  Utilizing the data set corresponding to an integrated luminosity of $3.19$
fb$^{-1}$ collected by the BESIII detector at a center-of-mass energy of 4.178
GeV, we perform an amplitude analysis of the $D_s^+\to\pi^+\pi^-\pi^+$ decay.
The sample contains 13,797 candidates with a signal purity of $\sim$80%. The
amplitude and phase of the contributing $\pi\pi$ ${\cal S}$ wave are measured
based on a quasi-model-independent approach, along with the amplitudes and
phases of the ${\cal P}$ and ${\cal D}$ waves parametrized by Breit-Wigner
models. The fit fractions of different intermediate decay channels are also
reported.
