C++ overhaul

[Enchufa2]

Whole algorithm rewritten in C++, which improves performance by a couple of orders of magnitude. In principle, tests still pass with few adjustments. But please test it carefully with known examples.

[codecov]

Codecov Report

❌ Patch coverage is 90.20772% with 33 lines in your changes missing coverage. Please review.
✅ Project coverage is 79.74%. Comparing base (e9f3dae) to head (3604a5a).

Files with missing lines	Patch %	Lines
src/taylor.h	69.04%	13 Missing ⚠️
src/nn2poly.cpp	92.64%	10 Missing ⚠️
R/plot_taylor_and_activation_potentials.R	0.00%	5 Missing ⚠️
src/partitions.cpp	91.42%	3 Missing ⚠️
src/partitions.h	97.40%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #77      +/-   ##
==========================================
+ Coverage   78.59%   79.74%   +1.15%     
==========================================
  Files          16       18       +2     
  Lines         710      780      +70     
==========================================
+ Hits          558      622      +64     
- Misses        152      158       +6     

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[Enchufa2]

Thought: we need to have a toy example computed by hand for the tests, simple enough to be doable, but complex enough to act as a gold standard to validate the algorithm. Something like

set.seed(1234)
(w <- list("tanh"   = matrix(rnorm(8, sd=0.3), nrow = 4, ncol = 2),
           "linear" = matrix(rnorm(3, sd=100), nrow = 3, ncol = 1)))
#> $tanh
#>             [,1]       [,2]
#> [1,] -0.36211972  0.1287374
#> [2,]  0.08322877  0.1518168
#> [3,]  0.32533235 -0.1724220
#> [4,] -0.70370931 -0.1639896
#> 
#> $linear
#>           [,1]
#> [1,] -56.44520
#> [2,] -89.00378
#> [3,] -47.71927
nn2poly::nn2poly(w, max_order = 4, taylor_orders = 5)
#> nn2poly p=3 max_order=4 (35 coefficients)
#>      Label         Value
#> 1        0 -31.659604601
#> 2        1 -13.647064990
#> 3        2 -17.397754477
#> 4        3  62.834901741
#> 5      1 1  -0.045760703
#> 6      1 2  -1.754732147
#> 7      1 3   2.816135856
#> 8      2 2  -2.636235198
#> 9      2 3  12.516969394
#> 10     3 3 -13.008416891
#> 11   1 1 1   0.060101496
#> 12   1 1 2  -0.081696362
#> 13   1 1 3  -0.374697060
#> 14   1 2 2  -0.081696362
#> 15   1 2 3  -1.230204385
#> 16   1 3 3  -0.374697060
#> 17   2 2 2   0.409603306
#> 18   2 2 3  -3.369221361
#> 19   2 3 3  -3.369221361
#> 20   3 3 3  -4.981328101
#> 21 1 1 1 1  -0.001144625
#> 22 1 1 1 2   0.026004139
#> 23 1 1 1 3  -0.025468972
#> 24 1 1 2 2   0.077681934
#> 25 1 1 2 3  -0.440929513
#> 26 1 1 3 3   0.427005053
#> 27 1 2 2 2   0.026004139
#> 28 1 2 2 3  -0.440929513
#> 29 1 2 3 3  -0.440929513
#> 30 1 3 3 3  -0.025468972
#> 31 2 2 2 2   0.237081539
#> 32 2 2 2 3  -2.096364041
#> 33 2 2 3 3   6.737475619
#> 34 2 3 3 3  -2.096364041
#> 35 3 3 3 3   5.266212538