  For the double power one dimensional nonlinear Schr{\"o}dinger equation, we
establish a complete classification of the stability or instability of standing
waves with positive frequencies. In particular, we fill out the gaps left open
by previous studies. Stability or instability follows from the analysis of the
slope criterion of Grillakis, Shatah and Strauss. The main new ingredients in
our approach are a reformulation of the slope and the explicit calculation of
the slope value in the zero-frequency case. Our theoretical results are
complemented with numerical experiments.
