def prox_likelihood_S(S, step, A=None, Y=None, prox_g=None, W=1):
    return prox_g((S - (step * grad_likelihood_S(S, A, Y, W=W))), step)
def prox_likelihood_S(S, step, A=None, Y=None, prox_g=None, W=1):
    return prox_g((S - (step * grad_likelihood_S(S, A, Y, W=W))), step)