class IPNDMScheduler(SchedulerMixin, ConfigMixin):
    """
    A fourth-order Improved Pseudo Linear Multistep scheduler.

    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
    methods the library implements for all schedulers such as loading and saving.

    Args:
        num_train_timesteps (`int`, defaults to 1000):
            The number of diffusion steps to train the model.
        trained_betas (`np.ndarray`, *optional*):
            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
    """

    order = 1

    @register_to_config
    def __init__(
        self, num_train_timesteps: int = 1000, trained_betas: Optional[Union[np.ndarray, List[float]]] = None
    ):
        # set `betas`, `alphas`, `timesteps`
        self.set_timesteps(num_train_timesteps)

        # standard deviation of the initial noise distribution
        self.init_noise_sigma = 1.0

        # For now we only support F-PNDM, i.e. the runge-kutta method
        # For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf
        # mainly at formula (9), (12), (13) and the Algorithm 2.
        self.pndm_order = 4

        # running values
        self.ets = []
        self._step_index = None
        self._begin_index = None

    @property
    def step_index(self):
        """
        The index counter for current timestep. It will increase 1 after each scheduler step.
        """
        return self._step_index

    @property
    def begin_index(self):
        """
        The index for the first timestep. It should be set from pipeline with `set_begin_index` method.
        """
        return self._begin_index

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.set_begin_index
    def set_begin_index(self, begin_index: int = 0):
        """
        Sets the begin index for the scheduler. This function should be run from pipeline before the inference.

        Args:
            begin_index (`int`):
                The begin index for the scheduler.
        """
        self._begin_index = begin_index

    def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
        """
        Sets the discrete timesteps used for the diffusion chain (to be run before inference).

        Args:
            num_inference_steps (`int`):
                The number of diffusion steps used when generating samples with a pre-trained model.
            device (`str` or `torch.device`, *optional*):
                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
        """
        self.num_inference_steps = num_inference_steps
        steps = torch.linspace(1, 0, num_inference_steps + 1)[:-1]
        steps = torch.cat([steps, torch.tensor([0.0])])

        if self.config.trained_betas is not None:
            self.betas = torch.tensor(self.config.trained_betas, dtype=torch.float32)
        else:
            self.betas = torch.sin(steps * math.pi / 2) ** 2

        self.alphas = (1.0 - self.betas**2) ** 0.5

        timesteps = (torch.atan2(self.betas, self.alphas) / math.pi * 2)[:-1]
        self.timesteps = timesteps.to(device)

        self.ets = []
        self._step_index = None
        self._begin_index = None

    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep
    def index_for_timestep(self, timestep, schedule_timesteps=None):
        if schedule_timesteps is None:
            schedule_timesteps = self.timesteps

        indices = (schedule_timesteps == timestep).nonzero()

        # The sigma index that is taken for the **very** first `step`
        # is always the second index (or the last index if there is only 1)
        # This way we can ensure we don't accidentally skip a sigma in
        # case we start in the middle of the denoising schedule (e.g. for image-to-image)
        pos = 1 if len(indices) > 1 else 0

        return indices[pos].item()

    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
    def _init_step_index(self, timestep):
        if self.begin_index is None:
            if isinstance(timestep, torch.Tensor):
                timestep = timestep.to(self.timesteps.device)
            self._step_index = self.index_for_timestep(timestep)
        else:
            self._step_index = self._begin_index

    def step(
        self,
        model_output: torch.Tensor,
        timestep: Union[int, torch.Tensor],
        sample: torch.Tensor,
        return_dict: bool = True,
    ) -> Union[SchedulerOutput, Tuple]:
        """
        Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
        the linear multistep method. It performs one forward pass multiple times to approximate the solution.

        Args:
            model_output (`torch.Tensor`):
                The direct output from learned diffusion model.
            timestep (`int`):
                The current discrete timestep in the diffusion chain.
            sample (`torch.Tensor`):
                A current instance of a sample created by the diffusion process.
            return_dict (`bool`):
                Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or tuple.

        Returns:
            [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
                If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
                tuple is returned where the first element is the sample tensor.
        """
        if self.num_inference_steps is None:
            raise ValueError(
                "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
            )
        if self.step_index is None:
            self._init_step_index(timestep)

        timestep_index = self.step_index
        prev_timestep_index = self.step_index + 1

        ets = sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
        self.ets.append(ets)

        if len(self.ets) == 1:
            ets = self.ets[-1]
        elif len(self.ets) == 2:
            ets = (3 * self.ets[-1] - self.ets[-2]) / 2
        elif len(self.ets) == 3:
            ets = (23 * self.ets[-1] - 16 * self.ets[-2] + 5 * self.ets[-3]) / 12
        else:
            ets = (1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4])

        prev_sample = self._get_prev_sample(sample, timestep_index, prev_timestep_index, ets)

        # upon completion increase step index by one
        self._step_index += 1

        if not return_dict:
            return (prev_sample,)

        return SchedulerOutput(prev_sample=prev_sample)

    def scale_model_input(self, sample: torch.Tensor, *args, **kwargs) -> torch.Tensor:
        """
        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
        current timestep.

        Args:
            sample (`torch.Tensor`):
                The input sample.

        Returns:
            `torch.Tensor`:
                A scaled input sample.
        """
        return sample

    def _get_prev_sample(self, sample, timestep_index, prev_timestep_index, ets):
        alpha = self.alphas[timestep_index]
        sigma = self.betas[timestep_index]

        next_alpha = self.alphas[prev_timestep_index]
        next_sigma = self.betas[prev_timestep_index]

        pred = (sample - sigma * ets) / max(alpha, 1e-8)
        prev_sample = next_alpha * pred + ets * next_sigma

        return prev_sample

    def __len__(self):
        return self.config.num_train_timesteps
/Users/nielsrogge/Documents/python_projecten/diffusers/src/diffusers/schedulers/scheduling_ipndm.py