Type design for PhasePoint and DualValue.

[yebai]

This PR aims at introducing some additional types that are discussed in #16. More specifically, the following types are introduced:

• PhasePoint: stores θ, r and cached Potential energy (and its gradient). Consider introduce the PhasePoint type #17
• DualValue: stores log density logπ(θ), and cache its gradient.
• LogDensityFunction: stores logπ and its gradient function ∂logπ∂θ.

TODOs

• Refactor numerical error handling code leapfrog using PhasePoint
• Remove DualFunction?
• Refactor build_tree using PhasePoint
• Return more information for each step Return more information for each step #59
• Add a Termination type.

[xukai92]

I updated the version in Project.toml from v0.1.2 to v0.1.3. You may want to merge with the master again.

Update: and an interface bug (f8226a7)

[xukai92]

Do you plan to address the problem of returning H_new for NUTS in this PR?

[yebai]

Do you plan to address the problem of returning H_new for NUTS in this PR?

yes, this will be addressed in this PR since PhasePoint caches H and its gradients.

[xukai92]

So for the purpose of #59, maybe we should consider here somehow make it flexible to return more information within a single step?

[xukai92]

Hi Hong, when can I do a review?

[yebai]

It's ready for a look!

[xukai92]

I commented on some places for discussion. Please take a look!

[yebai]

Ready for another look! @xukai92

[xukai92]

Looks great to me! Just wonder what's "bugfix" in the commit message of 435ac08 mean? I didn't see bugfix?

[yebai]

Looks great to me! Just wonder what's "bugfix" in the commit message of 435ac08 mean? I didn't see bugfix?

It refers to the leftover logπ (should be ℓπ).

[yebai]

Ready to merge from my side @xukai92

[xukai92]

Merged! Thanks for your great work!