wegamekinglc / Derivatives-Algorithms-Lib / 33946185017

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Skip Krylov iteration from an already-converged initial guess (#340)

curve_calibration_perf's APPROXIMATE case crashed with "CGSolve: numerical
breakdown: direct residual confirmation". Trace evidence: the failing penalty
solve started with ||b||=0.177, already far inside the caller's absolute
tolerance (sqrt(24)~=4.9), but CG — unlike BCG, which gained the initial
convergence short-circuit in #261 — iterated anyway. On the numerically
singular W+JtJ system (residuals scaled by 1/1e-10 swamp the smoothing
weights) the first alpha explodes along the near-null direction (residual
0.177 -> 139), the recursive and direct residuals decouple, and the DAL-64
confirmation guard fired on the marginal mismatch.

Return early for both solvers when the initial guess already satisfies the
requested tolerance: the guess is by definition an acceptable answer, and
refining it on a degenerate system is what produced the explosion. This also
makes a zero QP step reachable, exposing a latent secant-update bug: a zero
step made InnerProduct(dx,dx)=0 poison the Jacobian with NaN (0/0), surfacing
later as "CGSolve: non-finite input: b". Skip secant updates for zero steps in
both Jacobian implementations — a zero step carries no secant information.

Extend the initial-convergence count test, previously BCG-only, to CG.

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