





'''simple docstring'''


import math

import flax.linen as nn
import jax.numpy as jnp
def 							UpperCAmelCase_  (						__lowerCamelCase : jnp.ndarray     ,__lowerCamelCase : int     ,__lowerCamelCase : float = 1     ,__lowerCamelCase : float = 1     ,__lowerCamelCase : float = 1.0e4     ,__lowerCamelCase : bool = False     ,__lowerCamelCase : float = 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'
   lowercase_      :Optional[int]         =			float(embedding_dim // 2			)
   lowercase_      :Optional[int]         =			math.log(max_timescale / min_timescale			) / (num_timescales - freq_shift)
   lowercase_      :Union[str, Any]         =			min_timescale * jnp.exp(jnp.arange(__lowerCamelCase     ,dtype=jnp.floataa			) * -log_timescale_increment			)
   lowercase_      :List[Any]         =			jnp.expand_dims(__lowerCamelCase     ,1			) * jnp.expand_dims(__lowerCamelCase     ,0			)

   # scale embeddings
   lowercase_      :Optional[Any]         =			scale * emb

   if flip_sin_to_cos:
      lowercase_      :Any         =			jnp.concatenate([jnp.cos(__lowerCamelCase			), jnp.sin(__lowerCamelCase			)]     ,axis=1			)
   else:
      lowercase_      :List[str]         =			jnp.concatenate([jnp.sin(__lowerCamelCase			), jnp.cos(__lowerCamelCase			)]     ,axis=1			)
   lowercase_      :List[str]         =			jnp.reshape(__lowerCamelCase     ,[jnp.shape(__lowerCamelCase			)[0], embedding_dim]			)
   return signal
class 				a_       (    nn.Module							):
     __A								=      32
     __A								=      jnp.floataa





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





        """simple docstring"""




        lowercase_      :Union[str, Any]         =			nn.Dense(self.time_embed_dim     ,				dtype=self.dtype     ,				name="linear_1"						)(lowercase						)
        lowercase_      :List[Any]         =			nn.silu(lowercase						)
        lowercase_      :Optional[int]         =			nn.Dense(self.time_embed_dim     ,				dtype=self.dtype     ,				name="linear_2"						)(lowercase						)
        return temb







class 				a_       (    nn.Module							):
     __A								=      32
     __A								=      False
     __A								=      1





     @nn.compact
     def __call__(			self		: str     ,				lowercase		: Tuple						):





        """simple docstring"""




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









'''simple docstring'''


import numpy as np
def 							UpperCAmelCase_  (						__lowerCamelCase : str     ,__lowerCamelCase : Optional[Any]     ,__lowerCamelCase : int     ,__lowerCamelCase : List[str]     ,__lowerCamelCase : List[Any]			):
   lowercase_      :Dict         =			int(np.ceil((x_end - xa) / h			)			)
   lowercase_      :Optional[int]         =			np.zeros((n + 1,)			)
   lowercase_      :Tuple         =			ya
   lowercase_      :List[str]         =			xa

   for k in range(__lowerCamelCase			):
      lowercase_      :Any         =			f(__lowerCamelCase     ,y[k]			)
      lowercase_      :Optional[Any]         =			f(x + 0.5 * h     ,y[k] + 0.5 * h * ka			)
      lowercase_      :Optional[Any]         =			f(x + 0.5 * h     ,y[k] + 0.5 * h * ka			)
      lowercase_      :Any         =			f(x + h     ,y[k] + h * ka			)
      lowercase_      :Tuple         =			y[k] + (1 / 6) * h * (ka + 2 * ka + 2 * ka + ka)
      x += h

   return y


if __name__ == "__main__":
 import doctest

 doctest.testmod()


