


import torch
from torch import autograd







class 	_snake_case						(   autograd.Function							):




 @staticmethod
 def  SCREAMING_SNAKE_CASE__       (	_lowerCamelCase      ,						_lowerCamelCase      ,						_lowerCamelCase      ,						_lowerCamelCase					):
       a		:Optional[int]											= inputs.numel()
       a		:Optional[int]											= int(0.005 * nb_elems					) + 1
       if sigmoid:
             a		:str											= (torch.sigmoid(_lowerCamelCase					) > threshold).type(inputs.type()					)
       else:
             a		:Union[str, Any]											= (inputs > threshold).type(inputs.type()					)
       if mask.sum() < nb_min:
             # We limit the pruning so that at least 0.5% (half a percent) of the weights are remaining
             a		:Optional[int]											= inputs.flatten().kthvalue(max(nb_elems - nb_min      ,						1					)					).values
             a		:int											= (inputs > k_threshold).type(inputs.type()					)
       return mask




 @staticmethod
 def  SCREAMING_SNAKE_CASE__       (	_lowerCamelCase      ,						_lowerCamelCase					):
       return gradOutput, None, None







class 	_snake_case						(   autograd.Function							):




 @staticmethod
 def  SCREAMING_SNAKE_CASE__       (	_lowerCamelCase      ,						_lowerCamelCase      ,						_lowerCamelCase					):
       a		:Optional[Any]											= inputs.clone()
       a							,       a		:int											= inputs.flatten().sort(descending=_lowerCamelCase					)
       a		:Union[str, Any]											= int(threshold * inputs.numel()					)

       # flat_out and mask access the same memory.
       a		:Union[str, Any]											= mask.flatten()
       a		:int											= 0
       a		:str											= 1
       return mask




 @staticmethod
 def  SCREAMING_SNAKE_CASE__       (	_lowerCamelCase      ,						_lowerCamelCase					):
       return gradOutput, None







class 	_snake_case						(   _snake_case							):




 @staticmethod
 def  SCREAMING_SNAKE_CASE__       (	_lowerCamelCase      ,						_lowerCamelCase					):
       a		:Union[str, Any]											= inputs.clone()
       a							,       a		:str											= inputs.abs().flatten().sort(descending=_lowerCamelCase					)
       a		:Union[str, Any]											= int(threshold * inputs.numel()					)

       # flat_out and mask access the same memory.
       a		:Any											= mask.flatten()
       a		:Optional[int]											= 0
       a		:Any											= 1
       return mask









import numpy as np
def        __lowerCamelCase		(				UpperCAmelCase_		:	Optional[Any]		):




      """simple docstring"""





      a							,       a		:Union[str, Any]											= a.shape
      a		:Any											= min(UpperCAmelCase_				,						UpperCAmelCase_		)
      a		:Tuple											= np.eye(UpperCAmelCase_		)
      a		:Any											= a.copy()

      for k in range(t - 1		):
            # select a column of modified matrix A':
            a		:List[str]											= r[k:, [k]]
            # construct first basis vector
            a		:List[str]											= np.zeros_like(UpperCAmelCase_		)
            a		:List[Any]											= 1.0
            # determine scaling factor
            a		:Union[str, Any]											= np.linalg.norm(UpperCAmelCase_		)
            # construct vector v for Householder reflection
            a		:List[str]											= x + np.sign(x[0]		) * alpha * ea
            v /= np.linalg.norm(UpperCAmelCase_		)

            # construct the Householder matrix
            a		:Union[str, Any]											= np.eye(m - k		) - 2.0 * v @ v.T
            # pad with ones and zeros as necessary
            a		:Tuple											= np.block([[np.eye(UpperCAmelCase_		), np.zeros((k, m - k)		)], [np.zeros((m - k, k)		), q_k]]		)

            a		:List[Any]											= q @ q_k.T
            a		:int											= q_k @ r

      return q, r


if __name__ == "__main__":
     import doctest

     doctest.testmod()





