Yuhsuan/1277 fitting error

[YuHsuan-Hwang]

Description

• What is implemented or fixed? Mention the linked issue(s), if any.

1. Fixed image fitting error too small #1277 by implementing error calculations based on Condon (1997), which is also used by casa imfit.

   • When the beam table is empty, we assume the samples are independent and apply formulas in Condon (1997) section 2 eqn 21.
   • When the beam table is not empty, we assume there is correlated noise and apply formulas in Condon (1997) section 3 eqn 41 and 42.
   • If the beam table is not empty but the beam of the current plane is not found, we apply the first beam.
   • If the background offset is a free parameter during fitting, background offset error is calculated by the covariance matrix.

2. Changed from unweighted fitting to weighted fitting with the information of image standard deviation.

   • Please note that this will change the iteration number and the fitting results and thus the execution time.

3. Added calculation of integrated flux in the fitting result. This requires frontend branch Yuhsuan/fitting integrated flux carta-frontend#2229 and protobuf branch Yuhsuan/fitting integrated flux carta-protobuf#88.

   • Applied Condon (1997) section 2 eqn 21 and section 3 eqn 42 for the calculation.
   • Applicable only when image units are exactly "Jy/pixel" or "Jy/beam." The calculated flux unit is Jy.
   • When both amplitude and FWHM sizes of a component are fixed, the integrated flux becomes fixed.

• How does this PR solve the issue? Give a brief summary.

  • Obtained beam size, image unit, and image std (of the entire image or regions) in Frame.FitImage.
  • Obtained Median Absolute Deviation (MAD) as image std in ImageFitter.SolveSystem.
  • Applied weighted fitting (requires image std) in ImageFitter.SolveSystem.
  • Added error calculation (requires beam size and image std) and integrated flux calculation (requires image unit) in ImageFitter.CalculateErrors.

• Are there any companion PRs (frontend, protobuf)?

  • Yuhsuan/fitting integrated flux carta-frontend#2229
  • Yuhsuan/fitting integrated flux carta-protobuf#88

• Is there anything else that testers should know (e.g. exactly how to reproduce the issue)?

• ToDo

• code maintenance: add documentation in ImageFitter.h.

Checklist

• changelog updated / no changelog update needed
• e2e test passing / added corresponding fix
• protobuf updated to the latest dev commit / no protobuf update needed
• added reviewers and assignee
• added ZenHub estimate, milestone, and release

[YuHsuan-Hwang]

New changes:

• Added documentation in ImageFitter.h.
• Replaced std of the image / region with Median Absolute Deviation (MAD) calculation for weighted fitting and error calculation.
• Fixed incorrect center error calculation.

[kswang1029]

this is looking good. I have adjusted e2e tests accordingly.

[kswang1029]

need to divide a solid angle conversion factor as pi / 4.0 / ln(2.0) ~ 1.1330900354567985

flux = 2 * M_PI * fwhm_x * fwhm_y * SQ_FWHM_TO_SIGMA * amp / _beam_size / _beam_size / (M_PI / 4.0 / log(2.0))

[github-actions]

Package	Line Rate	Health
src.Cache	66%	➖
src.DataStream	52%	➖
src.FileList	67%	➖
src.Frame	50%	➖
src.HttpServer	42%	➖
src.ImageData	28%	❌
src.ImageFitter	83%	✔
src.ImageGenerators	43%	➖
src.ImageStats	76%	✔
src.Logger	44%	➖
src.Main	54%	➖
src.Region	18%	❌
src.Session	29%	❌
src.Table	52%	➖
src.ThreadingManager	87%	✔
src.Timer	85%	✔
src.Util	48%	➖
Summary	38% (7086 / 18700)	❌