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Automatic Continuation Method Robustness in recent versions #1903

@dpanici

Description

@dpanici

I have at least one case where the auto contination method worked in earlier desc versions but fails now

this works on v0.13.0 but not master (last time I checked)

from desc.geometry import FourierRZToroidalSurface
import numpy as np
surf = FourierRZToroidalSurface.from_input_file("../input.rotatingellipse.beta.240222_desc")

from desc.profiles import PowerSeriesProfile
PRES_SCALE = 7.957747154594767e+03
pressure = PowerSeriesProfile(params=np.array([1,-1])*PRES_SCALE, modes=[0,2],sym="even")
current = PowerSeriesProfile()
eqv = Equilibrium(surface=surf, pressure=pressure, current=current, Psi = -1.4652431000000077,L=12,M=12,N=12 )
eq = solve_continuation_automatic(eqv)[-1]

input.rotatingellipse.beta.240222_desc.txt

This one does not work on master, have not checked if it worked in the past:

@Mandelbr0t can you post the QH nfp4 one?

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