



'''simple docstring'''
import heapq


def 	lowercase_						( lowerCAmelCase__						:	Any      ,				lowerCAmelCase__						:	Optional[int]      ,				lowerCAmelCase__						:	Any			):

			"""simple docstring"""





			__UpperCAmelCase :   Union[str, Any]    					=  [(0, start)]  # cost from start node,end node
			__UpperCAmelCase :   Optional[int]    					=  set()
			while heap:
						(__UpperCAmelCase) :   List[Any]    					=  heapq.heappop(_UpperCamelCase			)
						if u in visited:
									continue
						visited.add(_UpperCamelCase			)
						if u == end:
									return cost
						for v, c in graph[u]:
									if v in visited:
												continue
									__UpperCAmelCase :   str    					=  cost + c
									heapq.heappush(_UpperCamelCase      ,				(next_item, v)			)
			return -1


_UpperCamelCase									=      {
    'A': [['B', 2], ['C', 5]],
    'B': [['A', 2], ['D', 3], ['E', 1], ['F', 1]],
    'C': [['A', 5], ['F', 3]],
    'D': [['B', 3]],
    'E': [['B', 4], ['F', 3]],
    'F': [['C', 3], ['E', 3]],
}
_UpperCamelCase									=      {
    'B': [['C', 1]],
    'C': [['D', 1]],
    'D': [['F', 1]],
    'E': [['B', 1], ['F', 3]],
    'F': [],
}
_UpperCamelCase									=      {
    'B': [['C', 1]],
    'C': [['D', 1]],
    'D': [['F', 1]],
    'E': [['B', 1], ['G', 2]],
    'F': [],
    'G': [['F', 1]],
}

_UpperCamelCase									=      dijkstra(G, '''E''', '''C''')
print(short_distance)  # E -- 3 --> F -- 3 --> C == 6

_UpperCamelCase									=      dijkstra(Ga, '''E''', '''F''')
print(short_distance)  # E -- 3 --> F == 3

_UpperCamelCase									=      dijkstra(Ga, '''E''', '''F''')
print(short_distance)  # E -- 2 --> G -- 1 --> F == 3

if __name__ == "__main__":
					import doctest

					doctest.testmod()









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

import flax
import jax.numpy as jnp
from scipy import integrate

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





@flax.struct.dataclass
class 							lowerCAmelCase_		:
		SCREAMING_SNAKE_CASE_       :			CommonSchedulerState

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

		# running values
		SCREAMING_SNAKE_CASE_       :			Optional[jnp.ndarray]					       =	None







		@classmethod
		def 					a_  (    cls  :   List[Any]       ,		UpperCAmelCase_  :   CommonSchedulerState       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   jnp.ndarray					)       ->		Optional[Any]:


						'''simple docstring'''







						return cls(common=UpperCAmelCase_       ,		init_noise_sigma=UpperCAmelCase_       ,		timesteps=UpperCAmelCase_       ,		sigmas=UpperCAmelCase_					)





@dataclass
class 							lowerCAmelCase_		(		lowercase_     ):
		SCREAMING_SNAKE_CASE_       :			LMSDiscreteSchedulerState





class 							lowerCAmelCase_		(		lowercase_							,		lowercase_     ):
		SCREAMING_SNAKE_CASE_       :			Union[str, Any]					       =	[e.name for e in FlaxKarrasDiffusionSchedulers]

		SCREAMING_SNAKE_CASE_       :			jnp.dtype







		@property
		def 					a_  (    self  :   Union[str, Any]					)       ->		List[Any]:


						'''simple docstring'''







						return True







		@register_to_config
		def __init__(    self  :   Optional[Any]       ,		UpperCAmelCase_  :   int = 1000       ,		UpperCAmelCase_  :   float = 0.0_001       ,		UpperCAmelCase_  :   float = 0.02       ,		UpperCAmelCase_  :   str = "linear"       ,		UpperCAmelCase_  :   Optional[jnp.ndarray] = None       ,		UpperCAmelCase_  :   str = "epsilon"       ,		UpperCAmelCase_  :   jnp.dtype = jnp.floataa       ,		)       ->		List[str]:


						'''simple docstring'''







						_UpperCAmelCase						:  str     					=	dtype







		def 					a_  (    self  :   Tuple       ,		UpperCAmelCase_  :   Optional[CommonSchedulerState] = None					)       ->		LMSDiscreteSchedulerState:


						'''simple docstring'''







						if common is None:
										_UpperCAmelCase						:  int     					=	CommonSchedulerState.create(self					)

						_UpperCAmelCase						:  Any     					=	jnp.arange(0       ,		self.config.num_train_timesteps					).round()[::-1]
						_UpperCAmelCase						:  Any     					=	((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5

						# standard deviation of the initial noise distribution
						_UpperCAmelCase						:  Dict     					=	sigmas.max()

						return LMSDiscreteSchedulerState.create(
						    common=UpperCAmelCase_       ,		init_noise_sigma=UpperCAmelCase_       ,		timesteps=UpperCAmelCase_       ,		sigmas=UpperCAmelCase_       ,		)







		def 					a_  (    self  :   Optional[Any]       ,		UpperCAmelCase_  :   LMSDiscreteSchedulerState       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   int					)       ->		jnp.ndarray:


						'''simple docstring'''







						((_UpperCAmelCase)					, )						:  Optional[Any]     					=	jnp.where(state.timesteps == timestep       ,		size=1					)
						_UpperCAmelCase						:  List[str]     					=	step_index[0]

						_UpperCAmelCase						:  List[Any]     					=	state.sigmas[step_index]
						_UpperCAmelCase						:  Union[str, Any]     					=	sample / ((sigma**2 + 1) ** 0.5)
						return sample







		def 					a_  (    self  :   List[Any]       ,		UpperCAmelCase_  :   LMSDiscreteSchedulerState       ,		UpperCAmelCase_  :   int       ,		UpperCAmelCase_  :   str       ,		UpperCAmelCase_  :   Union[str, Any]					)       ->		Union[str, Any]:


						'''simple docstring'''







						def lms_derivative(UpperCAmelCase_  :   Optional[int]					):
										_UpperCAmelCase						:  Optional[Any]     					=	1.0
										for k in range(UpperCAmelCase_					):
														if current_order == k:
																		continue
														prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k])
										return prod

						_UpperCAmelCase						:  Optional[Any]     					=	integrate.quad(UpperCAmelCase_       ,		state.sigmas[t]       ,		state.sigmas[t + 1]       ,		epsrel=1E-4					)[0]

						return integrated_coeff







		def 					a_  (    self  :   Dict       ,		UpperCAmelCase_  :   LMSDiscreteSchedulerState       ,		UpperCAmelCase_  :   int       ,		UpperCAmelCase_  :   Tuple = ()					)       ->		LMSDiscreteSchedulerState:


						'''simple docstring'''







						_UpperCAmelCase						:  List[str]     					=	jnp.linspace(self.config.num_train_timesteps - 1       ,		0       ,		UpperCAmelCase_       ,		dtype=self.dtype					)

						_UpperCAmelCase						:  Any     					=	jnp.floor(UpperCAmelCase_					).astype(jnp.intaa					)
						_UpperCAmelCase						:  Optional[Any]     					=	jnp.ceil(UpperCAmelCase_					).astype(jnp.intaa					)

						_UpperCAmelCase						:  str     					=	jnp.mod(UpperCAmelCase_       ,		1.0					)

						_UpperCAmelCase						:  Optional[Any]     					=	((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
						_UpperCAmelCase						:  Any     					=	(1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
						_UpperCAmelCase						:  Tuple     					=	jnp.concatenate([sigmas, jnp.array([0.0]       ,		dtype=self.dtype					)]					)

						_UpperCAmelCase						:  int     					=	timesteps.astype(jnp.intaa					)

						# initial running values
						_UpperCAmelCase						:  List[str]     					=	jnp.zeros((0,) + shape       ,		dtype=self.dtype					)

						return state.replace(
						    timesteps=UpperCAmelCase_       ,		sigmas=UpperCAmelCase_       ,		num_inference_steps=UpperCAmelCase_       ,		derivatives=UpperCAmelCase_       ,		)







		def 					a_  (    self  :   Tuple       ,		UpperCAmelCase_  :   LMSDiscreteSchedulerState       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   int       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   int = 4       ,		UpperCAmelCase_  :   bool = True       ,		)       ->		Union[FlaxLMSSchedulerOutput, Tuple]:


						'''simple docstring'''







						if state.num_inference_steps is None:
										raise ValueError(
										    '''Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'''					)

						_UpperCAmelCase						:  List[Any]     					=	state.sigmas[timestep]

						# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
						if self.config.prediction_type == "epsilon":
										_UpperCAmelCase						:  Optional[int]     					=	sample - sigma * model_output
						elif self.config.prediction_type == "v_prediction":
										# * c_out + input * c_skip
										_UpperCAmelCase						:  Tuple     					=	model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
						else:
										raise ValueError(
										    F'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'''					)

						# 2. Convert to an ODE derivative
						_UpperCAmelCase						:  Tuple     					=	(sample - pred_original_sample) / sigma
						_UpperCAmelCase						:  Tuple     					=	state.replace(derivatives=jnp.append(state.derivatives       ,		UpperCAmelCase_					)					)
						if len(state.derivatives					) > order:
										_UpperCAmelCase						:  Union[str, Any]     					=	state.replace(derivatives=jnp.delete(state.derivatives       ,		0					)					)

						# 3. Compute linear multistep coefficients
						_UpperCAmelCase						:  int     					=	min(timestep + 1       ,		UpperCAmelCase_					)
						_UpperCAmelCase						:  Optional[int]     					=	[self.get_lms_coefficient(UpperCAmelCase_       ,		UpperCAmelCase_       ,		UpperCAmelCase_       ,		UpperCAmelCase_					) for curr_order in range(UpperCAmelCase_					)]

						# 4. Compute previous sample based on the derivatives path
						_UpperCAmelCase						:  int     					=	sample + sum(
						    coeff * derivative for coeff, derivative in zip(UpperCAmelCase_       ,		reversed(state.derivatives					)					)					)

						if not return_dict:
										return (prev_sample, state)

						return FlaxLMSSchedulerOutput(prev_sample=UpperCAmelCase_       ,		state=UpperCAmelCase_					)







		def 					a_  (    self  :   Union[str, Any]       ,		UpperCAmelCase_  :   LMSDiscreteSchedulerState       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   jnp.ndarray       ,		)       ->		jnp.ndarray:


						'''simple docstring'''







						_UpperCAmelCase						:  Union[str, Any]     					=	state.sigmas[timesteps].flatten()
						_UpperCAmelCase						:  Union[str, Any]     					=	broadcast_to_shape_from_left(UpperCAmelCase_       ,		noise.shape					)

						_UpperCAmelCase						:  Any     					=	original_samples + noise * sigma

						return noisy_samples







		def __len__(    self  :   Dict					)       ->		Tuple:


						'''simple docstring'''







						return self.config.num_train_timesteps
