def METHOD_NAME(S1, S2, reduction='mean'):
    """Do Procrustes alignment and compute reconstruction error."""
    S1_hat = compute_similarity_transform_batch(S1, S2)
    re = np.sqrt(((S1_hat - S2)**2).sum(axis=-1)).mean(axis=-1)
    if reduction == 'mean':
        re = re.mean()
    elif reduction == 'sum':
        re = re.sum()
    return re