






'''simple docstring'''

import math

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






def 	_UpperCAmelCase    (  a		:	jnp.ndarray						,			a		:	int						,			a		:	float = 1						,			a		:	float = 1						,			a		:	float = 1.0e4						,			a		:	bool = False						,			a		:	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"
						lowercase_      :   Dict        =			float(embedding_dim // 2							)
						lowercase_      :   Tuple        =			math.log(max_timescale / min_timescale							) / (num_timescales - freq_shift)
						lowercase_      :   List[str]        =			min_timescale * jnp.exp(jnp.arange(a						,			dtype=jnp.floataa							) * -log_timescale_increment							)
						lowercase_      :   List[str]        =			jnp.expand_dims(a						,			1							) * jnp.expand_dims(a						,			0							)

						# scale embeddings
						lowercase_      :   str        =			scale * emb

						if flip_sin_to_cos:
												lowercase_      :   Union[str, Any]        =			jnp.concatenate([jnp.cos(a							), jnp.sin(a							)]						,			axis=1							)
						else:
												lowercase_      :   str        =			jnp.concatenate([jnp.sin(a							), jnp.cos(a							)]						,			axis=1							)
						lowercase_      :   Optional[Any]        =			jnp.reshape(a						,			[jnp.shape(a							)[0], embedding_dim]							)
						return signal






class 							__magic_name__     (	nn.Module				):







	"""simple docstring"""



	SCREAMING_SNAKE_CASE_					:      int        =  3_2
	SCREAMING_SNAKE_CASE_					:      jnp.dtype        =  jnp.floataa
	@nn.compact
	def __call__(							self  ,      _lowercase       )						->  Tuple:
							lowercase_      :   List[str]        =			nn.Dense(self.time_embed_dim  ,      dtype=self.dtype  ,      name='linear_1'       )(_lowercase       )
							lowercase_      :   Any        =			nn.silu(_lowercase       )
							lowercase_      :   int        =			nn.Dense(self.time_embed_dim  ,      dtype=self.dtype  ,      name='linear_2'       )(_lowercase       )
							return temb






class 							__magic_name__     (	nn.Module				):







	"""simple docstring"""



	SCREAMING_SNAKE_CASE_					:      int        =  3_2
	SCREAMING_SNAKE_CASE_					:      bool        =  False
	SCREAMING_SNAKE_CASE_					:      float        =  1
	@nn.compact
	def __call__(							self  ,      _lowercase       )						->  Any:
							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'''

def 	_UpperCAmelCase    (  a		:	str							)			->			str:





						"""simple docstring"""
						lowercase_      :   Dict        =			0

						# if input_string is "aba" than new_input_string become "a|b|a"
						lowercase_      :   Dict        =			''
						lowercase_      :   Any        =			''

						# append each character + "|" in new_string for range(0, length-1)
						for i in input_string[: len(a							) - 1]:
												new_input_string += i + "|"
						# append last character
						new_input_string += input_string[-1]

						# we will store the starting and ending of previous furthest ending palindromic
						# substring
						lowercase_  ,      lowercase_      :   Dict        =			0, 0

						# length[i] shows the length of palindromic substring with center i
						lowercase_      :   List[Any]        =			[1 for i in range(len(a							)							)]

						# for each character in new_string find corresponding palindromic string
						lowercase_      :   Dict        =			0
						for j in range(len(a							)							):
												lowercase_      :   Tuple        =			1 if j > r else min(length[l + r - j] // 2						,			r - j + 1							)
												while (
												    j - k >= 0
												    and j + k < len(a							)
												    and new_input_string[k + j] == new_input_string[j - k]
												):
																		k += 1

												lowercase_      :   int        =			2 * k - 1

												# does this string is ending after the previously explored end (that is r) ?
												# if yes the update the new r to the last index of this
												if j + k - 1 > r:
																		lowercase_      :   Tuple        =			j - k + 1  # noqa: E741
																		lowercase_      :   Tuple        =			j + k - 1

												# update max_length and start position
												if max_length < length[j]:
																		lowercase_      :   Tuple        =			length[j]
																		lowercase_      :   List[Any]        =			j

    # create that string
						lowercase_      :   str        =			new_input_string[start - max_length // 2 : start + max_length // 2 + 1]
						for i in s:
												if i != "|":
																		output_string += i

						return output_string


if __name__ == "__main__":
						import doctest

						doctest.testmod()
