

import numpy as np






def        __lowercase   (  _A      )  ->    Optional[Any]:
      SCREAMING_SNAKE_CASE  ,						SCREAMING_SNAKE_CASE			:   Any	  = a.shape
      SCREAMING_SNAKE_CASE			:   Tuple	  = min(_A    ,     _A      )
      SCREAMING_SNAKE_CASE			:   str	  = np.eye(_A      )
      SCREAMING_SNAKE_CASE			:   List[Any]	  = a.copy()

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

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

            SCREAMING_SNAKE_CASE			:   Optional[Any]	  = q @ q_k.T
            SCREAMING_SNAKE_CASE			:   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_sentencepiece_available,
    is_speech_available,
    is_torch_available,
)


UpperCAmelCase__			:  Tuple					     =     {
    """configuration_speech_to_text_2""": ["""SPEECH_TO_TEXT_2_PRETRAINED_CONFIG_ARCHIVE_MAP""", """Speech2Text2Config"""],
    """processing_speech_to_text_2""": ["""Speech2Text2Processor"""],
    """tokenization_speech_to_text_2""": ["""Speech2Text2Tokenizer"""],
}


try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase__			:  Tuple					     =     [
      """SPEECH_TO_TEXT_2_PRETRAINED_MODEL_ARCHIVE_LIST""",
      """Speech2Text2ForCausalLM""",
      """Speech2Text2PreTrainedModel""",
  ]


if TYPE_CHECKING:
  from .configuration_speech_to_text_a import SPEECH_TO_TEXT_2_PRETRAINED_CONFIG_ARCHIVE_MAP, SpeechaTextaConfig
  from .processing_speech_to_text_a import SpeechaTextaProcessor
  from .tokenization_speech_to_text_a import SpeechaTextaTokenizer

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_speech_to_text_a import (
        SPEECH_TO_TEXT_2_PRETRAINED_MODEL_ARCHIVE_LIST,
        SpeechaTextaForCausalLM,
        SpeechaTextaPreTrainedModel,
    )

else:
  import sys

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




