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feat: MaternSparse sparse Matérn (SPDE) precision regularization (phase 2 of #638) - #650
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…rectangular meshes nu = 1 (alpha = 2) precision H = coefficient * W^-1 c L^2 W^-1 with L = kappa^2 I - lap (5-point, reflecting edges, per-axis pixel scales) on the row-major rectangular mesh grid; c = e^T L^-2 e gives unit centre variance. Sparse H and factor R for the matrix-free path, dense H as a drop-in, exact log-det from the sparse LU of L. Non-rectangular meshes and nu != 1 raise NotImplementedError. Phase 2 of #638 (#646). Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Hand-built 4x3 L and c, SPD, log-det vs slogdet, coefficient scaling, weights path, Delaunay and nu errors, centre variance and decay, nojax import; PCG with the sparse Matérn H matches InversionInterferometerSparse to 1e-8 for two coefficients (#646). Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
This was referenced Oct 21, 2026
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This was referenced Oct 26, 2026
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Closes #646. Phase 2 of #638. Community proposal: PyAutoLabs/.github#39 (@HRSAstro), reference snippet section 3.
Summary
New
aa.reg.MaternSparse(coefficient, scale, nu=1.0, weights=None): the Matérn regularization as a sparse precision for rectangular meshes via the SPDE form (Lindgren, Rue & Lindström 2011). For ν = 1 (α = 2): H = coefficient · c · W⁻¹ L² W⁻¹ with L = κ² I − ∇² (5-point Laplacian with per-axis pixel scales, reflecting edges), κ = √(2ν)/scale, and c = eᵀL⁻²e so the centre variance is 1 (K(0) = 1 as for the dense kernel). It returns the sparse H (regularization_matrix_sparse_from) and its factor R = √c L W⁻¹ (regularization_factor_sparse_from, for phase 3's probe draws), the dense H on today's path (regularization_matrix_from, so it is a drop-in in an ordinary inversion), an exact log-det from the sparse LU of L, and sᵀHs. Non-rectangular meshes and ν ≠ 1 raiseNotImplementedError. Mesh pixel ordering verified row-major from the top-left onRectangularUniformand the adapt-density mesh. DenseMaternKerneluntouched. No priors config (fit wiring is phase 5).API Changes
Additive only:
aa.reg.MaternSparseandregularization.matern_sparse.rectangular_laplacian_sparse_from.See full details below.
Test Plan
test_autoarray/inversion/regularizations/test_matern_sparse.py(14 tests): hand-built 4×3 mesh L and c (neighbours found from coordinates, independent of index arithmetic) equal the class's sparse matrix; SPD; log-det vsnp.linalg.slogdet(2.5e-14 measured, 1e-10 tolerance; 4×3, 7×8, weighted); coefficient scaling; weights path = W⁻¹ c L² W⁻¹ by hand; Delaunay raises; ν ≠ 1 raises; centre variance 1 and monotonic decay along a row; subprocess no-JAX import.test_matrix_free_util.py: matrix-free PCG with the sparse H vs the dense-pathInversionInterferometerSparse(use_positive_only_solver=False) built with the sameMaternSparse: 9.0e-12 (coefficient 1.0) and 3.6e-11 (0.01), Witness target 1e-8; the inversion'sregularization_matrixequals the sparse H exactly.pytest test_autoarray/inversion -q→ 1053 passed, 4 xfailed.Heart YELLOW acknowledged by the human on 2026-10-21 (manifest drift 1 mismatch; release validation stale: source moved since rehearsal (PyAutoArray)).
Full API Changes (for automation & release notes)
Added
aa.reg.MaternSparse(coefficient, scale, nu=1.0, weights=None)—regularization_matrix_sparse_from,regularization_factor_sparse_from,regularization_matrix_from,log_det_regularization_matrix_term_from,regularization_term_from,regularization_weights_from,kernel_weights_from,mesh_shape_and_pixel_scales_from.autoarray.inversion.regularization.matern_sparse.rectangular_laplacian_sparse_from(shape_native, pixel_scales).Generated by the PyAutoLabs agent workflow.
🤖 Generated with Claude Code