human
I wrote the below code

    if (fun_jac is None):
        fun_jac_wrapped = None
    if (bc_jac is None):
        bc_jac_wrapped = None
    if (k == 0):
        def fun_p(x, y, _):
            return np.asarray(fun(x, y), dtype)
        def bc_wrapped(ya, yb, _):
            return np.asarray(bc(ya, yb), dtype)
        if (fun_jac is not None):
            def fun_jac_p(x, y, _):
                return (np.asarray(fun_jac(x, y), dtype), None)
        if (bc_jac is not None):
            def bc_jac_wrapped(ya, yb, _):
                (dbc_dya, dbc_dyb) = bc_jac(ya, yb)
                return (np.asarray(dbc_dya, dtype), np.asarray(dbc_dyb, dtype), None)
    else:
        def fun_p(x, y, p):
            return np.asarray(fun(x, y, p), dtype)
        def bc_wrapped(x, y, p):
            return np.asarray(bc(x, y, p), dtype)
        if (fun_jac is not None):
            def fun_jac_p(x, y, p):
                (df_dy, df_dp) = fun_jac(x, y, p)
                return (np.asarray(df_dy, dtype), np.asarray(df_dp, dtype))
        if (bc_jac is not None):
            def bc_jac_wrapped(ya, yb, p):
                (dbc_dya, dbc_dyb, dbc_dp) = bc_jac(ya, yb, p)
                return (np.asarray(dbc_dya, dtype), np.asarray(dbc_dyb, dtype), np.asarray(dbc_dp, dtype))
    if (S is None):
        fun_wrapped = fun_p
    else:
        def fun_wrapped(x, y, p):
            f = fun_p(x, y, p)
            if (x[0] == a):
                f[:, 0] = np.dot(D, f[:, 0])
                f[:, 1:] += (np.dot(S, y[:, 1:]) / (x[1:] - a))
            else:
                f += (np.dot(S, y) / (x - a))
            return f
    if (fun_jac is not None):
        if (S is None):
            fun_jac_wrapped = fun_jac_p
        else:
            Sr = S[:, :, np.newaxis]
            def fun_jac_wrapped(x, y, p):
                (df_dy, df_dp) = fun_jac_p(x, y, p)
                if (x[0] == a):
                    df_dy[:, :, 0] = np.dot(D, df_dy[:, :, 0])
                    df_dy[:, :, 1:] += (Sr / (x[1:] - a))
                else:
                    df_dy += (Sr /...

What's a good function header?

=====
Here's a good function header?
assistant
#Here's a good function header.

def wrap_functions(fun, bc, fun_jac, bc_jac, k, a, S, D, dtype):