# The theorycovariance module

The theorycovariance module deals with constructing, testing and outputting theory covariance matrices (covmats). Primarily, it is concerned with scale variation covariance matrices used to model missing higher order uncertainties. See the short and long NNPDF papers for in-depth information.

## Summary

• The module of validphys2 which deals with computation and interpretation of theoretical covariance matrices can be found in nnpdf/validphys2/src/validphys/theorycovariance/, which consists of three files:

1. construction.py: deals with construction of covariance matrices and associated quantities

2. output.py: plots and tables

3. tests.py: actions for validating the covariance matrices against the NNLO-NLO shift

• Theoretical covariance matrices are built according to the various prescriptions in Point prescriptions for theory covariance matrices.

• The prescription must be one of 3(f, r) point, 5(bar) point, 7(original) point or 9 point, see definitions. You can specify this using point_prescription: "x point" in the runcard. The translation of this flag into the relevant theoryids is handled by the scalevariations module in validphys.

• As input you need theories for the relevant scale combinations which correspond to the prescription. This information is taken from the scalevariations module, which consists of two files:

1. pointprescriptions.yaml: correspondence between each point prescription and the scale combinations that are used to construct it

2. scalevariationtheoryids.yaml: correspondence between each scale combination and a theoryid for a given central theoryid

• Renormalisation scales should be correlated within each process type. These process types are categorised as {DIS CC, DIS NC, Drell-Yan, Jets, Top}.

• Outputs includes tables and heat plots of theoretical and combined (theoretical + experimental) covariance matrices, comparisons of theoretical and experimental errors, and plots and tables of $$\chi^2$$ values.

• Various testing outputs also exist, including tables of eigenvalues, plots of eigenvectors and shift vs theory comparisons.