<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def _violinplot(val, shade, bw, ax, **kwargs_shade):
 """Auxiliary function to plot violinplots."""

    density, low_b, up_b = _fast_kde(val, bw=bw)
    x = np.linspace(low_b, up_b, len(density))

    x = np.concatenate([x, x[::-1]])
    density = np.concatenate([-density, density[::-1]])

    ax.fill_betweenx(x, density, alpha=shade, lw=0, **kwargs_shade)