



import math

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







def    _snake_case (       __snake_case					,  __snake_case					,  __snake_case = 1					,  __snake_case = 1					,  __snake_case = 1.0E4					,  __snake_case = False					,  __snake_case = 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_  :	Tuple				      =		float(embedding_dim // 2    )
      UpperCAmelCase_  :	List[Any]				      =		math.log(max_timescale / min_timescale    ) / (num_timescales - freq_shift)
      UpperCAmelCase_  :	List[Any]				      =		min_timescale * jnp.exp(jnp.arange(__snake_case					,  dtype=jnp.floataa    ) * -log_timescale_increment    )
      UpperCAmelCase_  :	Dict				      =		jnp.expand_dims(__snake_case					,  1    ) * jnp.expand_dims(__snake_case					,  0    )

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

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


class   snake_case_ (nn.Module  ):




       """simple docstring"""






       _lowerCamelCase			    =				32
       _lowerCamelCase			    =				jnp.floataa



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

             """simple docstring"""





             UpperCAmelCase_  :	Dict				      =		nn.Dense(self.time_embed_dim     ,dtype=self.dtype     ,name="linear_1")(lowercase)
             UpperCAmelCase_  :	int				      =		nn.silu(lowercase)
             UpperCAmelCase_  :	int				      =		nn.Dense(self.time_embed_dim     ,dtype=self.dtype     ,name="linear_2")(lowercase)
             return temb


class   snake_case_ (nn.Module  ):




       """simple docstring"""






       _lowerCamelCase			    =				32
       _lowerCamelCase			    =				False
       _lowerCamelCase			    =				1



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

             """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)





def    _snake_case (       __snake_case					,  __snake_case					,  __snake_case    )     ->     list:






      '''simple docstring'''







      UpperCAmelCase_  :	Any				      =		len(__snake_case    )
      UpperCAmelCase_  :	Tuple				      =		[[0] * n for i in range(__snake_case    )]
      for i in range(__snake_case    ):
            UpperCAmelCase_  :	Optional[Any]				      =		y_points[i]

      for i in range(2					,  __snake_case    ):
            for j in range(__snake_case					,  __snake_case    ):
                  UpperCAmelCase_  :	int				      =		(
                      (xa - x_points[j - i + 1]) * q[j][i - 1]
                      - (xa - x_points[j]) * q[j - 1][i - 1]
                  ) / (x_points[j] - x_points[j - i + 1])

      return [q[n - 1][n - 1], q]


if __name__ == "__main__":
   import doctest

   doctest.testmod()
