



# 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 						lowercase__      :

     """simple docstring"""






     __UpperCamelCase    :	CommonSchedulerState

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


     @classmethod
     def 		lowercase   ( cls :	Any   ,			__a :	CommonSchedulerState   ,			__a :	jnp.ndarray   ,			__a :	jnp.ndarray ):
      return cls(common=__A   ,			init_noise_sigma=__A   ,			timesteps=__A )



@dataclass
class 						lowercase__      (_lowercase						):

     """simple docstring"""






     __UpperCamelCase    :	DDPMSchedulerState



class 						lowercase__      (_lowercase						,      _lowercase						):

     """simple docstring"""






     __UpperCamelCase    :	Optional[int]		=       [e.name for e in FlaxKarrasDiffusionSchedulers]

     __UpperCamelCase    :	jnp.dtype


     @property
     def 		lowercase   ( self :	Tuple ):
      return True


     @register_to_config
     def __init__( self :	str   ,			__a :	int = 1_0_0_0   ,			__a :	float = 0.0001   ,			__a :	float = 0.02   ,			__a :	str = "linear"   ,			__a :	Optional[jnp.ndarray] = None   ,			__a :	str = "fixed_small"   ,			__a :	bool = True   ,			__a :	str = "epsilon"   ,			__a :	jnp.dtype = jnp.floataa   ,			):
      snake_case__				:							Dict      							= dtype


     def 		lowercase   ( self :	Optional[Any]   ,			__a :	Optional[CommonSchedulerState] = None ):
      if common is None:
       snake_case__				:							List[str]      							= CommonSchedulerState.create(self )

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

      snake_case__				:							Any      							= jnp.arange(0   ,			self.config.num_train_timesteps ).round()[::-1]

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


     def 		lowercase   ( self :	Any   ,			__a :	DDPMSchedulerState   ,			__a :	jnp.ndarray   ,			__a :	Optional[int] = None ):
      return sample


     def 		lowercase   ( self :	Dict   ,			__a :	DDPMSchedulerState   ,			__a :	int   ,			__a :	Tuple = () ):
      snake_case__				:							Dict      							= 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
      snake_case__				:							Dict      							= (jnp.arange(0   ,			__A ) * step_ratio).round()[::-1]

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


     def 		lowercase   ( self :	Optional[int]   ,			__a :	DDPMSchedulerState   ,			__a :	List[str]   ,			__a :	Union[str, Any]=None   ,			__a :	List[str]=None ):
      snake_case__				:							Dict      							= state.common.alphas_cumprod[t]
      snake_case__				:							Tuple      							= 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
      snake_case__				:							List[str]      							= (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

      if variance_type is None:
       snake_case__				:							List[str]      							= self.config.variance_type

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

      return variance


     def 		lowercase   ( self :	List[str]   ,			__a :	DDPMSchedulerState   ,			__a :	jnp.ndarray   ,			__a :	int   ,			__a :	jnp.ndarray   ,			__a :	Optional[jax.random.KeyArray] = None   ,			__a :	bool = True   ,			):
      snake_case__				:							Union[str, Any]      							= timestep

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

      if model_output.shape[1] == sample.shape[1] * 2 and self.config.variance_type in ["learned", "learned_range"]:
       snake_case__				:							Dict      							= jnp.split(__A   ,			sample.shape[1]   ,			axis=1 )
      else:
       snake_case__				:							Optional[int]      							= None

      # 1. compute alphas, betas
      snake_case__				:							Union[str, Any]      							= state.common.alphas_cumprod[t]
      snake_case__				:							str      							= jnp.where(t > 0   ,			state.common.alphas_cumprod[t - 1]   ,			jnp.array(1.0   ,			dtype=self.dtype ) )
      snake_case__				:							str      							= 1 - alpha_prod_t
      snake_case__				:							str      							= 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":
       snake_case__				:							Any      							= (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
      elif self.config.prediction_type == "sample":
       snake_case__				:							Union[str, Any]      							= model_output
      elif self.config.prediction_type == "v_prediction":
       snake_case__				:							List[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:
       snake_case__				:							Any      							= jnp.clip(__A   ,			-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
      snake_case__				:							Tuple      							= (alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
      snake_case__				:							List[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
      snake_case__				:							str      							= pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

      # 6. Add noise
      def random_variance():
       snake_case__				:							Dict      							= jax.random.split(__A   ,			num=1 )
       snake_case__				:							Dict      							= jax.random.normal(__A   ,			shape=model_output.shape   ,			dtype=self.dtype )
       return (self._get_variance(__A   ,			__A   ,			predicted_variance=__A ) ** 0.5) * noise

      snake_case__				:							Union[str, Any]      							= jnp.where(t > 0   ,			random_variance()   ,			jnp.zeros(model_output.shape   ,			dtype=self.dtype ) )

      snake_case__				:							Any      							= pred_prev_sample + variance

      if not return_dict:
       return (pred_prev_sample, state)

      return FlaxDDPMSchedulerOutput(prev_sample=__A   ,			state=__A )


     def 		lowercase   ( self :	Dict   ,			__a :	DDPMSchedulerState   ,			__a :	jnp.ndarray   ,			__a :	jnp.ndarray   ,			__a :	jnp.ndarray   ,			):
      return add_noise_common(state.common   ,			__A   ,			__A   ,			__A )


     def 		lowercase   ( self :	Optional[int]   ,			__a :	DDPMSchedulerState   ,			__a :	jnp.ndarray   ,			__a :	jnp.ndarray   ,			__a :	jnp.ndarray   ,			):
      return get_velocity_common(state.common   ,			__A   ,			__A   ,			__A )


     def __len__( self :	Any ):
      return self.config.num_train_timesteps







class      lowerCamelCase_      :




	def __init__(     self						:     Dict					,      __A						:     int					,      __A						:     Tuple					,      __A						:     List[Any]							):
		__A :			Optional[int]		    =			None
		__A :			Any		    =			None
		__A :			int		    =			graph

		self._normalize_graph(__A					,      __A							)
		__A :			str		    =			len(__A							)
		__A :			Optional[int]		    =			None




	def        lowerCAmelCase_       (     self						:     int					,      __A						:     Any					,      __A						:     Optional[Any]							):
		if sources is int:
			__A :			Dict		    =			[sources]
		if sinks is int:
			__A :			Optional[int]		    =			[sinks]

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

		__A :			str		    =			sources[0]
		__A :			Dict		    =			sinks[0]

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

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

			__A :			Any		    =			len(self.graph							) + 1
			for room in self.graph:
				room.append(0							)
			self.graph.append([0] * size							)
			for i in sinks:
				__A :			int		    =			max_input_flow
			__A :			Optional[Any]		    =			size - 1




	def        lowerCAmelCase_       (     self						:     Optional[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        lowerCAmelCase_       (     self						:     Optional[Any]					,      __A						:     Dict							):
		__A :			Dict		    =			algorithm(self							)






class      lowerCamelCase_      :




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




	def        lowerCAmelCase_       (     self						:     List[Any]							):
		if not self.executed:
			self._algorithm()
			__A :			Any		    =			True




	def        lowerCAmelCase_       (     self						:     List[str]							):
		pass






class      lowerCamelCase_      (	_lowercase	):




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




	def        lowerCAmelCase_       (     self						:     Any							):
		if not self.executed:
			raise Exception("""You should execute algorithm before using its result!"""							)

		return self.maximum_flow






class      lowerCamelCase_      (	_lowercase	):




	def __init__(     self						:     List[Any]					,      __A						:     Dict							):
		super().__init__(__A							)

		__A :			Tuple		    =			[[0] * self.verticies_count for i in range(self.verticies_count							)]

		__A :			Optional[Any]		    =			[0] * self.verticies_count
		__A :			Union[str, Any]		    =			[0] * self.verticies_count




	def        lowerCAmelCase_       (     self						:     int							):
		__A :			Optional[int]		    =			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
		__A :			List[str]		    =			[
		    i
		    for i in range(self.verticies_count							)
		    if i != self.source_index and i != self.sink_index
		]

		# move through list
		__A :			Dict		    =			0
		while i < len(__A							):
			__A :			List[Any]		    =			vertices_list[i]
			__A :			Optional[Any]		    =			self.heights[vertex_index]
			self.process_vertex(__A							)
			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(__A							)							)
				__A :			Any		    =			0
			else:
				i += 1

		__A :			Optional[int]		    =			sum(self.preflow[self.source_index]							)




	def        lowerCAmelCase_       (     self						:     Optional[Any]					,      __A						:     str							):
		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(__A					,      __A							)

			self.relabel(__A							)




	def        lowerCAmelCase_       (     self						:     Dict					,      __A						:     List[str]					,      __A						:     Optional[Any]							):
		__A :			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        lowerCAmelCase_       (     self						:     Optional[Any]					,      __A						:     Tuple							):
		__A :			Tuple		    =			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):
				__A :			Dict		    =			self.heights[to_index]

		if min_height is not None:
			__A :			Optional[int]		    =			min_height + 1


if __name__ == "__main__":
			UpperCAmelCase_							:					Union[str, Any]		 =   [0]
			UpperCAmelCase_							:					Dict		 =   [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],
			# ]
			UpperCAmelCase_							:					int		 =   [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

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

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





