






"""simple docstring"""


import numpy as np



def    lowerCAmelCase							(       __UpperCamelCase					):




  """simple docstring"""







  __A     ,       __A		     =					a.shape
  __A		     =					min(__UpperCamelCase						,			__UpperCamelCase					)
  __A		     =					np.eye(__UpperCamelCase					)
  __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(__UpperCamelCase					)
    __A		     =					1.0
    # determine scaling factor
    __A		     =					np.linalg.norm(__UpperCamelCase					)
    # construct vector v for Householder reflection
    __A		     =					x + np.sign(x[0]					) * alpha * ea
    v /= np.linalg.norm(__UpperCamelCase					)

    # 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(__UpperCamelCase					), 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, is_vision_available


_snake_case				=			{
    "configuration_oneformer": ["ONEFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP", "OneFormerConfig"],
    "processing_oneformer": ["OneFormerProcessor"],
}

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

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      _snake_case				=			[
          "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

      _snake_case				=			_LazyModule(__name__, globals()["__file__"], _import_structure)



