ksw/enhance image fitting performance by switching the solver from qr to cholesky

[kswang1029]

This is to address the performance concern from @Jordatious about the current 2D image fitting implementation by switching the default solver "qr" to "cholesky". You may refer to
https://www.gnu.org/software/gsl/doc/html/nls.html#c.gsl_multilarge_nlinear_solver.gsl_multifit_nlinear_solver_qr
https://www.gnu.org/software/gsl/doc/html/nls.html#c.gsl_multilarge_nlinear_solver.gsl_multifit_nlinear_solver_cholesky
to see the differences as also mentioned in the comment chain of the PR #1055.

With some tests, the performance boost in terms of elapsed time is reduced by ~66%. This is measured by testing single and triple gaussian fit with different image sizes. As for the fitting result accuracy, it appears to me that the two solvers give very similar solutions.

I also tried other methods to solve the trust region subproblem (https://www.gnu.org/software/gsl/doc/html/nls.html#solving-the-trust-region-subproblem-trs)
We use gsl_multifit_nlinear_trs_lm : Levenberg-Marquardt algorithm now:
gsl_multifit_nlinear_trs_lmaccel : Levenberg-Marquardt algorithm with geodesic acceleration --> slower. I don't provide the second directional derivative vector so it is using finite difference method for approximation
gsl_multifit_nlinear_trs_dogleg: dogleg algorithm --> slower
gsl_multifit_nlinear_trs_ddogleg: double dogleg algorithm --> slower
gsl_multifit_nlinear_trs_subspace2D: 2D subspace algorithm --> super fast and converged with just 1 iteration but the result is not correct. Not sure if I miss something configurable here

This PR is considered as a quick-and-dirty improvement of the fitting performance for the final v3 release. Open for comments on whether or not merging this.

[veggiesaurus]

Looks good. Can you provide some benchmarks with various image sizes?

[acdo2002]

I used Cypress to measure the performance.
The carta-cypress code is in "carta-cypress/cypress/integration/carta/2DGaussianFitting.spec.js" and the testing image (simple 1 component Gaussian image) is "Gaussian2Dimage.fits" in here.

The current backend dev branch:

It takes ~21sec to do the 2D image 1 component Gaussian fitting.

While in ksw branch:

It only takes 10sec to complete the same fitting.
I think the performance has significant improvement.

[veggiesaurus]

I used Cypress to measure the performance. The carta-cypress code is in "carta-cypress/cypress/integration/carta/2DGaussianFitting.spec.js" and the testing image (simple 1 component Gaussian image) is "Gaussian2Dimage.fits" in here.

Thanks @acdo2002. Can you run a similar test using the much larger HST image?

[acdo2002]

@veggiesaurus Yes, here is the result. I used the Abell 1689 HST public archive WFC3 image "ibja08020_drc.fits" (4131 x 4388 pix, 218MB), which is much larger than "Gaussian2Dimage.fits" (1000 x 1000 pix, 8MB)

The current dev branch:

It takes 180 sec (~3min) to derive a single component 2D gaussian fitting (fit the foreground star)

While in this ksw branch:

It only takes 67sec (~1min) to derive the same fitting result.