Chromatic delay similar to dispersion delay

[abhisrkckl]

This PR defines a chromatic delay (ChromaticCM) using CM, CM1, CM2, etc. similar to DispersionDM.

The delay is given by the following expression (consistent with tempo2):

cm * DMconst * (freq / 1 MHz)**(-alpha)

The chromatic index alpha is called TNCHROMIDX and it is a constant in time in this model.

I have also defined an abstract base class Chromatic similar to Dispersion so that piecewise-constant CM similar to DispersionDMX can be implemented in the future.

Partially implements #1661

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Codecov Report

Attention: Patch coverage is 65.89595% with 59 lines in your changes missing coverage. Please review.

Project coverage is 69.17%. Comparing base (178002e) to head (7f8a21b).
Report is 107 commits behind head on master.

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Files	Patch %	Lines
src/pint/models/chromatic_model.py	65.29%	52 Missing and 7 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1616      +/-   ##
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- Coverage   69.43%   69.17%   -0.26%     
==========================================
  Files         107      107              
  Lines       24925    25028     +103     
  Branches     4430     4455      +25     
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+ Hits        17306    17314       +8     
- Misses       6510     6591      +81     
- Partials     1109     1123      +14     

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[dlakaplan]

Should there be a DMX version of this?

[abhisrkckl]

Yes. I am also planning to do a piecewise model (like DMX), a Fourier model (like DMWaveX). and a GP model (like PLDMNoise).

[dlakaplan]

Good. Will those be separate or part of this?

[abhisrkckl]

I'll do them separately.

[abhisrkckl]

OK... I have compared the code carefully with TEMPO2 and it matches as far as I can tell.

Unfortunately, I couldn't actually do the comparison with tempo2 due to what I suspect is a bug in tempo2. Basically, the post-fit values for CM are not displayed on the terminal or written into an output par file. I have raised this issue in the IPTA slack.

For the time being I think this is ready for review.

[abhisrkckl]

Also, I have removed the chromatic index fitting code since it was not working consistently. This is probably because there is too much covariance with DM when the chromatic index is allowed to vary.

[abhisrkckl]

Example application on InPTA DR1 data of J1939+2134

Before fitting CM & CM1

CHI2R 3.2021938751881196
TRES 1.3759850757276195468

================

After fitting CM & CM1

CHI2R 1.5363535810916809
TRES 0.9524124603021290128

[dlakaplan]

Looks good. I don't see a test with a fit for CM1, though. Is that possible?

Similarly, would it make sense to do a fit for CM with alpha=-2 and show that it reproduces the DM fit?

[abhisrkckl]

Looks good. I don't see a test with a fit for CM1, though. Is that possible?
Similarly, would it make sense to do a fit for CM with alpha=-2 and show that it reproduces the DM fit?

Added both.

[abhisrkckl]

@dlakaplan I am done unless there is any other suggestion.