This function computes the psi_vec needed by the algorithm.
RSAVS_Get_Psi(y_vec, l_type = "L1", l_param = NULL)numeric vector
character string, type of loss function.
"L1": l-1 loss(absolute value loss)
"L2": l-2 loss(squared error loss)
"Huber": Huber loss. Its parameter is given in l_param.
Default value is "L1".
numeric vector containing necessary parameters of the corresponding loss function.
The default value is NULL.
the psi_vec
In the algorithm, when all \(\mu\) are shrinked to the same value, we have $$ \mu_0 = \mathrm{argmin}_{\mu} \sum_i\rho(y_i - \mu) $$ and $$ psi\_vec = (\psi(y_1 - \mu_0), \cdots, \psi(y_n - \mu_0)) $$ where \(\psi = \partial \rho\).
there is a SIGN different between this psi_vec and
\(\partial \rho\) w.r.t \(\mu\)
for non-differential loss like L1 at 0, the derivative at 0+ is returned.