Code and data for Retraction-Based Stability Bounds for Grassmann Optimization under Geometric Perturbations

Replication package for the paper "Retraction-Based Stability Bounds for Grassmann Optimization under Geometric Perturbations" by Pascal Kubwimana, B. Prabhakar Reddy and Jason M. Mkenyeleye (Department of Mathematics and Statistics, University of Dodoma). The paper derives an exact second-order comparison of the polar and QR retractions on the Grassmann manifold, showing that the polar quadratic drift term cancels identically while the QR term does not, and uses this to obtain a curvature-aware step-size stability threshold together with deterministic convergence and finite-time bounds under exact gradients. This archive contains the complete implementation, the random seeds, and the generated data behind every numerical result reported in the paper. Contents Implementation of the polar and QR retractions, the directional curvature factor, and the gradient-descent driver used throughout Section 6. full_results.csv (4,200 rows) — per-cell output of the Hopkins 155 motion-segmentation sweep of Section 6.7, covering both retractions across the step-size multipliers, with six random initializations per cell. Per-cell drift tables underlying the independent replication under generic tangent directions (Section 6.4) and the codimension-symmetry sweep (Section 6.6). Numerical verification of the expansion coefficients of Lemma 4.1. All random seeds and parameter settings, sufficient to reproduce the synthetic experiments of Sections 6.1–6.6 exactly. Reproducibility The full experimental protocol, including parameter settings and random-seed handling, is specified in Section 6 of the paper; all synthetic experiments are reproducible from that specification alone. The real-data study uses the publicly available Hopkins 155 motion-segmentation benchmark, which is not redistributed here and must be obtained from its original source. This version corresponds to the results as reported in the submitted manuscript and is fixed; it will not be amended.