


"""simple docstring"""




# DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim

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

import flax
import jax
import jax.numpy as jnp

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    add_noise_common,
    get_velocity_common,
)





@flax.struct.dataclass
class  _a							:
	_a  :  CommonSchedulerState

	# setable values
	_a  :  jnp.ndarray
	_a  :  jnp.ndarray
	_a  :  Optional[int]				   =							None




	@classmethod
	def 							UpperCAmelCase__( cls						:		Dict		, _SCREAMING_SNAKE_CASE						:		CommonSchedulerState		, _SCREAMING_SNAKE_CASE						:		jnp.ndarray		, _SCREAMING_SNAKE_CASE						:		jnp.ndarray		)->	Optional[Any]:
			return cls(common=_SCREAMING_SNAKE_CASE		, init_noise_sigma=_SCREAMING_SNAKE_CASE		, timesteps=_SCREAMING_SNAKE_CASE		)





@dataclass
class  _a							(    _lowercase):
	_a  :  DDPMSchedulerState





class  _a							(    _lowercase					,						_lowercase):
	_a  :  Any				   =							[e.name for e in FlaxKarrasDiffusionSchedulers]

	_a  :  jnp.dtype




	@property
	def 							UpperCAmelCase__( self						:		Tuple		)->	Any:
			return True




	@register_to_config
	def __init__( self						:		Optional[Any]		, _SCREAMING_SNAKE_CASE						:		int = 1000		, _SCREAMING_SNAKE_CASE						:		float = 0.0001		, _SCREAMING_SNAKE_CASE						:		float = 0.02		, _SCREAMING_SNAKE_CASE						:		str = "linear"		, _SCREAMING_SNAKE_CASE						:		Optional[jnp.ndarray] = None		, _SCREAMING_SNAKE_CASE						:		str = "fixed_small"		, _SCREAMING_SNAKE_CASE						:		bool = True		, _SCREAMING_SNAKE_CASE						:		str = "epsilon"		, _SCREAMING_SNAKE_CASE						:		jnp.dtype = jnp.floataa		, )->	Optional[int]:
			lowerCAmelCase__       :      List[Any]   					= dtype




	def 							UpperCAmelCase__( self						:		Dict		, _SCREAMING_SNAKE_CASE						:		Optional[CommonSchedulerState] = None		)->	DDPMSchedulerState:
			if common is None:
					lowerCAmelCase__       :      Optional[Any]   					= CommonSchedulerState.create(self		)

			# standard deviation of the initial noise distribution
			lowerCAmelCase__       :      str   					= jnp.array(1.0		, dtype=self.dtype		)

			lowerCAmelCase__       :      Optional[int]   					= jnp.arange(0		, self.config.num_train_timesteps		).round()[::-1]

			return DDPMSchedulerState.create(
			    common=_SCREAMING_SNAKE_CASE		, init_noise_sigma=_SCREAMING_SNAKE_CASE		, timesteps=_SCREAMING_SNAKE_CASE		, )




	def 							UpperCAmelCase__( self						:		Any		, _SCREAMING_SNAKE_CASE						:		DDPMSchedulerState		, _SCREAMING_SNAKE_CASE						:		jnp.ndarray		, _SCREAMING_SNAKE_CASE						:		Optional[int] = None		)->	jnp.ndarray:
			return sample




	def 							UpperCAmelCase__( self						:		Optional[Any]		, _SCREAMING_SNAKE_CASE						:		DDPMSchedulerState		, _SCREAMING_SNAKE_CASE						:		int		, _SCREAMING_SNAKE_CASE						:		Tuple = ()		)->	DDPMSchedulerState:
			lowerCAmelCase__       :      List[str]   					= self.config.num_train_timesteps // num_inference_steps
			# creates integer timesteps by multiplying by ratio
			# rounding to avoid issues when num_inference_step is power of 3
			lowerCAmelCase__       :      List[Any]   					= (jnp.arange(0		, _SCREAMING_SNAKE_CASE		) * step_ratio).round()[::-1]

			return state.replace(
			    num_inference_steps=_SCREAMING_SNAKE_CASE		, timesteps=_SCREAMING_SNAKE_CASE		, )




	def 							UpperCAmelCase__( self						:		str		, _SCREAMING_SNAKE_CASE						:		DDPMSchedulerState		, _SCREAMING_SNAKE_CASE						:		Tuple		, _SCREAMING_SNAKE_CASE						:		Union[str, Any]=None		, _SCREAMING_SNAKE_CASE						:		Dict=None		)->	Any:
			lowerCAmelCase__       :      int   					= state.common.alphas_cumprod[t]
			lowerCAmelCase__       :      List[str]   					= jnp.where(t > 0		, state.common.alphas_cumprod[t - 1]		, jnp.array(1.0		, dtype=self.dtype		)		)

			# For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
			# and sample from it to get previous sample
			# x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
			lowerCAmelCase__       :      List[Any]   					= (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

			if variance_type is None:
					lowerCAmelCase__       :      List[Any]   					= self.config.variance_type

			# hacks - were probably added for training stability
			if variance_type == "fixed_small":
					lowerCAmelCase__       :      Dict   					= jnp.clip(_SCREAMING_SNAKE_CASE		, a_min=1E-20		)
			# for rl-diffuser https://arxiv.org/abs/2205.09991
			elif variance_type == "fixed_small_log":
					lowerCAmelCase__       :      Any   					= jnp.log(jnp.clip(_SCREAMING_SNAKE_CASE		, a_min=1E-20		)		)
			elif variance_type == "fixed_large":
					lowerCAmelCase__       :      Optional[Any]   					= state.common.betas[t]
			elif variance_type == "fixed_large_log":
					# Glide max_log
					lowerCAmelCase__       :      str   					= jnp.log(state.common.betas[t]		)
			elif variance_type == "learned":
					return predicted_variance
			elif variance_type == "learned_range":
					lowerCAmelCase__       :      Dict   					= variance
					lowerCAmelCase__       :      str   					= state.common.betas[t]
					lowerCAmelCase__       :      Dict   					= (predicted_variance + 1) / 2
					lowerCAmelCase__       :      Union[str, Any]   					= frac * max_log + (1 - frac) * min_log

			return variance




	def 							UpperCAmelCase__( self						:		Union[str, Any]		, _SCREAMING_SNAKE_CASE						:		DDPMSchedulerState		, _SCREAMING_SNAKE_CASE						:		jnp.ndarray		, _SCREAMING_SNAKE_CASE						:		int		, _SCREAMING_SNAKE_CASE						:		jnp.ndarray		, _SCREAMING_SNAKE_CASE						:		Optional[jax.random.KeyArray] = None		, _SCREAMING_SNAKE_CASE						:		bool = True		, )->	Union[FlaxDDPMSchedulerOutput, Tuple]:
			lowerCAmelCase__       :      Optional[Any]   					= timestep

			if key is None:
					lowerCAmelCase__       :      str   					= jax.random.PRNGKey(0		)

			if model_output.shape[1] == sample.shape[1] * 2 and self.config.variance_type in ["learned", "learned_range"]:
					lowerCAmelCase__       :      List[str]   					= jnp.split(_SCREAMING_SNAKE_CASE		, sample.shape[1]		, axis=1		)
			else:
					lowerCAmelCase__       :      List[str]   					= None

			# 1. compute alphas, betas
			lowerCAmelCase__       :      str   					= state.common.alphas_cumprod[t]
			lowerCAmelCase__       :      Optional[int]   					= jnp.where(t > 0		, state.common.alphas_cumprod[t - 1]		, jnp.array(1.0		, dtype=self.dtype		)		)
			lowerCAmelCase__       :      Any   					= 1 - alpha_prod_t
			lowerCAmelCase__       :      Union[str, Any]   					= 1 - alpha_prod_t_prev

			# 2. compute predicted original sample from predicted noise also called
			# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
			if self.config.prediction_type == "epsilon":
					lowerCAmelCase__       :      str   					= (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
			elif self.config.prediction_type == "sample":
					lowerCAmelCase__       :      Dict   					= model_output
			elif self.config.prediction_type == "v_prediction":
					lowerCAmelCase__       :      str   					= (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
			else:
					raise ValueError(
					    F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` '
					    ''' for the FlaxDDPMScheduler.'''		)

			# 3. Clip "predicted x_0"
			if self.config.clip_sample:
					lowerCAmelCase__       :      Optional[Any]   					= jnp.clip(_SCREAMING_SNAKE_CASE		, -1		, 1		)

			# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
			# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
			lowerCAmelCase__       :      List[str]   					= (alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
			lowerCAmelCase__       :      Union[str, Any]   					= state.common.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

			# 5. Compute predicted previous sample µ_t
			# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
			lowerCAmelCase__       :      List[Any]   					= pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

			# 6. Add noise
			def random_variance():
					lowerCAmelCase__       :      Union[str, Any]   					= jax.random.split(_SCREAMING_SNAKE_CASE		, num=1		)
					lowerCAmelCase__       :      List[str]   					= jax.random.normal(_SCREAMING_SNAKE_CASE		, shape=model_output.shape		, dtype=self.dtype		)
					return (self._get_variance(_SCREAMING_SNAKE_CASE		, _SCREAMING_SNAKE_CASE		, predicted_variance=_SCREAMING_SNAKE_CASE		) ** 0.5) * noise

			lowerCAmelCase__       :      Any   					= jnp.where(t > 0		, random_variance()		, jnp.zeros(model_output.shape		, dtype=self.dtype		)		)

			lowerCAmelCase__       :      Union[str, Any]   					= pred_prev_sample + variance

			if not return_dict:
					return (pred_prev_sample, state)

			return FlaxDDPMSchedulerOutput(prev_sample=_SCREAMING_SNAKE_CASE		, state=_SCREAMING_SNAKE_CASE		)




	def 							UpperCAmelCase__( self						:		str		, _SCREAMING_SNAKE_CASE						:		DDPMSchedulerState		, _SCREAMING_SNAKE_CASE						:		jnp.ndarray		, _SCREAMING_SNAKE_CASE						:		jnp.ndarray		, _SCREAMING_SNAKE_CASE						:		jnp.ndarray		, )->	jnp.ndarray:
			return add_noise_common(state.common		, _SCREAMING_SNAKE_CASE		, _SCREAMING_SNAKE_CASE		, _SCREAMING_SNAKE_CASE		)




	def 							UpperCAmelCase__( self						:		str		, _SCREAMING_SNAKE_CASE						:		DDPMSchedulerState		, _SCREAMING_SNAKE_CASE						:		jnp.ndarray		, _SCREAMING_SNAKE_CASE						:		jnp.ndarray		, _SCREAMING_SNAKE_CASE						:		jnp.ndarray		, )->	jnp.ndarray:
			return get_velocity_common(state.common		, _SCREAMING_SNAKE_CASE		, _SCREAMING_SNAKE_CASE		, _SCREAMING_SNAKE_CASE		)




	def __len__( self						:		Optional[int]		)->	str:
			return self.config.num_train_timesteps








class  _a							:




	def __init__( self						:		str		, _SCREAMING_SNAKE_CASE						:		str		, _SCREAMING_SNAKE_CASE						:		Optional[int]		, _SCREAMING_SNAKE_CASE						:		List[Any]		)->	Tuple:
			lowerCAmelCase__       :      List[Any]   					= None
			lowerCAmelCase__       :      int   					= None
			lowerCAmelCase__       :      Union[str, Any]   					= graph

			self._normalize_graph(_SCREAMING_SNAKE_CASE		, _SCREAMING_SNAKE_CASE		)
			lowerCAmelCase__       :      Tuple   					= len(_SCREAMING_SNAKE_CASE		)
			lowerCAmelCase__       :      Optional[int]   					= None




	def 							UpperCAmelCase__( self						:		Union[str, Any]		, _SCREAMING_SNAKE_CASE						:		Optional[Any]		, _SCREAMING_SNAKE_CASE						:		Union[str, Any]		)->	Union[str, Any]:
			if sources is int:
					lowerCAmelCase__       :      List[Any]   					= [sources]
			if sinks is int:
					lowerCAmelCase__       :      Optional[Any]   					= [sinks]

			if len(_SCREAMING_SNAKE_CASE		) == 0 or len(_SCREAMING_SNAKE_CASE		) == 0:
					return

			lowerCAmelCase__       :      Union[str, Any]   					= sources[0]
			lowerCAmelCase__       :      Dict   					= sinks[0]

			# make fake vertex if there are more
			# than one source or sink
			if len(_SCREAMING_SNAKE_CASE		) > 1 or len(_SCREAMING_SNAKE_CASE		) > 1:
					lowerCAmelCase__       :      List[Any]   					= 0
					for i in sources:
							max_input_flow += sum(self.graph[i]		)

					lowerCAmelCase__       :      Any   					= len(self.graph		) + 1
					for room in self.graph:
							room.insert(0		, 0		)
					self.graph.insert(0		, [0] * size		)
					for i in sources:
							lowerCAmelCase__       :      Optional[Any]   					= max_input_flow
					lowerCAmelCase__       :      List[str]   					= 0

					lowerCAmelCase__       :      List[Any]   					= len(self.graph		) + 1
					for room in self.graph:
							room.append(0		)
					self.graph.append([0] * size		)
					for i in sinks:
							lowerCAmelCase__       :      str   					= max_input_flow
					lowerCAmelCase__       :      Tuple   					= size - 1




	def 							UpperCAmelCase__( self						:		Union[str, Any]		)->	Union[str, Any]:
			if self.maximum_flow_algorithm is None:
					raise Exception('''You need to set maximum flow algorithm before.'''		)
			if self.source_index is None or self.sink_index is None:
					return 0

			self.maximum_flow_algorithm.execute()
			return self.maximum_flow_algorithm.getMaximumFlow()




	def 							UpperCAmelCase__( self						:		str		, _SCREAMING_SNAKE_CASE						:		List[Any]		)->	int:
			lowerCAmelCase__       :      int   					= algorithm(self		)





class  _a							:




	def __init__( self						:		Optional[Any]		, _SCREAMING_SNAKE_CASE						:		Tuple		)->	Union[str, Any]:
			lowerCAmelCase__       :      Tuple   					= flow_network
			lowerCAmelCase__       :      Dict   					= flow_network.verticesCount
			lowerCAmelCase__       :      Optional[Any]   					= flow_network.sourceIndex
			lowerCAmelCase__       :      Optional[Any]   					= flow_network.sinkIndex
			# it's just a reference, so you shouldn't change
			# it in your algorithms, use deep copy before doing that
			lowerCAmelCase__       :      str   					= flow_network.graph
			lowerCAmelCase__       :      Optional[int]   					= False




	def 							UpperCAmelCase__( self						:		List[str]		)->	Dict:
			if not self.executed:
					self._algorithm()
					lowerCAmelCase__       :      Any   					= True




	def 							UpperCAmelCase__( self						:		Optional[Any]		)->	int:
			pass





class  _a							(    _lowercase):




	def __init__( self						:		Any		, _SCREAMING_SNAKE_CASE						:		List[Any]		)->	Union[str, Any]:
			super().__init__(_SCREAMING_SNAKE_CASE		)
			# use this to save your result
			lowerCAmelCase__       :      Dict   					= -1




	def 							UpperCAmelCase__( self						:		Any		)->	Optional[Any]:
			if not self.executed:
					raise Exception('''You should execute algorithm before using its result!'''		)

			return self.maximum_flow





class  _a							(    _lowercase):




	def __init__( self						:		Any		, _SCREAMING_SNAKE_CASE						:		List[str]		)->	List[str]:
			super().__init__(_SCREAMING_SNAKE_CASE		)

			lowerCAmelCase__       :      Any   					= [[0] * self.verticies_count for i in range(self.verticies_count		)]

			lowerCAmelCase__       :      Optional[Any]   					= [0] * self.verticies_count
			lowerCAmelCase__       :      str   					= [0] * self.verticies_count




	def 							UpperCAmelCase__( self						:		Any		)->	List[Any]:
			lowerCAmelCase__       :      Optional[Any]   					= self.verticies_count

			# push some substance to graph
			for nextvertex_index, bandwidth in enumerate(self.graph[self.source_index]		):
					self.preflow[self.source_index][nextvertex_index] += bandwidth
					self.preflow[nextvertex_index][self.source_index] -= bandwidth
					self.excesses[nextvertex_index] += bandwidth

			# Relabel-to-front selection rule
			lowerCAmelCase__       :      Any   					= [
			    i
			    for i in range(self.verticies_count		)
			    if i != self.source_index and i != self.sink_index
			]

			# move through list
			lowerCAmelCase__       :      str   					= 0
			while i < len(_SCREAMING_SNAKE_CASE		):
					lowerCAmelCase__       :      Union[str, Any]   					= vertices_list[i]
					lowerCAmelCase__       :      Any   					= self.heights[vertex_index]
					self.process_vertex(_SCREAMING_SNAKE_CASE		)
					if self.heights[vertex_index] > previous_height:
							# if it was relabeled, swap elements
							# and start from 0 index
							vertices_list.insert(0		, vertices_list.pop(_SCREAMING_SNAKE_CASE		)		)
							lowerCAmelCase__       :      Optional[Any]   					= 0
					else:
							i += 1

			lowerCAmelCase__       :      Optional[Any]   					= sum(self.preflow[self.source_index]		)




	def 							UpperCAmelCase__( self						:		List[str]		, _SCREAMING_SNAKE_CASE						:		Optional[Any]		)->	Optional[int]:
			while self.excesses[vertex_index] > 0:
					for neighbour_index in range(self.verticies_count		):
							# if it's neighbour and current vertex is higher
							if (
							    self.graph[vertex_index][neighbour_index]
							    - self.preflow[vertex_index][neighbour_index]
							    > 0
							    and self.heights[vertex_index] > self.heights[neighbour_index]
							):
									self.push(_SCREAMING_SNAKE_CASE		, _SCREAMING_SNAKE_CASE		)

					self.relabel(_SCREAMING_SNAKE_CASE		)




	def 							UpperCAmelCase__( self						:		int		, _SCREAMING_SNAKE_CASE						:		Optional[Any]		, _SCREAMING_SNAKE_CASE						:		Union[str, Any]		)->	Union[str, Any]:
			lowerCAmelCase__       :      Union[str, Any]   					= min(
			    self.excesses[from_index]		, self.graph[from_index][to_index] - self.preflow[from_index][to_index]		, )
			self.preflow[from_index][to_index] += preflow_delta
			self.preflow[to_index][from_index] -= preflow_delta
			self.excesses[from_index] -= preflow_delta
			self.excesses[to_index] += preflow_delta




	def 							UpperCAmelCase__( self						:		Optional[int]		, _SCREAMING_SNAKE_CASE						:		Any		)->	Optional[int]:
			lowerCAmelCase__       :      Optional[int]   					= None
			for to_index in range(self.verticies_count		):
					if (
					    self.graph[vertex_index][to_index]
					    - self.preflow[vertex_index][to_index]
					    > 0
					) and (min_height is None or self.heights[to_index] < min_height):
							lowerCAmelCase__       :      List[Any]   					= self.heights[to_index]

			if min_height is not None:
					lowerCAmelCase__       :      Optional[Any]   					= min_height + 1


if __name__ == "__main__":
		lowerCamelCase						=		[0]
		lowerCamelCase						=		[3]
		# graph = [
		#     [0, 0, 4, 6, 0, 0],
		#     [0, 0, 5, 2, 0, 0],
		#     [0, 0, 0, 0, 4, 4],
		#     [0, 0, 0, 0, 6, 6],
		#     [0, 0, 0, 0, 0, 0],
		#     [0, 0, 0, 0, 0, 0],
		# ]
		lowerCamelCase						=		[[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

		# prepare our network
		lowerCamelCase						=		FlowNetwork(graph, entrances, exits)
		# set algorithm
		flow_network.set_maximum_flow_algorithm(PushRelabelExecutor)
		# and calculate
		lowerCamelCase						=		flow_network.find_maximum_flow()

		print(f'''maximum flow is {maximum_flow}''')




