
"""simple docstring"""






from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean




def       A_  (				__lowercase	):

 # A local function to see if a dot lands in the circle.
 def is_in_circle(__lowercase						,	__lowercase	) -> bool:
  UpperCamelCase_     :					Dict   	=sqrt((x**2) + (y**2)	)
  # Our circle has a radius of 1, so a distance
  # greater than 1 would land outside the circle.
  return distance_from_centre <= 1

 # The proportion of guesses that landed in the circle
 UpperCamelCase_     :					List[Any]   	=mean(
     int(is_in_circle(uniform(-1.0						,	1.0	)						,	uniform(-1.0						,	1.0	)	)	)
     for _ in range(__lowercase	)	)
 # The ratio of the area for circle to square is pi/4.
 UpperCamelCase_     :					Any   	=proportion * 4
 print(F'''The estimated value of pi is {pi_estimate}'''	)
 print(F'''The numpy value of pi is {pi}'''	)
 print(F'''The total error is {abs(pi - pi_estimate	)}'''	)




def       A_  (				__lowercase						,	__lowercase						,	__lowercase = 0.0						,	__lowercase = 1.0						,	):
 return mean(
     function_to_integrate(uniform(__lowercase						,	__lowercase	)	) for _ in range(__lowercase	)	) * (max_value - min_value)




def       A_  (				__lowercase						,	__lowercase = 0.0						,	__lowercase = 1.0	):

 def identity_function(__lowercase	) -> float:
  return x

 UpperCamelCase_     :					Union[str, Any]   	=area_under_curve_estimator(
     __lowercase						,	__lowercase						,	__lowercase						,	__lowercase	)
 UpperCamelCase_     :					List[Any]   	=(max_value * max_value - min_value * min_value) / 2

 print('******************'	)
 print(F'''Estimating area under y=x where x varies from {min_value} to {max_value}'''	)
 print(F'''Estimated value is {estimated_value}'''	)
 print(F'''Expected value is {expected_value}'''	)
 print(F'''Total error is {abs(estimated_value - expected_value	)}'''	)
 print('******************'	)




def       A_  (				__lowercase	):

 def function_to_integrate(__lowercase	) -> float:
  return sqrt(4.0 - x * x	)

 UpperCamelCase_     :					Union[str, Any]   	=area_under_curve_estimator(
     __lowercase						,	__lowercase						,	0.0						,	2.0	)

 print('******************'	)
 print('Estimating pi using area_under_curve_estimator'	)
 print(F'''Estimated value is {estimated_value}'''	)
 print(F'''Expected value is {pi}'''	)
 print(F'''Total error is {abs(estimated_value - pi	)}'''	)
 print('******************'	)


if __name__ == "__main__":
 import doctest

 doctest.testmod()


"""simple docstring"""






import math

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




def       A_  (				__lowercase						,	__lowercase						,	__lowercase = 1						,	__lowercase = 1						,	__lowercase = 1.0e4						,	__lowercase = False						,	__lowercase = 1.0						,	):
 assert timesteps.ndim == 1, "Timesteps should be a 1d-array"
 assert embedding_dim % 2 == 0, F'''Embedding dimension {embedding_dim} should be even'''
 UpperCamelCase_     :					Optional[int]   	=float(embedding_dim // 2	)
 UpperCamelCase_     :					Optional[Any]   	=math.log(max_timescale / min_timescale	) / (num_timescales - freq_shift)
 UpperCamelCase_     :					List[Any]   	=min_timescale * jnp.exp(jnp.arange(__lowercase						,	dtype=jnp.floataa	) * -log_timescale_increment	)
 UpperCamelCase_     :					int   	=jnp.expand_dims(__lowercase						,	1	) * jnp.expand_dims(__lowercase						,	0	)

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

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





class 				a__					(						nn.Module       ):
     UpperCAmelCase__         =      32
     UpperCAmelCase__         =      jnp.floataa



     @nn.compact
     def __call__(							self :Optional[Any]      ,  _lowerCamelCase :List[str]   ):







      '''simple docstring'''



      UpperCamelCase_     :					Dict   	=nn.Dense(self.time_embed_dim      ,  dtype=self.dtype      ,  name='linear_1'   )(_lowerCamelCase   )
      UpperCamelCase_     :					Any   	=nn.silu(_lowerCamelCase   )
      UpperCamelCase_     :					Tuple   	=nn.Dense(self.time_embed_dim      ,  dtype=self.dtype      ,  name='linear_2'   )(_lowerCamelCase   )
      return temb





class 				a__					(						nn.Module       ):
     UpperCAmelCase__         =      32
     UpperCAmelCase__         =      False
     UpperCAmelCase__         =      1



     @nn.compact
     def __call__(							self :Union[str, Any]      ,  _lowerCamelCase :Dict   ):







      '''simple docstring'''



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