feat(numerics): add LU and Cholesky decompositions - #14
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backlundtransform wants to merge 2 commits into
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feat(numerics): add LU and Cholesky decompositions#14backlundtransform wants to merge 2 commits into
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backlundtransform
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Jul 27, 2026
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- LuDecomposition with partial pivoting (PA = LU): cached factorization with Solve for vector/list/matrix right-hand sides, Determinant, Inverse, IsSingular, Lower/Upper/PermutationMatrix
- CholeskyDecomposition (A = L*L^T) with IsPositiveDefinite, Solve, Determinant, Inverse
- Extension facade matrix.Lu() / matrix.Cholesky()
- Matrix.Inverse now uses LU internally (O(n^3) instead of adjugate O(n!)), same public API and error messages
- LinearSystemSolver overloads solve via LU substitution instead of computing the full inverse
- 25 new unit tests; full suite green (1486 passed)
- Check off LinearAlgebra roadmap Phase 1
- LuDecomposition with partial pivoting (P*A = L*U): cached factorization with Solve for vector/list/matrix right-hand sides, Determinant, Inverse, IsSingular, Lower/Upper/PermutationMatrix - CholeskyDecomposition (A = L*L^T) with IsPositiveDefinite, Solve, Determinant, Inverse - Extension facade matrix.Lu() / matrix.Cholesky() - Matrix.Inverse now uses LU internally (O(n^3) instead of adjugate O(n!)), same public API and error messages - LinearSystemSolver overloads solve via LU substitution instead of computing the full inverse - 25 new unit tests; full suite green (1486 passed) - Check off LinearAlgebra roadmap Phase 1 Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
- QrDecomposition via Householder reflections: economy Q/R, IsFullRank with relative tolerance, least squares Solve for overdetermined systems - EigenDecomposition (EISPACK/JAMA port): symmetric path via Householder tridiagonalization + implicit QL with shifts (ascending eigenvalues, orthonormal eigenvectors); non-symmetric path via Hessenberg reduction + shifted QR iteration with complex conjugate pair support (A*V = V*D with block diagonal D) - Extension facade matrix.Qr() / matrix.Eigen() - Quantum module migrated: SymmetricEigenSolver (Jacobi) removed, SchrodingerExtensions now uses the general EigenDecomposition - 24 new unit tests: Q orthonormality, eigenpair residuals, least squares vs normal equations, complex pairs, analytic Laplacian eigenvalues - Check off LinearAlgebra roadmap Phase 2 Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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