


'''simple docstring'''






import math

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


def       _snake_case     (  A				,					A				,					A = 1				,					A = 1				,					A = 1.0E4				,					A = False				,					A = 1.0				,					)		->					jnp.ndarray:
							assert timesteps.ndim == 1, "Timesteps should be a 1d-array"
							assert embedding_dim % 2 == 0, F"""Embedding dimension {embedding_dim} should be even"""
							lowerCAmelCase__      =			float(embedding_dim // 2 )
							lowerCAmelCase__      =			math.log(max_timescale / min_timescale ) / (num_timescales - freq_shift)
							lowerCAmelCase__      =			min_timescale * jnp.exp(jnp.arange(A				,					dtype=jnp.floataa ) * -log_timescale_increment )
							lowerCAmelCase__      =			jnp.expand_dims(A				,					1 ) * jnp.expand_dims(A				,					0 )

							# scale embeddings
							lowerCAmelCase__      =			scale * emb

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




class 	a__       (							nn.Module						):





							'''simple docstring'''






							lowercase__    :     int					=   3_2
							lowercase__    :     jnp.dtype					=   jnp.floataa







							@nn.compact
							def __call__(	self      ,					lowerCamelCase_     ) ->							str:
														lowerCAmelCase__      =			nn.Dense(self.time_embed_dim      ,					dtype=self.dtype      ,					name='''linear_1'''     )(lowerCamelCase_     )
														lowerCAmelCase__      =			nn.silu(lowerCamelCase_     )
														lowerCAmelCase__      =			nn.Dense(self.time_embed_dim      ,					dtype=self.dtype      ,					name='''linear_2'''     )(lowerCamelCase_     )
														return temb




class 	a__       (							nn.Module						):





							'''simple docstring'''






							lowercase__    :     int					=   3_2
							lowercase__    :     bool					=   False
							lowercase__    :     float					=   1







							@nn.compact
							def __call__(	self      ,					lowerCamelCase_     ) ->							Union[str, Any]:
														return get_sinusoidal_embeddings(
														    lowerCamelCase_      ,					embedding_dim=self.dim      ,					flip_sin_to_cos=self.flip_sin_to_cos      ,					freq_shift=self.freq_shift     )



'''simple docstring'''






import doctest
from collections import deque

import numpy as np




class 	a__       :





							'''simple docstring'''






							def __init__(	self     ) ->							None:
														lowerCAmelCase__      =			[2, 1, 2, -1]
														lowerCAmelCase__      =			[1, 2, 3, 4]







							def 						__SCREAMING_SNAKE_CASE							(	self     ) ->							list[float]:
														lowerCAmelCase__      =			len(self.first_signal     )
														lowerCAmelCase__      =			len(self.second_signal     )

														lowerCAmelCase__      =			max(lowerCamelCase_      ,					lowerCamelCase_     )

														# create a zero matrix of max_length x max_length
														lowerCAmelCase__      =			[[0] * max_length for i in range(lowerCamelCase_     )]

														# fills the smaller signal with zeros to make both signals of same length
														if length_first_signal < length_second_signal:
																					self.first_signal += [0] * (max_length - length_first_signal)
														elif length_first_signal > length_second_signal:
																					self.second_signal += [0] * (max_length - length_second_signal)
														for i in range(lowerCamelCase_     ):
																					lowerCAmelCase__      =			deque(self.second_signal     )
																					rotated_signal.rotate(lowerCamelCase_     )
																					for j, item in enumerate(lowerCamelCase_     ):
																												matrix[i][j] += item

        # multiply the matrix with the first signal
														lowerCAmelCase__      =			np.matmul(np.transpose(lowerCamelCase_     )      ,					np.transpose(self.first_signal     )     )

														# rounding-off to two decimal places
														return [round(lowerCamelCase_      ,					2     ) for i in final_signal]


if __name__ == "__main__":
		doctest.testmod()