ENH: Add itk::Math LDLT symmetric solve/inverse and vnl_cholesky engine GTest#6565
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hjmjohnson merged 3 commits intoJul 10, 2026
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Add itk::Math::SolveSymmetric and itk::Math::InverseSymmetric for symmetric (indefinite) linear systems and symmetric-matrix inversion, backed by Eigen's LDLT (Bunch-Kaufman) factorization. Overloads accept itk::Array2D/itk::Array and map the contiguous block through Eigen::Map with no copy; a matrix-RHS overload solves A X = B with a single factorization. ITK_MATH_HAS_SOLVE_SYMMETRIC advertises the capability so consumers can feature-test the header. itkMathLDLTGTest checks SPD and indefinite systems, the matrix-RHS solve and the symmetric inverse against a vnl reference.
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Adapt vxl core/vnl/algo/tests/test_cholesky.cxx into an ITK GoogleTest so the coverage runs in ITK CI and guards the native Cholesky engine that replaced the netlib LINPACK path (98f7498). Beyond the scavenged cases (inverse vs direct inverse, two-sided identity in both modes, known-solution solve), adds determinant, triangular-factor, rank-deficiency/rcond, and an equivalence check against the Eigen-backed itk::Math::SolveSymmetricPositiveDefinite. The suite defines ITK_LEGACY_TEST and compiles out under ITK_FUTURE_LEGACY_REMOVE, matching the vnl_cholesky deprecation guard. Follows the itkVnlSVDEngineGTest precedent (PR InsightSoftwareConsortium#6546). Tracking: InsightSoftwareConsortium#6403.
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Adds
itk::Math::SolveSymmetricanditk::Math::InverseSymmetric, backed by Eigen's LDLT (Bunch-Kaufman) factorization, for symmetric (indefinite) linear systems and symmetric-matrix inversion. Also scavenges vxltest_cholesky.cxxintoitkVnlCholeskyEngineGTestso the native Cholesky engine (98f7498) is covered in ITK CI, following theitkVnlSVDEngineGTestprecedent (#6546). Split out of #6564.API and rationale
SolveSymmetric(A, b)solvesA x = bfor symmetricA; a matrix-RHS overload solvesA X = Bwith a single factorization.InverseSymmetric(A)returns the symmetric inverse; it throws for singular input (LDLT pivot-diagonal check) rather than silently returning a pseudo-inverse.itk::Array2D/itk::Arrayand map the contiguous block throughEigen::Mapwith no copy.ITK_MATH_HAS_SOLVE_SYMMETRIClets consumers feature-test the header (#if __has_include(<itkMathLDLT.h>)).Test coverage and legacy-state behavior
itkMathLDLTGTest: SPD and indefinite systems, matrix-RHS solve, symmetric inverse, singular-input rejection, vnl-oracle cross-checks (float and double).itkVnlCholeskyEngineGTest(scavenged from vxltest_cholesky.cxx): inverse vs direct inverse, two-sided identity in default andestimate_conditionmodes, known-solution solve, determinant vs analytic, triangular-factor reconstruction, rank-deficiency/rcond, equivalence vsitk::Math::SolveSymmetricPositiveDefinite.ITK_LEGACY_TESTfor their vnl oracles and compile those out underITK_FUTURE_LEGACY_REMOVE, matching the vnl_cholesky deprecation guard already on main.ITK_LEGACY_REMOVE20/20 (0 deprecation warnings),ITK_FUTURE_LEGACY_REMOVE12/12 (deprecated-engine suites compiled out).