PerturbedEquilibrium - PERFORMANCE - Coarse-grid rzphi geometry in field reconstruction

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Summary

Speeds up FieldReconstruction.jl's R/Z/φ reconstruction by eliminating redundant and over-sampled equilibrium-geometry evaluation. reconstruct_physical_fields is ~2× faster (364 → 175 ms warm, DIII-D n=1, -t 6) at machine-precision accuracy.

Stacked on #263 (threading). This PR is based on performance/parallel-field-reconstruction and shows only the two geometry commits; retarget to develop once #263 merges.

Background

Profiling showed the field-reconstruction bottleneck is equilibrium bicubic-spline evaluation, not the mode-space linear algebra. Two issues:

1. _compute_rzphi_modes was called twice (ξ and b) and recomputed the identical (ψ,θ) transform matrices, which depend only on geometry.
2. The smooth geometry was sampled at every fine u_store ψ (npsi≈1158) when the rzphi bicubic only carries ~188 ψ-knots — a ~6× over-sampling.

Changes

• De-dup (53a88e8): split into _build_rzphi_geometry (built once) + _apply_rzphi_transform (per field). Byte-identical.
• Coarse-grid resample (a2e1cd4): sample the smooth rzphi primitives (r², η-offset, J, θ-derivatives) at the 188 rzphi_xs ψ-knots, build a single cubic Series interpolant in ψ (same convention as _build_metric_interp), and resample onto the fine grid — replacing 2-D bicubic evals with cheap 1-D cubic evals. ψ-derivatives come from differentiating the resample spline (resampling the bicubic ψ-derivatives directly rings to ~2600% near axis/edge, as they are only C¹).

Verification

• Accuracy: the R/Z/φ mode outputs (the only fields these functions affect) match a byte-identical baseline to ~1e-15 relative. NB: the regression harness does not track R/Z/φ, so this was validated by direct HDF5 comparison.
• Regression diiid_n1: 0-diff on all 30 tracked quantities.
• Threaded determinism: full gpec.h5 (239 numeric datasets) bit-identical across -t 1/2/6.

Scope notes

Reconstruction is a small fraction of total runtime (the stability ODE dominates), so the total-run speedup is modest; the win is largest for multi-n runs, scans, and repeated-response loops. I also implemented and benchmarked an area/b_n coarse-grid cache and DFT GEMM batching, but reverted both — measured net-negative (Series overhead at mthsurf=256; batching thin DFTs loses the per-ψ @threads parallelism, 175→255 ms).

🤖 Generated with Claude Code

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Verification: field reconstruction unchanged (machine precision)

Validated directly on the reconstruction mode-space outputs (which the regression harness does not track), comparing develop (incl. #263) vs this branch, both at -t 1 so the only difference is the coarse-grid geometry resample.

Only the six R/Z/φ outputs produced by _compute_rzphi_modes change at all, and only at the ~1e-15 level; every other field is exactly bit-identical.

field	max|Δ|	max rel	status
xi_psi, xi_psi_J, xi_theta, xi_zeta, xi_theta_reg, xi_zeta_reg	0.0	0.0	bit-identical
clebsch_psi, clebsch_psi1, clebsch_alpha	0.0	0.0	bit-identical
xi_cova_psi/theta/zeta, b_cova_psi/theta/zeta	0.0	0.0	bit-identical
b_n, xi_n, b_theta, b_zeta, b_theta_reg, b_zeta_reg, psi_area	0.0	0.0	bit-identical
xi_R	3.8e-17	1.0e-15	machine precision
xi_Z	4.9e-17	7.0e-16	machine precision
xi_phi	7.9e-17	1.6e-16	machine precision
b_R	1.6e-17	1.5e-15	machine precision
b_Z	1.7e-17	9.2e-16	machine precision
b_phi	8.7e-19	1.6e-16	machine precision

22/28 reconstruction fields exactly bit-identical; the remaining 6 (R/Z/φ) agree to ≤1.5e-15 relative. This matches expectation: the resample reproduces the bicubic on its native ψ-knots, and ψ-derivatives come from differentiating the resample spline.

Overlay below: m=2 and m=5 components of the R/Z/φ fields vs ψ — develop+#263 (solid lines) vs #264 coarse-grid (open circles). The circles land on the lines through all the resonant structure.