


'''simple docstring'''






import numpy as np






def 						_A					(lowerCAmelCase__	:Union[str, Any]		) ->	List[Any]:




     '''simple docstring'''



     _a         =				a.shape
     _a         =				min(lowercase__					,    lowercase__		)
     _a         =				np.eye(lowercase__		)
     _a         =				a.copy()

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

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

          _a         =				q @ q_k.T
          _a         =				q_k @ r

     return q, r


if __name__ == "__main__":
 import doctest

 doctest.testmod()





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


snake_case__  				=			{'configuration_qdqbert': ['QDQBERT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'QDQBertConfig']}

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			snake_case__  				=			[
			    'QDQBERT_PRETRAINED_MODEL_ARCHIVE_LIST',
			    'QDQBertForMaskedLM',
			    'QDQBertForMultipleChoice',
			    'QDQBertForNextSentencePrediction',
			    'QDQBertForQuestionAnswering',
			    'QDQBertForSequenceClassification',
			    'QDQBertForTokenClassification',
			    'QDQBertLayer',
			    'QDQBertLMHeadModel',
			    'QDQBertModel',
			    'QDQBertPreTrainedModel',
			    'load_tf_weights_in_qdqbert',
			]


if TYPE_CHECKING:
			from .configuration_qdqbert import QDQBERT_PRETRAINED_CONFIG_ARCHIVE_MAP, QDQBertConfig

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_qdqbert import (
						    QDQBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
						    QDQBertForMaskedLM,
						    QDQBertForMultipleChoice,
						    QDQBertForNextSentencePrediction,
						    QDQBertForQuestionAnswering,
						    QDQBertForSequenceClassification,
						    QDQBertForTokenClassification,
						    QDQBertLayer,
						    QDQBertLMHeadModel,
						    QDQBertModel,
						    QDQBertPreTrainedModel,
						    load_tf_weights_in_qdqbert,
						)


else:
			import sys

			snake_case__  				=			_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)


