How to use the pyodesys.util._ensure_4args function in pyodesys

try:
            if len(exprs) != ny:
                raise ValueError("Callback returned unexpected (%d) number of expressions: %d" % (ny, len(exprs)))
        except TypeError:
            raise ValueError("Callback did not return an array_like of expressions: %s" % str(exprs))

        cls._kwargs_roots_from_roots_cb(roots_cb, kwargs, x, _y, _p, be)

        if first_step_factory is not None:
            if 'first_step_exprs' in kwargs:
                raise ValueError("Cannot override first_step_exprs.")
            try:
                kwargs['first_step_expr'] = first_step_factory(x, _y, _p, be)
            except TypeError:
                kwargs['first_step_expr'] = _ensure_4args(first_step_factory)(x, _y, _p, be)
        if kwargs.get('dep_by_name', False):
            exprs = [exprs[k] for k in names]
        return cls(zip(y, exprs), x, kwargs.pop('params', None) if len(p) == 0 else p,
                   backend=be, names=names, **kwargs)

be = Backend(kwargs.pop('backend', None))
        names = tuple(kwargs.pop('names', ''))
        indep_name = indep_name or _get_indep_name(names)
        try:
            x = be.Symbol(indep_name, real=True)
        except TypeError:
            x = be.Symbol(indep_name)
        y = be.real_symarray('y', ny)
        p = be.real_symarray('p', nparams)
        _y = dict(zip(names, y)) if kwargs.get('dep_by_name', False) else y
        _p = dict(zip(kwargs['param_names'], p)) if kwargs.get('par_by_name', False) else p

        try:
            exprs = rhs(x, _y, _p, be)
        except TypeError:
            exprs = _ensure_4args(rhs)(x, _y, _p, be)

        try:
            if len(exprs) != ny:
                raise ValueError("Callback returned unexpected (%d) number of expressions: %d" % (ny, len(exprs)))
        except TypeError:
            raise ValueError("Callback did not return an array_like of expressions: %s" % str(exprs))

        cls._kwargs_roots_from_roots_cb(roots_cb, kwargs, x, _y, _p, be)

        if first_step_factory is not None:
            if 'first_step_exprs' in kwargs:
                raise ValueError("Cannot override first_step_exprs.")
            try:
                kwargs['first_step_expr'] = first_step_factory(x, _y, _p, be)
            except TypeError:
                kwargs['first_step_expr'] = _ensure_4args(first_step_factory)(x, _y, _p, be)

callables should have the signature ``f(x) -> expression`` in x
        roots_cb : callable
            Callback with signature ``roots(x, y[:], p[:], backend=math) -> r[:]``.
            Callback should return untransformed roots.
        \\*\\*kwargs :
            Keyword arguments passed onto :class:`TransformedSys`.

        """
        ny, nparams = _get_ny_nparams_from_kw(ny, nparams, kwargs)
        be = Backend(kwargs.pop('backend', None))
        x, = be.real_symarray('x', 1)
        y = be.real_symarray('y', ny)
        p = be.real_symarray('p', nparams)
        _y = dict(zip(kwargs['names'], y)) if kwargs.get('dep_by_name', False) else y
        _p = dict(zip(kwargs['param_names'], p)) if kwargs.get('par_by_name', False) else p
        exprs = _ensure_4args(cb)(x, _y, _p, be)
        if dep_transf_cbs is not None:
            dep_transf = [(fw(yi), bw(yi)) for (fw, bw), yi
                          in zip(dep_transf_cbs, y)]
        else:
            dep_transf = None

        if indep_transf_cbs is not None:
            indep_transf = indep_transf_cbs[0](x), indep_transf_cbs[1](x)
        else:
            indep_transf = None
        if kwargs.get('dep_by_name', False):
            exprs = [exprs[k] for k in kwargs['names']]

        cls._kwargs_roots_from_roots_cb(roots_cb, kwargs, x, _y, _p, be)

        return cls(list(zip(y, exprs)), x, dep_transf,

def _kwargs_roots_from_roots_cb(roots_cb, kwargs, x, _y, _p, be):
        if roots_cb is not None:
            if 'roots' in kwargs:
                raise ValueError("Keyword argument ``roots`` already given.")

            try:
                roots = roots_cb(x, _y, _p, be)
            except TypeError:
                roots = _ensure_4args(roots_cb)(x, _y, _p, be)

            kwargs['roots'] = roots

def __init__(self, f, jac=None, dfdx=None, jtimes=None, first_step_cb=None, roots_cb=None, nroots=None,
                 band=None, names=(), param_names=(), indep_name=None, description=None, dep_by_name=False,
                 par_by_name=False, latex_names=(), latex_param_names=(), latex_indep_name=None,
                 taken_names=None, pre_processors=None, post_processors=None, append_iv=False,
                 autonomous_interface=None, to_arrays_callbacks=None, autonomous_exprs=None,
                 _indep_autonomous_key=None, numpy=None, nnz=-1, **kwargs):
        self.f_cb = _ensure_4args(f)
        self.j_cb = _ensure_4args(jac) if jac is not None else None
        self.jtimes_cb = _ensure_4args(jtimes) if jtimes is not None else None
        self.dfdx_cb = dfdx
        self.first_step_cb = first_step_cb
        self.roots_cb = roots_cb
        self.nroots = nroots or 0
        if band is not None:
            if not band[0] >= 0 or not band[1] >= 0:
                raise ValueError("bands needs to be > 0 if provided")
        self.band = band
        self.nnz = nnz
        self.names = tuple(names or ())
        self.param_names = tuple(param_names or ())
        self.indep_name = indep_name
        self.description = description
        self.dep_by_name = dep_by_name
        self.par_by_name = par_by_name
        self.latex_names = tuple(latex_names or ())

def __init__(self, f, jac=None, dfdx=None, jtimes=None, first_step_cb=None, roots_cb=None, nroots=None,
                 band=None, names=(), param_names=(), indep_name=None, description=None, dep_by_name=False,
                 par_by_name=False, latex_names=(), latex_param_names=(), latex_indep_name=None,
                 taken_names=None, pre_processors=None, post_processors=None, append_iv=False,
                 autonomous_interface=None, to_arrays_callbacks=None, autonomous_exprs=None,
                 _indep_autonomous_key=None, numpy=None, nnz=-1, **kwargs):
        self.f_cb = _ensure_4args(f)
        self.j_cb = _ensure_4args(jac) if jac is not None else None
        self.jtimes_cb = _ensure_4args(jtimes) if jtimes is not None else None
        self.dfdx_cb = dfdx
        self.first_step_cb = first_step_cb
        self.roots_cb = roots_cb
        self.nroots = nroots or 0
        if band is not None:
            if not band[0] >= 0 or not band[1] >= 0:
                raise ValueError("bands needs to be > 0 if provided")
        self.band = band
        self.nnz = nnz
        self.names = tuple(names or ())
        self.param_names = tuple(param_names or ())
        self.indep_name = indep_name
        self.description = description
        self.dep_by_name = dep_by_name
        self.par_by_name = par_by_name

def __init__(self, original_system, analytic_factory, **kwargs):
        self._ori_sys = original_system
        self.analytic_factory = _ensure_4args(analytic_factory)
        roots = kwargs.pop('roots', self._ori_sys.roots)
        _be = self._ori_sys.be
        init_indep = self._ori_sys.init_indep or self._mk_init_indep(name=self._ori_sys.indep, be=self._ori_sys.be)
        init_dep = self._ori_sys.init_dep or self._ori_sys._mk_init_dep()
        if 'pre_processors' in kwargs or 'post_processors' in kwargs:
            raise NotImplementedError("Cannot override pre-/postprocessors")
        if 'backend' in kwargs and Backend(kwargs['backend']) != _be:
            raise ValueError("Cannot mix backends.")
        _pars = self._ori_sys.params
        if self._ori_sys.par_by_name:
            _pars = dict(zip(self._ori_sys.param_names, _pars))

        self.original_dep = self._ori_sys.dep
        _dep0 = (dict(zip(self.original_dep, init_dep)) if self._ori_sys.dep_by_name
                 else init_dep)
        self.analytic_exprs = self.analytic_factory(init_indep, _dep0, _pars, _be)