interp_poly op• 数据种类:signal → roots
• 调用:import mathops; mathops.poly_roots(coeffs, real_only=False, imag_tol=1e-09)(或 opsmath.get("poly_roots"))
多项式的全部根(系数按最高次在前)—— 含复根。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
Roots are the eigenvalues of the companion matrix (`np.roots`); the
polynomial must have degree ≥ 1 and a non-zero leading coefficient
(fail-closed: a zero leading coefficient means the stated degree is a lie —
trim it explicitly rather than have it silently dropped).
Returns complex128, sorted by real part then imaginary part
(deterministic). Complex answers are honest answers: `x² + 1` really does
have roots `±i`, and hiding them would misreport the polynomial. Pass
`real_only=True` to keep only roots whose imaginary part is negligible
(`|imag| <= imag_tol * max(1, |root|)`) and get them back as a sorted
float64 array — possibly empty, which is the correct answer for
`x² + 1`.
Numerical note: root-finding conditioning degrades with degree and with
clustered roots (a double root moves ~`sqrt(eps)` under coefficient
noise — Wilkinson's classic analysis); treat high-degree roots as
approximate. HALCON: no root-finding tuple operator.
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
roots 作为输入)—
interp_poly)interp_linear · interp_cubic · poly_fit · poly_eval
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