
'''simple docstring'''







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

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import FlaxSchedulerMixin, FlaxSchedulerOutput, broadcast_to_shape_from_left






@flax.struct.dataclass
class 					lowerCAmelCase__  :
					# setable values
					lowerCAmelCase_	  =	None
					lowerCAmelCase_	  =	None
					lowerCAmelCase_	  =	None






					@classmethod
					def       _snake_case       (  cls						):


											"""simple docstring"""





											return cls()







@dataclass
class 					lowerCAmelCase__  (    lowerCamelCase_	):
					lowerCAmelCase_	  =	42
					lowerCAmelCase_	  =	42
					lowerCAmelCase_	  =	None







class 					lowerCAmelCase__  (    lowerCamelCase_       ,		lowerCamelCase_	):






					@property
					def       _snake_case       (  self						):


											"""simple docstring"""





											return True






					@register_to_config
					def __init__(  self							,				__SCREAMING_SNAKE_CASE = 20_00							,				__SCREAMING_SNAKE_CASE = 0.15							,				__SCREAMING_SNAKE_CASE = 0.01							,				__SCREAMING_SNAKE_CASE = 13_48.0							,				__SCREAMING_SNAKE_CASE = 1E-5							,				__SCREAMING_SNAKE_CASE = 1							,				):


											"""simple docstring"""





											pass






					def       _snake_case       (  self						):


											"""simple docstring"""





											lowercase_      :	List[Any]						=			ScoreSdeVeSchedulerState.create()
											return self.set_sigmas(
											    snake_case__							,				self.config.num_train_timesteps							,				self.config.sigma_min							,				self.config.sigma_max							,				self.config.sampling_eps							,				)






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


											"""simple docstring"""





											lowercase_      :	Dict						=			sampling_eps if sampling_eps is not None else self.config.sampling_eps

											lowercase_      :	int						=			jnp.linspace(1							,				snake_case__							,				snake_case__						)
											return state.replace(timesteps=snake_case__						)






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


											"""simple docstring"""





											lowercase_      :	Optional[int]						=			sigma_min if sigma_min is not None else self.config.sigma_min
											lowercase_      :	List[Any]						=			sigma_max if sigma_max is not None else self.config.sigma_max
											lowercase_      :	Dict						=			sampling_eps if sampling_eps is not None else self.config.sampling_eps
											if state.timesteps is None:
																	lowercase_      :	int						=			self.set_timesteps(snake_case__							,				snake_case__							,				snake_case__						)

											lowercase_      :	Union[str, Any]						=			jnp.exp(jnp.linspace(jnp.log(snake_case__						)							,				jnp.log(snake_case__						)							,				snake_case__						)						)
											lowercase_      :	str						=			jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]						)

											return state.replace(discrete_sigmas=snake_case__							,				sigmas=snake_case__						)






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


											"""simple docstring"""





											return jnp.where(timesteps == 0							,				jnp.zeros_like(snake_case__						)							,				state.discrete_sigmas[timesteps - 1]						)






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


											"""simple docstring"""





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

											lowercase_      :	str						=			timestep * jnp.ones(
											    sample.shape[0]							,				)
											lowercase_      :	Dict						=			(timestep * (len(state.timesteps						) - 1)).long()

											lowercase_      :	Optional[int]						=			state.discrete_sigmas[timesteps]
											lowercase_      :	Optional[int]						=			self.get_adjacent_sigma(snake_case__							,				snake_case__							,				snake_case__						)
											lowercase_      :	Any						=			jnp.zeros_like(snake_case__						)
											lowercase_      :	Tuple						=			(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
											lowercase_      :	Union[str, Any]						=			diffusion.flatten()
											lowercase_      :	Optional[Any]						=			broadcast_to_shape_from_left(snake_case__							,				sample.shape						)
											lowercase_      :	Optional[Any]						=			drift - diffusion**2 * model_output

											#  equation 6: sample noise for the diffusion term of
											lowercase_      :	Any						=			random.split(snake_case__							,				num=1						)
											lowercase_      :	Dict						=			random.normal(key=snake_case__							,				shape=sample.shape						)
											lowercase_      :	Optional[int]						=			sample - drift  # subtract because `dt` is a small negative timestep
											# TODO is the variable diffusion the correct scaling term for the noise?
											lowercase_      :	Dict						=			prev_sample_mean + diffusion * noise  # add impact of diffusion field g

											if not return_dict:
																	return (prev_sample, prev_sample_mean, state)

											return FlaxSdeVeOutput(prev_sample=snake_case__							,				prev_sample_mean=snake_case__							,				state=snake_case__						)






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


											"""simple docstring"""





											if state.timesteps is None:
																	raise ValueError(
																	    '''`state.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
											lowercase_      :	List[str]						=			random.split(snake_case__							,				num=1						)
											lowercase_      :	List[Any]						=			random.normal(key=snake_case__							,				shape=sample.shape						)

											# compute step size from the model_output, the noise, and the snr
											lowercase_      :	Tuple						=			jnp.linalg.norm(snake_case__						)
											lowercase_      :	Dict						=			jnp.linalg.norm(snake_case__						)
											lowercase_      :	Optional[Any]						=			(self.config.snr * noise_norm / grad_norm) ** 2 * 2
											lowercase_      :	Optional[int]						=			step_size * jnp.ones(sample.shape[0]						)

											# compute corrected sample: model_output term and noise term
											lowercase_      :	Tuple						=			step_size.flatten()
											lowercase_      :	Optional[Any]						=			broadcast_to_shape_from_left(snake_case__							,				sample.shape						)
											lowercase_      :	int						=			sample + step_size * model_output
											lowercase_      :	Optional[Any]						=			prev_sample_mean + ((step_size * 2) ** 0.5) * noise

											if not return_dict:
																	return (prev_sample, state)

											return FlaxSdeVeOutput(prev_sample=snake_case__							,				state=snake_case__						)






					def __len__(  self						):


											"""simple docstring"""





											return self.config.num_train_timesteps







'''simple docstring'''




from itertools import combinations, product

def       __UpperCamelCase     (     _A     :					int       , _A     :					int       , _A     :					int       , _A     :					int					)     ->   bool:




	"""simple docstring"""





	if xa == ya == 0 or xa == ya == 0:
		return False
	lowerCAmelCase       :     Optional[Any]   				=			xa * xa + ya * ya
	lowerCAmelCase       :     Tuple   				=			xa * xa + ya * ya
	lowerCAmelCase       :     List[str]   				=			(xa - xa) * (xa - xa) + (ya - ya) * (ya - ya)
	return (
	    a_square + b_square == c_square
	    or a_square + c_square == b_square
	    or b_square + c_square == a_square
	)

def       __UpperCamelCase     (     _A     :					int = 50					)     ->   int:




	"""simple docstring"""





	return sum(
	    1
	    for pta, pta in combinations(product(range(limit + 1					)       , repeat=2					)       , 2					)
	    if is_right(*_A       , *_A					)					)


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