




"""simple docstring"""

from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils_flax import FlaxSchedulerMixin





@flax.struct.dataclass
class     lowercase_	:



 '''simple docstring'''
 UpperCAmelCase   :					Optional[int]				  =     None
 UpperCAmelCase   :					Optional[jnp.ndarray]				  =     None
 UpperCAmelCase   :					Optional[jnp.ndarray]				  =     None  # sigma(t_i)

 @classmethod
 def       lowerCAmelCase_							(			cls	:	str		):
       return cls()





@dataclass
class     lowercase_	(					__lowerCAmelCase							):



 '''simple docstring'''
 UpperCAmelCase   :					jnp.ndarray
 UpperCAmelCase   :					jnp.ndarray
 UpperCAmelCase   :					KarrasVeSchedulerState





class     lowercase_	(					__lowerCAmelCase      ,     __lowerCAmelCase							):



 '''simple docstring'''

 @property
 def       lowerCAmelCase_							(			self	:	Any		):
       return True

 @register_to_config
 def __init__(			self	:	Tuple   ,							_UpperCAmelCase	:	float = 0.02   ,							_UpperCAmelCase	:	float = 100   ,							_UpperCAmelCase	:	float = 1.007   ,							_UpperCAmelCase	:	float = 80   ,							_UpperCAmelCase	:	float = 0.05   ,							_UpperCAmelCase	:	float = 50   ,							):
       pass

 def       lowerCAmelCase_							(			self	:	Tuple		):
       return KarrasVeSchedulerState.create()

 def       lowerCAmelCase_							(			self	:	int   ,							_UpperCAmelCase	:	KarrasVeSchedulerState   ,							_UpperCAmelCase	:	int   ,							_UpperCAmelCase	:	Tuple = ()		):
       _A        =       jnp.arange(0   ,							_UpperCAmelCase		)[::-1].copy()
       _A        =       [
           (
               self.config.sigma_max**2
               * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
           )
           for i in timesteps
       ]

       return state.replace(
           num_inference_steps=_UpperCAmelCase   ,							schedule=jnp.array(_UpperCAmelCase   ,							dtype=jnp.floataa		)   ,							timesteps=_UpperCAmelCase   ,							)

 def       lowerCAmelCase_							(			self	:	Optional[Any]   ,							_UpperCAmelCase	:	KarrasVeSchedulerState   ,							_UpperCAmelCase	:	jnp.ndarray   ,							_UpperCAmelCase	:	float   ,							_UpperCAmelCase	:	random.KeyArray   ,							):
       if self.config.s_min <= sigma <= self.config.s_max:
             _A        =       min(self.config.s_churn / state.num_inference_steps   ,							2**0.5 - 1		)
       else:
             _A        =       0

       # sample eps ~ N(0, S_noise^2 * I)
       _A        =       random.split(_UpperCAmelCase   ,							num=1		)
       _A        =       self.config.s_noise * random.normal(key=_UpperCAmelCase   ,							shape=sample.shape		)
       _A        =       sigma + gamma * sigma
       _A        =       sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

       return sample_hat, sigma_hat

 def       lowerCAmelCase_							(			self	:	str   ,							_UpperCAmelCase	:	KarrasVeSchedulerState   ,							_UpperCAmelCase	:	jnp.ndarray   ,							_UpperCAmelCase	:	float   ,							_UpperCAmelCase	:	float   ,							_UpperCAmelCase	:	jnp.ndarray   ,							_UpperCAmelCase	:	bool = True   ,							):
       _A        =       sample_hat + sigma_hat * model_output
       _A        =       (sample_hat - pred_original_sample) / sigma_hat
       _A        =       sample_hat + (sigma_prev - sigma_hat) * derivative

       if not return_dict:
             return (sample_prev, derivative, state)

       return FlaxKarrasVeOutput(prev_sample=_UpperCAmelCase   ,							derivative=_UpperCAmelCase   ,							state=_UpperCAmelCase		)

 def       lowerCAmelCase_							(			self	:	Optional[Any]   ,							_UpperCAmelCase	:	KarrasVeSchedulerState   ,							_UpperCAmelCase	:	jnp.ndarray   ,							_UpperCAmelCase	:	float   ,							_UpperCAmelCase	:	float   ,							_UpperCAmelCase	:	jnp.ndarray   ,							_UpperCAmelCase	:	jnp.ndarray   ,							_UpperCAmelCase	:	jnp.ndarray   ,							_UpperCAmelCase	:	bool = True   ,							):
       _A        =       sample_prev + sigma_prev * model_output
       _A        =       (sample_prev - pred_original_sample) / sigma_prev
       _A        =       sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

       if not return_dict:
             return (sample_prev, derivative, state)

       return FlaxKarrasVeOutput(prev_sample=_UpperCAmelCase   ,							derivative=_UpperCAmelCase   ,							state=_UpperCAmelCase		)



 def       lowerCAmelCase_							(			self	:	Dict   ,							_UpperCAmelCase	:	KarrasVeSchedulerState   ,							_UpperCAmelCase	:	List[str]   ,							_UpperCAmelCase	:	Optional[int]   ,							_UpperCAmelCase	:	List[Any]		):
       raise NotImplementedError()







"""simple docstring"""

def 						_snake_case					( _snake_case							: int							)   -> list:






      '''simple docstring'''


      _A        =       int(_snake_case							)
      if n_element < 1:
            _A        =       ValueError('a should be a positive number'							)
            raise my_error

      _A        =       [1]
      _A       ,   _A       ,   _A        =       (0, 0, 0)
      _A        =       1
      while index < n_element:
            while hamming_list[i] * 2 <= hamming_list[-1]:
                  i += 1
            while hamming_list[j] * 3 <= hamming_list[-1]:
                  j += 1
            while hamming_list[k] * 5 <= hamming_list[-1]:
                  k += 1
            hamming_list.append(
                min(hamming_list[i] * 2    ,  hamming_list[j] * 3    ,  hamming_list[k] * 5							)							)
            index += 1
      return hamming_list


if __name__ == "__main__":
       a         =      input('''Enter the last number (nth term) of the Hamming Number Series: ''')
       print('''Formula of Hamming Number Series => 2^i * 3^j * 5^k''')
       a         =      hamming(int(n))
       print('''-----------------------------------------------------''')
       print(F'''The list with nth numbers is: {hamming_numbers}''')
       print('''-----------------------------------------------------''')

