






"""simple docstring"""
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 .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput

def 				snake_case      (   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_     : List[str]			     =					[]
			for i in range(A__						):
						UpperCAmelCase_     : str			     =					i / num_diffusion_timesteps
						UpperCAmelCase_     : Union[str, Any]			     =					(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 			UpperCamelCase_       (__A				,						__A     ):
	__magic_name__	      =				[e.name for e in KarrasDiffusionSchedulers]
	__magic_name__	      =				2





	@register_to_config
	def __init__(      self					: List[str]	,	lowerCAmelCase_					: int = 1_000	,	lowerCAmelCase_					: float = 0.0_0_0_8_5	,	lowerCAmelCase_					: float = 0.0_1_2	,	lowerCAmelCase_					: str = "linear"	,	lowerCAmelCase_					: Optional[Union[np.ndarray, List[float]]] = None	,	lowerCAmelCase_					: str = "epsilon"	,	lowerCAmelCase_					: str = "linspace"	,	lowerCAmelCase_					: int = 0	,	)						->			List[Any]:
				if trained_betas is not None:
							UpperCAmelCase_     : str			     =					torch.tensor(lowerCAmelCase_	,	dtype=torch.floataa						)
				elif beta_schedule == "linear":
							UpperCAmelCase_     : str			     =					torch.linspace(lowerCAmelCase_	,	lowerCAmelCase_	,	lowerCAmelCase_	,	dtype=torch.floataa						)
				elif beta_schedule == "scaled_linear":
							# this schedule is very specific to the latent diffusion model.
							UpperCAmelCase_     : str			     =					(
							    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_     : Dict			     =					betas_for_alpha_bar(lowerCAmelCase_						)
				else:
							raise NotImplementedError(f"""{beta_schedule} does is not implemented for {self.__class__}"""						)

				UpperCAmelCase_     : str			     =					1.0 - self.betas
				UpperCAmelCase_     : Optional[int]			     =					torch.cumprod(self.alphas	,	dim=0						)

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





	def      _SCREAMING_SNAKE_CASE      (      self					: Any	,	lowerCAmelCase_					: List[Any]	,	lowerCAmelCase_					: int=None						)						->			str:
				if schedule_timesteps is None:
							UpperCAmelCase_     : List[Any]			     =					self.timesteps

				UpperCAmelCase_     : Dict			     =					(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:
							UpperCAmelCase_     : Any			     =					1 if len(lowerCAmelCase_						) > 1 else 0
				else:
							UpperCAmelCase_     : Optional[int]			     =					timestep.cpu().item() if torch.is_tensor(lowerCAmelCase_						) else timestep
							UpperCAmelCase_     : List[Any]			     =					self._index_counter[timestep_int]

				return indices[pos].item()





	@property
	def      _SCREAMING_SNAKE_CASE      (      self					: Any						)						->			Dict:
				# standard deviation of the initial noise distribution
				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					: Optional[int]	,	lowerCAmelCase_					: torch.FloatTensor	,	lowerCAmelCase_					: Union[float, torch.FloatTensor]	,	)						->			torch.FloatTensor:
				UpperCAmelCase_     : Dict			     =					self.index_for_timestep(lowerCAmelCase_						)

				if self.state_in_first_order:
							UpperCAmelCase_     : Optional[int]			     =					self.sigmas[step_index]
				else:
							UpperCAmelCase_     : Tuple			     =					self.sigmas_interpol[step_index]

				UpperCAmelCase_     : Optional[int]			     =					sample / ((sigma**2 + 1) ** 0.5)
				return sample





	def      _SCREAMING_SNAKE_CASE      (      self					: Tuple	,	lowerCAmelCase_					: int	,	lowerCAmelCase_					: Union[str, torch.device] = None	,	lowerCAmelCase_					: Optional[int] = None	,	)						->			Dict:
				UpperCAmelCase_     : Optional[Any]			     =					num_inference_steps

				UpperCAmelCase_     : Any			     =					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":
							UpperCAmelCase_     : Any			     =					np.linspace(0	,	num_train_timesteps - 1	,	lowerCAmelCase_	,	dtype=lowerCAmelCase_						)[::-1].copy()
				elif self.config.timestep_spacing == "leading":
							UpperCAmelCase_     : int			     =					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_     : str			     =					(np.arange(0	,	lowerCAmelCase_						) * step_ratio).round()[::-1].copy().astype(lowerCAmelCase_						)
							timesteps += self.config.steps_offset
				elif self.config.timestep_spacing == "trailing":
							UpperCAmelCase_     : Any			     =					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_     : str			     =					(np.arange(lowerCAmelCase_	,	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_     : List[Any]			     =					np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5						)
				UpperCAmelCase_     : str			     =					torch.from_numpy(np.log(lowerCAmelCase_						)						).to(lowerCAmelCase_						)

				UpperCAmelCase_     : Optional[Any]			     =					np.interp(lowerCAmelCase_	,	np.arange(0	,	len(lowerCAmelCase_						)						)	,	lowerCAmelCase_						)
				UpperCAmelCase_     : str			     =					np.concatenate([sigmas, [0.0]]						).astype(np.floataa						)
				UpperCAmelCase_     : Optional[int]			     =					torch.from_numpy(lowerCAmelCase_						).to(device=lowerCAmelCase_						)

				# interpolate sigmas
				UpperCAmelCase_     : Optional[int]			     =					sigmas.log().lerp(sigmas.roll(1						).log()	,	0.5						).exp()

				UpperCAmelCase_     : Optional[int]			     =					torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2						), sigmas[-1:]]						)
				UpperCAmelCase_     : Tuple			     =					torch.cat(
				    [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2						), sigmas_interpol[-1:]]						)

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

				# interpolate timesteps
				UpperCAmelCase_     : List[str]			     =					self.sigma_to_t(lowerCAmelCase_						).to(lowerCAmelCase_	,	dtype=timesteps.dtype						)
				UpperCAmelCase_     : List[str]			     =					torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])	,	dim=-1						).flatten()

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

				UpperCAmelCase_     : int			     =					None

				# for exp beta schedules, such as the one for `pipeline_shap_e.py`
				# we need an index counter
				UpperCAmelCase_     : Optional[int]			     =					defaultdict(lowerCAmelCase_						)





	def      _SCREAMING_SNAKE_CASE      (      self					: Union[str, Any]	,	lowerCAmelCase_					: List[Any]						)						->			Optional[int]:
				# get log sigma
				UpperCAmelCase_     : Optional[Any]			     =					sigma.log()

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

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

				UpperCAmelCase_     : Any			     =					self.log_sigmas[low_idx]
				UpperCAmelCase_     : Optional[int]			     =					self.log_sigmas[high_idx]

				# interpolate sigmas
				UpperCAmelCase_     : List[Any]			     =					(low - log_sigma) / (low - high)
				UpperCAmelCase_     : Optional[int]			     =					w.clamp(0	,	1						)

				# transform interpolation to time range
				UpperCAmelCase_     : Optional[int]			     =					(1 - w) * low_idx + w * high_idx
				UpperCAmelCase_     : Any			     =					t.view(sigma.shape						)
				return t





	@property
	def      _SCREAMING_SNAKE_CASE      (      self					: Optional[int]						)						->			Any:
				return self.sample is None





	def      _SCREAMING_SNAKE_CASE      (      self					: Union[str, Any]	,	lowerCAmelCase_					: Union[torch.FloatTensor, np.ndarray]	,	lowerCAmelCase_					: Union[float, torch.FloatTensor]	,	lowerCAmelCase_					: Union[torch.FloatTensor, np.ndarray]	,	lowerCAmelCase_					: bool = True	,	)						->			Union[SchedulerOutput, Tuple]:
				UpperCAmelCase_     : List[Any]			     =					self.index_for_timestep(lowerCAmelCase_						)

				# advance index counter by 1
				UpperCAmelCase_     : Dict			     =					timestep.cpu().item() if torch.is_tensor(lowerCAmelCase_						) else timestep
				self._index_counter[timestep_int] += 1

				if self.state_in_first_order:
							UpperCAmelCase_     : List[Any]			     =					self.sigmas[step_index]
							UpperCAmelCase_     : Optional[int]			     =					self.sigmas_interpol[step_index + 1]
							UpperCAmelCase_     : List[Any]			     =					self.sigmas[step_index + 1]
				else:
							# 2nd order / KDPM2's method
							UpperCAmelCase_     : Union[str, Any]			     =					self.sigmas[step_index - 1]
							UpperCAmelCase_     : Any			     =					self.sigmas_interpol[step_index]
							UpperCAmelCase_     : int			     =					self.sigmas[step_index]

				# 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
				UpperCAmelCase_     : Union[str, Any]			     =					0
				UpperCAmelCase_     : Optional[int]			     =					sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

				# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
				if self.config.prediction_type == "epsilon":
							UpperCAmelCase_     : Tuple			     =					sigma_hat if self.state_in_first_order else sigma_interpol
							UpperCAmelCase_     : Dict			     =					sample - sigma_input * model_output
				elif self.config.prediction_type == "v_prediction":
							UpperCAmelCase_     : Dict			     =					sigma_hat if self.state_in_first_order else sigma_interpol
							UpperCAmelCase_     : Optional[int]			     =					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
							UpperCAmelCase_     : Tuple			     =					(sample - pred_original_sample) / sigma_hat
							# 3. delta timestep
							UpperCAmelCase_     : Dict			     =					sigma_interpol - sigma_hat

							# store for 2nd order step
							UpperCAmelCase_     : Any			     =					sample
				else:
							# DPM-Solver-2
							# 2. Convert to an ODE derivative for 2nd order
							UpperCAmelCase_     : Optional[int]			     =					(sample - pred_original_sample) / sigma_interpol

							# 3. delta timestep
							UpperCAmelCase_     : Tuple			     =					sigma_next - sigma_hat

							UpperCAmelCase_     : int			     =					self.sample
							UpperCAmelCase_     : List[str]			     =					None

				UpperCAmelCase_     : Dict			     =					sample + derivative * dt

				if not return_dict:
							return (prev_sample,)

				return SchedulerOutput(prev_sample=lowerCAmelCase_						)





	def      _SCREAMING_SNAKE_CASE      (      self					: List[str]	,	lowerCAmelCase_					: torch.FloatTensor	,	lowerCAmelCase_					: torch.FloatTensor	,	lowerCAmelCase_					: torch.FloatTensor	,	)						->			torch.FloatTensor:
				# Make sure sigmas and timesteps have the same device and dtype as original_samples
				UpperCAmelCase_     : List[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_     : str			     =					self.timesteps.to(original_samples.device	,	dtype=torch.floataa						)
							UpperCAmelCase_     : Dict			     =					timesteps.to(original_samples.device	,	dtype=torch.floataa						)
				else:
							UpperCAmelCase_     : Dict			     =					self.timesteps.to(original_samples.device						)
							UpperCAmelCase_     : Dict			     =					timesteps.to(original_samples.device						)

				UpperCAmelCase_     : Union[str, Any]			     =					[self.index_for_timestep(lowerCAmelCase_	,	lowerCAmelCase_						) for t in timesteps]

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

				UpperCAmelCase_     : List[Any]			     =					original_samples + noise * sigma
				return noisy_samples





	def __len__(      self					: Optional[Any]						)						->			Any:
				return self.config.num_train_timesteps











"""simple docstring"""
def 				snake_case      (   A__	,A__						):
			# "extended trapezoidal rule"
			# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
			UpperCAmelCase_     : Dict			     =					(boundary[1] - boundary[0]) / steps
			UpperCAmelCase_     : Optional[int]			     =					boundary[0]
			UpperCAmelCase_     : str			     =					boundary[1]
			UpperCAmelCase_     : Tuple			     =					make_points(A__	,A__	,A__						)
			UpperCAmelCase_     : List[str]			     =					0.0
			y += (h / 2.0) * f(A__						)
			for i in x_i:
						# print(i)
						y += h * f(A__						)
			y += (h / 2.0) * f(A__						)
			return y

def 				snake_case      (   A__	,A__	,A__						):
			UpperCAmelCase_     : Union[str, Any]			     =					a + h
			while x < (b - h):
						yield x
						UpperCAmelCase_     : Optional[Any]			     =					x + h

def 				snake_case      (   A__						):  # enter your function here
			UpperCAmelCase_     : Dict			     =					(x - 0) * (x - 0)
			return y

def 				snake_case      (   ):
			UpperCAmelCase_     : Dict			     =					0.0  # Lower bound of integration
			UpperCAmelCase_     : Optional[int]			     =					1.0  # Upper bound of integration
			UpperCAmelCase_     : Dict			     =					10.0  # define number of steps or resolution
			UpperCAmelCase_     : List[Any]			     =					[a, b]  # define boundary of integration
			UpperCAmelCase_     : Union[str, Any]			     =					method_a(A__	,A__						)
			print(F"""y = {y}"""						)


if __name__ == "__main__":
			main()



