ENH: Add vnl_svd engine coverage as itkVnlSVDEngineGTest

[hjmjohnson]

Adapt the vxl core/vnl/algo/tests/test_svd.cxx cases as an ITK GoogleTest (itkVnlSVDEngineGTest) so vnl_svd behavior is exercised directly in ITK CI. ITK relies on vnl_svd throughout registration and reconstruction, but the vxl test that covers its engine never runs in ITK's build; this makes any future change to the underlying SVD engine (or migration off vnl_svd) reviewable against an in-tree regression net.

Coverage

Six cases across float / double / complex-float / complex-double:

• Hilbert-matrix inversion (ill-conditioned accuracy)
• Least-squares parabola fit (solve)
• Rank and nullspace extraction on rank-deficient inputs
• Identity singular values
• U·W·Vᴴ recomposition
• nullvector() correctness

Testing performed

Built and run locally against current main (f2c LINPACK svdc engine), macOS arm64, clang: 6/6 pass. pre-commit run --all-files clean.

[greptile-apps]

Greptile Summary

This PR adds direct GoogleTest coverage for the vnl_svd engine in ITK. The main changes are:

• New itkVnlSVDEngineGTest.cxx coverage for inversion, least-squares solve, rank/nullspace, singular values, recomposition, and nullvector behavior.
• Test coverage across float, double, std::complex<float>, and std::complex<double> cases.
• Registration of the new test source in the existing ITKCommon GoogleTest driver.

Confidence Score: 5/5

Safe to merge with minimal risk.

The change is test-only, follows the existing ITKCommon GoogleTest registration pattern, and does not add production or security-sensitive code. No blocking or non-blocking issues were identified.

No files require special attention.

T-Rex Logs

What T-Rex did

• T-Rex ran the requested verification to validate the contract, but its local artifact references were not uploaded.

_{Ran code and verified through T-Rex}

Important Files Changed

Filename	Overview
Modules/Core/Common/test/CMakeLists.txt	Registers the new itkVnlSVDEngineGTest.cxx source in the existing ITKCommon GoogleTest driver.
Modules/Core/Common/test/itkVnlSVDEngineGTest.cxx	Adds deterministic GoogleTest coverage for vnl_svd inversion, solve, rank/nullspace, recomposition, singular values, and nullvector behavior across real and complex scalar types.

Sequence Diagram

%%{init: {'theme': 'neutral'}}%%
sequenceDiagram
participant CMake as ITKCommon CMake
participant Driver as ITKCommonGTests
participant Test as itkVnlSVDEngineGTest
participant SVD as vnl_svd

CMake->>Driver: add itkVnlSVDEngineGTest.cxx
Driver->>Test: run VnlSVDEngine test cases
Test->>SVD: construct from real/complex matrices
SVD-->>Test: inverse/solve/rank/nullspace/recompose results
Test->>Test: assert residuals and singular values

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sequenceDiagram
participant CMake as ITKCommon CMake
participant Driver as ITKCommonGTests
participant Test as itkVnlSVDEngineGTest
participant SVD as vnl_svd

CMake->>Driver: add itkVnlSVDEngineGTest.cxx
Driver->>Test: run VnlSVDEngine test cases
Test->>SVD: construct from real/complex matrices
SVD-->>Test: inverse/solve/rank/nullspace/recompose results
Test->>Test: assert residuals and singular values

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_{Reviews (1): Last reviewed commit: "ENH: Add vnl_svd engine coverage as itkV..." | Re-trigger Greptile}

[hjmjohnson]

Downstream forest validation — SVD engine swap is invisible to consumers

Validated this change against 13 downstream ITK consumers built on top of f386a36bbe (this PR's head). All 13 build clean and every SVD code path with test coverage passes — 58/58 SVD-path tests, 0 regressions, 0 sign flips.

Build matrix — 13 consumers vs. this PR's ITK

Consumer	Build	SVD exposure
ANTs	✅ built	Wahba/Kabsch rotation, JointFusion pinverse, tensor decompose
BRAINSTools	✅ built	rotation orthonormalization, DTI recon, DWI gradients
elastix	✅ built	thin-plate-spline svd.inverse, PCA metrics
SimpleITK	✅ built	wraps LandmarkBasedTransformInitializer
c3d	✅ built	Procrustes U·Vᵀ, affine solve, GLM pinverse
Plastimatch	✅ built	RBF svd.solve, sphere/plane fit
OpenIGTLink	✅ built	none
OpenIGTLinkIO	✅ built	none
vtkAddon	✅ built	none
IGSIO	✅ built	spin-calibration Procrustes V·Uᵀ
PlusLib	✅ built	phantom/probe calibration, plane nullvector
Slicer	✅ built	fiducial registration, DTI FS-affine inverse
SlicerExtensions	✅ built	none (descriptor bundle)

BRAINSTools SuperBuild reached [22/22] Completed and installed every binary; a harness rc=1 was traced to a post-build TBB link step, not a compile/link error.

Functional test results — SVD code paths exercised

Tool	Tests	Result	SVD path proven
BRAINSTools	28 / 28	✅ pass	SVD orthonormalization, constellation aligner, gradient-sign preservation
ANTs	10 / 10	✅ pass	rotation registration (Wahba V·Uᵀ) + SyN-with-time
Plastimatch	18 / 18	✅ pass	Wendland + Gauss RBF svd.solve
elastix	2 / 2	✅ pass	thin-plate-spline svd.inverse
PlusLib	via matrix	✅ pass	plane/sphere/phantom fits — assertions sign-invariant by design
Slicer	via matrix	✅ pass	fiducial registration, ResampleDTIVolume baselines

Why the risk is bounded

• Every asserted SVD path is sign-invariant. Tested call sites consume SVD as an intermediate — inverse, solve, pinverse, U·Vᵀ rotation, reconstruction — or compare registration output against a tolerance. None assert on raw singular-vector signs, the only quantity Eigen and LINPACK legitimately differ on.
• The sharp edge is tested — with fabs(). The shared RANSAC PlaneParametersEstimator::nullvector() is byte-identical in Plastimatch and PlusLib. PlusLib's PlaneEstimationTest asserts fabs(dot(known, computed)) > 0.9962, so a flipped normal still passes — the exact invariance the swap relies on, pre-encoded by a domain expert.
• "Untested" residue is upstream, not a forest gap. The few raw-vector paths without tests (ANTs tensor-decompose / surface-curvature / SCCAN, BRAINSTools' disabled DTI-recon add_test, elastix PCA) have no assertion tests upstream — they live in example / CLI / diagnostic code.
• Accuracy proxy agrees. Eigen-vs-LINPACK on identical matrices: sign-invariant operations agree to ≤1.7e-13 (below every test tolerance); raw U/V differ by sign only. The functional results confirm the proxy end-to-end.

[dzenanz]

I can't devote time to carefully reviewing this.