Gradients/derivatives in econforge interpolators

[Mv77]

This PR adds the capability to compute first-order derivatives of n-dimensional interpolators for my wrapper of econforge.interpolation.py.

It works but:

• We should only merge after Pablo has released the new version of econforge.interpolation.py. The current version one gets through pip has a bug. See Documentation for derivatives EconForge/interpolation.py#94. This PR depends on the version of econforge.interpolation currently in their master branch.
• There are various improvements I'd like to make.

---

• Tests for new functionality/models or Tests to reproduce the bug-fix in code.
• Updated documentation of features that add new functionality.
• Update CHANGELOG.md with major/minor changes.

[Mv77]

Improvements I'd like to make:

• Add the option to evaluate derivatives w.r.t a single dimension (not the full gradient).
• Add the option to simultaneously evaluate the function and its derivatives with the same function call. (to save time in figuring indices out).
• Update requirements to use the version of interpolation.py that does not have the bug.

[llorracc]

This is great!

Though, failing some build tests...

[Mv77]

Yes!

The reason is that the current version of econforge/interpolation.py that HARK pulls has not fixed the bug! (I think we need to ask Pablo to make a release and require the new version when he does).

[llorracc]

Q: If you ask for the derivative exactly at a kink point (where the answer is in principle $\infty$), what does it return?

Or, are piecewise linear splines not allowed?

[Mv77]

Q: If you ask for the derivative exactly at a kink point (where the answer is in principle ∞), what does it return?

I just checked, and it calculates derivatives 'backwards' (using the previous point). Consider the following example

x = np.array([0.,1.,2.,3.,4.])
y = np.array([0.,0.,1.,3.,6.])

interp = LinearFast(y, [x])
grad = interp.gradient(x)
print(grad)

It creates a piecewise linear function. The derivative at 1 is (0 from the left) or (1 from the right). The derivative at 2 is (1 from the left) or (2 from the right). And so on. Here is what I get:

grad = array([0., 0., 1., 2., 3.])

So it's using left-differences.

---

Or, are piecewise linear splines not allowed?

Yes they are, and they are in fact the only thing I am using at the moment. I have not explored higher order splines.

[llorracc]

Hmmm, I guess that's better than $\infty$ or $-\infty$ for preventing the computer blowing up. But maybe it SHOULD blow up if you ask for a derivative at a point where it is undefined ...

[Mv77]

Hmmm, I guess that's better than ∞ or −∞ for preventing the computer blowing up. But maybe it SHOULD blow up if you ask for a derivative at a point where it is undefined ...

But we would not want to go around blowing up our---or other people's---computers!

[Mv77]

@MridulS , @sbenthall , this PR relies on the latest release of Pablo's interpolation.py, which is 2.2.2. There was a bug in previous versions, so if people get the wrong version they will be getting incorrect derivatives.

How do I reflect that in HARK's requirements? Is it a matter only of writing interpolation >= 2.2.2 in requirements.txt or should I do something else?

[MridulS]

How do I reflect that in HARK's requirements? Is it a matter only of writing interpolation >= 2.2.2 in requirements.txt or should I do something else?

Yeah, that will make sure that HARK installed via github is depending on interpolation >= 2.2.2. But we need to make a new release to make sure if someone does pip install ... they get the proper version of interpolation.

[Mv77]

How do I reflect that in HARK's requirements? Is it a matter only of writing interpolation >= 2.2.2 in requirements.txt or should I do something else?

Yeah, that will make sure that HARK installed via github is depending on interpolation >= 2.2.2. But we need to make a new release to make sure if someone does pip install ... they get the proper version of interpolation.

Well the good thing is that none of the content currently in HARK depends on the buggy derivatives, those are only used by elements introduced in this PR. So even without a HARK release people won't be getting bugs from HARK. But when we do roll out these new features we have to enforce interpolation>=2.2.2

[codecov-commenter]

Codecov Report

Merging #1157 (06ebf28) into master (4f950f0) will increase coverage by 0.24%.
The diff coverage is 92.85%.

@@            Coverage Diff             @@
##           master    #1157      +/-   ##
==========================================
+ Coverage   73.33%   73.58%   +0.24%     
==========================================
  Files          72       72              
  Lines       11387    11465      +78     
==========================================
+ Hits         8351     8436      +85     
+ Misses       3036     3029       -7     

Impacted Files	Coverage Δ
HARK/econforgeinterp.py	82.85% <72.72%> (-17.15%)	⬇️
HARK/interpolation.py	43.29% <100.00%> (+0.76%)	⬆️
HARK/tests/test_econforgeinterp.py	100.00% <100.00%> (ø)

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[Mv77]

Bleh. Current tests are failing in windows because interpolation.py requieres a package "curses" that is included in base Python for other OSs but not for Windows.

How on earth do I handle that requirement...

Edit: The requirement was accidental, Pablo has patched the issue.

[Mv77]

After Pablo's patch this is now ready to review.

[Mv77]

@llorracc @sbenthall @alanlujan91, could anyone review this? It's ready to go

[alanlujan91]

Great PR, left a few comments. Looking forward to implementing this on other models.

[Mv77]

@alanlujan91 thanks for the great suggestions. The last couple of commits address them all. Don't merge this in yet, I think Chris wanted to chat about it first.

[Mv77]

@alanlujan91 approves and I've discussed @llorracc 's questions with him over email, so I'll go ahead and merge. Thanks everyone!