'''simple docstring'''





import math

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





def 	lowerCAmelCase_				(					snake_case_       : jnp.ndarray					,    snake_case_       : int					,    snake_case_       : float = 1					,    snake_case_       : float = 1					,    snake_case_       : float = 1.0E4					,    snake_case_       : bool = False					,    snake_case_       : 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"""
     UpperCAmelCase_           =   float(embedding_dim // 2			)
     UpperCAmelCase_           =   math.log(max_timescale / min_timescale			) / (num_timescales - freq_shift)
     UpperCAmelCase_           =   min_timescale * jnp.exp(jnp.arange(snake_case_					,    dtype=jnp.floataa			) * -log_timescale_increment			)
     UpperCAmelCase_           =   jnp.expand_dims(snake_case_					,    1			) * jnp.expand_dims(snake_case_					,    0			)

     # scale embeddings
     UpperCAmelCase_           =   scale * emb

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




class        __A      ( nn.Module	):
    a__       :						int          =  32
    a__       :						jnp.dtype          =  jnp.floataa



    @nn.compact
    def __call__(self    :    Dict   ,			__a    :    Tuple ):
         UpperCAmelCase_           =   nn.Dense(self.time_embed_dim   ,			dtype=self.dtype   ,			name="linear_1" )(__a )
         UpperCAmelCase_           =   nn.silu(__a )
         UpperCAmelCase_           =   nn.Dense(self.time_embed_dim   ,			dtype=self.dtype   ,			name="linear_2" )(__a )
         return temb




class        __A      ( nn.Module	):
    a__       :						int          =  32
    a__       :						bool          =  False
    a__       :						float          =  1



    @nn.compact
    def __call__(self    :    Optional[Any]   ,			__a    :    List[Any] ):
         return get_sinusoidal_embeddings(
             __a   ,			embedding_dim=self.dim   ,			flip_sin_to_cos=self.flip_sin_to_cos   ,			freq_shift=self.freq_shift )





'''simple docstring'''





def 	lowerCAmelCase_				(					snake_case_       : int					,    snake_case_       : int			)    ->      int:


     '''simple docstring'''




     return x if y == 0 else greatest_common_divisor(snake_case_					,    x % y			)





def 	lowerCAmelCase_				(					snake_case_       : int					,    snake_case_       : int			)    ->      int:


     '''simple docstring'''




     return (x * y) // greatest_common_divisor(snake_case_					,    snake_case_			)





def 	lowerCAmelCase_				(					snake_case_       : int = 20			)    ->      int:


     '''simple docstring'''




     UpperCAmelCase_           =   1
     for i in range(1					,    n + 1			):
          UpperCAmelCase_           =   lcm(snake_case_					,    snake_case_			)
     return g


if __name__ == "__main__":
    print(f"{solution() = }")




