
'''simple docstring'''
from transformers import PretrainedConfig






class   snake_case__					(			__SCREAMING_SNAKE_CASE				):







		"""simple docstring"""

		lowerCamelCase           =	"""custom"""



		def __init__(			self							: Optional[int]     ,  UpperCamelCase__							: Union[str, Any]=1     ,  **UpperCamelCase__							: Optional[Any]			)	-> int:






				"""simple docstring"""







				snake_case     :					Optional[int]     =	attribute
				super().__init__(**UpperCamelCase__			)







class   snake_case__					(			__SCREAMING_SNAKE_CASE				):







		"""simple docstring"""

		lowerCamelCase           =	"""custom"""



		def __init__(			self							: int     ,  UpperCamelCase__							: Union[str, Any]=1     ,  **UpperCamelCase__							: Optional[Any]			)	-> Any:






				"""simple docstring"""







				snake_case     :					Dict     =	attribute




'''simple docstring'''
import numpy as np




def       _UpperCamelCase	(					SCREAMING_SNAKE_CASE__ )     ->       Optional[Any]:


		'''simple docstring'''


		snake_case ,snake_case     :					str     =	a.shape
		snake_case     :					Union[str, Any]     =	min(SCREAMING_SNAKE_CASE__   ,					SCREAMING_SNAKE_CASE__ )
		snake_case     :					List[Any]     =	np.eye(SCREAMING_SNAKE_CASE__ )
		snake_case     :					Union[str, Any]     =	a.copy()

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

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

				snake_case     :					int     =	q @ q_k.T
				snake_case     :					Dict     =	q_k @ r

		return q, r


if __name__ == "__main__":
						import doctest

						doctest.testmod()


