






"""simple docstring"""



# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion
import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import SchedulerMixin
from diffusers.utils import BaseOutput, deprecate





@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
class 					_UpperCAmelCase       ( _A							):
					SCREAMING_SNAKE_CASE_		:				torch.FloatTensor
					SCREAMING_SNAKE_CASE_		:				Optional[torch.FloatTensor]							    =   None



def 						lowercase    (				__snake_case				: Union[str, Any]		,					__snake_case				: List[str]=0.999		,					__snake_case				: str="cosine"		,					):
		if alpha_transform_type == "cosine":

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

		elif alpha_transform_type == "exp":

				def alpha_bar_fn(__snake_case				: Union[str, Any]	):
						return math.exp(t * -12.0	)

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

		lowercase_ : Optional[Any]							       =   []
		for i in range(__snake_case	):
				lowercase_ : int							       =   i / num_diffusion_timesteps
				lowercase_ : Optional[int]							       =   (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 					_UpperCAmelCase       ( _A   ,						_A							):
					SCREAMING_SNAKE_CASE_		:				Any							    =   1




					@register_to_config
					def __init__(				self     :						Any    ,						A     :						int = 10_00    ,						A     :						float = 0.0001    ,						A     :						float = 0.02    ,						A     :						str = "linear"    ,						A     :						Optional[Union[np.ndarray, List[float]]] = None    ,						A     :						bool = True    ,						A     :						bool = True    ,						A     :						int = 0    ,						A     :						str = "epsilon"    ,						A     :						float = 1.0    ,						**A     :						Union[str, Any]    ,						)  ->  Any:
							if kwargs.get('''set_alpha_to_one'''    ,						A   ) is not None:
									lowercase_ : List[Any]							       =   (
									    '''The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead.'''
									)
									deprecate('''set_alpha_to_one'''    ,						'''1.0.0'''    ,						A    ,						standard_warn=A   )
									lowercase_ : List[str]							       =   kwargs['''set_alpha_to_one''']
							if trained_betas is not None:
									lowercase_ : List[str]							       =   torch.tensor(A    ,						dtype=torch.floataa   )
							elif beta_schedule == "linear":
									lowercase_ : Any							       =   torch.linspace(A    ,						A    ,						A    ,						dtype=torch.floataa   )
							elif beta_schedule == "scaled_linear":
									# this schedule is very specific to the latent diffusion model.
									lowercase_ : Dict							       =   (
									    torch.linspace(beta_start**0.5    ,						beta_end**0.5    ,						A    ,						dtype=torch.floataa   ) ** 2
									)
							elif beta_schedule == "squaredcos_cap_v2":
									# Glide cosine schedule
									lowercase_ : Union[str, Any]							       =   betas_for_alpha_bar(A   )
							else:
									raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}'''   )

							lowercase_ : List[Any]							       =   1.0 - self.betas
							lowercase_ : Optional[Any]							       =   torch.cumprod(self.alphas    ,						dim=0   )

							# At every step in inverted ddim, we are looking into the next alphas_cumprod
							# For the final step, there is no next alphas_cumprod, and the index is out of bounds
							# `set_alpha_to_zero` decides whether we set this parameter simply to zero
							# in this case, self.step() just output the predicted noise
							# or whether we use the final alpha of the "non-previous" one.
							lowercase_ : Tuple							       =   torch.tensor(0.0   ) if set_alpha_to_zero else self.alphas_cumprod[-1]

							# standard deviation of the initial noise distribution
							lowercase_ : Optional[int]							       =   1.0

							# setable values
							lowercase_ : Optional[int]							       =   None
							lowercase_ : Tuple							       =   torch.from_numpy(np.arange(0    ,						A   ).copy().astype(np.intaa   )   )




					def   A  (				self     :						Any    ,						A     :						torch.FloatTensor    ,						A     :						Optional[int] = None   )  ->  torch.FloatTensor:
							return sample




					def   A  (				self     :						int    ,						A     :						int    ,						A     :						Union[str, torch.device] = None   )  ->  Any:

							if num_inference_steps > self.config.num_train_timesteps:
									raise ValueError(
									    F'''`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:'''
									    F''' {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle'''
									    F''' maximal {self.config.num_train_timesteps} timesteps.'''   )

							lowercase_ : Optional[int]							       =   num_inference_steps
							lowercase_ : Union[str, 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
							lowercase_ : Dict							       =   (np.arange(0    ,						A   ) * step_ratio).round().copy().astype(np.intaa   )
							lowercase_ : str							       =   torch.from_numpy(A   ).to(A   )
							self.timesteps += self.config.steps_offset




					def   A  (				self     :						Union[str, Any]    ,						A     :						torch.FloatTensor    ,						A     :						int    ,						A     :						torch.FloatTensor    ,						A     :						float = 0.0    ,						A     :						bool = False    ,						A     :						Optional[torch.FloatTensor] = None    ,						A     :						bool = True    ,						)  ->  Union[DDIMSchedulerOutput, Tuple]:
							# 1. get previous step value (=t+1)
							lowercase_ : Optional[int]							       =   timestep + self.config.num_train_timesteps // self.num_inference_steps

							# 2. compute alphas, betas
							# change original implementation to exactly match noise levels for analogous forward process
							lowercase_ : List[str]							       =   self.alphas_cumprod[timestep]
							lowercase_ : Tuple							       =   (
							    self.alphas_cumprod[prev_timestep]
							    if prev_timestep < self.config.num_train_timesteps
							    else self.final_alpha_cumprod
							)

							lowercase_ : Dict							       =   1 - alpha_prod_t

							# 3. compute predicted original sample from predicted noise also called
							# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
							if self.config.prediction_type == "epsilon":
									lowercase_ : Union[str, Any]							       =   (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
									lowercase_ : List[Any]							       =   model_output
							elif self.config.prediction_type == "sample":
									lowercase_ : Tuple							       =   model_output
									lowercase_ : int							       =   (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
							elif self.config.prediction_type == "v_prediction":
									lowercase_ : int							       =   (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
									lowercase_ : Union[str, Any]							       =   (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
							else:
									raise ValueError(
									    F'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or'''
									    ''' `v_prediction`'''   )

							# 4. Clip or threshold "predicted x_0"
							if self.config.clip_sample:
									lowercase_ : Union[str, Any]							       =   pred_original_sample.clamp(
									    -self.config.clip_sample_range    ,						self.config.clip_sample_range   )

							# 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
							lowercase_ : Optional[int]							       =   (1 - alpha_prod_t_prev) ** 0.5 * pred_epsilon

							# 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
							lowercase_ : int							       =   alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

							if not return_dict:
									return (prev_sample, pred_original_sample)
							return DDIMSchedulerOutput(prev_sample=A    ,						pred_original_sample=A   )






					def __len__(				self     :						str   )  ->  Tuple:
							return self.config.num_train_timesteps











"""simple docstring"""



from __future__ import annotations

__A		:       List[Any]  				=		[-10, -5, 0, 5, 5.1, 11, 13, 21, 3, 4, -21, -10, -5, -1, 0]
__A		:       str  				=		[-5, 0, 5, 5.1, 11, 13, 21, -1, 4, -1, -10, -5, -1, 0, -1]



def 						lowercase    (				__snake_case				: list[float]	):
		lowercase_ : List[str]							       =   []
		lowercase_ : List[Any]							       =   len(__snake_case	)

		for i in range(__snake_case	):
				lowercase_ : float							       =   -1
				for j in range(i + 1		,					__snake_case	):
						if arr[i] < arr[j]:
								lowercase_ : List[str]							       =   arr[j]
								break
				result.append(__snake_case	)
		return result



def 						lowercase    (				__snake_case				: list[float]	):
		lowercase_ : List[str]							       =   []
		for i, outer in enumerate(__snake_case	):
				lowercase_ : float							       =   -1
				for inner in arr[i + 1 :]:
						if outer < inner:
								lowercase_ : List[Any]							       =   inner
								break
				result.append(__snake_case	)
		return result



def 						lowercase    (				__snake_case				: list[float]	):
		lowercase_ : List[str]							       =   len(__snake_case	)
		lowercase_ : list[float]							       =   []
		lowercase_ : list[float]							       =   [-1] * arr_size

		for index in reversed(range(__snake_case	)	):
				if stack:
						while stack[-1] <= arr[index]:
								stack.pop()
								if not stack:
										break
				if stack:
						lowercase_ : Optional[Any]							       =   stack[-1]
				stack.append(arr[index]	)
		return result


if __name__ == "__main__":
						from doctest import testmod
						from timeit import timeit

						testmod()
						print(next_greatest_element_slow(arr))
						print(next_greatest_element_fast(arr))
						print(next_greatest_element(arr))

						__A		:       int  				=		(
						    '''from __main__ import arr, next_greatest_element_slow, '''
						    '''next_greatest_element_fast, next_greatest_element'''
						)
						print(
						    '''next_greatest_element_slow():''',
						    timeit('''next_greatest_element_slow(arr)''', setup=setup),
						)
						print(
						    '''next_greatest_element_fast():''',
						    timeit('''next_greatest_element_fast(arr)''', setup=setup),
						)
						print(
						    '''     next_greatest_element():''',
						    timeit('''next_greatest_element(arr)''', setup=setup),
						)



