

import numpy as np
def 					a				(      A__     :       List[Any]					)   ->				List[Any]:





      """simple docstring"""



      _lowercase	,	_lowercase     	=a.shape
      _lowercase     	=min(_A				,       _A					)
      _lowercase     	=np.eye(_A					)
      _lowercase     	=a.copy()

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

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

            _lowercase     	=q @ q_k.T
            _lowercase     	=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, is_vision_available


lowercase_     =       {
    'configuration_oneformer': ['ONEFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP', 'OneFormerConfig'],
    'processing_oneformer': ['OneFormerProcessor'],
}

try:
  if not is_vision_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  lowercase_     =       ['OneFormerImageProcessor']

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  lowercase_     =       [
      'ONEFORMER_PRETRAINED_MODEL_ARCHIVE_LIST',
      'OneFormerForUniversalSegmentation',
      'OneFormerModel',
      'OneFormerPreTrainedModel',
  ]

if TYPE_CHECKING:
  from .configuration_oneformer import ONEFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP, OneFormerConfig
  from .processing_oneformer import OneFormerProcessor

  try:
    if not is_vision_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .image_processing_oneformer import OneFormerImageProcessor
  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_oneformer import (
        ONEFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
        OneFormerForUniversalSegmentation,
        OneFormerModel,
        OneFormerPreTrainedModel,
    )


else:
  import sys

  lowercase_     =       _LazyModule(__name__, globals()['__file__'], _import_structure)


