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Polish weakly joined clusters in the PowerMean soft covers - #105
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Balancing rows and columns determines the log products across a cluster of rows and columns joined to the rest of the support only by entries of weight w (r^p) to about max(tol, eps)/w, so rescaling A by exact powers of two changed the products of the PowerMean soft covers by up to O(1) across the weakest joins. After the Newton steps converge, the solver now polishes the cover: clusters are the components of the entries above thresholds spaced a factor of 10 apart in weight, and each cluster is shifted to its exact 1-D minimizer over its joining entries, swept Gauss-Seidel per level, finest first, alternating two hierarchies offset by half a level. The Newton test is checked again afterwards, so the returned cover still satisfies it. The asymmetric and symmetric solvers share the polish through the double cover of the symmetric support. On four SuiteSparse Jacobians the products now agree between presentations to 1e-13 or better at p = 1, 2, 4, 8; on problems without weak joins the polish is one no-op pass. `soft_cover` and `soft_symcover` gain `maxpolish` (default 100) bounding the polish passes, and `PowerMeanStats` gains `shift`, the largest cluster shift of the last pass, which reports the residual when the budget runs out (with a warning). Assisted-by: Claude Fable 5.1 <noreply@anthropic.com> Assisted-by: Claude Opus 5.5 <noreply@anthropic.com>
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Balancing rows and columns determines the log products across a cluster joined to the rest of the support only by entries of weight w to about max(tol, eps)/w, so rescaling by powers of two changed the products of the PowerMean soft covers by up to O(1) across the weakest joins. After the Newton steps converge, the solver now polishes those clusters by exact shifts over a hierarchy of weak joins, then re-checks the Newton test.
On four SuiteSparse Jacobians the products agree between presentations to 1e-13 or better at p = 1, 2, 4, 8; problems without weak joins pay one no-op pass. New:
maxpolishkeyword,shiftfield inPowerMeanStats, and a warning when the polish budget ends unsettled.Assisted-by: Claude Fable 5.1 noreply@anthropic.com