





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


A__:  Any       					=					logging.get_logger(__name__)  # pylint: disable=invalid-name




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

      """simple docstring"""


      UpperCamelCase__       						=   42
      UpperCamelCase__       						=   None



def 							lowerCAmelCase_				(    A_  ,A_=0.999  ,A_="cosine"  ,):






    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}")

    UpperCamelCase__:					Dict												=      []
    for i in range(snake_case__):
        UpperCamelCase__:					Dict												=      i / num_diffusion_timesteps
        UpperCamelCase__:					Any												=      (i + 1) / num_diffusion_timesteps
        betas.append(min(1 - alpha_bar_fn(snake_case__) / alpha_bar_fn(snake_case__)  ,snake_case__))
    return torch.tensor(snake_case__  ,dtype=torch.floataa)




class    _a  (  _a		,	_a):

      """simple docstring"""


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






      @register_to_config
      def __init__(						self:	Tuple					,  __lowerCamelCase:	int = 1000					,  __lowerCamelCase:	float = 0.0_001					,  __lowerCamelCase:	float = 0.02					,  __lowerCamelCase:	str = "linear"					,  __lowerCamelCase:	Optional[Union[np.ndarray, List[float]]] = None					,  __lowerCamelCase:	str = "epsilon"					,  __lowerCamelCase:	str = "linspace"					,  __lowerCamelCase:	int = 0					,  ):
          '''simple docstring'''


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

          UpperCamelCase__:					Union[str, Any]												=      1.0 - self.betas
          UpperCamelCase__:					Dict												=      torch.cumprod(self.alphas					,  dim=0			)

          UpperCamelCase__:					int												=      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5			)
          UpperCamelCase__:					Any												=      np.concatenate([sigmas[::-1], [0.0]]			).astype(np.floataa			)
          UpperCamelCase__:					str												=      torch.from_numpy(__lowerCamelCase			)

          # setable values
          UpperCamelCase__:					str												=      None
          UpperCamelCase__:					Optional[int]												=      np.linspace(0					,  num_train_timesteps - 1					,  __lowerCamelCase					,  dtype=__lowerCamelCase			)[::-1].copy()
          UpperCamelCase__:					Union[str, Any]												=      torch.from_numpy(__lowerCamelCase			)
          UpperCamelCase__:					Dict												=      False






      @property
      def 	UpperCAmelCase_   (						self:	Any			):
          '''simple docstring'''


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

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






      def 	UpperCAmelCase_   (						self:	Optional[Any]					,  __lowerCamelCase:	torch.FloatTensor					,  __lowerCamelCase:	Union[float, torch.FloatTensor]			):
          '''simple docstring'''


          if isinstance(__lowerCamelCase					,  torch.Tensor			):
              UpperCamelCase__:					Any												=      timestep.to(self.timesteps.device			)
          UpperCamelCase__:					List[Any]												=      (self.timesteps == timestep).nonzero().item()
          UpperCamelCase__:					List[str]												=      self.sigmas[step_index]
          UpperCamelCase__:					Union[str, Any]												=      sample / ((sigma**2 + 1) ** 0.5)
          UpperCamelCase__:					str												=      True
          return sample






      def 	UpperCAmelCase_   (						self:	List[Any]					,  __lowerCamelCase:	int					,  __lowerCamelCase:	Union[str, torch.device] = None			):
          '''simple docstring'''


          UpperCamelCase__:					List[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":
              UpperCamelCase__:					Any												=      np.linspace(0					,  self.config.num_train_timesteps - 1					,  __lowerCamelCase					,  dtype=__lowerCamelCase			)[
                  ::-1
              ].copy()
          elif self.config.timestep_spacing == "leading":
              UpperCamelCase__:					List[Any]												=      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
              UpperCamelCase__:					int												=      (np.arange(0					,  __lowerCamelCase			) * step_ratio).round()[::-1].copy().astype(__lowerCamelCase			)
              timesteps += self.config.steps_offset
          elif self.config.timestep_spacing == "trailing":
              UpperCamelCase__:					Dict												=      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
              UpperCamelCase__:					int												=      (np.arange(self.config.num_train_timesteps					,  0					,  -step_ratio			)).round().copy().astype(__lowerCamelCase			)
              timesteps -= 1
          else:
              raise ValueError(
                  F"{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'."			)

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






      def 	UpperCAmelCase_   (						self:	int					,  __lowerCamelCase:	torch.FloatTensor					,  __lowerCamelCase:	Union[float, torch.FloatTensor]					,  __lowerCamelCase:	torch.FloatTensor					,  __lowerCamelCase:	Optional[torch.Generator] = None					,  __lowerCamelCase:	bool = True					,  ):
          '''simple docstring'''


          if (
              isinstance(__lowerCamelCase					,  __lowerCamelCase			)
              or isinstance(__lowerCamelCase					,  torch.IntTensor			)
              or isinstance(__lowerCamelCase					,  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(__lowerCamelCase					,  torch.Tensor			):
              UpperCamelCase__:					str												=      timestep.to(self.timesteps.device			)

          UpperCamelCase__:					Tuple												=      (self.timesteps == timestep).nonzero().item()
          UpperCamelCase__:					str												=      self.sigmas[step_index]

          # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
          if self.config.prediction_type == "epsilon":
              UpperCamelCase__:					Any												=      sample - sigma * model_output
          elif self.config.prediction_type == "v_prediction":
              # * c_out + input * c_skip
              UpperCamelCase__:					int												=      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`"			)

          UpperCamelCase__:					Union[str, Any]												=      self.sigmas[step_index]
          UpperCamelCase__:					Optional[int]												=      self.sigmas[step_index + 1]
          UpperCamelCase__:					Optional[int]												=      (sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
          UpperCamelCase__:					Tuple												=      (sigma_to**2 - sigma_up**2) ** 0.5

          # 2. Convert to an ODE derivative
          UpperCamelCase__:					Dict												=      (sample - pred_original_sample) / sigma

          UpperCamelCase__:					Tuple												=      sigma_down - sigma

          UpperCamelCase__:					int												=      sample + derivative * dt

          UpperCamelCase__:					Any												=      model_output.device
          UpperCamelCase__:					Any												=      randn_tensor(model_output.shape					,  dtype=model_output.dtype					,  device=__lowerCamelCase					,  generator=__lowerCamelCase			)

          UpperCamelCase__:					Optional[Any]												=      prev_sample + noise * sigma_up

          if not return_dict:
              return (prev_sample,)

          return EulerAncestralDiscreteSchedulerOutput(
              prev_sample=__lowerCamelCase					,  pred_original_sample=__lowerCamelCase			)






      def 	UpperCAmelCase_   (						self:	str					,  __lowerCamelCase:	torch.FloatTensor					,  __lowerCamelCase:	torch.FloatTensor					,  __lowerCamelCase:	torch.FloatTensor					,  ):
          '''simple docstring'''


          UpperCamelCase__:					str												=      self.sigmas.to(device=original_samples.device					,  dtype=original_samples.dtype			)
          if original_samples.device.type == "mps" and torch.is_floating_point(__lowerCamelCase			):
              # mps does not support float64
              UpperCamelCase__:					Optional[int]												=      self.timesteps.to(original_samples.device					,  dtype=torch.floataa			)
              UpperCamelCase__:					int												=      timesteps.to(original_samples.device					,  dtype=torch.floataa			)
          else:
              UpperCamelCase__:					Optional[int]												=      self.timesteps.to(original_samples.device			)
              UpperCamelCase__:					List[str]												=      timesteps.to(original_samples.device			)

          UpperCamelCase__:					Dict												=      [(schedule_timesteps == t).nonzero().item() for t in timesteps]

          UpperCamelCase__:					Dict												=      sigmas[step_indices].flatten()
          while len(sigma.shape			) < len(original_samples.shape			):
              UpperCamelCase__:					Optional[int]												=      sigma.unsqueeze(-1			)

          UpperCamelCase__:					Optional[Any]												=      original_samples + noise * sigma
          return noisy_samples






      def __len__(						self:	str			):
          '''simple docstring'''


          return self.config.num_train_timesteps








def 							lowerCAmelCase_				(    A_  ,A_  ,A_):
    UpperCamelCase__:					Optional[int]												=      [1 / first_term]
    UpperCamelCase__:					int												=      1 / first_term
    for _ in range(number_of_terms - 1):
        first_term += common_difference
        arithmetic_progression.append(A_)
    UpperCamelCase__:					str												=      [1 / step for step in arithmetic_progression]
    return sum(A_)


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   print(sum_of_harmonic_progression(1 / 2, 2, 2))

