Issue1499 speed up DFA calculations

[jhmigueles]

Fixes #1499 => This PR proposes a vectorized approach to Detrended Fluctuation Analysis (DFA). The implementation replaces nested loops and repeated lm.fit calls with matrix algebra, significantly improving performance, especially for short epoch lengths, while maintaining the exact same output.

Epoch	Current GGIR	New proposal	Speed up
60 sec	15.65 sec	3.09 sec	5x
5 sec	19.25 min	8.11 sec	142x

If finally accepted, the DFA function would not be called as the analyses are directly conducted in the SSP function, so the DFA function could be removed.

Fixes #1501 => Now, the PR also includes the calculation of alpha_1 and alpha_2 and related output estimates (SSP, ABI, SSP_short, ABI_short, SSP_long, ABI_long, and SSP_diff). The documentation has been updated to describe the new indices calculated.

Checklist before merging:

• Existing tests still work (check by running the test suite, e.g. from RStudio).
• Added tests (if you added functionality) or fixed existing test (if you fixed a bug).
• Clean code has been attempted, e.g. intuitive object names and no code redundancy.
• Documentation updated:
  • Function documentation
  • Chapter vignettes for GitHub IO
  • Vignettes for CRAN
• Corresponding issue tagged in PR message. If no issue exist, please create an issue and tag it.
• Updated release notes in inst/NEWS.Rd with a user-readable summary. Please, include references to relevant issues or PR discussions.
• If you think you made a significant contribution, add your name to the contributors lists in the DESCRIPTION, zenodo.json, and inst/CITATION files.
• GGIR parameters were added/removed. If yes, please also complete checklist below.

If NEW GGIR parameter(s) were added then these NEW parameter(s) are:

• documented in man/GGIR.Rd
• included with a default in R/load_params.R
• included with value class check in R/check_params.R
• included in table of vignettes/GGIRParameters.Rmd with references to the GGIR parts the parameter is used in.
• mentioned in NEWS.Rd as NEW parameter

If GGIR parameter(s) were deprecated these parameter(s) are:

• documented as deprecated in man/GGIR.Rd
• removed from R/load_params.R
• removed from R/check_params.R
• removed from table in vignettes/GGIRParameters.Rmd
• mentioned as deprecated parameter in NEWS.Rd
• added to the list in R/extract_params.R with deprecated parameters such that these do not produce warnings when found in old config.csv files.

[vincentvanhees]

Thanks Jairo, great to see you were able to speed it up the code. Ian and I worked only with 1 minute epoch data and for us speed was acceptable at the time. So, probably that is why I did not make more effort to speed it up.

Before I do the review, could you please consider the following:

Function DFA appears to be no longer used (?) and still has the inefficient for-loop, while the new code inside function SSP is essentially what DFA does but this is not communicated. Would it not be better to keep the new functionality inside DFA such that SSP remains largely unchanged and it is clear to everyone that this PR only makes local changes to the DFA step focussed on speed and does not revise the general logic of how SSP and DFA work together?

I recognise new code snippets from SSP that came from DFA, and it is reassuring that the unit-tests are not changed, but with so many new lines it would almost seem the algorithm itself is new.

[jhmigueles]

That makes sense. As the SSP function was rather short I thought of simplifying things and doing the whole process there, but keeping the current structure is easier for review and for future references to the code. I will organize the code to keep the fluctuation calculations in DFA and the slope extraction in SSP, thanks for the suggestion!

I will push the updates shortly.