




import numpy as np


def 		_lowerCamelCase					(       UpperCamelCase				)      ->		Any:





  """simple docstring"""





  _lowercase  ,       _lowercase:			List[str]      =     a.shape
  _lowercase:			Tuple      =     min(UpperCamelCase       ,  UpperCamelCase				)
  _lowercase:			int      =     np.eye(UpperCamelCase				)
  _lowercase:			Union[str, Any]      =     a.copy()

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

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

    _lowercase:			Optional[int]      =     q @ q_k.T
    _lowercase:			Tuple      =     q_k @ r

  return q, r


if __name__ == "__main__":
   import doctest

   doctest.testmod()






from typing import TYPE_CHECKING

# rely on isort to merge the imports
from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available, is_torch_available


UpperCAmelCase__    :							List[str]       		=     {
    'configuration_ernie_m': ['ERNIE_M_PRETRAINED_CONFIG_ARCHIVE_MAP', 'ErnieMConfig'],
}

try:
   if not is_sentencepiece_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase__    :							Any       		=     ['ErnieMTokenizer']

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase__    :							Dict       		=     [
       'ERNIE_M_PRETRAINED_MODEL_ARCHIVE_LIST',
       'ErnieMForMultipleChoice',
       'ErnieMForQuestionAnswering',
       'ErnieMForSequenceClassification',
       'ErnieMForTokenClassification',
       'ErnieMModel',
       'ErnieMPreTrainedModel',
       'ErnieMForInformationExtraction',
   ]


if TYPE_CHECKING:
   from .configuration_ernie_m import ERNIE_M_PRETRAINED_CONFIG_ARCHIVE_MAP, ErnieMConfig

   try:
      if not is_sentencepiece_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_ernie_m import ErnieMTokenizer

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_ernie_m import (
          ERNIE_M_PRETRAINED_MODEL_ARCHIVE_LIST,
          ErnieMForInformationExtraction,
          ErnieMForMultipleChoice,
          ErnieMForQuestionAnswering,
          ErnieMForSequenceClassification,
          ErnieMForTokenClassification,
          ErnieMModel,
          ErnieMPreTrainedModel,
      )


else:
   import sys

   UpperCAmelCase__    :							List[Any]       		=     _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
