# Condition number selection of structuresΒΆ

Here, a large pool of randomized structures is used, after which we try to select an optimal small subset of structures for training. Optimal subset refers to the subset that has the smallest condition number for the linear problem

\[\boldsymbol{X}\boldsymbol{w} = \boldsymbol{y}\]

where \(\boldsymbol{X}\) is the sensing matrix (cluster-vectors), \(\boldsymbol{w}\) the solution (ECIs) and \(\boldsymbol{y}\) the target values (DFT energies).

This procedure is illustrated in a tutorial on the icet homepage.