Recent merges made fro worrying terminal output about max(u) and step counts

[logan-nc]

We've had a lot of merges lately. The DIII-D-like example terminal output now looks like this:

DCON START
----------------------------------
[ Info: Forcing hamada coordinate jacobian exponents: power_*
Equilibrium file: examples/DIIID-like_ideal_example/TKMKR_D3Dlike_default_Hmode.geqdsk
--> Processing EFIT g-file: examples/DIIID-like_ideal_example/TKMKR_D3Dlike_default_Hmode.geqdsk
--> Parsed from header: nw=257, nh=257
   Magnetic axis found at R = 1.74306, Z = -0.00640
   Inboard separatrix found at R = 1.057797647321493.
   Outboard separatrix found at R = 2.3014488562570796.
[ Info: Setting psilim via dmlim: initial qlim = 5.331263230452014, dmlim = 0.2
Evaluating Mercier criterion
Run parameters:
   q0 = 1.065, qmin = 1.065, qmax = 5.331, q95 = 4.292
   qlim = 5.20000, psilim = 0.990798921
   betat = 0.013, betan = -1.368, betap1 = 0.612
   mlow =  -12, mhigh =   21, mpert =   34, mband =   33
   nlow =    1, nhigh =    1, npert =    1
   Computing F, G, and K Matrices
Integrating Euler-Lagrange equation
   ψ = 0.000,  q = 1.065
   ψ = 0.551,  q= 2.000,  max(u) = 1.20e+36,  steps = 40
   ψ = 0.811,  q= 3.000,  max(u) = 1.02e+39,  steps = 77
   ψ = 0.926,  q= 4.000,  max(u) = 2.20e+41,  steps = 110
   ψ = 0.986,  q= 5.000,  max(u) = 3.27e+42,  steps = 142
   ψ = 0.991,  q= 5.200,  max(u) = 1.05e+41,  steps = 145
Evaluating fixed-boundary stability criterion
┌ Warning: W inverse matrix was non-Hermitian beyond tolerance at 4 integration step(s)
└ @ JPEC.DCON ~/Code/JPEC_ode/src/DCON/FixedBoundaryStability.jl:32
Computing free boundary energies
[ Info: Using no wall
Least Stable Eigenmode Energies:
  Plasma = -3.949e-02 +2.014e-05i
  Vacuum = +1.740e+00 -1.165e-16i
  Total  = +1.701e+00 +2.014e-05i
All free-boundary modes stable for n = 1.
Writing saved data to euler.h5
----------------------------------
Run time: 6.486e+00 seconds
Normal termination.

The final answer is consistent with what it has historically been, however,

• The max(u) values are now huge. Recall DCON keeps these bellow ~1e3 or 1e4 usually. I suspect the Make ode integration bounds more clear #87 merge may have resulted in this?
• The step count is now small. It should be 900+. I think this is from the Julia speedups #124 merge that only saves every 10th step now. Do we have a separate counter for the total number of steps? Do we want to add one?

[logan-nc]

It is also funky that betan is negative. How long has that been true?

[jhalpern30]

• The max(u) values are now huge. Recall DCON keeps these bellow ~1e3 or 1e4 usually. I suspect the Make ode integration bounds more clear #87 merge may have resulted in this?

Note on this. I think you're confusing max(u) with ucrit, which defaults to 1e4. ucrit is the ratio of the maximum to minimum norm of the solution vectors, and this is what DCON keeps to below 1e3-1e4. max(u) is an unphysical diagnostic that I added before the first DCON PR to give something else to compare across runs other than the final eigenvalue to confirm we didn't break anything

[logan-nc]

ok. so the action items are to remove the unphysical max(u) diagnostic and report the actual number of integrator steps rather than the number of saved steps