Reconstruction of nonlinear fluctuations in the rms of the cosmic matter field. The solid curves represent $\log {\sigma }_{NL}^{-1}$ as a function of M and are reconstructed from measurements of median prolaticity deduced from the shape of the halos (as a function of the halo mass) and from the universal relations between median prolaticity and $\log {\sigma }_{NL}^{-1}$. The agreement with the expected nonlinear fluctuations (dotted lines) of the cosmic matter field derived from simulations and calculated with Power-grid at z = 0 is excellent. We have also plotted (dashed lines) $\log {\sigma }_L^{-1}(M)$ for comparison: the shape measurements undoubtedly give information about the nonlinear fluctuations of the cosmic matter champ that are distinct from the linear fluctuations on the scale of the DM halo.