How to use the torchdiffeq._impl.solvers.AdaptiveStepsizeODESolver function in torchdiffeq

f0 = tuple(k_[0] for k_ in k)
    f1 = tuple(k_[-1] for k_ in k)
    return _interp_fit(y0, y1, y_mid, f0, f1, dt)


def _abs_square(x):
    return torch.mul(x, x)


def _ta_append(list_of_tensors, value):
    """Append a value to the end of a list of PyTorch tensors."""
    list_of_tensors.append(value)
    return list_of_tensors


class AdaptiveHeunSolver(AdaptiveStepsizeODESolver):

    def __init__(
        self, func, y0, rtol, atol, first_step=None, safety=0.9, ifactor=10.0, dfactor=0.2, max_num_steps=2**31 - 1,
        **unused_kwargs
    ):
        _handle_unused_kwargs(self, unused_kwargs)
        del unused_kwargs

        self.func = func
        self.y0 = y0
        self.rtol = rtol if _is_iterable(rtol) else [rtol] * len(y0)
        self.atol = atol if _is_iterable(atol) else [atol] * len(y0)
        self.first_step = first_step
        self.safety = _convert_to_tensor(safety, dtype=torch.float64, device=y0[0].device)
        self.ifactor = _convert_to_tensor(ifactor, dtype=torch.float64, device=y0[0].device)
        self.dfactor = _convert_to_tensor(dfactor, dtype=torch.float64, device=y0[0].device)

f0 = tuple(k_[0] for k_ in k)
    f1 = tuple(k_[-1] for k_ in k)
    return _interp_fit(y0, y1, y_mid, f0, f1, dt)


def _abs_square(x):
    return torch.mul(x, x)


def _ta_append(list_of_tensors, value):
    """Append a value to the end of a list of PyTorch tensors."""
    list_of_tensors.append(value)
    return list_of_tensors


class Dopri5Solver(AdaptiveStepsizeODESolver):

    def __init__(
        self, func, y0, rtol, atol, first_step=None, safety=0.9, ifactor=10.0, dfactor=0.2, max_num_steps=2**31 - 1,
        **unused_kwargs
    ):
        _handle_unused_kwargs(self, unused_kwargs)
        del unused_kwargs

        self.func = func
        self.y0 = y0
        self.rtol = rtol if _is_iterable(rtol) else [rtol] * len(y0)
        self.atol = atol if _is_iterable(atol) else [atol] * len(y0)
        self.first_step = first_step
        self.safety = _convert_to_tensor(safety, dtype=torch.float64, device=y0[0].device)
        self.ifactor = _convert_to_tensor(ifactor, dtype=torch.float64, device=y0[0].device)
        self.dfactor = _convert_to_tensor(dfactor, dtype=torch.float64, device=y0[0].device)