



"""simple docstring"""






import numpy as np






def 	snake_case__  (						__lowerCamelCase							:       Tuple      ):
			"""simple docstring"""
			lowerCamelCase__						:						Any						      =a.shape
			lowerCamelCase__						:						Tuple						      =min(_A				,						_A      )
			lowerCamelCase__						:						str						      =np.eye(_A      )
			lowerCamelCase__						:						List[Any]						      =a.copy()

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

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

						lowerCamelCase__						:						Optional[Any]						      =q @ q_k.T
						lowerCamelCase__						:						Dict						      =q_k @ r

			return q, r


if __name__ == "__main__":
		import doctest

		doctest.testmod()







from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available


UpperCAmelCase__			:  Dict					     =     {"""configuration_hubert""": ["""HUBERT_PRETRAINED_CONFIG_ARCHIVE_MAP""", """HubertConfig"""]}

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase__			:  Union[str, Any]					     =     [
      """HUBERT_PRETRAINED_MODEL_ARCHIVE_LIST""",
      """HubertForCTC""",
      """HubertForSequenceClassification""",
      """HubertModel""",
      """HubertPreTrainedModel""",
  ]


try:
  if not is_tf_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase__			:  List[Any]					     =     [
      """TF_HUBERT_PRETRAINED_MODEL_ARCHIVE_LIST""",
      """TFHubertForCTC""",
      """TFHubertModel""",
      """TFHubertPreTrainedModel""",
  ]

if TYPE_CHECKING:
  from .configuration_hubert import HUBERT_PRETRAINED_CONFIG_ARCHIVE_MAP, HubertConfig

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_hubert import (
        HUBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
        HubertForCTC,
        HubertForSequenceClassification,
        HubertModel,
        HubertPreTrainedModel,
    )

  try:
    if not is_tf_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_tf_hubert import (
        TF_HUBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
        TFHubertForCTC,
        TFHubertModel,
        TFHubertPreTrainedModel,
    )


else:
  import sys

  UpperCAmelCase__			:  str					     =     _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)




