




# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

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

import torch

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



@dataclass
class    lowercase_		(SCREAMING_SNAKE_CASE__ ):
						lowerCAmelCase__			      =42
						lowerCAmelCase__			      =42



class    lowercase_		(SCREAMING_SNAKE_CASE__							,	SCREAMING_SNAKE_CASE__ ):
						lowerCAmelCase__			      =1



						@register_to_config
						def __init__(			self	:   Union[str, Any]					,							snake_case__	:   int = 20_00					,							snake_case__	:   float = 0.15					,							snake_case__	:   float = 0.01					,							snake_case__	:   float = 13_48.0					,							snake_case__	:   float = 1e-5					,							snake_case__	:   int = 1					,							):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							sigma_max

								# setable values
								SCREAMING_SNAKE_CASE_					      =							None

								self.set_sigmas(snake_case__					,							snake_case__					,							snake_case__					,							snake_case__  )



						def 	__a					(			self	:   Optional[int]					,							snake_case__	:   torch.FloatTensor					,							snake_case__	:   Optional[int] = None  ):

								"""simple docstring"""

								return sample



						def 	__a					(			self	:   Dict					,							snake_case__	:   int					,							snake_case__	:   float = None					,							snake_case__	:   Union[str, torch.device] = None  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							sampling_eps if sampling_eps is not None else self.config.sampling_eps

								SCREAMING_SNAKE_CASE_					      =							torch.linspace(1					,							snake_case__					,							snake_case__					,							device=snake_case__  )



						def 	__a					(			self	:   Union[str, Any]					,							snake_case__	:   int					,							snake_case__	:   float = None					,							snake_case__	:   float = None					,							snake_case__	:   float = None  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							sigma_min if sigma_min is not None else self.config.sigma_min
								SCREAMING_SNAKE_CASE_					      =							sigma_max if sigma_max is not None else self.config.sigma_max
								SCREAMING_SNAKE_CASE_					      =							sampling_eps if sampling_eps is not None else self.config.sampling_eps
								if self.timesteps is None:
										self.set_timesteps(snake_case__					,							snake_case__  )

								SCREAMING_SNAKE_CASE_					      =							sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
								SCREAMING_SNAKE_CASE_					      =							torch.exp(torch.linspace(math.log(snake_case__  )					,							math.log(snake_case__  )					,							snake_case__  )  )
								SCREAMING_SNAKE_CASE_					      =							torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]  )



						def 	__a					(			self	:   Any					,							snake_case__	:   int					,							snake_case__	:   List[str]  ):

								"""simple docstring"""

								return torch.where(
								    timesteps == 0					,							torch.zeros_like(t.to(timesteps.device  )  )					,							self.discrete_sigmas[timesteps - 1].to(timesteps.device  )					,							)



						def 	__a					(			self	:   Union[str, Any]					,							snake_case__	:   torch.FloatTensor					,							snake_case__	:   int					,							snake_case__	:   torch.FloatTensor					,							snake_case__	:   Optional[torch.Generator] = None					,							snake_case__	:   bool = True					,							):

								"""simple docstring"""

								if self.timesteps is None:
										raise ValueError(
										    '`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'  )

								SCREAMING_SNAKE_CASE_					      =							timestep * torch.ones(
								    sample.shape[0]					,							device=sample.device  )  # torch.repeat_interleave(timestep, sample.shape[0])
								SCREAMING_SNAKE_CASE_					      =							(timestep * (len(self.timesteps  ) - 1)).long()

								# mps requires indices to be in the same device, so we use cpu as is the default with cuda
								SCREAMING_SNAKE_CASE_					      =							timesteps.to(self.discrete_sigmas.device  )

								SCREAMING_SNAKE_CASE_					      =							self.discrete_sigmas[timesteps].to(sample.device  )
								SCREAMING_SNAKE_CASE_					      =							self.get_adjacent_sigma(snake_case__					,							snake_case__  ).to(sample.device  )
								SCREAMING_SNAKE_CASE_					      =							torch.zeros_like(snake_case__  )
								SCREAMING_SNAKE_CASE_					      =							(sigma**2 - adjacent_sigma**2) ** 0.5

								# equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
								# also equation 47 shows the analog from SDE models to ancestral sampling methods
								SCREAMING_SNAKE_CASE_					      =							diffusion.flatten()
								while len(diffusion.shape  ) < len(sample.shape  ):
										SCREAMING_SNAKE_CASE_					      =							diffusion.unsqueeze(-1  )
								SCREAMING_SNAKE_CASE_					      =							drift - diffusion**2 * model_output

								#  equation 6: sample noise for the diffusion term of
								SCREAMING_SNAKE_CASE_					      =							randn_tensor(
								    sample.shape					,							layout=sample.layout					,							generator=snake_case__					,							device=sample.device					,							dtype=sample.dtype  )
								SCREAMING_SNAKE_CASE_					      =							sample - drift  # subtract because `dt` is a small negative timestep
								# TODO is the variable diffusion the correct scaling term for the noise?
								SCREAMING_SNAKE_CASE_					      =							prev_sample_mean + diffusion * noise  # add impact of diffusion field g

								if not return_dict:
										return (prev_sample, prev_sample_mean)

								return SdeVeOutput(prev_sample=snake_case__					,							prev_sample_mean=snake_case__  )



						def 	__a					(			self	:   int					,							snake_case__	:   torch.FloatTensor					,							snake_case__	:   torch.FloatTensor					,							snake_case__	:   Optional[torch.Generator] = None					,							snake_case__	:   bool = True					,							):

								"""simple docstring"""

								if self.timesteps is None:
										raise ValueError(
										    '`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'  )

								# For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
								# sample noise for correction
								SCREAMING_SNAKE_CASE_					      =							randn_tensor(sample.shape					,							layout=sample.layout					,							generator=snake_case__  ).to(sample.device  )

								# compute step size from the model_output, the noise, and the snr
								SCREAMING_SNAKE_CASE_					      =							torch.norm(model_output.reshape(model_output.shape[0]					,							-1  )					,							dim=-1  ).mean()
								SCREAMING_SNAKE_CASE_					      =							torch.norm(noise.reshape(noise.shape[0]					,							-1  )					,							dim=-1  ).mean()
								SCREAMING_SNAKE_CASE_					      =							(self.config.snr * noise_norm / grad_norm) ** 2 * 2
								SCREAMING_SNAKE_CASE_					      =							step_size * torch.ones(sample.shape[0]  ).to(sample.device  )
								# self.repeat_scalar(step_size, sample.shape[0])

								# compute corrected sample: model_output term and noise term
								SCREAMING_SNAKE_CASE_					      =							step_size.flatten()
								while len(step_size.shape  ) < len(sample.shape  ):
										SCREAMING_SNAKE_CASE_					      =							step_size.unsqueeze(-1  )
								SCREAMING_SNAKE_CASE_					      =							sample + step_size * model_output
								SCREAMING_SNAKE_CASE_					      =							prev_sample_mean + ((step_size * 2) ** 0.5) * noise

								if not return_dict:
										return (prev_sample,)

								return SchedulerOutput(prev_sample=snake_case__  )



						def 	__a					(			self	:   Tuple					,							snake_case__	:   torch.FloatTensor					,							snake_case__	:   torch.FloatTensor					,							snake_case__	:   torch.FloatTensor					,							):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							timesteps.to(original_samples.device  )
								SCREAMING_SNAKE_CASE_					      =							self.discrete_sigmas.to(original_samples.device  )[timesteps]
								SCREAMING_SNAKE_CASE_					      =							(
								    noise * sigmas[:, None, None, None]
								    if noise is not None
								    else torch.randn_like(snake_case__  ) * sigmas[:, None, None, None]
								)
								SCREAMING_SNAKE_CASE_					      =							noise + original_samples
								return noisy_samples






						def __len__(			self	:   Any  ):

								"""simple docstring"""

								return self.config.num_train_timesteps





from __future__ import annotations

import math


def 					_a							(					lowerCAmelCase )->	bool:

		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(lowerCAmelCase ) + 1 )    ,						6 ):
				if number % i == 0 or number % (i + 2) == 0:
						return False
		return True


SCREAMING_SNAKE_CASE:     List[str]									= [num for num in range(3, 1_0_0_0_0_1, 2) if not is_prime(num)]


def 					_a							(					lowerCAmelCase )->	list[int]:
		if not isinstance(lowerCAmelCase    ,						lowerCAmelCase ):
				raise ValueError('n must be an integer' )
		if n <= 0:
				raise ValueError('n must be >= 0' )

		SCREAMING_SNAKE_CASE_					      =							[]
		for num in range(len(lowerCAmelCase ) ):
				SCREAMING_SNAKE_CASE_					      =							0
				while 2 * i * i <= odd_composites[num]:
						SCREAMING_SNAKE_CASE_					      =							odd_composites[num] - 2 * i * i
						if is_prime(lowerCAmelCase ):
								break
						i += 1
				else:
						list_nums.append(odd_composites[num] )
						if len(lowerCAmelCase ) == n:
								return list_nums

		return []


def 					_a							(					)->	int:
		return compute_nums(1 )[0]


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