conv_observed_order — CONVERGE `verification` op

• 数据种类:无 → table(仅由参数决定的算子 —— 不接受图像或数据输入)

• 调用: import fullseye as fs; fs.ledger.conv_observed_order(phi=None, h=None, r=None, n_cells=None, dim=None) -> 'dict'(要直接调用实现,import converge; converge.conv_observed_order(phi=None, h=None, r=None, n_cells=None, dim=None) -> 'dict';从台账取用则 opsconverge.get("conv_observed_order"))

用法

由三个系统加密的解求表观收敛阶 p（Celik 等 2008，式 3）。

> 以下的详细说明为原文 —— 摘要与标题已翻译。

phi = (phi1, phi2, phi3) on grids 1 (finest) .. 3 (coarsest). The refinement is given by exactly one of h = (h1, h2, h3) representative cell sizes, r = (r21, r32) with r21 = h2/h1 and r32 = h3/h2, or n_cells = (N1, N2, N3) with dim (h from Celik eqs. (1)-(2)). With eps32 = phi3 - phi2 and eps21 = phi2 - phi1 (Step 3):

p = |ln|eps32/eps21| + q(p)| / ln(r21) (3a)

q(p) = ln((r21^p - s) / (r32^p - s)) (3b)

s = sign(eps32 / eps21) (3c)

solved by fixed-point iteration from the first term (q = 0) with iterate_fixed_point (plain, as the paper prescribes; |p_k+1 - p_k| <= 1e-13, at most 1000 steps). q = 0 when r is constant. s = -1 flags oscillatory convergence (reported, not refused — Celik keeps the absolute values so the extrapolation goes toward h = 0).

Refusal: eps21 or eps32 "very close" to zero (|eps| <= 1e-12 * max|phi|) — Celik: the procedure does not work there (oscillation or an exact solution; refine further) — and a fixed-point iteration for p that does not converge.

Defaults: the first column of Celik et al. 2008 Table 1 (p = 1.53).

详细使用指南

• convergent_computation 族使用指南

参考(示例数据、文献)

• 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。

可运行的示例(实际调用该算子并已验证的样例)

• (暂无)

类型可衔接的下一个算子(可接受 `table` 作为输入)

—

同类别(`verification`)

conv_gci

*Provenance: converge.py — CONVERGE 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*

conv_observed_order — CONVERGE verification op

用法