


import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

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




def SCREAMING_SNAKE_CASE_  (				__lowerCamelCase:		List[str]  ,			__lowerCamelCase:		Union[str, Any]=0.999  ,			__lowerCamelCase:		Optional[Any]="cosine"  ,			):







	'''simple docstring'''



	if alpha_transform_type == "cosine":

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

	elif alpha_transform_type == "exp":

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

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

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







class     __lowerCamelCase     (  UpperCAmelCase__							,   UpperCAmelCase__     ):


							"""simple docstring"""

							lowerCAmelCase__          =				[e.name for e in KarrasDiffusionSchedulers]
							lowerCAmelCase__          =				2




							@register_to_config
							def __init__(  self						,       UpperCAmelCase = 1000						,       UpperCAmelCase = 0.00085						,       UpperCAmelCase = 0.012						,       UpperCAmelCase = "linear"						,       UpperCAmelCase = None						,       UpperCAmelCase = "epsilon"						,       UpperCAmelCase = "linspace"						,       UpperCAmelCase = 0						,       )     ->       int:






								'''simple docstring'''






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

								lowercase_			 = 1.0 - self.betas
								lowercase_			 = torch.cumprod(self.alphas						,       dim=0  )

								#  set all values
								self.set_timesteps(snake_case_						,       snake_case_						,       snake_case_  )




							def 				A__      (  self						,       UpperCAmelCase						,       UpperCAmelCase=None  )     ->       List[str]:






								'''simple docstring'''






								if schedule_timesteps is None:
									lowercase_			 = self.timesteps

								lowercase_			 = (schedule_timesteps == timestep).nonzero()

								# The sigma index that is taken for the **very** first `step`
								# is always the second index (or the last index if there is only 1)
								# This way we can ensure we don't accidentally skip a sigma in
								# case we start in the middle of the denoising schedule (e.g. for image-to-image)
								if len(self._index_counter  ) == 0:
									lowercase_			 = 1 if len(snake_case_  ) > 1 else 0
								else:
									lowercase_			 = timestep.cpu().item() if torch.is_tensor(snake_case_  ) else timestep
									lowercase_			 = self._index_counter[timestep_int]

								return indices[pos].item()




							@property
							def 				A__      (  self  )     ->       List[Any]:






								'''simple docstring'''






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

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




							def 				A__      (  self						,       UpperCAmelCase						,       UpperCAmelCase						,       )     ->       Optional[Any]:






								'''simple docstring'''






								lowercase_			 = self.index_for_timestep(snake_case_  )

								if self.state_in_first_order:
									lowercase_			 = self.sigmas[step_index]
								else:
									lowercase_			 = self.sigmas_interpol[step_index - 1]

								lowercase_			 = sample / ((sigma**2 + 1) ** 0.5)
								return sample




							def 				A__      (  self						,       UpperCAmelCase						,       UpperCAmelCase = None						,       UpperCAmelCase = None						,       )     ->       Any:






								'''simple docstring'''






								lowercase_			 = num_inference_steps

								lowercase_			 = num_train_timesteps or self.config.num_train_timesteps

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

								lowercase_			 = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5  )
								lowercase_			 = torch.from_numpy(np.log(snake_case_  )  ).to(snake_case_  )

								lowercase_			 = np.interp(snake_case_						,       np.arange(0						,       len(snake_case_  )  )						,       snake_case_  )
								lowercase_			 = np.concatenate([sigmas, [0.0]]  ).astype(np.floataa  )
								lowercase_			 = torch.from_numpy(snake_case_  ).to(device=snake_case_  )

								# compute up and down sigmas
								lowercase_			 = sigmas.roll(-1  )
								lowercase_			 = 0.0
								lowercase_			 = (sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
								lowercase_			 = (sigmas_next**2 - sigmas_up**2) ** 0.5
								lowercase_			 = 0.0

								# compute interpolated sigmas
								lowercase_			 = sigmas.log().lerp(sigmas_down.log()						,       0.5  ).exp()
								lowercase_			 = 0.0

								# set sigmas
								lowercase_			 = torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2  ), sigmas[-1:]]  )
								lowercase_			 = torch.cat(
								    [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2  ), sigmas_interpol[-1:]]  )
								lowercase_			 = torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2  ), sigmas_up[-1:]]  )
								lowercase_			 = torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2  ), sigmas_down[-1:]]  )

								if str(snake_case_  ).startswith("mps"  ):
									# mps does not support float64
									lowercase_			 = torch.from_numpy(snake_case_  ).to(snake_case_						,       dtype=torch.floataa  )
								else:
									lowercase_			 = torch.from_numpy(snake_case_  ).to(snake_case_  )

								lowercase_			 = self.sigma_to_t(snake_case_  ).to(snake_case_						,       dtype=timesteps.dtype  )
								lowercase_			 = torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])						,       dim=-1  ).flatten()

								lowercase_			 = torch.cat([timesteps[:1], interleaved_timesteps]  )

								lowercase_			 = None

								# for exp beta schedules, such as the one for `pipeline_shap_e.py`
								# we need an index counter
								lowercase_			 = defaultdict(snake_case_  )




							def 				A__      (  self						,       UpperCAmelCase  )     ->       Optional[int]:






								'''simple docstring'''






								lowercase_			 = sigma.log()

								# get distribution
								lowercase_			 = log_sigma - self.log_sigmas[:, None]

								# get sigmas range
								lowercase_			 = dists.ge(0  ).cumsum(dim=0  ).argmax(dim=0  ).clamp(max=self.log_sigmas.shape[0] - 2  )
								lowercase_			 = low_idx + 1

								lowercase_			 = self.log_sigmas[low_idx]
								lowercase_			 = self.log_sigmas[high_idx]

								# interpolate sigmas
								lowercase_			 = (low - log_sigma) / (low - high)
								lowercase_			 = w.clamp(0						,       1  )

								# transform interpolation to time range
								lowercase_			 = (1 - w) * low_idx + w * high_idx
								lowercase_			 = t.view(sigma.shape  )
								return t




							@property
							def 				A__      (  self  )     ->       Any:






								'''simple docstring'''






								return self.sample is None




							def 				A__      (  self						,       UpperCAmelCase						,       UpperCAmelCase						,       UpperCAmelCase						,       UpperCAmelCase = None						,       UpperCAmelCase = True						,       )     ->       Optional[Any]:






								'''simple docstring'''






								lowercase_			 = self.index_for_timestep(snake_case_  )

								# advance index counter by 1
								lowercase_			 = timestep.cpu().item() if torch.is_tensor(snake_case_  ) else timestep
								self._index_counter[timestep_int] += 1

								if self.state_in_first_order:
									lowercase_			 = self.sigmas[step_index]
									lowercase_			 = self.sigmas_interpol[step_index]
									lowercase_			 = self.sigmas_up[step_index]
									lowercase_			 = self.sigmas_down[step_index - 1]
								else:
									# 2nd order / KPDM2's method
									lowercase_			 = self.sigmas[step_index - 1]
									lowercase_			 = self.sigmas_interpol[step_index - 1]
									lowercase_			 = self.sigmas_up[step_index - 1]
									lowercase_			 = self.sigmas_down[step_index - 1]

								# currently only gamma=0 is supported. This usually works best anyways.
								# We can support gamma in the future but then need to scale the timestep before
								# passing it to the model which requires a change in API
								lowercase_			 = 0
								lowercase_			 = sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

								lowercase_			 = model_output.device
								lowercase_			 = randn_tensor(model_output.shape						,       dtype=model_output.dtype						,       device=snake_case_						,       generator=snake_case_  )

								# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
								if self.config.prediction_type == "epsilon":
									lowercase_			 = sigma_hat if self.state_in_first_order else sigma_interpol
									lowercase_			 = sample - sigma_input * model_output
								elif self.config.prediction_type == "v_prediction":
									lowercase_			 = sigma_hat if self.state_in_first_order else sigma_interpol
									lowercase_			 = model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
									    sample / (sigma_input**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`'  )

								if self.state_in_first_order:
									# 2. Convert to an ODE derivative for 1st order
									lowercase_			 = (sample - pred_original_sample) / sigma_hat
									# 3. delta timestep
									lowercase_			 = sigma_interpol - sigma_hat

									# store for 2nd order step
									lowercase_			 = sample
									lowercase_			 = dt
									lowercase_			 = sample + derivative * dt
								else:
									# DPM-Solver-2
									# 2. Convert to an ODE derivative for 2nd order
									lowercase_			 = (sample - pred_original_sample) / sigma_interpol
									# 3. delta timestep
									lowercase_			 = sigma_down - sigma_hat

									lowercase_			 = self.sample
									lowercase_			 = None

									lowercase_			 = sample + derivative * dt
									lowercase_			 = prev_sample + noise * sigma_up

								if not return_dict:
									return (prev_sample,)

								return SchedulerOutput(prev_sample=snake_case_  )




							def 				A__      (  self						,       UpperCAmelCase						,       UpperCAmelCase						,       UpperCAmelCase						,       )     ->       List[str]:






								'''simple docstring'''






								lowercase_			 = self.sigmas.to(device=original_samples.device						,       dtype=original_samples.dtype  )
								if original_samples.device.type == "mps" and torch.is_floating_point(snake_case_  ):
									# mps does not support float64
									lowercase_			 = self.timesteps.to(original_samples.device						,       dtype=torch.floataa  )
									lowercase_			 = timesteps.to(original_samples.device						,       dtype=torch.floataa  )
								else:
									lowercase_			 = self.timesteps.to(original_samples.device  )
									lowercase_			 = timesteps.to(original_samples.device  )

								lowercase_			 = [self.index_for_timestep(snake_case_						,       snake_case_  ) for t in timesteps]

								lowercase_			 = sigmas[step_indices].flatten()
								while len(sigma.shape  ) < len(original_samples.shape  ):
									lowercase_			 = sigma.unsqueeze(-1  )

								lowercase_			 = original_samples + noise * sigma
								return noisy_samples




							def __len__(  self  )     ->       int:






								'''simple docstring'''






								return self.config.num_train_timesteps








"""simple docstring"""




def 		UpperCAmelCase__						(	_UpperCAmelCase					,   _UpperCAmelCase   ):






  """simple docstring"""





  A_    :			List[str]									=    (boundary[1] - boundary[0]) / steps
  A_    :			Optional[int]									=    boundary[0]
  A_    :			Optional[int]									=    boundary[1]
  A_    :			Any									=    make_points(_UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase   )
  A_    :			Dict									=    0.0
  y += (h / 3.0) * f(_UpperCAmelCase   )
  A_    :			Optional[int]									=    2
  for i in x_i:
    y += (h / 3) * (4 - 2 * (cnt % 2)) * f(_UpperCAmelCase   )
    cnt += 1
  y += (h / 3.0) * f(_UpperCAmelCase   )
  return y





def 		UpperCAmelCase__						(	_UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase   ):






  """simple docstring"""





  A_    :			Optional[Any]									=    a + h
  while x < (b - h):
    yield x
    A_    :			Dict									=    x + h





def 		UpperCAmelCase__						(	_UpperCAmelCase   ):  # enter your function here






  """simple docstring"""





  A_    :			List[Any]									=    (x - 0) * (x - 0)
  return y





def 		UpperCAmelCase__						(	):






  """simple docstring"""





  A_    :			int									=    0.0  # Lower bound of integration
  A_    :			int									=    1.0  # Upper bound of integration
  A_    :			Tuple									=    10.0  # define number of steps or resolution
  A_    :			List[str]									=    [a, b]  # define boundary of integration
  A_    :			Optional[Any]									=    method_a(_UpperCAmelCase					,   _UpperCAmelCase   )
  print(f"""y = {y}"""   )


if __name__ == "__main__":
   main()