Farthest point sampling method

[AKaiser85]

The method selects those N structures form the training-set that are farthest from each other in terms of a distance norm in symmetry function values. To this end, it collects all symmetry function values for a single structure into a vector "allG", sorts allG, and calculates the distance 1/n*|allG[i]-allG[j]| for structures with the same number of atoms and elements.

This application was inspired by
https://doi.org/10.1063/1.5024611

[codecov-commenter]

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Codecov Report

❌ Patch coverage is 92.00000% with 14 lines in your changes missing coverage. Please review.
✅ Project coverage is 60.56%. Comparing base (af08e78) to head (d21ab22).
⚠️ Report is 377 commits behind head on master.

Files with missing lines	Patch %	Lines
src/application/nnp-fps.cpp	93.71%	10 Missing ⚠️
src/libnnp/Structure.cpp	75.00%	4 Missing ⚠️
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Additional details and impacted files

@@            Coverage Diff             @@
##           master      #13      +/-   ##
==========================================
+ Coverage   58.33%   60.56%   +2.22%     
==========================================
  Files          78       70       -8     
  Lines       11380    10040    -1340     
==========================================
- Hits         6639     6081     -558     
+ Misses       4741     3959     -782     

Flag	Coverage Δ
cpp	60.56% <92.00%> (+1.22%)	⬆️
python	?

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[singraber]

I have a little difficulty understanding the reasoning behind the ordering of allG in Structure.cpp:
https://github.com/AKaiser85/n2p2/blob/d21ab22a9cb75765e3952dd14162f517414a5287/src/libnnp/Structure.cpp#L888-L893

    // sort them elementwise
    for (vector<vector<float>>::iterator it1 = allG.begin();
         it1 != allG.end(); ++it1)
    {
        sort(it1->begin(), it1->end());
    }

because it shuffles completely the order of symmetry functions and atoms... I have to think about it...

[singraber]

I think it would be reasonable to move the farthest point sampling from the level of structures to the atomic level, i.e. compare not combined symmetry function vectors of entire structures but rather atomic environment fingerprints of individual atoms.