# Copyright 2022 Zhejiang University Team and The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import math
from typing import Tuple, Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import SchedulerMixin, SchedulerOutput


class IPNDMScheduler(SchedulerMixin, ConfigMixin):
    """
    Improved Pseudo numerical methods for diffusion models (iPNDM) ported from @crowsonkb's amazing k-diffusion
    [library](https://github.com/crowsonkb/v-diffusion-pytorch/blob/987f8985e38208345c1959b0ea767a625831cc9b/diffusion/sampling.py#L296)

    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
    [`~SchedulerMixin.from_pretrained`] functions.

    For more details, see the original paper: https://arxiv.org/abs/2202.09778

    Args:
        num_train_timesteps (`int`): number of diffusion steps used to train the model.
    """

    order = 1

    @register_to_config
    def __init__(self, num_train_timesteps: int = 1000):
        # 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 = []

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

        Args:
            num_inference_steps (`int`):
                the number of diffusion steps used when generating samples with a pre-trained model.
        """
        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])])

        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 = []

    def step(
        self,
        model_output: torch.FloatTensor,
        timestep: int,
        sample: torch.FloatTensor,
        return_dict: bool = True,
    ) -> Union[SchedulerOutput, Tuple]:
        """
        Step function propagating the sample with the linear multi-step method. This has one forward pass with multiple
        times to approximate the solution.

        Args:
            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
            timestep (`int`): current discrete timestep in the diffusion chain.
            sample (`torch.FloatTensor`):
                current instance of sample being created by diffusion process.
            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class

        Returns:
            [`~scheduling_utils.SchedulerOutput`] or `tuple`: [`~scheduling_utils.SchedulerOutput`] if `return_dict` is
            True, otherwise a `tuple`. When returning a tuple, 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"
            )

        timestep_index = (self.timesteps == timestep).nonzero().item()
        prev_timestep_index = timestep_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)

        if not return_dict:
            return (prev_sample,)

        return SchedulerOutput(prev_sample=prev_sample)

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

        Args:
            sample (`torch.FloatTensor`): input sample

        Returns:
            `torch.FloatTensor`: 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
