Sparse pullback for big performance gain

[unalmis]

If this will not be merged then all bounce integrals should be removed per #2225

• Resolves Sparsity preserving pullbacks #2168 .
  • Yields factor of $N \times$ improvement in memory and compute speed to get Jacobian $R^{N \times M}$ of map $f \colon R^M \to R^N$. Basically if you had some expensive function, with proper application throughout you could get Jacobian for around the cost you'd get a single row before.
  • $N^2$ for check pointed funs
  • Even if you are only doing a single vjp, it is much faster and more memory effecient due to reasons discussed in links threads.
• Removes
  • bounce1d optimization.
  • Unneeded flags (is_reshaped, is_fourier) that users said were confusing (backwards compatible) as well as the developer flags Bref, Lref that should not be there.
• Previously, pitch_batch_size was getting ignored. This fixes that by adding strip_dim0 flag to batch_map.
• Switch resolution to per field period to simplify use and analysis #2182
• Resolves the fixme comment so that gradients are consistent #2185

notes

• They are decorator functions, so it is non-invasive and can improves many objective such as bounce, balloon, qs, omni, surface integral, free surface etc, but more generally can apply to any atomic computation. Trivial to use now that I have done all the math and resolved implementation sharp bits.
• for example the 4d singular integral kernel can be reduced to 2d pullback
• For this PR, I only apply the decorator at one point in bounce. Because itsdone at intermediate point I needed to change some code. Note the CI benchmarks won't show that improvement since those objectives were onto $R^1$, but benchmarking with tensor-board indeed shows the factor of $N$ improvement in speed and memory computing the Jacobian. And this is not yet applied to the full pipeline. See Single contangent pullback through compute pipeline #2171 .
• Unrelated to this PR since it's always been like this, but computing the proximal projection Jacobian with Force balance constraint is more expensive that computing the bigger unconstrained Jacobian since the svd solve is way more expensive now than computing a vjp of bounce integrals. Perhaps the decorator could be applied to stuff there; I didn't look.
• If the partial summation in Poloidal FFT Implementation #1508 is done so that the the transforms are factorized then we can extend the pullback wrappers to include the spectral to real space transform on each surface to by decorating the larger function with a sparse_pullback as well. Or use Fourier-Chebysev as i had suggested in Making transforms more efficient #1243 to make it simpler. This would have thr advantage of further reducing memory.
• This should renew interest in Upsample data above midplane to full grid assuming stellarator symmetry #1206 and Compute function and gradient simultaneously for reverse mode #1872 and Generalize toroidal angle beyond phi cylindrical #465.

[ddudt]

I haven't reviewed all the code yet, but I think this introduces some breaking changes. I'm not sure what the best solution is: ideally we would keep support for forward mode, but we at least need to add more error handling.

[unalmis]

#2170 (comment)

#2170 (comment)

[unalmis]

@ddudt @daniel-dudt it works in forward mode now.

[unalmis]

@dpanici when will this be merged?

[unalmis]

@ddudt when will this be merged

[unalmis]

It's needed for #2257

[unalmis]

@f0uriest when will this be merged?