def   __lowercase	(		lowerCamelCase   :	list[list[int | float]]      ):
 UpperCamelCase_   :		Optional[Any]					=   len(__UpperCAmelCase      )
 UpperCamelCase_   :		Dict					=   len(matrix[0]      )
 UpperCamelCase_   :		List[Any]					=   min(__UpperCAmelCase    ,    __UpperCAmelCase      )

 for row in range(__UpperCAmelCase      ):
  # Check if diagonal element is not zero
  if matrix[row][row] != 0:
   # Eliminate all the elements below the diagonal
   for col in range(row + 1    ,    __UpperCAmelCase      ):
    UpperCamelCase_   :		Tuple					=   matrix[col][row] / matrix[row][row]
    for i in range(__UpperCAmelCase    ,    __UpperCAmelCase      ):
     matrix[col][i] -= multiplier * matrix[row][i]
  else:
   # Find a non-zero diagonal element to swap rows
   UpperCamelCase_   :		Optional[Any]					=   True
   for i in range(row + 1    ,    __UpperCAmelCase      ):
    if matrix[i][row] != 0:
     UpperCamelCase_,					UpperCamelCase_   :		List[str]					=   matrix[i], matrix[row]
     UpperCamelCase_   :		Tuple					=   False
     break
   if reduce:
    rank -= 1
    for i in range(__UpperCAmelCase      ):
     UpperCamelCase_   :		List[str]					=   matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
   row -= 1

 return rank


if __name__ == "__main__":
   import doctest

   doctest.testmod()









from typing import TYPE_CHECKING

from ....utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowerCamelCase__					:  Optional[int]      							=				{'configuration_mmbt': ['MMBTConfig']}

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   lowerCamelCase__					:  Any      							=				['MMBTForClassification', 'MMBTModel', 'ModalEmbeddings']


if TYPE_CHECKING:
   from .configuration_mmbt import MMBTConfig

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_mmbt import MMBTForClassification, MMBTModel, ModalEmbeddings

else:
   import sys

   lowerCamelCase__					:  str      							=				_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)