Periodic parameters improvement by rotating them

[segasai]

I am thinking about potential improvement of how dynesty deals with periodic parameters. Currently the periodicity is ignored when ellipsoid bounds are constructed, which will lead to modes being split for example if they wrap around. (i.e. 2 period parameters with the center at zero will make 4 modes)

I'm thinking about transforming the points before making the ellipsoidal bounds. I.e. i x is periodic parameter, its' better to work with it in space of (x-x0)mod 1 where x0 is chosen such as to put points in the center of the cube.

I don't yet know if the change can be made in localised way to not make the code too complex and slow down the non-periodic cases. IMO the implementation of the feature should not bee too complex, otherwise it's not worth it.

Feedback/patches/ideas welcome.

PS the best rotation of the for 1d set of points is the rotation that puts the biggest gap between points at zero. Something like this:

x=(1+np.random.normal(size=10)*.1)%1
print(x)
xind = np.argsort(x)
x_sort = np.concatenate(([x[xind[-1]]-1],x[xind]))
bestpos = np.argmax(np.diff(x_sort))
cen = (x_sort[bestpos] + x_sort[bestpos + 1]) / 2.
x_transform = (x + 2 - cen)%1
print (x_transform)
>>> [0.07819544 0.07965051 0.13322925 0.92580754 0.10810778 0.90248174 0.9690383  0.01715838 0.10589642 0.11196911]
>>> [0.56033994 0.56179501 0.61537375 0.40795205 0.59025229 0.38462625
 0.45118281 0.49930289 0.58804092 0.59411362]