Optimize GEK.jl

[Spinachboul]

• Changes made in the model *

1. Matrix Operations Optimization:

   • Utilized LinearAlgebra functions for matrix inversion to improve efficiency.

2. Loop Optimization:

   • Utilized @inbounds and @simd macros for loop bounds-check elimination and vectorization, respectively, to enhance performance.

3. Calculations are reused:

   • Moved common calculations outside loops to avoid redundancy and improve efficiency.

4. Redundant Checks:

   • Moved the check for sample repetition outside the constructor function to eliminate redundant checks and improve readability.

5. Consolidation of Functions:

   • Removed duplicate _calc_gek_coeffs function and consolidated its logic into a single function to enhance maintainability.

6. Optimized Constructor:

   • Streamlined the constructor function to improve readability and efficiency.

7. Added Dimension Checking:

   • Added a _check_dimension function to ensure the input dimension matches the surrogate dimension, improving robustness.

Testing yet to be performed after after appropriate review by the maintainers

@ChrisRackauckas and @sathvikbhagavan

[ChrisRackauckas]

I'm not sure I see what in these changes would actually improve performance? Can you show a benchmark and a flamegraph?

[Spinachboul]

Sure! I'll do that soon

[Spinachboul]

@ChrisRackauckas and @sathvikbhagavan I have drafted this PR since while benchmarking, I could only find some differences/improvements in terms of time and space I have attached a pdf describing the differences between my code and the original code. The sphere benchmarking will be done soon, withing a couple of days!! Differences table.pdf