from __future__ import annotations

from collections.abc import Generator







def     A__	(       __A						):







    '''simple docstring'''
    if not isinstance(__A ,			__A						) or n < 1:
        raise Exception("""Sequence only defined for positive integers"""						)

    yield n
    while n != 1:
        if n % 2 == 0:
            n //= 2
        else:
            _lowerCamelCase  :		List[str]			    =    3 * n + 1
        yield n







def     A__	(       ):







    '''simple docstring'''
    _lowerCamelCase  :		List[str]			    =    43
    _lowerCamelCase  :		Optional[int]			    =    tuple(collatz_sequence(__A						)						)
    print(__A						)
    print(F"""Collatz sequence from {n} took {len(__A						)} steps."""						)


if __name__ == "__main__":
    main()





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

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, logging, randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin


lowerCAmelCase      :				Dict     			=logging.get_logger(__name__)  # pylint: disable=invalid-name




@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class 						__snake_case						(			__lowerCAmelCase		):





      '''simple docstring'''






      _snake_case     		=							42
      _snake_case     		=							None







def     A__	(       __A ,			__A=0.999 ,			__A="cosine" ,			):







    '''simple docstring'''
    if alpha_transform_type == "cosine":

        def alpha_bar_fn(__A						):
            return math.cos((t + 0.008) / 1.008 * math.pi / 2						) ** 2

    elif alpha_transform_type == "exp":

        def alpha_bar_fn(__A						):
            return math.exp(t * -12.0						)

    else:
        raise ValueError(F"""Unsupported alpha_tranform_type: {alpha_transform_type}"""						)

    _lowerCamelCase  :		int			    =    []
    for i in range(__A						):
        _lowerCamelCase  :		Optional[int]			    =    i / num_diffusion_timesteps
        _lowerCamelCase  :		int			    =    (i + 1) / num_diffusion_timesteps
        betas.append(min(1 - alpha_bar_fn(__A						) / alpha_bar_fn(__A						) ,			__A						)						)
    return torch.tensor(__A ,			dtype=torch.floataa						)




class 						__snake_case						(			__lowerCAmelCase			,	__lowerCAmelCase		):





      '''simple docstring'''






      _snake_case     		=							[e.name for e in KarrasDiffusionSchedulers]
      _snake_case     		=							1



      @register_to_config
      def __init__(       self  :					Tuple     ,	_UpperCamelCase  :					int = 1000     ,	_UpperCamelCase  :					float = 0.0_0_0_1     ,	_UpperCamelCase  :					float = 0.0_2     ,	_UpperCamelCase  :					str = "linear"     ,	_UpperCamelCase  :					Optional[Union[np.ndarray, List[float]]] = None     ,	_UpperCamelCase  :					str = "epsilon"     ,	_UpperCamelCase  :					str = "linspace"     ,	_UpperCamelCase  :					int = 0     ,	)					->Optional[int]:


          """simple docstring"""


          if trained_betas is not None:
              _lowerCamelCase  :		List[str]			    =    torch.tensor(_UpperCamelCase     ,	dtype=torch.floataa)
          elif beta_schedule == "linear":
              _lowerCamelCase  :		List[str]			    =    torch.linspace(_UpperCamelCase     ,	_UpperCamelCase     ,	_UpperCamelCase     ,	dtype=torch.floataa)
          elif beta_schedule == "scaled_linear":
              # this schedule is very specific to the latent diffusion model.
              _lowerCamelCase  :		int			    =    (
                  torch.linspace(beta_start**0.5     ,	beta_end**0.5     ,	_UpperCamelCase     ,	dtype=torch.floataa) ** 2
              )
          elif beta_schedule == "squaredcos_cap_v2":
              # Glide cosine schedule
              _lowerCamelCase  :		Any			    =    betas_for_alpha_bar(_UpperCamelCase)
          else:
              raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}""")

          _lowerCamelCase  :		Tuple			    =    1.0 - self.betas
          _lowerCamelCase  :		int			    =    torch.cumprod(self.alphas     ,	dim=0)

          _lowerCamelCase  :		Tuple			    =    np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
          _lowerCamelCase  :		Dict			    =    np.concatenate([sigmas[::-1], [0.0]]).astype(np.floataa)
          _lowerCamelCase  :		Tuple			    =    torch.from_numpy(_UpperCamelCase)

          # setable values
          _lowerCamelCase  :		List[str]			    =    None
          _lowerCamelCase  :		int			    =    np.linspace(0     ,	num_train_timesteps - 1     ,	_UpperCamelCase     ,	dtype=_UpperCamelCase)[::-1].copy()
          _lowerCamelCase  :		Optional[Any]			    =    torch.from_numpy(_UpperCamelCase)
          _lowerCamelCase  :		Tuple			    =    False



      @property
      def 						_SCREAMING_SNAKE_CASE     (       self  :					List[str])					->Dict:


          """simple docstring"""


          if self.config.timestep_spacing in ["linspace", "trailing"]:
              return self.sigmas.max()

          return (self.sigmas.max() ** 2 + 1) ** 0.5



      def 						_SCREAMING_SNAKE_CASE     (       self  :					int     ,	_UpperCamelCase  :					torch.FloatTensor     ,	_UpperCamelCase  :					Union[float, torch.FloatTensor])					->torch.FloatTensor:


          """simple docstring"""


          if isinstance(_UpperCamelCase     ,	torch.Tensor):
              _lowerCamelCase  :		Optional[int]			    =    timestep.to(self.timesteps.device)
          _lowerCamelCase  :		Tuple			    =    (self.timesteps == timestep).nonzero().item()
          _lowerCamelCase  :		str			    =    self.sigmas[step_index]
          _lowerCamelCase  :		List[str]			    =    sample / ((sigma**2 + 1) ** 0.5)
          _lowerCamelCase  :		str			    =    True
          return sample



      def 						_SCREAMING_SNAKE_CASE     (       self  :					Tuple     ,	_UpperCamelCase  :					int     ,	_UpperCamelCase  :					Union[str, torch.device] = None)					->int:


          """simple docstring"""


          _lowerCamelCase  :		Union[str, Any]			    =    num_inference_steps

          # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
          if self.config.timestep_spacing == "linspace":
              _lowerCamelCase  :		Any			    =    np.linspace(0     ,	self.config.num_train_timesteps - 1     ,	_UpperCamelCase     ,	dtype=_UpperCamelCase)[
                  ::-1
              ].copy()
          elif self.config.timestep_spacing == "leading":
              _lowerCamelCase  :		Tuple			    =    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
              _lowerCamelCase  :		List[Any]			    =    (np.arange(0     ,	_UpperCamelCase) * step_ratio).round()[::-1].copy().astype(_UpperCamelCase)
              timesteps += self.config.steps_offset
          elif self.config.timestep_spacing == "trailing":
              _lowerCamelCase  :		List[str]			    =    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
              _lowerCamelCase  :		str			    =    (np.arange(self.config.num_train_timesteps     ,	0     ,	-step_ratio)).round().copy().astype(_UpperCamelCase)
              timesteps -= 1
          else:
              raise ValueError(
                  F"""{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'.""")

          _lowerCamelCase  :		Tuple			    =    np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
          _lowerCamelCase  :		Union[str, Any]			    =    np.interp(_UpperCamelCase     ,	np.arange(0     ,	len(_UpperCamelCase))     ,	_UpperCamelCase)
          _lowerCamelCase  :		Optional[int]			    =    np.concatenate([sigmas, [0.0]]).astype(np.floataa)
          _lowerCamelCase  :		Dict			    =    torch.from_numpy(_UpperCamelCase).to(device=_UpperCamelCase)
          if str(_UpperCamelCase).startswith("""mps"""):
              # mps does not support float64
              _lowerCamelCase  :		List[str]			    =    torch.from_numpy(_UpperCamelCase).to(_UpperCamelCase     ,	dtype=torch.floataa)
          else:
              _lowerCamelCase  :		Any			    =    torch.from_numpy(_UpperCamelCase).to(device=_UpperCamelCase)



      def 						_SCREAMING_SNAKE_CASE     (       self  :					Union[str, Any]     ,	_UpperCamelCase  :					torch.FloatTensor     ,	_UpperCamelCase  :					Union[float, torch.FloatTensor]     ,	_UpperCamelCase  :					torch.FloatTensor     ,	_UpperCamelCase  :					Optional[torch.Generator] = None     ,	_UpperCamelCase  :					bool = True     ,	)					->Union[EulerAncestralDiscreteSchedulerOutput, Tuple]:


          """simple docstring"""


          if (
              isinstance(_UpperCamelCase     ,	_UpperCamelCase)
              or isinstance(_UpperCamelCase     ,	torch.IntTensor)
              or isinstance(_UpperCamelCase     ,	torch.LongTensor)
          ):
              raise ValueError(
                  (
                      """Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"""
                      """ `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"""
                      """ one of the `scheduler.timesteps` as a timestep."""
                  )     ,	)

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

          if isinstance(_UpperCamelCase     ,	torch.Tensor):
              _lowerCamelCase  :		Optional[Any]			    =    timestep.to(self.timesteps.device)

          _lowerCamelCase  :		Optional[int]			    =    (self.timesteps == timestep).nonzero().item()
          _lowerCamelCase  :		Union[str, Any]			    =    self.sigmas[step_index]

          # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
          if self.config.prediction_type == "epsilon":
              _lowerCamelCase  :		int			    =    sample - sigma * model_output
          elif self.config.prediction_type == "v_prediction":
              # * c_out + input * c_skip
              _lowerCamelCase  :		Optional[Any]			    =    model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
          elif self.config.prediction_type == "sample":
              raise NotImplementedError("""prediction_type not implemented yet: sample""")
          else:
              raise ValueError(
                  F"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`""")

          _lowerCamelCase  :		Tuple			    =    self.sigmas[step_index]
          _lowerCamelCase  :		int			    =    self.sigmas[step_index + 1]
          _lowerCamelCase  :		Tuple			    =    (sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
          _lowerCamelCase  :		List[Any]			    =    (sigma_to**2 - sigma_up**2) ** 0.5

          # 2. Convert to an ODE derivative
          _lowerCamelCase  :		List[Any]			    =    (sample - pred_original_sample) / sigma

          _lowerCamelCase  :		Tuple			    =    sigma_down - sigma

          _lowerCamelCase  :		Optional[int]			    =    sample + derivative * dt

          _lowerCamelCase  :		int			    =    model_output.device
          _lowerCamelCase  :		List[Any]			    =    randn_tensor(model_output.shape     ,	dtype=model_output.dtype     ,	device=_UpperCamelCase     ,	generator=_UpperCamelCase)

          _lowerCamelCase  :		List[Any]			    =    prev_sample + noise * sigma_up

          if not return_dict:
              return (prev_sample,)

          return EulerAncestralDiscreteSchedulerOutput(
              prev_sample=_UpperCamelCase     ,	pred_original_sample=_UpperCamelCase)



      def 						_SCREAMING_SNAKE_CASE     (       self  :					Optional[Any]     ,	_UpperCamelCase  :					torch.FloatTensor     ,	_UpperCamelCase  :					torch.FloatTensor     ,	_UpperCamelCase  :					torch.FloatTensor     ,	)					->torch.FloatTensor:


          """simple docstring"""


          _lowerCamelCase  :		Any			    =    self.sigmas.to(device=original_samples.device     ,	dtype=original_samples.dtype)
          if original_samples.device.type == "mps" and torch.is_floating_point(_UpperCamelCase):
              # mps does not support float64
              _lowerCamelCase  :		str			    =    self.timesteps.to(original_samples.device     ,	dtype=torch.floataa)
              _lowerCamelCase  :		Union[str, Any]			    =    timesteps.to(original_samples.device     ,	dtype=torch.floataa)
          else:
              _lowerCamelCase  :		Union[str, Any]			    =    self.timesteps.to(original_samples.device)
              _lowerCamelCase  :		List[str]			    =    timesteps.to(original_samples.device)

          _lowerCamelCase  :		Optional[int]			    =    [(schedule_timesteps == t).nonzero().item() for t in timesteps]

          _lowerCamelCase  :		List[Any]			    =    sigmas[step_indices].flatten()
          while len(sigma.shape) < len(original_samples.shape):
              _lowerCamelCase  :		Optional[Any]			    =    sigma.unsqueeze(-1)

          _lowerCamelCase  :		List[str]			    =    original_samples + noise * sigma
          return noisy_samples




      def __len__(       self  :					Dict)					->str:


          """simple docstring"""


          return self.config.num_train_timesteps




