`FourierPlanarCoil` still gives NaN gradient when axis is vertical

[dario-panici]

I thought we had fixed this before #1456 but I guess not?

from desc.coils import FourierPlanarCoil
from desc.objectives import ObjectiveFunction, CoilLength
from desc.optimize import Optimizer

coil = FourierPlanarCoil(normal=[0,0,1])
opt = Optimizer("lsq-exact")

obj = ObjectiveFunction(CoilLength(coil))

# Works fine, no Nan
opt.optimize(coil,objective=obj,verbose=3,maxiter=2);


coil = FourierPlanarCoil(normal=[1e-18,1e-18,1])
opt = Optimizer("lsq-exact")

obj = ObjectiveFunction(CoilLength(coil))
# Nan Optimality when normal is close but not quite vertical
opt.optimize(coil,objective=obj,verbose=3,maxiter=2);

• No NaN in forward mode
• No NaN if the normal is [2e-8, 2e-8, 1], but NaN when the first two components are anything less than 2e-8
  • points to handling of the allclose here which depends on the dotproduct I guess? though these are not aligned with negative Z axis...

Our current tests dont catch this, if I add

      test([0, 1e-8, 1])  # nearly parallel
      test([0, 1e-8, -1])  # nearly antiparallel

to our test for this, these fail.

[YigitElma]

I think this is due to round-off error during dot product. For [0, 1e-8, 1], dot product becomes 1*1 + 1e-8*1e-8= 1 + 1e-16 and this is rounded to simply 1 (due to float64). Maybe we can prune the very small terms from the dot product before actually computing it?