


'''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 			a      (			__a ,					__a=0.9_9_9 ,					__a="cosine" ,					)  ->	Optional[int]:



					'''simple docstring'''






					if alpha_transform_type == "cosine":

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

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

					UpperCamelCase__   :Union[str, Any]												= []
					for i in range(a__   ):
										UpperCamelCase__   :int												= i / num_diffusion_timesteps
										UpperCamelCase__   :List[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    lowercase	(							A__	,		A__					):

		"""simple docstring"""

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




		@register_to_config
		def __init__(		self    ,   UpperCamelCase_ = 1000    ,   UpperCamelCase_ = 0.00085    ,   UpperCamelCase_ = 0.012    ,   UpperCamelCase_ = "linear"    ,   UpperCamelCase_ = None    ,   UpperCamelCase_ = "epsilon"    ,   UpperCamelCase_ = False    ,   UpperCamelCase_ = False    ,   UpperCamelCase_ = 1.0    ,   UpperCamelCase_ = "linspace"    ,   UpperCamelCase_ = 0    ,   ):

							'''simple docstring'''


							if trained_betas is not None:
												UpperCamelCase__   :Optional[int]												= torch.tensor(_snake_case    ,   dtype=torch.floataa							)
							elif beta_schedule == "linear":
												UpperCamelCase__   :Union[str, Any]												= 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.
												UpperCamelCase__   :int												= (
												    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
												UpperCamelCase__   :List[Any]												= betas_for_alpha_bar(_snake_case    ,   alpha_transform_type='''cosine'''							)
							elif beta_schedule == "exp":
												UpperCamelCase__   :Tuple												= betas_for_alpha_bar(_snake_case    ,   alpha_transform_type='''exp'''							)
							else:
												raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}'''							)

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

							#  set all values
							self.set_timesteps(_snake_case    ,   _snake_case    ,   _snake_case							)
							UpperCamelCase__   :Tuple												= use_karras_sigmas




		def     lowerCAmelCase__				(		self    ,   UpperCamelCase_    ,   UpperCamelCase_=None							):

							'''simple docstring'''


							if schedule_timesteps is None:
												UpperCamelCase__   :Tuple												= self.timesteps

							UpperCamelCase__   :Optional[int]												= (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__   :int												= 1 if len(_snake_case							) > 1 else 0
							else:
												UpperCamelCase__   :Optional[int]												= timestep.cpu().item() if torch.is_tensor(_snake_case							) else timestep
												UpperCamelCase__   :Optional[int]												= self._index_counter[timestep_int]

							return indices[pos].item()




		@property
		def     lowerCAmelCase__				(		self							):

							'''simple docstring'''


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

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




		def     lowerCAmelCase__				(		self    ,   UpperCamelCase_    ,   UpperCamelCase_    ,   ):

							'''simple docstring'''


							UpperCamelCase__   :str												= self.index_for_timestep(_snake_case							)

							UpperCamelCase__   :int												= self.sigmas[step_index]
							UpperCamelCase__   :Tuple												= sample / ((sigma**2 + 1) ** 0.5)
							return sample




		def     lowerCAmelCase__				(		self    ,   UpperCamelCase_    ,   UpperCamelCase_ = None    ,   UpperCamelCase_ = None    ,   ):

							'''simple docstring'''


							UpperCamelCase__   :Tuple												= num_inference_steps

							UpperCamelCase__   :Union[str, 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    ,   _snake_case    ,   dtype=_snake_case							)[::-1].copy()
							elif self.config.timestep_spacing == "leading":
												UpperCamelCase__   :Dict												= 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    ,   _snake_case							) * step_ratio).round()[::-1].copy().astype(_snake_case							)
												timesteps += self.config.steps_offset
							elif self.config.timestep_spacing == "trailing":
												UpperCamelCase__   :Optional[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__   :Any												= (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\'.'''							)

							UpperCamelCase__   :Optional[Any]												= np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
							UpperCamelCase__   :str												= np.log(_snake_case							)
							UpperCamelCase__   :int												= np.interp(_snake_case    ,   np.arange(0    ,   len(_snake_case							)							)    ,   _snake_case							)

							if self.config.use_karras_sigmas:
												UpperCamelCase__   :int												= self._convert_to_karras(in_sigmas=_snake_case    ,   num_inference_steps=self.num_inference_steps							)
												UpperCamelCase__   :Dict												= np.array([self._sigma_to_t(_snake_case    ,   _snake_case							) for sigma in sigmas]							)

							UpperCamelCase__   :Union[str, Any]												= np.concatenate([sigmas, [0.0]]							).astype(np.floataa							)
							UpperCamelCase__   :Dict												= torch.from_numpy(_snake_case							).to(device=_snake_case							)
							UpperCamelCase__   :Union[str, Any]												= torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2							), sigmas[-1:]]							)

							UpperCamelCase__   :str												= torch.from_numpy(_snake_case							)
							UpperCamelCase__   :Dict												= torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2							)]							)

							if str(_snake_case							).startswith('''mps'''							):
												# mps does not support float64
												UpperCamelCase__   :List[str]												= timesteps.to(_snake_case    ,   dtype=torch.floataa							)
							else:
												UpperCamelCase__   :Optional[Any]												= timesteps.to(device=_snake_case							)

							# empty dt and derivative
							UpperCamelCase__   :List[str]												= None
							UpperCamelCase__   :Union[str, Any]												= None

							# for exp beta schedules, such as the one for `pipeline_shap_e.py`
							# we need an index counter
							UpperCamelCase__   :List[str]												= defaultdict(_snake_case							)




		def     lowerCAmelCase__				(		self    ,   UpperCamelCase_    ,   UpperCamelCase_							):

							'''simple docstring'''


							UpperCamelCase__   :Optional[Any]												= np.log(_snake_case							)

							# get distribution
							UpperCamelCase__   :Dict												= log_sigma - log_sigmas[:, np.newaxis]

							# get sigmas range
							UpperCamelCase__   :Union[str, Any]												= np.cumsum((dists >= 0)    ,   axis=0							).argmax(axis=0							).clip(max=log_sigmas.shape[0] - 2							)
							UpperCamelCase__   :int												= low_idx + 1

							UpperCamelCase__   :Dict												= log_sigmas[low_idx]
							UpperCamelCase__   :Any												= log_sigmas[high_idx]

							# interpolate sigmas
							UpperCamelCase__   :int												= (low - log_sigma) / (low - high)
							UpperCamelCase__   :List[str]												= np.clip(_snake_case    ,   0    ,   1							)

							# transform interpolation to time range
							UpperCamelCase__   :int												= (1 - w) * low_idx + w * high_idx
							UpperCamelCase__   :str												= t.reshape(sigma.shape							)
							return t




		def     lowerCAmelCase__				(		self    ,   UpperCamelCase_    ,   UpperCamelCase_							):

							'''simple docstring'''


							UpperCamelCase__   :str												= in_sigmas[-1].item()
							UpperCamelCase__   :Tuple												= in_sigmas[0].item()

							UpperCamelCase__   :Any												= 7.0  # 7.0 is the value used in the paper
							UpperCamelCase__   :Union[str, Any]												= np.linspace(0    ,   1    ,   _snake_case							)
							UpperCamelCase__   :Any												= sigma_min ** (1 / rho)
							UpperCamelCase__   :Dict												= sigma_max ** (1 / rho)
							UpperCamelCase__   :str												= (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
							return sigmas




		@property
		def     lowerCAmelCase__				(		self							):

							'''simple docstring'''


							return self.dt is None




		def     lowerCAmelCase__				(		self    ,   UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_ = True    ,   ):

							'''simple docstring'''


							UpperCamelCase__   :Optional[Any]												= self.index_for_timestep(_snake_case							)

							# advance index counter by 1
							UpperCamelCase__   :List[Any]												= timestep.cpu().item() if torch.is_tensor(_snake_case							) else timestep
							self._index_counter[timestep_int] += 1

							if self.state_in_first_order:
												UpperCamelCase__   :int												= self.sigmas[step_index]
												UpperCamelCase__   :List[str]												= self.sigmas[step_index + 1]
							else:
												# 2nd order / Heun's method
												UpperCamelCase__   :List[str]												= self.sigmas[step_index - 1]
												UpperCamelCase__   :Any												= 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__   :Optional[Any]												= 0
							UpperCamelCase__   :Dict												= 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__   :Dict												= sigma_hat if self.state_in_first_order else sigma_next
												UpperCamelCase__   :str												= sample - sigma_input * model_output
							elif self.config.prediction_type == "v_prediction":
												UpperCamelCase__   :Tuple												= sigma_hat if self.state_in_first_order else sigma_next
												UpperCamelCase__   :Optional[Any]												= model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
												    sample / (sigma_input**2 + 1)
												)
							elif self.config.prediction_type == "sample":
												UpperCamelCase__   :List[str]												= model_output
							else:
												raise ValueError(
												    F'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'''							)

							if self.config.clip_sample:
												UpperCamelCase__   :Optional[Any]												= pred_original_sample.clamp(
												    -self.config.clip_sample_range    ,   self.config.clip_sample_range							)

							if self.state_in_first_order:
												# 2. Convert to an ODE derivative for 1st order
												UpperCamelCase__   :List[str]												= (sample - pred_original_sample) / sigma_hat
												# 3. delta timestep
												UpperCamelCase__   :List[Any]												= sigma_next - sigma_hat

												# store for 2nd order step
												UpperCamelCase__   :Union[str, Any]												= derivative
												UpperCamelCase__   :str												= dt
												UpperCamelCase__   :Tuple												= sample
							else:
												# 2. 2nd order / Heun's method
												UpperCamelCase__   :Union[str, Any]												= (sample - pred_original_sample) / sigma_next
												UpperCamelCase__   :Optional[int]												= (self.prev_derivative + derivative) / 2

												# 3. take prev timestep & sample
												UpperCamelCase__   :Any												= self.dt
												UpperCamelCase__   :Tuple												= self.sample

												# free dt and derivative
												# Note, this puts the scheduler in "first order mode"
												UpperCamelCase__   :Optional[int]												= None
												UpperCamelCase__   :List[str]												= None
												UpperCamelCase__   :int												= None

							UpperCamelCase__   :List[Any]												= sample + derivative * dt

							if not return_dict:
												return (prev_sample,)

							return SchedulerOutput(prev_sample=_snake_case							)




		def     lowerCAmelCase__				(		self    ,   UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_    ,   ):

							'''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(_snake_case							):
												# mps does not support float64
												UpperCamelCase__   :Tuple												= self.timesteps.to(original_samples.device    ,   dtype=torch.floataa							)
												UpperCamelCase__   :int												= timesteps.to(original_samples.device    ,   dtype=torch.floataa							)
							else:
												UpperCamelCase__   :Optional[Any]												= self.timesteps.to(original_samples.device							)
												UpperCamelCase__   :Any												= timesteps.to(original_samples.device							)

							UpperCamelCase__   :Optional[Any]												= [self.index_for_timestep(_snake_case    ,   _snake_case							) for t in timesteps]

							UpperCamelCase__   :List[str]												= sigmas[step_indices].flatten()
							while len(sigma.shape							) < len(original_samples.shape							):
												UpperCamelCase__   :List[Any]												= sigma.unsqueeze(-1							)

							UpperCamelCase__   :Any												= original_samples + noise * sigma
							return noisy_samples




		def __len__(		self							):

							'''simple docstring'''


							return self.config.num_train_timesteps

from math import ceil


def     __lowerCAmelCase			(			a__ = 1001  )       ->  int:
				__a										=    1

				for i in range(1						,    int(ceil(n / 2.0  )  )  ):
								__a										=    2 * i + 1
								__a										=    2 * i
								__a										=    total + 4 * odd**2 - 6 * even

				return total


if __name__ == "__main__":
					import sys

					if len(sys.argv) == 1:
										print(solution())
					else:
										try:
															A     :	List[Any]    = int(sys.argv[1])
															print(solution(n))
										except ValueError:
															print('Invalid entry - please enter a number')