






import math

import flax.linen as nn
import jax.numpy as jnp



def       _SCREAMING_SNAKE_CASE    (			__lowercase :      jnp.ndarray      ,					__lowercase :      int      ,					__lowercase :      float = 1      ,					__lowercase :      float = 1      ,					__lowercase :      float = 1.0E4      ,					__lowercase :      bool = False      ,					__lowercase :      float = 1.0      ,					)    ->   jnp.ndarray:





    """simple docstring"""

    assert timesteps.ndim == 1, "Timesteps should be a 1d-array"
    assert embedding_dim % 2 == 0, f"Embedding dimension {embedding_dim} should be even"
    __A       =						float(embedding_dim // 2     )
    __A       =						math.log(max_timescale / min_timescale     ) / (num_timescales - freq_shift)
    __A       =						min_timescale * jnp.exp(jnp.arange(__lowercase      ,					dtype=jnp.floataa     ) * -log_timescale_increment     )
    __A       =						jnp.expand_dims(__lowercase      ,					1     ) * jnp.expand_dims(__lowercase      ,					0     )

    # scale embeddings
    __A       =						scale * emb

    if flip_sin_to_cos:
        __A       =						jnp.concatenate([jnp.cos(__lowercase     ), jnp.sin(__lowercase     )]      ,					axis=1     )
    else:
        __A       =						jnp.concatenate([jnp.sin(__lowercase     ), jnp.cos(__lowercase     )]      ,					axis=1     )
    __A       =						jnp.reshape(__lowercase      ,					[jnp.shape(__lowercase     )[0], embedding_dim]     )
    return signal


class    __lowercase   (						nn.Module	):







     '''simple docstring'''
     SCREAMING_SNAKE_CASE     =					32
     SCREAMING_SNAKE_CASE     =					jnp.floataa




     @nn.compact
     def __call__(					self							:      List[str]			,						UpperCamelCase_							:      Optional[int]					):


         """simple docstring"""



         __A       =						nn.Dense(self.time_embed_dim			,						dtype=self.dtype			,						name="""linear_1"""					)(UpperCamelCase_					)
         __A       =						nn.silu(UpperCamelCase_					)
         __A       =						nn.Dense(self.time_embed_dim			,						dtype=self.dtype			,						name="""linear_2"""					)(UpperCamelCase_					)
         return temb


class    __lowercase   (						nn.Module	):







     '''simple docstring'''
     SCREAMING_SNAKE_CASE     =					32
     SCREAMING_SNAKE_CASE     =					False
     SCREAMING_SNAKE_CASE     =					1




     @nn.compact
     def __call__(					self							:      int			,						UpperCamelCase_							:      List[Any]					):


         """simple docstring"""



         return get_sinusoidal_embeddings(
             UpperCamelCase_			,						embedding_dim=self.dim			,						flip_sin_to_cos=self.flip_sin_to_cos			,						freq_shift=self.freq_shift					)












from __future__ import annotations

from typing import Generic, TypeVar

__a   :							str						= TypeVar("T")


class    __lowercase   (						Generic[T]	):







     '''simple docstring'''




     def __init__(					self							:      Any			,						UpperCamelCase_							:      T					):


         """simple docstring"""



         __A       =						data
         __A       =						self
         __A       =						0


class    __lowercase   (						Generic[T]	):







     '''simple docstring'''




     def __init__(					self							:      Optional[Any]					):


         """simple docstring"""



         __A       =						{}




     def 		lowerCAmelCase_  (					self							:      Union[str, Any]			,						UpperCamelCase_							:      T					):


         """simple docstring"""



         __A       =						DisjointSetTreeNode(UpperCamelCase_					)




     def 		lowerCAmelCase_  (					self							:      List[Any]			,						UpperCamelCase_							:      T					):


         """simple docstring"""



         __A       =						self.map[data]
         if elem_ref != elem_ref.parent:
             __A       =						self.find_set(elem_ref.parent.data					)
         return elem_ref.parent




     def 		lowerCAmelCase_  (					self							:      int			,						UpperCamelCase_							:      DisjointSetTreeNode[T]			,						UpperCamelCase_							:      DisjointSetTreeNode[T]					):


         """simple docstring"""



         if nodea.rank > nodea.rank:
             __A       =						nodea
         else:
             __A       =						nodea
             if nodea.rank == nodea.rank:
                 nodea.rank += 1





     def 		lowerCAmelCase_  (					self							:      Tuple			,						UpperCamelCase_							:      T			,						UpperCamelCase_							:      T					):


         """simple docstring"""



         self.link(self.find_set(UpperCamelCase_					)			,						self.find_set(UpperCamelCase_					)					)


class    __lowercase   (						Generic[T]	):







     '''simple docstring'''




     def __init__(					self							:      Optional[int]					):


         """simple docstring"""



         __A       =						{}




     def 		lowerCAmelCase_  (					self							:      int			,						UpperCamelCase_							:      T					):


         """simple docstring"""



         if node not in self.connections:
             __A       =						{}




     def 		lowerCAmelCase_  (					self							:      Dict			,						UpperCamelCase_							:      T			,						UpperCamelCase_							:      T			,						UpperCamelCase_							:      int					):


         """simple docstring"""



         self.add_node(UpperCamelCase_					)
         self.add_node(UpperCamelCase_					)
         __A       =						weight
         __A       =						weight





     def 		lowerCAmelCase_  (					self							:      Dict					):


         """simple docstring"""



         __A       =						[]
         __A       =						set()
         for start in self.connections:
             for end in self.connections[start]:
                 if (start, end) not in seen:
                     seen.add((end, start)					)
                     edges.append((start, end, self.connections[start][end])					)
         edges.sort(key=lambda UpperCamelCase_					: x[2]					)

         # creating the disjoint set
         __A       =						DisjointSetTree[T]()
         for node in self.connections:
             disjoint_set.make_set(UpperCamelCase_					)

         # MST generation
         __A       =						0
         __A       =						0
         __A       =						GraphUndirectedWeighted[T]()
         while num_edges < len(self.connections					) - 1:
             __A     ,						__A     ,						__A       =						edges[index]
             index += 1
             __A       =						disjoint_set.find_set(UpperCamelCase_					)
             __A       =						disjoint_set.find_set(UpperCamelCase_					)
             if parent_u != parent_v:
                 num_edges += 1
                 graph.add_edge(UpperCamelCase_			,						UpperCamelCase_			,						UpperCamelCase_					)
                 disjoint_set.union(UpperCamelCase_			,						UpperCamelCase_					)
         return graph




