AI 中文总结
anyakrakusuma库用对数域Sinkhorn - Knopp迭代解决离散静态薛定谔桥问题，重建点云间熵插值。经四个理想化平面案例测试，该方法在特定参数下效果良好，残差小，能恢复重新定向，为相关研究提供了有效工具。
AI 中文摘要
我们展示了anyakrakusuma，一个开源Python库，它通过对数域Sinkhorn - Knopp迭代解决离散静态薛定谔桥问题（最优传输的熵正则化对应问题），并重建两个经验点云之间的熵插值。求解器与诊断管道配对，通过信息论和几何度量来表征最优耦合和中间分布。我们在四个理想化平面案例上测试该库，涵盖圆到圆的扩张、螺旋到混合的碎片化、两个卫星的刚性重新定向以及利萨如曲线到三叶结的变形。对数域公式在研究的参数下是必要的，在成本与正则化比率达到400且吉布斯核在其大部分范围内下溢双精度的情况下，迭代在每种情况下仍达到$10^{-9}$的边际残差和单位边际保真度。残差历史在每次迭代收缩因子介于$0.966$和$0.976$之间时，在大约八个数量级上几何衰减，这些是定点附近的局部速率，比最坏情况的希尔伯特度量界低多个数量级。协方差分析在主轴不可观测的近各向同性的掩蔽区间内，将施加的90度重新定向恢复到$0.07^\circ$以内，大约比其不确定性小40倍。报告诊断时明确关注每个诊断定义良好的区域，包括仅在开放插值区间有意义微分熵。所展示的案例是构建而非测量的；对经验点云的定量应用需要进一步研究。
英文摘要
We present anyakrakusuma, an open-source Python library that solves the discrete static Schrödinger bridge problem, the entropically regularized counterpart of optimal transport, through a log-domain Sinkhorn--Knopp iteration and reconstructs the entropic interpolation between two empirical point clouds. The solver is paired with a diagnostic pipeline that characterizes the optimal coupling and the intermediate distributions through information-theoretic and geometric measures. We exercise the library on four idealized planar cases spanning a circle-to-circle dilation, a spiral-to-mixture fragmentation, a rigid reorientation of two moons, and a Lissajous-to-trefoil deformation. The log-domain formulation is necessary rather than merely convenient at the parameters studied, where the cost-to-regularization ratio reaches four hundred and the Gibbs kernel underflows double precision across most of its range; the iteration nonetheless attains a marginal residual of $10^{-9}$ and unit marginal fidelity in every case. Residual histories decay geometrically over approximately eight decades at per-iteration contraction factors between $0.966$ and $0.976$, which are local rates near the fixed point that lie many orders of magnitude below the worst-case Hilbert-metric bound. The covariance analysis recovers an imposed ninety-degree reorientation to within $0.07^\circ$, roughly forty times smaller than its uncertainty, across a masked interval of near-isotropy on which the principal axis is unobservable. The diagnostics are reported with explicit attention to the regimes in which each is well defined, including the differential entropy, which is meaningful only on the open interpolation interval. The presented cases are constructed rather than measured; quantitative application to empirical point clouds requires further study.
Comments22 pages, 4 figures, 5 tables
