Fmm prec plot

[Yrisch]

Description:
This PR fix the MASE test done in #774. It now follows what was actually done in NDSPMHD. It also adds a new routine in test_gravity.f90 that tests relative errors and performance of SFMM and FMM compared to direct sum on a plummer sphere with N particles varying between 10³ and 10⁶. A switch to toggle SFMM and FMM has been added for this purpose. However, the option is not shown in the infiles to stay with SFMM as the default.

Components modified:

• Setup (src/setup)
• Main code (src/main)
• Moddump utilities (src/utils/moddump)
• Analysis utilities (src/utils/analysis)
• Test suite (src/tests)
• Documentation (docs/)
• Build/CI (build/ or github actions)

Type of change:

• Bug fix
• Physics improvements
• Better initial conditions
• Performance improvements
• Documentation update
• Better testing
• Code cleanup / refactor
• Other (please describe)

Testing:
Changed the mase tolerance. No new physics...

Did you run the bots? no

Did you update relevant documentation in the docs directory? no

Did you add comments such that the purpose of the code is understandable? yes

[gemini-code-assist]

Summary of Changes

Hello @Yrisch, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request significantly enhances the robustness and analytical capabilities of the gravity solver tests. It addresses an existing bug in the MASE test by refining its calculation and tightening its tolerance, ensuring more accurate and stringent evaluations. Furthermore, it introduces a sophisticated new testing framework that allows for detailed performance and precision comparisons between SFMM, FMM, and direct summation across a range of particle numbers and accuracy settings, providing valuable data for understanding the methods' characteristics. The changes also include internal mechanisms for controlling the gravity solver and random number generation, primarily to support these new testing features.

Highlights

• MASE Test Fix and Tolerance Adjustment: The Mean Absolute Scaled Error (MASE) test, originally from PR (testgrav) added unit test for acceleration in Plummer sphere #774, has been corrected to align with the methodology used in NDSPMHD. The calculation of MASE has been revised, and the tolerance for this test has been significantly tightened from 1.2e-1 to 8.e-4, leading to a much stricter evaluation criterion.
• SFMM/FMM Switch for Testing: A new neigh_switch integer variable has been introduced in neigh_kdtree.f90 to allow toggling between Smoothed Fast Multipole Method (SFMM) and Fast Multipole Method (FMM) implementations. While this switch is configurable internally for testing purposes, it is intentionally not exposed in the input files to maintain SFMM as the default method for users.
• Centralized Random Seed for Monte Carlo Particle Generation: The random seed for Monte Carlo particle placement in set_sphere.f90 has been centralized into a public module variable iseed_mc. This allows for reproducible and controlled random number generation across multiple test realisations, improving the reliability of statistical tests.
• New Performance and Precision Plotting Routine: A comprehensive new routine (plot_SFMM and get_plummer_prec_perf) has been added to test_gravity.f90. This routine systematically evaluates the relative errors and performance of SFMM and FMM compared to direct summation on a Plummer sphere. It tests varying particle counts (from 10^3 to 10^6) and different tree accuracy parameters, outputting data suitable for plotting performance and precision curves.

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[gemini-code-assist]

Code Review

This pull request addresses a MASE test fix and introduces a new routine to evaluate the precision and performance of SFMM and FMM against direct summation on a Plummer sphere. The changes involve refactoring the neighbor-finding logic to use a neigh_switch variable, making the random seed for Monte Carlo simulations configurable, and updating the MASE calculation. The new plot_SFMM and get_plummer_prec_perf subroutines provide valuable testing capabilities for the gravity solver.

[gemini-code-assist]

The assignment fxyz_dir = fxyzu(1:3,1:npart) is repeated three times consecutively. This is redundant and can be simplified to a single assignment to improve efficiency and readability.

fxyz_dir = fxyzu(1:3,1:npart)