



"""simple docstring"""






from __future__ import annotations

import matplotlib.pyplot as plt  # type: ignore
import numpy

# initial triangle of Koch snowflake
_lowercase			:			Dict										=						numpy.array([0, 0])
_lowercase			:			int										=						numpy.array([0.5, 0.8_660_254])
_lowercase			:			Optional[int]										=						numpy.array([1, 0])
_lowercase			:			int										=						[VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]






def 					snake_case__       (		__lowerCamelCase    :   list[numpy.ndarray]							,		__lowerCamelCase    :   int     ):
			"""simple docstring"""
			lowerCamelCase__		:		Tuple		     =initial_vectors
			for _ in range(__lowerCamelCase     ):
						lowerCamelCase__		:		Dict		     =iteration_step(__lowerCamelCase     )
			return vectors






def 					snake_case__       (		__lowerCamelCase    :   list[numpy.ndarray]     ):
			"""simple docstring"""
			lowerCamelCase__		:		str		     =[]
			for i, start_vector in enumerate(vectors[:-1]     ):
						lowerCamelCase__		:		Any		     =vectors[i + 1]
						new_vectors.append(__lowerCamelCase     )
						lowerCamelCase__		:		List[Any]		     =end_vector - start_vector
						new_vectors.append(start_vector + difference_vector / 3     )
						new_vectors.append(
						    start_vector + difference_vector / 3 + rotate(difference_vector / 3							,		60     )     )
						new_vectors.append(start_vector + difference_vector * 2 / 3     )
			new_vectors.append(vectors[-1]     )
			return new_vectors






def 					snake_case__       (		__lowerCamelCase    :   numpy.ndarray							,		__lowerCamelCase    :   float     ):
			"""simple docstring"""
			lowerCamelCase__		:		Tuple		     =numpy.radians(__lowerCamelCase     )
			lowerCamelCase__     ,       lowerCamelCase__		:		Optional[Any]		     =numpy.cos(__lowerCamelCase     ), numpy.sin(__lowerCamelCase     )
			lowerCamelCase__		:		int		     =numpy.array(((c, -s), (s, c))     )
			return numpy.dot(__lowerCamelCase							,		__lowerCamelCase     )






def 					snake_case__       (		__lowerCamelCase    :   list[numpy.ndarray]     ):
			"""simple docstring"""
			lowerCamelCase__		:		Optional[int]		     =plt.gca()
			axes.set_aspect('''equal'''     )

			# matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
			# y-coordinates as inputs, which are constructed from the vector-list using
			# zip()
			lowerCamelCase__     ,       lowerCamelCase__		:		int		     =zip(*__lowerCamelCase     )
			plt.plot(__lowerCamelCase							,		__lowerCamelCase     )
			plt.show()


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		_lowercase			:			List[Any]										=						iterate(INITIAL_VECTORS, 5)
		plot(processed_vectors)









"""simple docstring"""






import math

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






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

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

			if flip_sin_to_cos:
						lowerCamelCase__		:		int		     =jnp.concatenate([jnp.cos(__lowerCamelCase     ), jnp.sin(__lowerCamelCase     )]							,		axis=1     )
			else:
						lowerCamelCase__		:		List[str]		     =jnp.concatenate([jnp.sin(__lowerCamelCase     ), jnp.cos(__lowerCamelCase     )]							,		axis=1     )
			lowerCamelCase__		:		str		     =jnp.reshape(__lowerCamelCase							,		[jnp.shape(__lowerCamelCase     )[0], embedding_dim]     )
			return signal

class 	__SCREAMING_SNAKE_CASE     (				nn.Module       ):


					'''simple docstring'''





					_a             =							3_2
					_a             =							jnp.floataa



					@nn.compact
					def __call__(	self							:  Optional[Any],  lowerCamelCase							:  int					)-> Any:
								lowerCamelCase__		:		Optional[Any]		     =nn.Dense(self.time_embed_dim,  dtype=self.dtype,  name='''linear_1'''					)(lowerCamelCase					)
								lowerCamelCase__		:		List[str]		     =nn.silu(lowerCamelCase					)
								lowerCamelCase__		:		Any		     =nn.Dense(self.time_embed_dim,  dtype=self.dtype,  name='''linear_2'''					)(lowerCamelCase					)
								return temb





class 	__SCREAMING_SNAKE_CASE     (				nn.Module       ):


					'''simple docstring'''





					_a             =							3_2
					_a             =							False
					_a             =							1



					@nn.compact
					def __call__(	self							:  Any,  lowerCamelCase							:  int					)-> int:
								return get_sinusoidal_embeddings(
								    lowerCamelCase,  embedding_dim=self.dim,  flip_sin_to_cos=self.flip_sin_to_cos,  freq_shift=self.freq_shift					)




