Utility Classes

Apart from the operator classes, eko also provides some utility classes which are e.g. used in yadism

eko.thresholds.ThresholdsAtlas
- Implementation of the flavor number scheme and the quark thresholds both for the eko.couplings.Couplings and the operators
When running in VFNS it is important to specify the number of flavors active at each given scale, since the evolution path can be different depending of the chosen setting. This path is determined by eko.thresholds.ThresholdsAtlas.path().

Let us consider two examples to better illustrate how it works. Imagine to have a boundary condition q2_ref=1, nf_ref=3 with heavy quarks mass matching scales at: mc=2, mb=3, mt=4 and would like to evolve your object (PDF or \(a_s\)) to an higher scale (say q2_to=49). The corresponding ThresholdsAtlas will look like:
```
ThresholdsAtlas [0.00e+00 - 4.00e+00 - 9.00e+00 - 16.00e+00 - inf], ref=1.000000000000001 @ 3
```
and the evolution path will be given by:
```
[PathSegment(1 -> 4, nf=3), PathSegment(4 -> 9, nf=4), PathSegment(9 -> 16, nf=5), PathSegment(16 -> 49, nf=6)]
```
where automatically the number of flavors active in each eko.thresholds.PathSegment is determined according with the specified matching scales.

However some more complicated situations can arise when the boundary conditions are not given with the same prescription of the eko.thresholds.ThresholdAtlas. Let’s now consider as boundary condition q2_ref=64 with nf_ref=3:
```
ThresholdsAtlas [0.00e+00 - 4.00e+00 - 9.00e+00 - 16.00e+00 - inf], ref=64.000000000000001 @ 3
```
Again we would like to evolve to q2_to=49 but now giving a different number of active flavors to the final scale. Some possible paths are:
- a path to q2_to=49 with nf=6 which is given by the following list of eko.thresholds.PathSegment :
  [PathSegment(64 -> 4, nf=3), PathSegment(4 -> 9, nf=4), PathSegment(9 -> 16, nf=5), PathSegment(16 -> 49, nf=6)]
  and it’s determined according to the list of heavy quark thresholds. This path is default option when the argument nf_to is not given.
- A path to q2_to=49 enforcing nf=4:
  [PathSegment(64 -> 4, nf=3), PathSegment(4 -> 49, nf=4)]
- A path to q2_to=49 enforcing nf=3 which will simply contain a single eko.thresholds.PathSegment:
  [PathSegment(64 -> 49, nf=3)]
In the first two cases as first step, you go back to the closest matching scale (closest in nf), running in nf=3, since that is what has been specified in the boundary conditions. Then you are back in the flavor flow, and you cross all the other scales going according to the prescription given by the eko.thresholds.ThresholdAtlas. While in the third example you go directly to the final scale, since there is no matching scale in the middle. You can notice that eko.thresholds.ThresholdsAtlas.path() are always ordered according to nf and not q2 scales. This property is used in VFNS to determine if the matchings are done for an increasing or decreasing number of light flavors.
eko.couplings.Couplings: Implementation of the Strong Coupling
eko.interpolation.InterpolatorDispatcher: Implementation of the Interpolation