Equilibrium - BUGFIX! - Build F and P of g-file and IMAS equilibria from the tabulated FF′ and p′

[d-burg]

Release note

• Audience: users
• Numerical impact: every g-file (efit, efit_arclength, efit_by_inversion) and IMAS result moves. On the DIII-D-like example: Δ′ diagonal up to 15 %, free-boundary energy 0.6 %, SLAYER γ 6 %, NTV torque 2.8 %. Solovev is unchanged. (harness @ b3f412f)
• Migration: re-pin local baselines for g-file and IMAS cases; set profile_source = "values" in [Equilibrium] to reproduce earlier results exactly.

F and P of a g-file or IMAS equilibrium are now the integrals of the file's FF′ and p′, anchored at the boundary values, instead of the tabulated F and P. Differentiating a tabulated F amplified its rounding error into the current gradient, which put noise of several units on Δ′ for 257-node files written in single precision. Closes #504.

What changed

• read_efit and read_imas fill the F and P columns of the 1D table through one helper (integrate_profile_derivatives), always for both profiles together. Everything downstream is untouched and still differentiates one spline.
• New [Equilibrium] key profile_source: "derivatives" (default) or "values" (previous behaviour, bit-identical to develop).
• The reader logs the largest interior difference between the rebuilt and tabulated profiles and warns above 1e-4 of F or 5 % of the peak pressure. It falls back to "values" with a warning when the derivative arrays are absent, all zero, non-finite, or opposite in sign for only one of the two profiles.

Regression report

regress --cases diiid_n1,diiid_n1_riccati,diiid_slayer_n1,diiid_error_field,diiid_multi_n,efit_fixedbdy_separatrix,gal_resistive_diiid,gal_resistive_pe,solovev_n1 --refs 0e68a0553,b3f412f35 --force (julia 1.11.9, x86_64, pinned manifest, 8 threads).

case / quantity                               develop 0e68a0553   b3f412f35        diff
diiid_n1_riccati   (12 changed, 5 unchanged)
  delta prime (BVP diagonal)                  [5 elem]            [5 elem]         14.68%
  delta prime (raw side-major)                [10 elem]           [10 elem]        3.10%
  total energy Re(et[1])                      8.037194e-01        7.988495e-01     0.61%
  q0 / q95 / beta_n                                                                4e-6 / 4e-6 / 0.08%
diiid_n1           (42 changed, 11 unchanged)
  total energy Re(et[1])                      8.012318e-01        7.961432e-01     0.64%
  plasma energy Re(ep[1])                     -1.348486e+00       -1.361062e+00    0.93%
  island half-widths                          [5 elem]            [5 elem]         0.50%
  NTV torque FGAR [N.m]                       5.296746e-01        5.446895e-01     2.83%
  PE toroidal torque                          5.087465e-02        -5.063447e-02    sign flip (see notes)
diiid_slayer_n1    (12 changed, 5 unchanged)
  SLAYER gamma_Hz [2/1,3/1,4/1]               [3 elem]            [3 elem]         6.04%
  SLAYER omega_Hz [2/1,3/1,4/1]               [3 elem]            [3 elem]         0.12%
gal_resistive_diiid (7 changed, 3 unchanged)
  gal PEST3 Delta diagonal                    [4 elem]            [4 elem]         0.40%
  ||gal Delta_coil block||                    2.453508e+02        2.478311e+02     1.01%
diiid_error_field  (7 changed, 1 unchanged)
  EFC whole-field NTV torque per kAt^2        [1 elem]            [1 elem]         2.83%
  EFC rotation-scan shifts [rad/s]            [9 elem]            [9 elem]         50.00%  (see notes)
  EFC residual torque against rotation        [9 elem]            [9 elem]         65.79%  (see notes)
diiid_multi_n      (14 changed, 5 unchanged)   largest change 0.22%
efit_fixedbdy_separatrix (3 changed)           q0, q95, beta_n at 1e-9
gal_resistive_pe   8 quantities N/A on both refs
solovev_n1         22 unchanged

Unit tests on the same commit: equilibrium 305/305, IMAS 32/32, rerun-from-h5 40/40.

Validation beyond the harness

• Old route is exact: profile_source = "values" gives develop's Δ′(2/1) to every digit on two files.
• Same equilibrium state, two g-files (five pairs, inputs agree to 1e-5; see Equilibrium - g-file reader differentiates FPOL and PRES and discards FFPRIM and PPRIME, putting rounding noise on Δ′ #504): the gap in Δ′(2/1) was 3.7 rms on develop. With this change on a fixed grid (ldp, mpsi = 256) it is 0.027 rms.
• Fortran cross-check: on the in-repo TkMkr_D3Dlike_Hmode.geqdsk with F rebuilt from FF′, Julia and Fortran STRIDE give Δ′(2/1) of 7.27 and 7.28. Fortran GPEC has the same defect and will need the same fix.
• Grad-Shafranov consistency: on the files' own (R,Z) grids, ψ(R,Z) follows FF′/p′ and not the node-scale structure of the differentiated F (regression coefficient 0.07 ± 0.02 over 24 files, where 0 means FF′/p′ and 1 means the differentiated profiles).

Notes for reviewers

• End nodes are used as written. TokaMaker's FF′ and p′ have an axis-node spike and a last-node drop. Δ′(2/1) and 3/1 are insensitive to how these are integrated; an edge 4/1 entry moves by up to 0.4 with the spline end condition. Alternatives (for example extrapolating the two end nodes) are untested and left for a follow-up.
• This does not remove the auto grid's own sensitivity. On the two-pass auto grid the same-state gap is still 0.1–0.3 rms with identical knot counts, against 0.027 on the fixed grid.
• diiid_n1 PE toroidal torque changes sign (+0.0509 → −0.0506). The same flip is recorded under grid refinement in PE toroidal torque changes sign under grid refinement while its magnitude stays stable to ~1% #370; I have not investigated it here.
• diiid_error_field rotation-scan quantities move 50–66 %. The scan shifts themselves change, which suggests a discrete choice moved; not investigated.
• IMAS: Equilibrium - BUGFIX! - Place read_imas profiles on the stored psi grid #499 and Equilibrium - BUGFIX - Select the rectangular profiles_2d by grid_type in read_imas #476 edit read_imas too; the overlap is the block that builds the 1D table.
• Pinned values in Regression - FEATURE! - ⚠️ Golden values: committed pins with provisional tolerances #397 and any local baselines built on the example g-file will need re-pinning.
• Suggested regression case: one case with profile_source = "values", so the previous numbers stay tracked. Not added here.
• The upstream cause of the largest errors is TokaMaker writing g-files in single precision; that is separate from this PR.

⚠️ Requires third-party human review before merging. Do not merge without an approving review.

---

🤖 Generated with Claude Code

[github-actions]

This pull request is missing a reviewer.

If you are not ready to name them, mark this pull request as a draft.
docs/development/contributors.md suggests lead developers to ask.
Merging is not blocked here, but no pull request may be merged without human review.

[github-actions]

This pull request is missing a reviewer.

If you are not ready to name them, mark this pull request as a draft.
docs/development/contributors.md suggests lead developers to ask.
Merging is not blocked here, but no pull request may be merged without human review.

[d-burg]

Parking this PR. OpenFUSIONToolkit/OpenFUSIONToolkit#358 fixes the noise at the writer, and with double-precision g-files develop gives clean Δ′ without this change. Integrating FF′ and p′ also moves surfaces near pedestal kinks by more than the noise it removes (cubic, trapezoid and Akima rules disagree there by several units). Results and the open points are in #504. The one CI failure is the Δ′(2/1) pin of the in-repo example, which this change moves by design; it is left as is while the PR is parked.