New effective eccentric mchirp parameter

[rahuldhurkunde]

Added a new eccentric mchirp parameter as defined in arXiv:2107.14736.

Standard information about the request

This is a: new feature

This change affects: the offline search.

This change changes:result presentation / plotting

Motivation

A new effective mchirp-e parameter might be better for eccentric searches, i.e. may lead to better bank placement.

Contents

Added a new method in conversions.py

Testing performed

Reproduced the Figure 3. in the paper.

Additional notes

• The author of this pull request confirms they will adhere to the code of conduct

[ahnitz]

@rahuldhurkunde Nice. I might suggest two things.

(1) (minor) is there a better name than 'ecc mchirp'?
(2) Is it possible to write an inverse function? e.g. give back the mchirp from the 'ecc mchirp' + ecc.

[rahuldhurkunde]

@ahnitz The inverse function requires a root solver. So to avoid adding a scipy dependency, I had to include a new bisection root solver function: solve_root.

Simple testing seems to be working:

>>> conversions.ecc_mchirp_from_mchirp_ecc(20.0, 0.2)
20.668174895333745
>>> conversions._mchirp_from_ecc_mchirp_ecc(20.668174895333745, 0.2)
19.999999648528163

Sorry I can't think of any better name for the new parameter. Happy to change if you have any suggestions.

[rahuldhurkunde]

@ahnitz I've dropped the e^6 term, simplified the inversion to a quadratic one and renamed the new parameter to Emchirp.

[rahuldhurkunde]

I've bring back the cubic term, and performed some quick testing on 50000 points. In short, both the functions work well and this looks ready to merge from my end.

--- Testing Conversions for 50000 points ---
Using ranges from plot_ecc_mchirp.py:
  ecc: [0.0, 0.6]
  ecc_mchirp: [5.0, 80.0]

Timing (total for 50000 points):
  mchirp_from_ecc_mchirp_ecc (Inverse): 0.003358 s
  ecc_mchirp_from_mchirp_ecc (Forward): 0.002018 s

Validity Check (Round-trip):
  Number of NaNs in recovered mchirp: 0
  Max absolute difference in mchirp: 2.13e-14
  Mean absolute difference in mchirp: 6.26e-16

  RESULT: SUCCESS - The inverse function is valid in this range.

[yi-fan-wang]

@rahuldhurkunde I have a PR #5328, where I try to enable fitting the noise trigger rate with respect to eccentricity. I think it'd be good to think about adding eccentricity mchirp as well