathops; mathops.poly_fit(x, y, degree);从台账取用则 opsmath.get("poly_fit"))
最小二乘多项式拟合,并记录其条件数。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
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).
mathops 的每个算子都先校验输入再计算(不让任何东西无声通过):
• complex 输入一律 ValueError —— 强制转成 float64 会无声丢掉虚部(numpy 只发一个 ComplexWarning,然后返回一个「看着合理却是错的」实数)。请显式写出 .real/.imag/abs(),或改用支持复数的 complexops。
• 含被掩元素的 masked array 一律 ValueError —— 拒绝「剥掉掩码直接使用下面原值」的隐式转换。请显式选择填充还是丢弃。
• 所有输入中的 NaN/Inf 一律 ValueError(明确给出个数后拒绝 —— 它会污染整个结果)。
• 形状严格:不对 1-D 与 2-D 做隐式提升或广播(向量槽位收到矩阵、矩阵槽位收到向量都是 ValueError;请显式 reshape)。
• 尺寸上限:接受矩阵的算子与 stat_histogram 的 bins,超过 mathops.MAX_ELEMENTS(2^26 ≈ 6700 万个元素)即 ValueError。
• 示例数据目录(下载 URL / 许可证) —— 2-D 用 skimage.data(BSD/公有领域)加合成图,3-D 给出真实数据源(Stanford/PDS 等)的下载 URL。
• 算子来历与参考文献 —— 该算子族所依据的研究/方法出处。
• 算法的正典(作者、年份)与用途见上面的族使用指南。
• 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 作为输入)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
interp_poly)interp_linear · interp_cubic · interp_scattered · poly_eval · poly_roots
*Provenance: mathops.py — MATH 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.