ENH: Eigen-backed Levenberg-Marquardt; remove netlib MINPACK

[hjmjohnson]

Migrates the Levenberg-Marquardt path from the vendored netlib MINPACK to Eigen's MINPACK-port Levenberg-Marquardt (unsupported/Eigen/NonLinearOptimization), part of the ITKv7 VNL→Eigen numerics direction (#6403, #6230). itk::LevenbergMarquardtOptimizer is now Eigen-backed, vnl_levenberg_marquardt is auto-routed to the same Eigen engine with its public API unchanged, and the now-unused netlib minpack/ sources are deleted.

Both engines are MINPACK lmdif/lmder ports, so the result is numerically equivalent (residuals agree to machine precision on every converged problem) while Eigen is faster.

Note

Direct downstream callers of vnl_levenberg_marquardt are unaffected. The public header is unchanged; the only direct consumer found across the build forest — Plastimatch's RANSAC SphereParametersEstimator (SlicerRT) — compiles, links, and runs unchanged against this branch (verified locally).

Important

This is an ITK-vendored-only divergence from upstream VXL: itkvnl_algo gains a header-only Eigen3 dependency that cannot be carried to standalone VXL (which has no Eigen), and the netlib deletion cannot stand alone in VXL either. UpdateFromUpstream must re-apply the whole change on each VXL/Eigen re-sync. No change is pushed to the vxl extraction fork.

What changed (3 commits)

1. COMP: Vendor Eigen unsupported modules — NonLinearOptimization, LevenbergMarquardt, NumericalDiff under itkeigen/unsupported/, registered in UpdateFromUpstream.sh, with install rules. Verified MPL2-clean (compiles under EIGEN_MPL2_ONLY, which CI enables).
2. ENH: Eigen-backed L-M for itk::LevenbergMarquardtOptimizer — a narrow, Eigen-free engine interface (itkEigenLevenbergMarquardtEngine, raw-pointer residual/Jacobian callbacks; no Eigen in the header per ENH: Master tracking — Eigen3 third-party design for ITK 6.x #6230) driven through the existing MultipleValuedVnlCostFunctionAdaptor. GetOptimizer()/InternalOptimizerType retained behind itkLegacyMacro (GetOptimizer() returns nullptr). New GoogleTest (Rosenbrock ±Jacobian, linear least-squares); legacy test drives the optimizer through its own API.
3. COMP: Re-back vnl_levenberg_marquardt on Eigen; remove netlib MINPACK — public API preserved verbatim (minimize*, MINPACK return codes, iteration/eval counts, start/end RMS, diagnose_outcome, get_JtJ via the R-factor + permutation from the Eigen solve). Deletes the 9 netlib minpack/ routines (sole consumer was vnl_levenberg_marquardt).

Performance / accuracy gate

Conditioning sweep (exponential-sum least squares; single-threaded, Release, median of N reps), Eigen vs netlib through the same optimizer:

• Speed: Eigen faster in every case (~10–45%), equal-or-fewer iterations.
• Accuracy: equivalent — on every converged problem the residuals agree to machine precision (e.g. at cond(J) ≈ 1.6e16: 4.460e-9 vs 4.460e-9), with identical convergence behavior. Cases where a naive benchmark suggested a difference were traced to a too-small iteration cap on a numerically-singular (cond ≈ 1e17) problem where both engines fail to converge — not an accuracy difference.

Validated locally: full ITK build (0 failures), all 24 vnl_algo tests, vnl_algo_test_levenberg_marquardt, the ITK optimizer GoogleTest + legacy test, and the Plastimatch-usage compile/link/run.

[hjmjohnson]

Downstream validation (Plastimatch): the Eigen L-M migration + netlib-MINPACK deletion builds and runs correctly in Plastimatch (radiotherapy registration), a real consumer with a direct vnl_levenberg_marquardt call site. Its bundled RANSAC sphere-estimator unit test — which drives vnl_levenberg_marquardt via GeometricLeastSquaresEstimate — now executes and passes against this branch, and the full test suite passes 579/579.

Why Plastimatch is a meaningful target

• libs/ransac/SphereParametersEstimator.txx calls vnl_levenberg_marquardt directly — the exact symbol this PR re-backs onto Eigen after deleting netlib MINPACK.
• Plastimatch does not use itk::LevenbergMarquardtOptimizer itself (it wires LBFGS/LBFGSB, RegularStepGradientDescent, Amoeba, versor optimizers), so the itk:: class is not runtime-exercised here; the vnl_levenberg_marquardt path is now both compile- and runtime-validated, and the broader ITKOptimizers/registration framework is runtime-validated.

Direct vnl_levenberg_marquardt runtime coverage (now executing)

Plastimatch ships libs/ransac/Testing/SphereParametersEstimatorTest.cxx but never builds it (upstream doesn't add_subdirectory the RANSAC test dir, and nothing else instantiates the template). Registering it in ctest makes the L-M path actually run. It fits a sphere through noisy synthetic points and compares the geometric (L-M) estimate to ground truth in 2D/3D/4D:

Geometric least squares estimate [c,r]:
        [-977.61, -887.49, 652.87, 621.13, 399.56]
         Distance between estimated and known sphere centers [0=correct]: 0.54
         Difference between estimated and known sphere radius [0=correct]: 0.11
ransac-sphere-estimator .......... Passed

(First real compilation of SphereParametersEstimator.h also surfaced an unrelated modern-ITK gap — itkNewMacro(Self) now needs a trailing ; — which is a Plastimatch-side fix, not an ITK regression.)

Full test results — 579/579, 0 failed, 0 skipped

Built against this branch's ITK (USE_SYSTEM_ITK, ccache) in the itk_forest_build_testbed; ran the full Plastimatch ctest suite:

100% tests passed, 0 tests failed out of 579

No tests reported Not Run / Skipped / Disabled. The ITK-registration family ran with real timings on synthetic phantoms and matched committed baselines (-stats + -check):

Test	Optimizer exercised	Result
plm-reg-itk-translation	versor / RegularStepGradientDescent	Passed
plm-reg-itk-rigid-a	versor rigid	Passed
plm-reg-itk-similarity	similarity	Passed
plm-reg-itk-bspline	LBFGS / LBFGSB	Passed
plm-reg-itk-demons (+ diff/logd/sym-logd)	demons	Passed
ransac-sphere-estimator	vnl_levenberg_marquardt	Passed

[dzenanz]

Looks good on a quick glance.