



'''simple docstring'''



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

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 			_SCREAMING_SNAKE_CASE				:
			# setable values
			A__								=  None
			A__								=  None
			A__								=  None



			@classmethod
			def 				lowerCAmelCase (     cls		:						Union[str, Any]			)      ->      List[Any]:
							"""simple docstring"""





							return cls()






@dataclass
class 			_SCREAMING_SNAKE_CASE				(lowercase__      ):
			A__								=  42
			A__								=  42
			A__								=  None






class 			_SCREAMING_SNAKE_CASE				(lowercase__,	lowercase__      ):



			@property
			def 				lowerCAmelCase (     self		:						Dict			)      ->      str:
							"""simple docstring"""





							return True



			@register_to_config
			def __init__(     self		:						List[str]    ,			__UpperCamelCase		:						int = 2000    ,			__UpperCamelCase		:						float = 0.15    ,			__UpperCamelCase		:						float = 0.01    ,			__UpperCamelCase		:						float = 1348.0    ,			__UpperCamelCase		:						float = 1e-5    ,			__UpperCamelCase		:						int = 1    ,			)      ->      Optional[Any]:
							"""simple docstring"""





							pass



			def 				lowerCAmelCase (     self		:						Union[str, Any]			)      ->      List[Any]:
							"""simple docstring"""





							snake_case__      :   str      =    ScoreSdeVeSchedulerState.create()
							return self.set_sigmas(
							    __UpperCamelCase    ,			self.config.num_train_timesteps    ,			self.config.sigma_min    ,			self.config.sigma_max    ,			self.config.sampling_eps    ,			)



			def 				lowerCAmelCase (     self		:						Union[str, Any]    ,			__UpperCamelCase		:						ScoreSdeVeSchedulerState    ,			__UpperCamelCase		:						int    ,			__UpperCamelCase		:						Tuple = ()    ,			__UpperCamelCase		:						float = None			)      ->      ScoreSdeVeSchedulerState:
							"""simple docstring"""





							snake_case__      :   str      =    sampling_eps if sampling_eps is not None else self.config.sampling_eps

							snake_case__      :   Dict      =    jnp.linspace(1    ,			__UpperCamelCase    ,			__UpperCamelCase			)
							return state.replace(timesteps=__UpperCamelCase			)



			def 				lowerCAmelCase (     self		:						Optional[int]    ,			__UpperCamelCase		:						ScoreSdeVeSchedulerState    ,			__UpperCamelCase		:						int    ,			__UpperCamelCase		:						float = None    ,			__UpperCamelCase		:						float = None    ,			__UpperCamelCase		:						float = None    ,			)      ->      ScoreSdeVeSchedulerState:
							"""simple docstring"""





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

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

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



			def 				lowerCAmelCase (     self		:						Optional[int]    ,			__UpperCamelCase		:						Any    ,			__UpperCamelCase		:						Optional[int]    ,			__UpperCamelCase		:						List[Any]			)      ->      Optional[int]:
							"""simple docstring"""





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



			def 				lowerCAmelCase (     self		:						Tuple    ,			__UpperCamelCase		:						ScoreSdeVeSchedulerState    ,			__UpperCamelCase		:						jnp.ndarray    ,			__UpperCamelCase		:						int    ,			__UpperCamelCase		:						jnp.ndarray    ,			__UpperCamelCase		:						random.KeyArray    ,			__UpperCamelCase		:						bool = True    ,			)      ->      Union[FlaxSdeVeOutput, Tuple]:
							"""simple docstring"""





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

							snake_case__      :   Optional[int]      =    timestep * jnp.ones(
							    sample.shape[0]    ,			)
							snake_case__      :   List[str]      =    (timestep * (len(state.timesteps			) - 1)).long()

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

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



			def 				lowerCAmelCase (     self		:						Union[str, Any]    ,			__UpperCamelCase		:						ScoreSdeVeSchedulerState    ,			__UpperCamelCase		:						jnp.ndarray    ,			__UpperCamelCase		:						jnp.ndarray    ,			__UpperCamelCase		:						random.KeyArray    ,			__UpperCamelCase		:						bool = True    ,			)      ->      Union[FlaxSdeVeOutput, Tuple]:
							"""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
							snake_case__      :   Union[str, Any]      =    random.split(__UpperCamelCase    ,			num=1			)
							snake_case__      :   int      =    random.normal(key=__UpperCamelCase    ,			shape=sample.shape			)

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

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

							if not return_dict:
											return (prev_sample, state)

							return FlaxSdeVeOutput(prev_sample=__UpperCamelCase    ,			state=__UpperCamelCase			)







			def __len__(     self		:						Optional[int]			)      ->      Tuple:
							"""simple docstring"""





							return self.config.num_train_timesteps










import math


class  lowerCamelCase     :






			'''simple docstring'''





			def __init__(			self      : Dict							,    lowerCamelCase_      : int							,    lowerCamelCase_      : int							,    lowerCamelCase_      : int							,    lowerCamelCase_      : Union[str, Any]	)    -> Optional[Any]:
								__magic_name__				:						Union[str, Any]     				=				x
								__magic_name__				:						Optional[int]     				=				y
								__magic_name__				:						List[str]     				=				step_size
								__magic_name__				:						Union[str, Any]     				=				function_to_optimize

			def 				UpperCAmelCase__							(			self      : int	)    -> int:
								return self.function(self.x							,    self.y	)

			def 				UpperCAmelCase__							(			self      : Dict	)    -> Any:
								__magic_name__				:						Optional[int]     				=				self.step_size
								return [
								    SearchProblem(lowerCamelCase_							,    lowerCamelCase_							,    lowerCamelCase_							,    self.function	)
								    for x, y in (
								        (self.x - step_size, self.y - step_size),
								        (self.x - step_size, self.y),
								        (self.x - step_size, self.y + step_size),
								        (self.x, self.y - step_size),
								        (self.x, self.y + step_size),
								        (self.x + step_size, self.y - step_size),
								        (self.x + step_size, self.y),
								        (self.x + step_size, self.y + step_size),
								    )
								]

			def __hash__(			self      : Dict	)    -> Tuple:
								return hash(str(self	)	)

			def __eq__(			self      : List[str]							,    lowerCamelCase_      : Dict	)    -> Union[str, Any]:
								if isinstance(lowerCamelCase_							,    lowerCamelCase_	):
													return hash(str(self	)	) == hash(str(lowerCamelCase_	)	)
								return False


			def __str__(			self      : Tuple	)    -> Tuple:
								return F'''x: {self.x} y: {self.y}'''







def 		lowercase__ (		__A:						int				,__A:						bool = True				,__A:						float = math.inf				,__A:						float = -math.inf				,__A:						float = math.inf				,__A:						float = -math.inf				,__A:						bool = False				,__A:						int = 1_0_0_0_0				,):





					'''simple docstring'''






					__magic_name__				:						Union[str, Any]     				=				search_prob
					__magic_name__				:						int     				=				[]  # list to store the current score at each iteration
					__magic_name__				:						Any     				=				0
					__magic_name__				:						Optional[Any]     				=				False
					__magic_name__				:						Dict     				=				set()
					while not solution_found and iterations < max_iter:
										visited.add(__A					)
										iterations += 1
										__magic_name__				:						int     				=				current_state.score()
										scores.append(__A					)
										__magic_name__				:						Union[str, Any]     				=				current_state.get_neighbors()
										__magic_name__				:						str     				=				-math.inf
										__magic_name__				:						Optional[Any]     				=				math.inf
										__magic_name__				:						Any     				=				None  # to hold the next best neighbor
										for neighbor in neighbors:
															if neighbor in visited:
																				continue  # do not want to visit the same state again
															if (
															    neighbor.x > max_x
															    or neighbor.x < min_x
															    or neighbor.y > max_y
															    or neighbor.y < min_y
															):
																				continue  # neighbor outside our bounds
															__magic_name__				:						Tuple     				=				neighbor.score() - current_score
															if find_max:  # finding max
																				# going to direction with greatest ascent
																				if change > max_change and change > 0:
																									__magic_name__				:						List[str]     				=				change
																									__magic_name__				:						List[str]     				=				neighbor
															else:  # finding min
																				# to direction with greatest descent
																				if change < min_change and change < 0:
																									__magic_name__				:						List[Any]     				=				change
																									__magic_name__				:						Optional[int]     				=				neighbor
										if next_state is not None:
															# we found at least one neighbor which improved the current state
															__magic_name__				:						Any     				=				next_state
										else:
															# since we have no neighbor that improves the solution we stop the search
															__magic_name__				:						List[str]     				=				True

					if visualization:
										from matplotlib import pyplot as plt

										plt.plot(range(__A					)				,__A					)
										plt.xlabel('''Iterations'''					)
										plt.ylabel('''Function values'''					)
										plt.show()

					return current_state


if __name__ == "__main__":
	import doctest

	doctest.testmod()







	def 		lowercase__ (		__A:						Optional[Any]				,__A:						str					):





						'''simple docstring'''






						return (x**2) + (y**2)

	# starting the problem with initial coordinates (3, 4)
	__lowerCamelCase :    Any      						=      SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
	__lowerCamelCase :    Any      						=      hill_climbing(prob, find_max=False)
	print(
	    '''The minimum score for f(x, y) = x^2 + y^2 found via hill climbing: '''
	    F"""{local_min.score()}"""
	)

	# starting the problem with initial coordinates (12, 47)
	__lowerCamelCase :    Optional[int]      						=      SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
	__lowerCamelCase :    Union[str, Any]      						=      hill_climbing(
	    prob, find_max=False, max_x=1_00, min_x=5, max_y=50, min_y=-5, visualization=True
	)
	print(
	    '''The minimum score for f(x, y) = x^2 + y^2 with the domain 100 > x > 5 '''
	    F"""and 50 > y > - 5 found via hill climbing: {local_min.score()}"""
	)







	def 		lowercase__ (		__A:						List[Any]				,__A:						int					):





						'''simple docstring'''






						return (3 * x**2) - (6 * y)

	__lowerCamelCase :    List[str]      						=      SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
	__lowerCamelCase :    Optional[int]      						=      hill_climbing(prob, find_max=True)
	print(
	    '''The maximum score for f(x, y) = x^2 + y^2 found via hill climbing: '''
	    F"""{local_min.score()}"""
	)



