# Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
# Copyright 2022 Stanford 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.
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#
#     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.
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# limitations under the License.

# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion

import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import paddle

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils import SchedulerMixin


@dataclass
# Copied from ppdiffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
class DDIMSchedulerOutput(BaseOutput):
    """
    Output class for the scheduler's step function output.

    Args:
        prev_sample (`paddle.Tensor` of shape `(batch_size, num_channels, height, width)` for images):
            Computed sample (x_{t-1}) of previous timestep. `prev_sample` should be used as next model input in the
            denoising loop.
        pred_original_sample (`paddle.Tensor` of shape `(batch_size, num_channels, height, width)` for images):
            The predicted denoised sample (x_{0}) based on the model output from the current timestep.
            `pred_original_sample` can be used to preview progress or for guidance.
    """

    prev_sample: paddle.Tensor
    pred_original_sample: Optional[paddle.Tensor] = None


def betas_for_alpha_bar(num_diffusion_timesteps,
                        max_beta=0.999) -> paddle.Tensor:
    """
    Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of
    (1-beta) over time from t = [0,1].

    Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up
    to that part of the diffusion process.


    Args:
        num_diffusion_timesteps (`int`): the number of betas to produce.
        max_beta (`float`): the maximum beta to use; use values lower than 1 to
                     prevent singularities.

    Returns:
        betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
    """

    def alpha_bar(time_step):
        return math.cos((time_step + 0.008) / 1.008 * math.pi / 2)**2

    betas = []
    for i in range(num_diffusion_timesteps):
        t1 = i / num_diffusion_timesteps
        t2 = (i + 1) / num_diffusion_timesteps
        betas.append(min(1 - alpha_bar(t2) / alpha_bar(t1), max_beta))
    return paddle.to_tensor(betas)


class DDIMScheduler(SchedulerMixin, ConfigMixin):
    """
    Denoising diffusion implicit models is a scheduler that extends the denoising procedure introduced in denoising
    diffusion probabilistic models (DDPMs) with non-Markovian guidance.

    [`~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`.
    [`~ConfigMixin`] also provides general loading and saving functionality via the [`~ConfigMixin.save_config`] and
    [`~ConfigMixin.from_config`] functions.

    For more details, see the original paper: https://arxiv.org/abs/2010.02502

    Args:
        num_train_timesteps (`int`): number of diffusion steps used to train the model.
        beta_start (`float`): the starting `beta` value of inference.
        beta_end (`float`): the final `beta` value.
        beta_schedule (`str`):
            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
            `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
        trained_betas (`np.ndarray`, optional):
            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
        clip_sample (`bool`, default `True`):
            option to clip predicted sample between -1 and 1 for numerical stability.
        set_alpha_to_one (`bool`, default `True`):
            each diffusion step uses the value of alphas product at that step and at the previous one. For the final
            step there is no previous alpha. When this option is `True` the previous alpha product is fixed to `1`,
            otherwise it uses the value of alpha at step 0.
        steps_offset (`int`, default `0`):
            an offset added to the inference steps. You can use a combination of `offset=1` and
            `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in
            stable diffusion.

    """

    @register_to_config
    def __init__(
        self,
        num_train_timesteps: int = 1000,
        beta_start: float = 0.0001,
        beta_end: float = 0.02,
        beta_schedule: str = "linear",
        trained_betas: Optional[np.ndarray] = None,
        clip_sample: bool = True,
        set_alpha_to_one: bool = True,
        steps_offset: int = 0,
    ):
        if trained_betas is not None:
            self.betas = paddle.to_tensor(trained_betas)
        elif beta_schedule == "linear":
            self.betas = paddle.linspace(beta_start,
                                         beta_end,
                                         num_train_timesteps,
                                         dtype="float32")
        elif beta_schedule == "scaled_linear":
            # this schedule is very specific to the latent diffusion model.
            self.betas = (paddle.linspace(beta_start**0.5,
                                          beta_end**0.5,
                                          num_train_timesteps,
                                          dtype="float32")**2)
        elif beta_schedule == "squaredcos_cap_v2":
            # Glide cosine schedule
            self.betas = betas_for_alpha_bar(num_train_timesteps)
        else:
            raise NotImplementedError(
                f"{beta_schedule} does is not implemented for {self.__class__}")

        self.alphas = 1.0 - self.betas
        self.alphas_cumprod = paddle.cumprod(self.alphas, 0)

        # At every step in ddim, we are looking into the previous alphas_cumprod
        # For the final step, there is no previous alphas_cumprod because we are already at 0
        # `set_alpha_to_one` decides whether we set this parameter simply to one or
        # whether we use the final alpha of the "non-previous" one.
        self.final_alpha_cumprod = paddle.to_tensor(
            1.0) if set_alpha_to_one else self.alphas_cumprod[0]

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

        # setable values
        self.num_inference_steps = None
        self.timesteps = paddle.to_tensor(
            np.arange(0, num_train_timesteps)[::-1].copy().astype("int64"))

    def scale_model_input(self,
                          sample: paddle.Tensor,
                          timestep: Optional[int] = None) -> paddle.Tensor:
        """
        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
        current timestep.

        Args:
            sample (`paddle.Tensor`): input sample
            timestep (`int`, optional): current timestep

        Returns:
            `paddle.Tensor`: scaled input sample
        """
        return sample

    def _get_variance(self, timestep, prev_timestep):
        alpha_prod_t = self.alphas_cumprod[timestep]
        alpha_prod_t_prev = self.alphas_cumprod[
            prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
        beta_prod_t = 1 - alpha_prod_t
        beta_prod_t_prev = 1 - alpha_prod_t_prev

        variance = (beta_prod_t_prev /
                    beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

        return variance

    def set_timesteps(self, num_inference_steps: int):
        """
        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
        step_ratio = self.config.num_train_timesteps // self.num_inference_steps
        # creates integer timesteps by multiplying by ratio
        # casting to int to avoid issues when num_inference_step is power of 3
        timesteps = (np.arange(0, num_inference_steps) *
                     step_ratio).round()[::-1].copy().astype("int64")
        self.timesteps = paddle.to_tensor(timesteps)
        self.timesteps += self.config.steps_offset

    def step(
        self,
        model_output: paddle.Tensor,
        timestep: int,
        sample: paddle.Tensor,
        eta: float = 0.0,
        use_clipped_model_output: bool = False,
        return_dict: bool = True,
    ) -> Union[DDIMSchedulerOutput, 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 (`paddle.Tensor`): direct output from learned diffusion model.
            timestep (`int`): current discrete timestep in the diffusion chain.
            sample (`paddle.Tensor`):
                current instance of sample being created by diffusion process.
            eta (`float`): weight of noise for added noise in diffusion step.
            use_clipped_model_output (`bool`): TODO
            return_dict (`bool`): option for returning tuple rather than DDIMSchedulerOutput class

        Returns:
            [`~schedulers.scheduling_utils.DDIMSchedulerOutput`] or `tuple`:
            [`~schedulers.scheduling_utils.DDIMSchedulerOutput`] 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"
            )

        # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
        # Ideally, read DDIM paper in-detail understanding

        # Notation (<variable name> -> <name in paper>
        # - pred_noise_t -> e_theta(x_t, t)
        # - pred_original_sample -> f_theta(x_t, t) or x_0
        # - std_dev_t -> sigma_t
        # - eta -> η
        # - pred_sample_direction -> "direction pointing to x_t"
        # - pred_prev_sample -> "x_t-1"

        # 1. get previous step value (=t-1)
        prev_timestep = timestep - self.config.num_train_timesteps // self.num_inference_steps

        # 2. compute alphas, betas
        alpha_prod_t = self.alphas_cumprod[timestep]
        alpha_prod_t_prev = self.alphas_cumprod[
            prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod

        beta_prod_t = 1 - alpha_prod_t

        # 3. compute predicted original sample from predicted noise also called
        # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        pred_original_sample = (sample - beta_prod_t**
                                (0.5) * model_output) / alpha_prod_t**(0.5)

        # 4. Clip "predicted x_0"
        if self.config.clip_sample:
            pred_original_sample = paddle.clip(pred_original_sample, -1, 1)

        # 5. compute variance: "sigma_t(η)" -> see formula (16)
        # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
        variance = self._get_variance(timestep, prev_timestep)
        std_dev_t = eta * variance**(0.5)

        if use_clipped_model_output:
            # the model_output is always re-derived from the clipped x_0 in Glide
            model_output = (sample - alpha_prod_t**
                            (0.5) * pred_original_sample) / beta_prod_t**(0.5)

        # 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        pred_sample_direction = (1 - alpha_prod_t_prev -
                                 std_dev_t**2)**(0.5) * model_output

        # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        prev_sample = alpha_prod_t_prev**(
            0.5) * pred_original_sample + pred_sample_direction

        if eta > 0:
            # randn_like does not support seed https://github.com/pytorch/pytorch/issues/27072
            noise = paddle.randn(model_output.shape, dtype=model_output.dtype)
            variance = self._get_variance(timestep,
                                          prev_timestep)**(0.5) * eta * noise

            prev_sample = prev_sample + variance

        if not return_dict:
            return (prev_sample, )

        return DDIMSchedulerOutput(prev_sample=prev_sample,
                                   pred_original_sample=pred_original_sample)

    def add_noise(
        self,
        original_samples: paddle.Tensor,
        noise: paddle.Tensor,
        timesteps: paddle.Tensor,
    ) -> paddle.Tensor:
        # Make sure alphas_cumprod and timestep have same dtype as original_samples
        self.alphas_cumprod = self.alphas_cumprod.astype(original_samples.dtype)

        sqrt_alpha_prod = self.alphas_cumprod[timesteps]**0.5
        sqrt_alpha_prod = sqrt_alpha_prod.flatten()
        while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
            sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)

        sqrt_one_minus_alpha_prod = (1 - self.alphas_cumprod[timesteps])**0.5
        sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
        while len(sqrt_one_minus_alpha_prod.shape) < len(
                original_samples.shape):
            sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)

        noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
        return noisy_samples

    def __len__(self):
        return self.config.num_train_timesteps
