EQUIL, RDCON, PENTRC - FEATURE - Monotone (pchip) fits for the tabulated Zeff and kinetic profiles

[StuartBenjamin]

Builds on #296. Fits the tabulated Zeff profile (RDCON MRE terms) and the PENTRC kinetic profile table (also read by DCON with kin_flag) with a monotone cubic (pchip) instead of a cubic spline. These tables have pedestal-scale gradients and no derivatives. A cubic spline overshoots and rings there; pchip cannot overshoot between points.

Changes

• spline_fit_pchip (equil/spline.f): monotone cubic Hermite fit with the same slopes as scipy's PchipInterpolator, for 2 or more points.
• Used for Zeff (rdcon/mercier.f) and in read_kin (pentrc/inputs.f90).
• Zeff tables need 2 points instead of 4 (the cubic spline's "extrap" end condition needed 4). A scalar Zeff becomes a flat 2-point table.
• Unit test regression/spline_tests/test_spline_pchip.f90 (manual, not in CI): matches scipy to 1e-7 (values) and 1e-6 (slopes); 2-point tables are exact.

Effect on results

case	#296 (cubic spline)	this PR
CI Solovev kinetic, PENTRC torque / dW_k	5.3208e-3 / 2.333e-5	+0.97 % / +24.5 %
CI Solovev ideal, PENTRC torque / dW_k	2.0476e-3 / 7.741e-6	+1.6 % / −21 %
CI Solovev kinetic, DCON W_t (kin_flag)	16.6519	16.6534
DIIID_ideal, DIIID_resistive, CI Solovev ideal DCON		identical
RDCON MRE, flat Zeff		identical to 3e-16
RDCON MRE, Zeff profile 1.5 → 3.0		mufrac 1.9 %, Δ′ identical

The PENTRC changes are an edge artifact of the example kinetic.txt, which ends at ψ_N = 0.998 with T = 0.59 eV. PENTRC samples the table fit on a regular grid up to ψ_N = 1. There T is 1.4e-6 eV with the cubic spline and 1e-4 eV with pchip, so logΛ < 0 and ν is huge and negative at that node in both cases. PENTRC's regular-grid spline of ν (still a cubic spline) rings from that node far inward. pchip makes the edge value ~1000× smaller, so the ringing shrinks (ν_i at ψ_N = 0.87: 1.4e9 before, 3.9e6 now, against 1.5e6 in the core), but ν stays unphysical near the edge either way. n, T and ω_E change by ~1e-6.

Scripts: pchip_profiles_scripts.zip run_split_tests.sh OUTDIR runs the cases above (edit the build paths at the top), and cmpnc.py compares the netCDF files.

Dependencies

Contains #296. Conflicts with #297 only where both append code (equil/spline.f: keep both, spline_fit_pchip becomes subprogram 25; the spline-test makefile and .gitignore: build both tests).

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[matt-pharr]

@StuartBenjamin this touches the splines, so I am going to need a bit to review this because that is the well from which we all drink :)

[matt-pharr]

This actually mostly just creates a new class of spline so it might be easy, and its main implications are for PENTRC which @logan-nc might have some thoughts on.

[logan-nc]

Skimming - I like the concept of this type of spline for the input profiles, and I like the minimal highly-independent implementation.

@StuartBenjamin, can you post some plots showing these ringings you describe in the top description and the fix? These would be very helpful now and for future reference.

[StuartBenjamin]

In short the pchip doesn't make a huge difference unless you've got a sparse or bumpy input

The PENTRC thing that the robot identified in the PR report is a separate issue (see #321 fresh and ready to be investigated):
pr300_plots_scripts.zip

I wrote this PR because I wanted a bulltproof spline that I didn't have to worry about, it's marginal gain if you have well behaved profiles already