Timing model derivatives are mean-subtracted

[aarchiba]

model.d_phase_d_param() returns a derivative whose mean is zero. This is wrong if one is working with absolute phases - if the model contains TZRMJD, all derivatives should be exactly zero there. This arose in #1261, where test_derivative_equals_numerical began failing when comparing returned phases to numerical derivatives.

[aarchiba]

Here's a notebook that demonstrates the problem - sorry it's a PDF, I can't upload notebooks directly. absphase.pdf

[aarchiba]

How this interacts with Fitter objects is not so clear - I think we treat TZRMJD differently from every other parameter, so the Fitter might or might not care whether the derivative there is zero.

[aarchiba]

The way PINT computes phase (relative or absolute) is complicated and confusing and poses real challenges for handling pulse numbers (see issues #1034, #589, #512 and PR #443 for examples).

[paulray]

Here's a notebook that demonstrates the problem - sorry it's a PDF, I can't upload notebooks directly.

Yeah, I've been working on a similar notebook. Note that there is also model.d_phase_d_param_num() so you don't have to use numdifftools.

[aarchiba]

I trust numdifftools to give accurate but slow answers. Also not to have the same assumptions baked into it as our analytic derivatives.

[abhisrkckl]

Is this still a problem?

TODO: Investigate further if this issue still persists. TODO: AD with JAX instead of numdifftools

[abhisrkckl]

Related #1303