
'''simple docstring'''







import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

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


_lowercase				:						str												= logging.get_logger(__name__)  # pylint: disable=invalid-name






@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class 				lowerCAmelCase__     (						lowerCamelCase_  ):
					lowerCAmelCase_       =  42
					lowerCAmelCase_       =  None







def       snake_case_	(       __SCREAMING_SNAKE_CASE      :				Union[str, Any]   ,   __SCREAMING_SNAKE_CASE      :				List[str]=0.999   ,   __SCREAMING_SNAKE_CASE      :				Any="cosine"   ,   ):



						"""simple docstring"""





						if alpha_transform_type == "cosine":

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

						elif alpha_transform_type == "exp":

												def alpha_bar_fn(__SCREAMING_SNAKE_CASE      :				List[Any]							):
																		return math.exp(t * -12.0							)

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

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






class 				lowerCAmelCase__     (						lowerCamelCase_					,		lowerCamelCase_  ):
					lowerCAmelCase_       =  [e.name for e in KarrasDiffusionSchedulers]
					lowerCAmelCase_       =  1






					@register_to_config
					def __init__(     self       ,							__SCREAMING_SNAKE_CASE = 10_00       ,							__SCREAMING_SNAKE_CASE = 0.0_001       ,							__SCREAMING_SNAKE_CASE = 0.02       ,							__SCREAMING_SNAKE_CASE = "linear"       ,							__SCREAMING_SNAKE_CASE = None       ,							__SCREAMING_SNAKE_CASE = "epsilon"       ,							__SCREAMING_SNAKE_CASE = "linear"       ,							__SCREAMING_SNAKE_CASE = False       ,							__SCREAMING_SNAKE_CASE = "linspace"       ,							__SCREAMING_SNAKE_CASE = 0       ,							):


											"""simple docstring"""





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

											lowercase_			:  Union[str, Any]									= 1.0 - self.betas
											lowercase_			:  Tuple									= torch.cumprod(self.alphas       ,							dim=0	)

											lowercase_			:  int									= np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5	)
											lowercase_			:  Dict									= np.concatenate([sigmas[::-1], [0.0]]	).astype(np.floataa	)
											lowercase_			:  int									= torch.from_numpy(__SCREAMING_SNAKE_CASE	)

											# setable values
											lowercase_			:  Optional[int]									= None
											lowercase_			:  Optional[Any]									= np.linspace(0       ,							num_train_timesteps - 1       ,							__SCREAMING_SNAKE_CASE       ,							dtype=__SCREAMING_SNAKE_CASE	)[::-1].copy()
											lowercase_			:  Optional[Any]									= torch.from_numpy(__SCREAMING_SNAKE_CASE	)
											lowercase_			:  Any									= False
											lowercase_			:  Any									= use_karras_sigmas






					@property
					def 			_snake_case					(     self	):


											"""simple docstring"""





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

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






					def 			_snake_case					(     self       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE	):


											"""simple docstring"""





											if isinstance(__SCREAMING_SNAKE_CASE       ,							torch.Tensor	):
																	lowercase_			:  Union[str, Any]									= timestep.to(self.timesteps.device	)
											lowercase_			:  str									= (self.timesteps == timestep).nonzero().item()
											lowercase_			:  Optional[int]									= self.sigmas[step_index]

											lowercase_			:  List[str]									= sample / ((sigma**2 + 1) ** 0.5)

											lowercase_			:  Any									= True
											return sample






					def 			_snake_case					(     self       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE = None	):


											"""simple docstring"""





											lowercase_			:  Optional[Any]									= num_inference_steps

											# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
											if self.config.timestep_spacing == "linspace":
																	lowercase_			:  Any									= np.linspace(0       ,							self.config.num_train_timesteps - 1       ,							__SCREAMING_SNAKE_CASE       ,							dtype=__SCREAMING_SNAKE_CASE	)[
																	    ::-1
																	].copy()
											elif self.config.timestep_spacing == "leading":
																	lowercase_			:  str									= 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_			:  List[Any]									= (np.arange(0       ,							__SCREAMING_SNAKE_CASE	) * step_ratio).round()[::-1].copy().astype(__SCREAMING_SNAKE_CASE	)
																	timesteps += self.config.steps_offset
											elif self.config.timestep_spacing == "trailing":
																	lowercase_			:  List[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_			:  List[Any]									= (np.arange(self.config.num_train_timesteps       ,							0       ,							-step_ratio	)).round().copy().astype(__SCREAMING_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_			:  Optional[Any]									= np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5	)
											lowercase_			:  Optional[Any]									= np.log(__SCREAMING_SNAKE_CASE	)

											if self.config.interpolation_type == "linear":
																	lowercase_			:  str									= np.interp(__SCREAMING_SNAKE_CASE       ,							np.arange(0       ,							len(__SCREAMING_SNAKE_CASE	)	)       ,							__SCREAMING_SNAKE_CASE	)
											elif self.config.interpolation_type == "log_linear":
																	lowercase_			:  List[str]									= torch.linspace(np.log(sigmas[-1]	)       ,							np.log(sigmas[0]	)       ,							num_inference_steps + 1	).exp()
											else:
																	raise ValueError(
																	    F'''{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either'''
																	    ''' \'linear\' or \'log_linear\''''	)

											if self.use_karras_sigmas:
																	lowercase_			:  Any									= self._convert_to_karras(in_sigmas=__SCREAMING_SNAKE_CASE       ,							num_inference_steps=self.num_inference_steps	)
																	lowercase_			:  str									= np.array([self._sigma_to_t(__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE	) for sigma in sigmas]	)

											lowercase_			:  str									= np.concatenate([sigmas, [0.0]]	).astype(np.floataa	)
											lowercase_			:  List[str]									= torch.from_numpy(__SCREAMING_SNAKE_CASE	).to(device=__SCREAMING_SNAKE_CASE	)
											if str(__SCREAMING_SNAKE_CASE	).startswith('''mps'''	):
																	# mps does not support float64
																	lowercase_			:  Union[str, Any]									= torch.from_numpy(__SCREAMING_SNAKE_CASE	).to(__SCREAMING_SNAKE_CASE       ,							dtype=torch.floataa	)
											else:
																	lowercase_			:  List[Any]									= torch.from_numpy(__SCREAMING_SNAKE_CASE	).to(device=__SCREAMING_SNAKE_CASE	)






					def 			_snake_case					(     self       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE	):


											"""simple docstring"""





											lowercase_			:  Any									= np.log(__SCREAMING_SNAKE_CASE	)

											# get distribution
											lowercase_			:  Optional[Any]									= log_sigma - log_sigmas[:, np.newaxis]

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

											lowercase_			:  int									= log_sigmas[low_idx]
											lowercase_			:  Union[str, Any]									= log_sigmas[high_idx]

											# interpolate sigmas
											lowercase_			:  Any									= (low - log_sigma) / (low - high)
											lowercase_			:  int									= np.clip(__SCREAMING_SNAKE_CASE       ,							0       ,							1	)

											# transform interpolation to time range
											lowercase_			:  Union[str, Any]									= (1 - w) * low_idx + w * high_idx
											lowercase_			:  Tuple									= t.reshape(sigma.shape	)
											return t






					def 			_snake_case					(     self       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE	):


											"""simple docstring"""





											lowercase_			:  float									= in_sigmas[-1].item()
											lowercase_			:  float									= in_sigmas[0].item()

											lowercase_			:  Optional[Any]									= 7.0  # 7.0 is the value used in the paper
											lowercase_			:  List[str]									= np.linspace(0       ,							1       ,							__SCREAMING_SNAKE_CASE	)
											lowercase_			:  Optional[Any]									= sigma_min ** (1 / rho)
											lowercase_			:  List[str]									= sigma_max ** (1 / rho)
											lowercase_			:  Optional[int]									= (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
											return sigmas






					def 			_snake_case					(     self       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE = 0.0       ,							__SCREAMING_SNAKE_CASE = 0.0       ,							__SCREAMING_SNAKE_CASE = float('''inf'''	)       ,							__SCREAMING_SNAKE_CASE = 1.0       ,							__SCREAMING_SNAKE_CASE = None       ,							__SCREAMING_SNAKE_CASE = True       ,							):


											"""simple docstring"""





											if (
											    isinstance(__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE	)
											    or isinstance(__SCREAMING_SNAKE_CASE       ,							torch.IntTensor	)
											    or isinstance(__SCREAMING_SNAKE_CASE       ,							torch.LongTensor	)
											):
																	raise ValueError(
																	    (
																	        '''Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to'''
																	        ''' `EulerDiscreteScheduler.step()` is not supported. Make sure to pass'''
																	        ''' one of the `scheduler.timesteps` as a timestep.'''
																	    )       ,							)

											if not self.is_scale_input_called:
																	logger.warning(
																	    '''The `scale_model_input` function should be called before `step` to ensure correct denoising. '''
																	    '''See `StableDiffusionPipeline` for a usage example.'''	)

											if isinstance(__SCREAMING_SNAKE_CASE       ,							torch.Tensor	):
																	lowercase_			:  List[str]									= timestep.to(self.timesteps.device	)

											lowercase_			:  str									= (self.timesteps == timestep).nonzero().item()
											lowercase_			:  Optional[Any]									= self.sigmas[step_index]

											lowercase_			:  str									= min(s_churn / (len(self.sigmas	) - 1)       ,							2**0.5 - 1	) if s_tmin <= sigma <= s_tmax else 0.0

											lowercase_			:  Optional[Any]									= randn_tensor(
											    model_output.shape       ,							dtype=model_output.dtype       ,							device=model_output.device       ,							generator=__SCREAMING_SNAKE_CASE	)

											lowercase_			:  str									= noise * s_noise
											lowercase_			:  Union[str, Any]									= sigma * (gamma + 1)

											if gamma > 0:
																	lowercase_			:  Optional[int]									= sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

											# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
											# NOTE: "original_sample" should not be an expected prediction_type but is left in for
											# backwards compatibility
											if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
																	lowercase_			:  List[str]									= model_output
											elif self.config.prediction_type == "epsilon":
																	lowercase_			:  Dict									= sample - sigma_hat * model_output
											elif self.config.prediction_type == "v_prediction":
																	# * c_out + input * c_skip
																	lowercase_			:  Optional[int]									= model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
											else:
																	raise ValueError(
																	    F'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'''	)

											# 2. Convert to an ODE derivative
											lowercase_			:  Union[str, Any]									= (sample - pred_original_sample) / sigma_hat

											lowercase_			:  int									= self.sigmas[step_index + 1] - sigma_hat

											lowercase_			:  Dict									= sample + derivative * dt

											if not return_dict:
																	return (prev_sample,)

											return EulerDiscreteSchedulerOutput(prev_sample=__SCREAMING_SNAKE_CASE       ,							pred_original_sample=__SCREAMING_SNAKE_CASE	)






					def 			_snake_case					(     self       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE       ,							):


											"""simple docstring"""





											lowercase_			:  Tuple									= self.sigmas.to(device=original_samples.device       ,							dtype=original_samples.dtype	)
											if original_samples.device.type == "mps" and torch.is_floating_point(__SCREAMING_SNAKE_CASE	):
																	# mps does not support float64
																	lowercase_			:  Dict									= self.timesteps.to(original_samples.device       ,							dtype=torch.floataa	)
																	lowercase_			:  Any									= timesteps.to(original_samples.device       ,							dtype=torch.floataa	)
											else:
																	lowercase_			:  Optional[Any]									= self.timesteps.to(original_samples.device	)
																	lowercase_			:  int									= timesteps.to(original_samples.device	)

											lowercase_			:  str									= [(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

											lowercase_			:  Dict									= original_samples + noise * sigma
											return noisy_samples






					def __len__(     self	):


											"""simple docstring"""





											return self.config.num_train_timesteps





'''simple docstring'''







import math
def       snake_case_	(       __SCREAMING_SNAKE_CASE      :				int							):



						"""simple docstring"""





						if 1 < number < 4:
												# 2 and 3 are primes
												return True
						elif number < 2 or number % 2 == 0 or number % 3 == 0:
												# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
												return False

						# All primes number are in format of 6k +/- 1
						for i in range(5   ,   int(math.sqrt(__SCREAMING_SNAKE_CASE							) + 1							)   ,   6							):
												if number % i == 0 or number % (i + 2) == 0:
																		return False
						return True
def       snake_case_	(       __SCREAMING_SNAKE_CASE      :				int = 2000000							):



						"""simple docstring"""





						return sum(num for num in range(3   ,   __SCREAMING_SNAKE_CASE   ,   2							) if is_prime(__SCREAMING_SNAKE_CASE							)							) + 2 if n > 2 else 0


if __name__ == "__main__":
							print(f"""{solution() = }""")



