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In this note we describe how to complement the neutrino evolution matrixcalculated at a given energy and trajectory with additional information whichallows to reliably extrapolate it to nearby energies or trajectories withoutrepeating the full computation. Our method works for arbitrary matter densityprofiles, can be applied to any propagation model described by an Hamiltonian,and exactly guarantees the unitarity of the evolution matrix. As astraightforward application, we show how to enhance the calculation of thetheoretical predictions for experimentally measured quantities, so that theyremain accurate even in the presence of fast neutrino oscillations.Furthermore, the ability to "move around" a given energy and trajectory opensthe door to precise interpolation of the oscillation amplitudes within a gridof tabulated values, with potential benefits for the computation speed ofMonte-Carlo codes. We also provide a set of examples to illustrate the mostprominent features of our approach.

From ray to spray: augmenting amplitudes and taming fast oscillations in fully numerical neutrino codes