




import numpy as np

def       UpperCAmelCase_							(   __UpperCAmelCase		:			str							)      ->				Optional[Any]:
      SCREAMING_SNAKE_CASE_		,				SCREAMING_SNAKE_CASE_					=    a.shape
      SCREAMING_SNAKE_CASE_					=    min(__UpperCAmelCase    ,    __UpperCAmelCase							)
      SCREAMING_SNAKE_CASE_					=    np.eye(__UpperCAmelCase							)
      SCREAMING_SNAKE_CASE_					=    a.copy()

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

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

            SCREAMING_SNAKE_CASE_					=    q @ q_k.T
            SCREAMING_SNAKE_CASE_					=    q_k @ r

      return q, r


if __name__ == "__main__":
     import doctest

     doctest.testmod()





import warnings

from ...utils import logging
from .image_processing_detr import DetrImageProcessor


lowerCamelCase__				:     Optional[Any]			       =							logging.get_logger(__name__)





class  lowerCamelCase_							(   _SCREAMING_SNAKE_CASE      ):


 '''simple docstring'''







 def __init__(							self						:	Dict       ,       *_lowerCAmelCase						:	str       ,       **_lowerCAmelCase						:	List[str]		):
       warnings.warn(
           'The class DetrFeatureExtractor is deprecated and will be removed in version 5 of Transformers.'
           ' Please use DetrImageProcessor instead.'       ,       _lowerCAmelCase       ,       )
       super().__init__(*_lowerCAmelCase       ,       **_lowerCAmelCase		)