code: 
  
  
  import numpy as np
  from numpy import floataa
  from numpy.typing import NDArray
  def 							_UpperCAmelCase       (UpperCamelCase__  :						NDArray[floataa]       ,							UpperCamelCase__  :						NDArray[floataa]		):
         _A					,    _A   : Any       					=				np.shape(UpperCamelCase__		)
  
         _A   : NDArray[floataa]       					=				np.zeros((rows, 1)       ,							dtype=UpperCamelCase__		)
         for row in reversed(range(UpperCamelCase__		)		):
                _A   : int       					=				0
                for col in range(row + 1       ,							UpperCamelCase__		):
                       total += coefficients[row, col] * x[col]
  
                _A   : Optional[Any]       					=				(vector[row] - total) / coefficients[row, row]
  
         return x
  def 							_UpperCAmelCase       (UpperCamelCase__  :						NDArray[floataa]       ,							UpperCamelCase__  :						NDArray[floataa]		):
         _A					,    _A   : Optional[Any]       					=				np.shape(UpperCamelCase__		)
         if rows != columns:
                return np.array(()       ,							dtype=UpperCamelCase__		)
  
         # augmented matrix
         _A   : NDArray[floataa]       					=				np.concatenate((coefficients, vector)       ,							axis=1		)
         _A   : List[str]       					=				augmented_mat.astype("float64"		)
  
         # scale the matrix leaving it triangular
         for row in range(rows - 1		):
                _A   : str       					=				augmented_mat[row, row]
                for col in range(row + 1       ,							UpperCamelCase__		):
                       _A   : Dict       					=				augmented_mat[col, row] / pivot
                       augmented_mat[col, :] -= factor * augmented_mat[row, :]
  
         _A   : Any       					=				retroactive_resolution(
             augmented_mat[:, 0:columns]       ,							augmented_mat[:, columns : columns + 1]		)
  
         return x
  
  
  if __name__ == "__main__":
      import doctest
  
      doctest.testmod()
  
style_context: 
  
  
  from typing import TYPE_CHECKING
  
  from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available
  
  
  lowerCAmelCase__   	=				{'configuration_detr': ['DETR_PRETRAINED_CONFIG_ARCHIVE_MAP', 'DetrConfig', 'DetrOnnxConfig']}
  
  try:
      if not is_vision_available():
          raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
      pass
  else:
      lowerCAmelCase__   	=				['DetrFeatureExtractor']
      lowerCAmelCase__   	=				['DetrImageProcessor']
  
  try:
      if not is_torch_available():
          raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
      pass
  else:
      lowerCAmelCase__   	=				[
          'DETR_PRETRAINED_MODEL_ARCHIVE_LIST',
          'DetrForObjectDetection',
          'DetrForSegmentation',
          'DetrModel',
          'DetrPreTrainedModel',
      ]
  
  
  if TYPE_CHECKING:
      from .configuration_detr import DETR_PRETRAINED_CONFIG_ARCHIVE_MAP, DetrConfig, DetrOnnxConfig
  
      try:
          if not is_vision_available():
              raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
          pass
      else:
          from .feature_extraction_detr import DetrFeatureExtractor
          from .image_processing_detr import DetrImageProcessor
  
      try:
          if not is_torch_available():
              raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
          pass
      else:
          from .modeling_detr import (
              DETR_PRETRAINED_MODEL_ARCHIVE_LIST,
              DetrForObjectDetection,
              DetrForSegmentation,
              DetrModel,
              DetrPreTrainedModel,
          )
  
  else:
      import sys
  
      lowerCAmelCase__   	=				_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
  