See the concurvity help file for GAMs and the last two measures in particular, applied to the rest of model or done pairwise. Not exactly sure how the measures work, but the second measure seems to based on fitted values norms of fitted values i.e., |\bm{X}\bm{\beta}|^2 and the third measures is based more on the Frobenius norm of basis itself. Both the second and third measures in mgcv are computed use QR decompositions.
See the concurvity help file for GAMs and the last two measures in particular, applied to the rest of model or done pairwise. Not exactly sure how the measures work, but the second measure seems to based on fitted values norms of fitted values i.e., |\bm{X}\bm{\beta}|^2 and the third measures is based more on the Frobenius norm of basis itself. Both the second and third measures in mgcv are computed use QR decompositions.