





'''simple docstring'''


import math

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


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

    # scale embeddings
    _lowerCAmelCase						      =   scale * emb

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

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




 @nn.compact
 def __call__(						self      ,  _lowerCAmelCase		)     ->				Optional[Any]:
     _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  lowerCAmelCase_		(		nn.Module		):
 __lowerCamelCase    :				int								=       32
 __lowerCamelCase    :				bool								=       False
 __lowerCamelCase    :				float								=       1




 @nn.compact
 def __call__(						self      ,  _lowerCAmelCase		)     ->				List[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'''


from __future__ import annotations

import math
def 						lowerCamelCase__   (				a    ,	a							):
						__snake_case						 =   u
						for i in range(1    ,	a							):
												__snake_case						 =   temp * (u - i)
						return temp
def 						lowerCamelCase__   (				):
						__snake_case						 =   int(input('enter the numbers of values: '							)							)
						__snake_case						 =   []
						for _ in range(a							):
												y.append([]							)
						for i in range(a							):
												for j in range(a							):
																		y[i].append(a							)
																		__snake_case						 =   0

						print('enter the values of parameters in a list: '							)
						__snake_case						 =   list(map(a    ,	input().split()							)							)

						print('enter the values of corresponding parameters: '							)
						for i in range(a							):
												__snake_case						 =   float(input()							)

						__snake_case						 =   int(input('enter the value to interpolate: '							)							)
						__snake_case						 =   (value - x[0]) / (x[1] - x[0])

						# for calculating forward difference table

						for i in range(1    ,	a							):
												for j in range(n - i							):
																		__snake_case						 =   y[j + 1][i - 1] - y[j][i - 1]

						__snake_case						 =   y[0][0]
						for i in range(1    ,	a							):
												summ += (ucal(a    ,	a							) * y[0][i]) / math.factorial(a							)

						print(f'the value at {value} is {summ}'							)


if __name__ == "__main__":
	main()

