One concern (not related to this commit) is that there is no foolproof way to automatically generate a good set of ak/bk levels, and when creating an entirely novel set of levels some degree of hand-tuning is necessary to avoid stability problems. Xi Chen had developed a tool which can help, and interpolating from predefined level sets is usually pretty good, but some user discretion is needed when making new level sets.
There is no a priori way to ensure stability but typically we can examine the differences in delp and delz in a variety of situations, which is what Xi's tool does. We could run tests to ensure that the differences do not exceed some tolerance. This might be a good way forward; furthermore smoothing can be applied to improve the smoothness and stability of the selected coordinate.
One concern (not related to this commit) is that there is no foolproof way to automatically generate a good set of ak/bk levels, and when creating an entirely novel set of levels some degree of hand-tuning is necessary to avoid stability problems. Xi Chen had developed a tool which can help, and interpolating from predefined level sets is usually pretty good, but some user discretion is needed when making new level sets.
There is no a priori way to ensure stability but typically we can examine the differences in delp and delz in a variety of situations, which is what Xi's tool does. We could run tests to ensure that the differences do not exceed some tolerance. This might be a good way forward; furthermore smoothing can be applied to improve the smoothness and stability of the selected coordinate.
( Per discussion in #36 )