
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  A			(   lowercase       ,			lowercase=0.9_9_9       ,			lowercase="cosine"       ,			)  ->    int:
		'''simple docstring'''

		if alpha_transform_type == "cosine":

				def alpha_bar_fn(lowercase					):
						return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2					) ** 2

		elif alpha_transform_type == "exp":

				def alpha_bar_fn(lowercase					):
						return math.exp(t * -1_2.0					)

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

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


class 							lowercase   (						_SCREAMING_SNAKE_CASE    ,  _SCREAMING_SNAKE_CASE  ):
		__lowercase			:			Optional[int]      	=							[e.name for e in KarrasDiffusionSchedulers]
		__lowercase			:			Union[str, Any]      	=							2



		@register_to_config
		def __init__(					self							, A_ = 1_000							, A_ = 0.0_0085							, A_ = 0.012							, A_ = "linear"							, A_ = None							, A_ = "epsilon"							, A_ = "linspace"							, A_ = 0							, )    ->   Optional[Any]:
				"""simple docstring"""
				if trained_betas is not None:
						UpperCamelCase            =	torch.tensor(A_							, dtype=torch.floataa			)
				elif beta_schedule == "linear":
						UpperCamelCase            =	torch.linspace(A_							, A_							, A_							, dtype=torch.floataa			)
				elif beta_schedule == "scaled_linear":
						# this schedule is very specific to the latent diffusion model.
						UpperCamelCase            =	(
						    torch.linspace(beta_start**0.5							, beta_end**0.5							, A_							, dtype=torch.floataa			) ** 2
						)
				elif beta_schedule == "squaredcos_cap_v2":
						# Glide cosine schedule
						UpperCamelCase            =	betas_for_alpha_bar(A_			)
				else:
						raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}'''			)

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

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



		def __UpperCamelCase					(					self							, A_							, A_=None			)    ->   Dict:
				"""simple docstring"""
				if schedule_timesteps is None:
						UpperCamelCase            =	self.timesteps

				UpperCamelCase            =	(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            =	1 if len(A_			) > 1 else 0
				else:
						UpperCamelCase            =	timestep.cpu().item() if torch.is_tensor(A_			) else timestep
						UpperCamelCase            =	self._index_counter[timestep_int]

				return indices[pos].item()



		@property
		def __UpperCamelCase					(					self			)    ->   str:
				"""simple docstring"""
				# 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 __UpperCamelCase					(					self							, A_							, A_							, )    ->   torch.FloatTensor:
				"""simple docstring"""
				UpperCamelCase            =	self.index_for_timestep(A_			)

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

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



		def __UpperCamelCase					(					self							, A_							, A_ = None							, A_ = None							, )    ->   Optional[int]:
				"""simple docstring"""
				UpperCamelCase            =	num_inference_steps

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

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

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

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

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

				if str(A_			).startswith('mps'			):
						# mps does not support float64
						UpperCamelCase            =	torch.from_numpy(A_			).to(A_							, dtype=torch.floataa			)
				else:
						UpperCamelCase            =	torch.from_numpy(A_			).to(A_			)

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

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

				UpperCamelCase            =	None

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



		def __UpperCamelCase					(					self							, A_			)    ->   Dict:
				"""simple docstring"""
				# get log sigma
				UpperCamelCase            =	sigma.log()

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

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

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

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

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



		@property
		def __UpperCamelCase					(					self			)    ->   Optional[int]:
				"""simple docstring"""
				return self.sample is None



		def __UpperCamelCase					(					self							, A_							, A_							, A_							, A_ = None							, A_ = True							, )    ->   Union[SchedulerOutput, Tuple]:
				"""simple docstring"""
				UpperCamelCase            =	self.index_for_timestep(A_			)

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

				if self.state_in_first_order:
						UpperCamelCase            =	self.sigmas[step_index]
						UpperCamelCase            =	self.sigmas_interpol[step_index]
						UpperCamelCase            =	self.sigmas_up[step_index]
						UpperCamelCase            =	self.sigmas_down[step_index - 1]
				else:
						# 2nd order / KPDM2's method
						UpperCamelCase            =	self.sigmas[step_index - 1]
						UpperCamelCase            =	self.sigmas_interpol[step_index - 1]
						UpperCamelCase            =	self.sigmas_up[step_index - 1]
						UpperCamelCase            =	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
				UpperCamelCase            =	0
				UpperCamelCase            =	sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

				UpperCamelCase            =	model_output.device
				UpperCamelCase            =	randn_tensor(model_output.shape							, dtype=model_output.dtype							, device=A_							, generator=A_			)

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

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

						UpperCamelCase            =	self.sample
						UpperCamelCase            =	None

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

				if not return_dict:
						return (prev_sample,)

				return SchedulerOutput(prev_sample=A_			)



		def __UpperCamelCase					(					self							, A_							, A_							, A_							, )    ->   torch.FloatTensor:
				"""simple docstring"""
				# Make sure sigmas and timesteps have the same device and dtype as original_samples
				UpperCamelCase            =	self.sigmas.to(device=original_samples.device							, dtype=original_samples.dtype			)
				if original_samples.device.type == "mps" and torch.is_floating_point(A_			):
						# mps does not support float64
						UpperCamelCase            =	self.timesteps.to(original_samples.device							, dtype=torch.floataa			)
						UpperCamelCase            =	timesteps.to(original_samples.device							, dtype=torch.floataa			)
				else:
						UpperCamelCase            =	self.timesteps.to(original_samples.device			)
						UpperCamelCase            =	timesteps.to(original_samples.device			)

				UpperCamelCase            =	[self.index_for_timestep(A_							, A_			) for t in timesteps]

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

				UpperCamelCase            =	original_samples + noise * sigma
				return noisy_samples



		def __len__(					self			)    ->   Dict:
				"""simple docstring"""
				return self.config.num_train_timesteps


from __future__ import annotations


def  A			(   lowercase       ,			lowercase					)  ->    int:
		'''simple docstring'''

		UpperCamelCase      ,    UpperCamelCase            =	0, len(lowercase					) - 1
		while start_ind <= end_ind:
				if array[start_ind] == search_item:
						return start_ind
				elif array[end_ind] == search_item:
						return end_ind
				else:
						start_ind += 1
						end_ind -= 1
    # returns -1 if search_item is not found in array
		return -1


if __name__ == "__main__":
					print(double_linear_search(list(range(100)), 40))
