  We compute the first four perturbative coefficients of the internal energy
for the twisted reduced principal chiral model (TRPCM) using numerical
stochastic perturbation theory (NSPT). This matrix model has the same large $N$
limit as the ordinary principal chiral model (PCM) at infinite volume. Indeed,
we verify that the first three coefficients match the analytic result for the
PCM coefficients at large $N$ with a precision of three to four significant
digits. The fourth coefficient also matches our own NSPT calculation of the
corresponding PCM coefficient at large $N$. The finite-$N$ corrections to all
coefficients beyond the leading order are smaller for TRPCM than for PCM. We
analyze the variance to determine the feasibility of extending the calculations
to higher orders.
