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]

Codecov Report

Merging #13 into master will increase coverage by 1.08%.
The diff coverage is 92.00%.

@@            Coverage Diff             @@
##           master      #13      +/-   ##
==========================================
+ Coverage   58.33%   59.42%   +1.08%     
==========================================
  Files          78       79       +1     
  Lines       11380    11555     +175     
==========================================
+ Hits         6639     6866     +227     
+ Misses       4741     4689      -52     

Flag	Coverage Δ
#cpp	60.56% <92.00%> (+1.22%)	⬆️
#python	59.42% <92.00%> (+1.08%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files	Coverage Δ
src/libnnp/Structure.cpp	66.60% <75.00%> (+0.47%)	⬆️
src/application/nnp-fps.cpp	93.71% <93.71%> (ø)
src/libnnp/SymmetryFunction.cpp	94.77% <0.00%> (+0.74%)	⬆️
src/libnnp/SymmetryFunctionAngularNarrow.cpp	84.54% <0.00%> (+0.90%)	⬆️
src/libnnp/SymmetryFunctionRadial.cpp	78.51% <0.00%> (+1.65%)	⬆️
src/libnnp/SymmetryFunctionAngularWide.cpp	82.29% <0.00%> (+2.39%)	⬆️
src/libnnp/Mode.cpp	72.56% <0.00%> (+4.86%)	⬆️
src/libnnp/Element.cpp	84.97% <0.00%> (+9.84%)	⬆️

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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.