




'''simple docstring'''





import math

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


def 					UpperCamelCase_(     snake_case							:	jnp.ndarray							,    snake_case							:	int							,    snake_case							:	float = 1							,    snake_case							:	float = 1							,    snake_case							:	float = 1.0e4							,    snake_case							:	bool = False							,    snake_case							:	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'
							snake_case_      =				float(embedding_dim // 2					)
							snake_case_      =				math.log(max_timescale / min_timescale					) / (num_timescales - freq_shift)
							snake_case_      =				min_timescale * jnp.exp(jnp.arange(snake_case							,    dtype=jnp.floataa					) * -log_timescale_increment					)
							snake_case_      =				jnp.expand_dims(snake_case							,    1					) * jnp.expand_dims(snake_case							,    0					)

							# scale embeddings
							snake_case_      =				scale * emb

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




class 			_snake_case		(     nn.Module							):
			lowerCAmelCase_					:				int							=   32
			lowerCAmelCase_					:				jnp.dtype							=   jnp.floataa




			@nn.compact
			def __call__( self    ,							a__							)    ->    List[Any]:

										'''simple docstring'''




										snake_case_      =				nn.Dense(self.time_embed_dim    ,							dtype=self.dtype    ,							name="linear_1"							)(a__							)
										snake_case_      =				nn.silu(a__							)
										snake_case_      =				nn.Dense(self.time_embed_dim    ,							dtype=self.dtype    ,							name="linear_2"							)(a__							)
										return temb




class 			_snake_case		(     nn.Module							):
			lowerCAmelCase_					:				int							=   32
			lowerCAmelCase_					:				bool							=   False
			lowerCAmelCase_					:				float							=   1




			@nn.compact
			def __call__( self    ,							a__							)    ->    Any:

										'''simple docstring'''




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










'''simple docstring'''





from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403


def 					UpperCamelCase_(     snake_case							:	str							,    snake_case							:	complex							,    snake_case							:	str = "x"							,    snake_case							:	float = 1_0**-1_0							,    snake_case							:	int = 1							,    ):

							'''simple docstring'''






							snake_case_      =				symbols(snake_case					)
							snake_case_      =				lambdify(snake_case							,    snake_case					)
							snake_case_      =				lambdify(snake_case							,    diff(snake_case							,    snake_case					)					)

							snake_case_      =				starting_point

							while True:
														if diff_function(snake_case					) != 0:
																					snake_case_      =				prev_guess - multiplicity * func(snake_case					) / diff_function(
																					    snake_case					)
														else:
																					raise ZeroDivisionError("Could not find root"					) from None

														# Precision is checked by comparing the difference of consecutive guesses
														if abs(next_guess - prev_guess					) < precision:
																					return next_guess

														snake_case_      =				next_guess


# Let's Execute
if __name__ == "__main__":
		# Find root of trigonometric function
		# Find value of pi
		print(F"The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}")

		# Find root of polynomial
		# Find fourth Root of 5
		print(F"The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5j)}")

		# Find value of e
		print(
		    "The root of log(y) - 1 = 0 is ",
		    F"{newton_raphson('log(y) - 1', 2, variable='y')}",
		)

		# Exponential Roots
		print(
		    "The root of exp(x) - 1 = 0 is",
		    F"{newton_raphson('exp(x) - 1', 10, precision=0.0_0_5)}",
		)

		# Find root of cos(x)
		print(F"The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}")




