Refactor code to have a single Ellipsoid class
#616
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Start implementing gravity field with a permutation matrix to sort out the semiaxes.
Update the elliptical integrals for oblates so they assume that `a == b > c`. Simplify the permutation matrix since now we don't need to take care of oblates as a special case.
Remove quite a lot of tests since we now have a single ellipsoid class.
It makes it more explicit about what's happening with the semiaxes. The permutation matrix should match that sorting, but we can cover that in tests.
Update the magnetic code to use the single `Ellipsoid` class, make use of the permutation matrix, and update the internal demagnetization tensor equations for the oblate ellipsoid defined as `a == b > c`.
Do this to differentiate it from just the rotation matrix, since it also includes the permutation one.
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The permutation matrix used wasn't right: we need to apply a proper rotation matrix (with 90 degrees) to ensure that the local coordinate system is a right-handed one.
Test ellipsoids defined with semiaxes passed in arbitrary orders against equivalent ellipsoids defined with ``a >= b >= c``, but with necessary rotations.
After changing the definition of the oblate to `a == b > c`, we need to change the condition for oblates in such function.
Fix the numerical instabilities of gravity fields produced by triaxial ellipsoids that approximate a prolate and an oblate ellipsoid. Fallback to the prolate and oblate solutions when two of the three semiaxes are close enough to each other.
Fallback to the prolate and oblate solutions for the internal demagnetization tensor when triaxial has two semiaxes close enough to each other.
Use the ratio instead of a static delta, so we are sure we are comparing the two different codes and not just triggering the numerical instability fix that falls back to the spherical solutions.
Use the ratio instead of a static delta, so we are sure we are comparing the two different codes and not just triggering the numerical instability fix that falls back to the spherical solutions.
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Refactor the ellipsoid code to have a single
Ellipsoidclass that can represent any type of ellipsoid. Ditch the specific classes for each ellipsoid type. Update the forward modelling code for gravity and magnetics. Make use of an extra rotation matrix that aligns the x, y, z local coordinate system to the ellipsoid's semiaxes in decreasing order, soa >= b >= c. Modify the analytic solutions for oblate ellipsoids in such way that they are defined bya == b > c(instead ofa < b = cas Takahashi et al. and Clark et al. do). Make rotation angles andcenteras optional arguments for theEllipsoidclass. Fix numerical instabilities of triaxial ellipsoids when they approximate prolate or oblate ellipsoids (when two semiaxes lengths are close enough to each other). Update the tests and add a few more for the new bits of code.Relevant issues/PRs:
Part of #594