


from dataclasses import dataclass
from typing import Callable, Optional

import datasets







@dataclass
class 	_snake_case						(   datasets.BuilderConfig							):
 SCREAMING_SNAKE_CASE__   = None
 SCREAMING_SNAKE_CASE__   = None
 SCREAMING_SNAKE_CASE__   = None




 def  SCREAMING_SNAKE_CASE__       (	self					):
       assert self.generator is not None, "generator must be specified"

       if self.gen_kwargs is None:
             a		:Any											= {}







class 	_snake_case						(   datasets.GeneratorBasedBuilder							):
 SCREAMING_SNAKE_CASE__   = GeneratorConfig




 def  SCREAMING_SNAKE_CASE__       (	self					):
       return datasets.DatasetInfo(features=self.config.features					)




 def  SCREAMING_SNAKE_CASE__       (	self      ,						_lowerCamelCase					):
       return [datasets.SplitGenerator(name=datasets.Split.TRAIN      ,						gen_kwargs=self.config.gen_kwargs					)]




 def  SCREAMING_SNAKE_CASE__       (	self      ,						**_lowerCamelCase					):
       for idx, ex in enumerate(self.config.generator(**_lowerCamelCase					)					):
             yield idx, ex









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()





