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[WIP] Integrability constraints for flavour basis fits

Emanuele Roberto Nocera requested to merge integ into flavbasis

Created by: tgiani

First attempt to solve issue #761 (closed), not sure if this is the best way of doing this. We want to add a term to the loss function like for example

\lambda_{T_3} \sum_i (x_i*T_3(x_i,Q_0))^2,  [1]

with something like

x_i = 1e-6, 1e-5, 1e-4.

To do this we may use the same code already implemented for positivity datasets with some small variations.

Eq. [1] can be seen as the squared value of the theory prediction for a single datapoint dataset. This fake observable is defined by the FK table

{xGrid______________________________________________________
1.0000000000000000e-06
1.0000000000000000e-05
1.0000000000000000e-04

{FastKernel_________________________________________________
0       0       0       0       0       0       0       0       0       0       0       1.00000000      0       0       0       0
0       1       0       0       0       0       0       0       0       0       0       1.00000000      0       0       0       0
0       2       0       0       0       0       0       0       0       0       0       1.00000000      0       0       0       0

The other distributions for which we want a term like the one of Eq.[1] will correspond to analogous FK tables with the columns of 1 in a different position (for x^2*g and x^2*sgm we need to multiply also for the corresponding x value). We can then define some fake one-point positivity observables, denoted for example like INTEGXT3, implementing them in buildmaster and adding to the theory the corresponding FK. Doing this we can treat them almost as if they were positivity observables. The only difference should be the specific expression of the term we need to add at the loss function. In the case of a true positivity obs is an elu function of the theory prediction, while in this case it's the square of the theory prediction, as given in Eq.[1].

In these first commits I ve tried to do this considering only the distribution T_3 as an example, adding a new observable among the posdates. As FK table I ve used the one above (I ve literally pasted it under the preamble of a true FK table, I guess there is a better way of doing these..just to test the idea)

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