Table 1: Means and Pearson correlation coefficient $r_{\rm p}^2$ of the decomposition order $n_{\max}$, the scale size $\beta $, the flux F, the components of the ellipticity $\epsilon $, and the axis ratio r of the true shapelet model (denoted by 0) and the reconstruction using the two implementations. $\langle R_{\rm s}\rangle$ is the mean distance in shapelet space between the true model and the reconstructions (defined in 16). In the last line the mean centroid shift between the model and the reconstruction is given; consider that the IDL implementation iteratively corrects the centroid, whereas the C++ implementation keeps it fixed.
  Model C++ IDL
$\langle n_{\max}\rangle$ 8 9.791 11.969
$r_{\rm p}^2(\beta^0,\beta)$ 1 0.984 0.949
$\langle F\rangle$ 8.478 8.478 8.406
$r_{\rm p}^2(F^0,F)$ 1 0.999 0.811
$r_{\rm p}^2(\epsilon_1^0,\epsilon_1)$ 1 0.999 0.894
$r_{\rm p}^2(\epsilon_2^0,\epsilon_2)$ 1 0.999 0.976
$r_{\rm p}^2(r^0,r)$ 1 0.989 0.771
$\langle R_{\rm s}\rangle$ 0 0.025 0.040
$\langle \vert\Delta {\vec x}_{\rm c}\vert\rangle$ 0 0.580 0.549


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