code: 
  '''simple docstring'''
  from typing import TYPE_CHECKING
  
  from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available
  
  
  lowercase__						=		{
      "configuration_flava": [
          "FLAVA_PRETRAINED_CONFIG_ARCHIVE_MAP",
          "FlavaConfig",
          "FlavaImageCodebookConfig",
          "FlavaImageConfig",
          "FlavaMultimodalConfig",
          "FlavaTextConfig",
      ],
  }
  
  try:
  						if not is_vision_available():
  												raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
  						pass
  else:
  						lowercase__						=		["FlavaFeatureExtractor"]
  						lowercase__						=		["FlavaImageProcessor"]
  						lowercase__						=		["FlavaProcessor"]
  
  try:
  						if not is_torch_available():
  												raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
  						pass
  else:
  						lowercase__						=		[
  						    "FLAVA_PRETRAINED_MODEL_ARCHIVE_LIST",
  						    "FlavaForPreTraining",
  						    "FlavaImageCodebook",
  						    "FlavaImageModel",
  						    "FlavaModel",
  						    "FlavaMultimodalModel",
  						    "FlavaPreTrainedModel",
  						    "FlavaTextModel",
  						]
  
  if TYPE_CHECKING:
  						from .configuration_flava import (
  						    FLAVA_PRETRAINED_CONFIG_ARCHIVE_MAP,
  						    FlavaConfig,
  						    FlavaImageCodebookConfig,
  						    FlavaImageConfig,
  						    FlavaMultimodalConfig,
  						    FlavaTextConfig,
  						)
  
  						try:
  												if not is_vision_available():
  																		raise OptionalDependencyNotAvailable()
  						except OptionalDependencyNotAvailable:
  												pass
  						else:
  												from .feature_extraction_flava import FlavaFeatureExtractor
  												from .image_processing_flava import FlavaImageProcessor
  												from .processing_flava import FlavaProcessor
  
  						try:
  												if not is_torch_available():
  																		raise OptionalDependencyNotAvailable()
  						except OptionalDependencyNotAvailable:
  												pass
  						else:
  												from .modeling_flava import (
  												    FLAVA_PRETRAINED_MODEL_ARCHIVE_LIST,
  												    FlavaForPreTraining,
  												    FlavaImageCodebook,
  												    FlavaImageModel,
  												    FlavaModel,
  												    FlavaMultimodalModel,
  												    FlavaPreTrainedModel,
  												    FlavaTextModel,
  												)
  
  else:
  						import sys
  
  						lowercase__						=		_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)
  
  
  
style_context: 
  '''simple docstring'''
  import numpy as np
  
  
  
  
  def       _UpperCamelCase	(					SCREAMING_SNAKE_CASE__ )     ->       Optional[Any]:
  
  
  		'''simple docstring'''
  
  
  		snake_case ,snake_case     :					str     =	a.shape
  		snake_case     :					Union[str, Any]     =	min(SCREAMING_SNAKE_CASE__   ,					SCREAMING_SNAKE_CASE__ )
  		snake_case     :					List[Any]     =	np.eye(SCREAMING_SNAKE_CASE__ )
  		snake_case     :					Union[str, Any]     =	a.copy()
  
  		for k in range(t - 1 ):
  				# select a column of modified matrix A':
  				snake_case     :					Union[str, Any]     =	r[k:, [k]]
  				# construct first basis vector
  				snake_case     :					str     =	np.zeros_like(SCREAMING_SNAKE_CASE__ )
  				snake_case     :					List[str]     =	1.0
  				# determine scaling factor
  				snake_case     :					int     =	np.linalg.norm(SCREAMING_SNAKE_CASE__ )
  				# construct vector v for Householder reflection
  				snake_case     :					Optional[int]     =	x + np.sign(x[0] ) * alpha * ea
  				v /= np.linalg.norm(SCREAMING_SNAKE_CASE__ )
  
  				# construct the Householder matrix
  				snake_case     :					Tuple     =	np.eye(m - k ) - 2.0 * v @ v.T
  				# pad with ones and zeros as necessary
  				snake_case     :					int     =	np.block([[np.eye(SCREAMING_SNAKE_CASE__ ), np.zeros((k, m - k) )], [np.zeros((m - k, k) ), q_k]] )
  
  				snake_case     :					int     =	q @ q_k.T
  				snake_case     :					Dict     =	q_k @ r
  
  		return q, r
  
  
  if __name__ == "__main__":
  						import doctest
  
  						doctest.testmod()
  
  
  