  In this paper, we focus on Stochastic Amplitude Flow (SAF) for phase
retrieval, a stochastic gradient descent for the amplitude-based squared loss.
While the convergence to a critical point of (nonstochastic) Amplitude Flow is
well-understood, SAF is a much less studied algorithm. We close this gap by
deriving the convergence guarantees for SAF based on the contributions for
Amplitude Flow and analysis for stochastic gradient descent. These results are
then applied to two more algorithms, which can be seen as instances of SAF. The
first is an extension of the Kaczmarz method for phase retrieval. The second is
Ptychographic Iterative Engine, which is a popular algorithm for ptychography,
a special case of phase retrieval with the short-time Fourier transform.
  Keywords: phase retrieval, Amplitude Flow, stochastic gradient descent,
ptychography, Ptychographic Iterative Engine, Kaczmarz method.
