'''simple docstring'''






from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
_UpperCAmelCase    :     Optional[Any]         =       2_99_79_24_58

# Symbols
_UpperCAmelCase       ,  _UpperCAmelCase       ,  _UpperCAmelCase       ,  _UpperCAmelCase    :     Optional[int]         =       symbols('''ct x y z''')





def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			Any				):
     if velocity > c:
          raise ValueError('Speed must not exceed light speed 299,792,458 [m/s]!'				)
     elif velocity < 1:
          # Usually the speed should be much higher than 1 (c order of magnitude)
          raise ValueError('Speed must be greater than or equal to 1!'				)

     return velocity / c





def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			Union[str, Any]				):
     return 1 / sqrt(1 - beta(__lowercase				) ** 2				)





def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			List[Any]				):
     return np.array(
         [
             [gamma(__lowercase				), -gamma(__lowercase				) * beta(__lowercase				), 0, 0],
             [-gamma(__lowercase				) * beta(__lowercase				), gamma(__lowercase				), 0, 0],
             [0, 0, 1, 0],
             [0, 0, 0, 1],
         ]				)





def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			Dict   ,		__snake_case							:			int = None				):
     # Ensure event is not empty
     if event is None:
          _A    		=  np.array([ct, x, y, z]				)  # Symbolic four vector
     else:
          event[0] *= c  # x0 is ct (speed of light * time)

     return transformation_matrix(__lowercase				) @ event


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   # Example of symbolic vector:
   _UpperCAmelCase    :     List[str]         =       transform(29_97_92_45)
   print('''Example of four vector: ''')
   print(F'''ct\' = {four_vector[0]}''')
   print(F'''x\' = {four_vector[1]}''')
   print(F'''y\' = {four_vector[2]}''')
   print(F'''z\' = {four_vector[3]}''')

   # Substitute symbols with numerical values
   _UpperCAmelCase    :     List[Any]         =       {ct: c, x: 1, y: 1, z: 1}
   _UpperCAmelCase    :     Optional[int]         =       [four_vector[i].subs(sub_dict) for i in range(4)]

   print(F'''\n{numerical_vector}''')





"""simple docstring"""






import math

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




def       A_  (				__lowercase						,	__lowercase						,	__lowercase = 1						,	__lowercase = 1						,	__lowercase = 1.0e4						,	__lowercase = False						,	__lowercase = 1.0						,	):
 assert timesteps.ndim == 1, "Timesteps should be a 1d-array"
 assert embedding_dim % 2 == 0, F'''Embedding dimension {embedding_dim} should be even'''
 UpperCamelCase_     :					Optional[int]   	=float(embedding_dim // 2	)
 UpperCamelCase_     :					Optional[Any]   	=math.log(max_timescale / min_timescale	) / (num_timescales - freq_shift)
 UpperCamelCase_     :					List[Any]   	=min_timescale * jnp.exp(jnp.arange(__lowercase						,	dtype=jnp.floataa	) * -log_timescale_increment	)
 UpperCamelCase_     :					int   	=jnp.expand_dims(__lowercase						,	1	) * jnp.expand_dims(__lowercase						,	0	)

 # scale embeddings
 UpperCamelCase_     :					List[str]   	=scale * emb

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





class 				a__					(						nn.Module       ):
     UpperCAmelCase__         =      32
     UpperCAmelCase__         =      jnp.floataa



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







      '''simple docstring'''



      UpperCamelCase_     :					Dict   	=nn.Dense(self.time_embed_dim      ,  dtype=self.dtype      ,  name='linear_1'   )(_lowerCamelCase   )
      UpperCamelCase_     :					Any   	=nn.silu(_lowerCamelCase   )
      UpperCamelCase_     :					Tuple   	=nn.Dense(self.time_embed_dim      ,  dtype=self.dtype      ,  name='linear_2'   )(_lowerCamelCase   )
      return temb





class 				a__					(						nn.Module       ):
     UpperCAmelCase__         =      32
     UpperCAmelCase__         =      False
     UpperCAmelCase__         =      1



     @nn.compact
     def __call__(							self :Union[str, Any]      ,  _lowerCamelCase :Dict   ):







      '''simple docstring'''



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