Improve root-finding convergence with bisection and log-scale formulation - #38
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Summary of Changes
polyfc: Replaced unconstrained Levenberg-Marquardt withoptimistix.Bisectionon the bounded domain[0, Phi_max]. Because the residual function is strictly monotonic and bounded, this provides guaranteed 100% convergence with no overshooting or domain errors.polyc: UpdatedReq_polycto solve forlog(Req)using the log-ratio residuallog(Req + Rbound) - log(Rtot). This prevents negative receptor concentrations during intermediate iterations and stabilizes gradients across wide dynamic ranges.Req_solve: Initialized the solver with the 1:1 binding equilibrium estimate instead of a zero vector, starting the solver near the true root and reducing iterations.valentbind/test/test_edge_cases.pycovering high-affinity/high-valency multivalent mixtures (f=12, wide affinity ranges).All 16 unit tests, static type checks (
make ty), and Ruff lint/formatting checks pass.