
class 		UpperCamelCase__  :
   def __init__(self			: int       ):
    __a			:  str		    =  0
    __a			:  Union[str, Any]		    =  0
    __a			:  List[str]		    =  {}
   def 				lowerCAmelCase      (self			: Any ,    snake_case_			: List[Any]       ):
    if vertex not in self.adjacency:
     __a			:  Union[str, Any]		    =  {}
     self.num_vertices += 1
   def 				lowerCAmelCase      (self			: int ,    snake_case_			: Tuple ,    snake_case_			: List[str] ,    snake_case_			: Dict       ):
    self.add_vertex(snake_case_       )
    self.add_vertex(snake_case_       )

    if head == tail:
     return

    __a			:  Tuple		    =  weight
    __a			:  Tuple		    =  weight
   def 				lowerCAmelCase      (self			: Union[str, Any]       ):
    __a			:  Any		    =  self.get_edges()
    for edge in edges:
     __a    ,	__a    ,	__a			:  List[Any]		    =  edge
     edges.remove((tail, head, weight)       )
    for i in range(len(snake_case_       )       ):
     __a			:  str		    =  list(edges[i]       )

    edges.sort(key=lambda snake_case_       : e[2]       )
    for i in range(len(snake_case_       ) - 1       ):
     if edges[i][2] >= edges[i + 1][2]:
      __a			:  Optional[int]		    =  edges[i][2] + 1
    for edge in edges:
     __a    ,	__a    ,	__a			:  List[str]		    =  edge
     __a			:  Any		    =  weight
     __a			:  str		    =  weight
   def __str__(self			: Dict       ):
    __a			:  Dict		    =  ''''''
    for tail in self.adjacency:
     for head in self.adjacency[tail]:
      __a			:  Union[str, Any]		    =  self.adjacency[head][tail]
      string += f"{head} -> {tail} == {weight}\n"
    return string.rstrip('''\n'''       )
   def 				lowerCAmelCase      (self			: Optional[Any]       ):
    __a			:  Optional[Any]		    =  []
    for tail in self.adjacency:
     for head in self.adjacency[tail]:
      output.append((tail, head, self.adjacency[head][tail])       )
    return output
   def 				lowerCAmelCase      (self			: Union[str, Any]       ):
    return self.adjacency.keys()
   @staticmethod
   def 				lowerCAmelCase      (snake_case_			: Any=None ,    snake_case_			: Optional[int]=None       ):
    __a			:  Optional[int]		    =  Graph()
    if vertices is None:
     __a			:  str		    =  []
    if edges is None:
     __a			:  Union[str, Any]		    =  []
    for vertex in vertices:
     g.add_vertex(snake_case_       )
    for edge in edges:
     g.add_edge(*snake_case_       )
    return g



   class 		UpperCamelCase__  :
      def __init__(self			: Optional[Any]       ):
       __a			:  str		    =  {}
       __a			:  int		    =  {}
      def __len__(self			: Tuple       ):
       return len(self.parent       )
      def 				lowerCAmelCase      (self			: Any ,    snake_case_			: Tuple       ):
       if item in self.parent:
        return self.find(snake_case_       )

       __a			:  Tuple		    =  item
       __a			:  str		    =  0
       return item
      def 				lowerCAmelCase      (self			: List[str] ,    snake_case_			: Any       ):
       if item not in self.parent:
        return self.make_set(snake_case_       )
       if item != self.parent[item]:
        __a			:  Optional[int]		    =  self.find(self.parent[item]       )
       return self.parent[item]







      def 				lowerCAmelCase      (self			: str ,    snake_case_			: Union[str, Any] ,    snake_case_			: Dict       ):
       __a			:  Optional[int]		    =  self.find(snake_case_       )
       __a			:  Optional[int]		    =  self.find(snake_case_       )

       if roota == roota:
        return roota

       if self.rank[roota] > self.rank[roota]:
        __a			:  List[Any]		    =  roota
        return roota

       if self.rank[roota] < self.rank[roota]:
        __a			:  str		    =  roota
        return roota

       if self.rank[roota] == self.rank[roota]:
        self.rank[roota] += 1
        __a			:  Any		    =  roota
        return roota
       return None





   @staticmethod
   def 				lowerCAmelCase      (snake_case_			: Optional[Any]       ):
    __a			:  int		    =  graph.num_vertices

    __a			:  List[str]		    =  Graph.UnionFind()
    __a			:  Tuple		    =  []
    while num_components > 1:
     __a			:  Optional[Any]		    =  {}
     for vertex in graph.get_vertices():
      __a			:  Dict		    =  -1

     __a			:  Dict		    =  graph.get_edges()
     for edge in edges:
      __a    ,	__a    ,	__a			:  int		    =  edge
      edges.remove((tail, head, weight)       )
     for edge in edges:
      __a    ,	__a    ,	__a			:  Optional[Any]		    =  edge
      __a			:  Optional[int]		    =  union_find.find(snake_case_       )
      __a			:  Optional[int]		    =  union_find.find(snake_case_       )
      if seta != seta:
       if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
        __a			:  int		    =  [head, tail, weight]

       if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
        __a			:  Tuple		    =  [head, tail, weight]
     for vertex in cheap_edge:
      if cheap_edge[vertex] != -1:
       __a    ,	__a    ,	__a			:  Optional[Any]		    =  cheap_edge[vertex]
       if union_find.find(snake_case_       ) != union_find.find(snake_case_       ):
        union_find.union(snake_case_ ,    snake_case_       )
        mst_edges.append(cheap_edge[vertex]       )
        __a			:  List[str]		    =  num_components - 1
    __a			:  List[Any]		    =  Graph.build(edges=snake_case_       )
    return mst


# 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 		UpperCamelCase__  :
   _SCREAMING_SNAKE_CASE				:							CommonSchedulerState

   # setable values
   _SCREAMING_SNAKE_CASE				:							jnp.ndarray
   _SCREAMING_SNAKE_CASE				:							jnp.ndarray
   _SCREAMING_SNAKE_CASE				:							Optional[int]     	=				None
   @classmethod
   def 				lowerCAmelCase      (cls			: int ,    snake_case_			: CommonSchedulerState ,    snake_case_			: jnp.ndarray ,    snake_case_			: jnp.ndarray       ):
    return cls(common=snake_case_ ,    init_noise_sigma=snake_case_ ,    timesteps=snake_case_       )





@dataclass
class 		UpperCamelCase__  (	__lowercase   ):
   _SCREAMING_SNAKE_CASE				:							DDPMSchedulerState





class 		UpperCamelCase__  (	__lowercase   ,__lowercase   ):
   _SCREAMING_SNAKE_CASE				:							str     	=				[e.name for e in FlaxKarrasDiffusionSchedulers]

   _SCREAMING_SNAKE_CASE				:							jnp.dtype
   @property
   def 				lowerCAmelCase      (self			: Optional[Any]       ):
    return True
   @register_to_config
   def __init__(self			: Any ,    snake_case_			: int = 1_0_0_0 ,    snake_case_			: float = 0.0001 ,    snake_case_			: float = 0.02 ,    snake_case_			: str = "linear" ,    snake_case_			: Optional[jnp.ndarray] = None ,    snake_case_			: str = "fixed_small" ,    snake_case_			: bool = True ,    snake_case_			: str = "epsilon" ,    snake_case_			: jnp.dtype = jnp.floataa ,    ):
    __a			:  str		    =  dtype
   def 				lowerCAmelCase      (self			: Any ,    snake_case_			: Optional[CommonSchedulerState] = None       ):
    if common is None:
     __a			:  Optional[Any]		    =  CommonSchedulerState.create(self       )

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

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

    return DDPMSchedulerState.create(
        common=snake_case_ ,    init_noise_sigma=snake_case_ ,    timesteps=snake_case_ ,    )
   def 				lowerCAmelCase      (self			: Dict ,    snake_case_			: DDPMSchedulerState ,    snake_case_			: jnp.ndarray ,    snake_case_			: Optional[int] = None       ):
    return sample
   def 				lowerCAmelCase      (self			: List[Any] ,    snake_case_			: DDPMSchedulerState ,    snake_case_			: int ,    snake_case_			: Tuple = ()       ):
    __a			:  Tuple		    =  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
    __a			:  Any		    =  (jnp.arange(0 ,    snake_case_       ) * step_ratio).round()[::-1]

    return state.replace(
        num_inference_steps=snake_case_ ,    timesteps=snake_case_ ,    )
   def 				lowerCAmelCase      (self			: List[Any] ,    snake_case_			: DDPMSchedulerState ,    snake_case_			: Optional[Any] ,    snake_case_			: List[str]=None ,    snake_case_			: Union[str, Any]=None       ):
    __a			:  Optional[Any]		    =  state.common.alphas_cumprod[t]
    __a			:  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
    __a			:  Optional[int]		    =  (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

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

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

    return variance
   def 				lowerCAmelCase      (self			: Any ,    snake_case_			: DDPMSchedulerState ,    snake_case_			: jnp.ndarray ,    snake_case_			: int ,    snake_case_			: jnp.ndarray ,    snake_case_			: Optional[jax.random.KeyArray] = None ,    snake_case_			: bool = True ,    ):
    __a			:  int		    =  timestep

    if key is None:
     __a			:  Any		    =  jax.random.PRNGKey(0       )

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

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

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

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

    __a			:  Tuple		    =  pred_prev_sample + variance

    if not return_dict:
     return (pred_prev_sample, state)

    return FlaxDDPMSchedulerOutput(prev_sample=snake_case_ ,    state=snake_case_       )
   def 				lowerCAmelCase      (self			: List[str] ,    snake_case_			: DDPMSchedulerState ,    snake_case_			: jnp.ndarray ,    snake_case_			: jnp.ndarray ,    snake_case_			: jnp.ndarray ,    ):
    return add_noise_common(state.common ,    snake_case_ ,    snake_case_ ,    snake_case_       )
   def 				lowerCAmelCase      (self			: str ,    snake_case_			: DDPMSchedulerState ,    snake_case_			: jnp.ndarray ,    snake_case_			: jnp.ndarray ,    snake_case_			: jnp.ndarray ,    ):
    return get_velocity_common(state.common ,    snake_case_ ,    snake_case_ ,    snake_case_       )







   def __len__(self			: List[str]       ):
    return self.config.num_train_timesteps
