import warnings
from typing import Tuple, Union

import torch
from diffusers.schedulers.scheduling_lms_discrete import \
    LMSDiscreteScheduler as _LMSDiscreteScheduler
from diffusers.schedulers.scheduling_lms_discrete import \
    LMSDiscreteSchedulerOutput


class LMSDiscreteScheduler(_LMSDiscreteScheduler):

    def step(
        self,
        model_output: torch.FloatTensor,
        step_index: int,
        sample: torch.FloatTensor,
        order: int = 4,
        return_dict: bool = True,
    ) -> Union[LMSDiscreteSchedulerOutput, Tuple]:
        """
        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
        process from the learned model outputs (most often the predicted noise).

        Args:
            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
            timestep (`float`): current timestep in the diffusion chain.
            sample (`torch.FloatTensor`):
                current instance of sample being created by diffusion process.
            order: coefficient for multi-step inference.
            return_dict (`bool`): option for returning tuple rather than LMSDiscreteSchedulerOutput class

        Returns:
            [`~schedulers.scheduling_utils.LMSDiscreteSchedulerOutput`] or `tuple`:
            [`~schedulers.scheduling_utils.LMSDiscreteSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`.
            When returning a tuple, the first element is the sample tensor.

        """
        if not self.is_scale_input_called:
            warnings.warn(
                "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
                "See `StableDiffusionPipeline` for a usage example."
            )

        sigma = self.sigmas[step_index]

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        if self.config.prediction_type == "epsilon":
            pred_original_sample = sample - sigma * model_output
        elif self.config.prediction_type == "v_prediction":
            # * c_out + input * c_skip
            pred_original_sample = model_output * \
                (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
        else:
            raise ValueError(
                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"
            )

        # 2. Convert to an ODE derivative
        derivative = (sample - pred_original_sample) / sigma
        self.derivatives.append(derivative)
        if len(self.derivatives) > order:
            self.derivatives.pop(0)

        # 3. Compute linear multistep coefficients
        order = min(step_index + 1, order)
        lms_coeffs = [self.get_lms_coefficient(
            order, step_index, curr_order) for curr_order in range(order)]

        # 4. Compute previous sample based on the derivatives path
        prev_sample = sample + sum(
            coeff * derivative for coeff, derivative in zip(lms_coeffs, reversed(self.derivatives))
        )

        if not return_dict:
            return (prev_sample,)

        return LMSDiscreteSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_sample)

    def scale_model_input(
        self, 
        sample: torch.FloatTensor,
        iteration: int
    ) -> torch.FloatTensor:
        """
        Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the K-LMS algorithm.

        Args:
            sample (`torch.FloatTensor`): input sample
            timestep (`float` or `torch.FloatTensor`): the current timestep in the diffusion chain

        Returns:
            `torch.FloatTensor`: scaled input sample
        """
        sample = sample / ((self.sigmas[iteration]**2 + 1) ** 0.5)
        self.is_scale_input_called = True
        return sample