treedater

New features

• **Sparse node-time solver (clsSolver = "sparse"), now the default.** The temporally-constrained least-squares step that estimates internal-node times is now solved with a sparse tree-Laplacian **Goldfarb–Idnani dual active-set** instead of forming and solving a dense quadratic program. Each step applies L⁻¹ to one constraint column (an O(n) sparse solve) and updates a small dense Schur factor. End-to-end this is roughly 6× faster than the dense solver on a real 1,000-tip relaxed-clock fit and ~15× at 2,000 tips, while returning numerically identical estimates (tMRCA/rate agree with the dense solver to ~1e-8 or better). Because it is a *dual* method, it also converges on **degenerate** constraint sets — many linearly-dependent binding constraints, common on large, non-clock-like trees — by exchanging constraints, where the earlier primal active-set had to fall back to the dense quadprog solver (e.g. ~14× faster than that fallback at 4,000 tips). The dense solver is available as clsSolver = "quadprog", and "mgcv" is unchanged. The sparse path requires the **Matrix** package (a recommended package shipped with R) and falls back to "quadprog" automatically if it is unavailable or fails, so a result is always produced. See notes/sparse-active-set.md for details.